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THE TEXAS JOURNAL OF SCIENCE

Volume XXXV

1983

Published by

THE TEXAS ACADEMY OF SCIENCE

THE TEXAS JOURNAL OF SCIENCE

Volume XXXV, No. 1

March 1983

CONTENTS

Instructions to Authors . . . . . 3

Modeling Systolic Mitral Valve Motion: A Tool for Clarifying Mitral Valve Prolapse. By Jon F. Hunter, David P. Seaton, William M. Lively,

Gerald E. Miller, and David L. Stoner . . . 5

Thin Layer Chromatography of Nitrogen Heterocycles on a Modified

Silica Gel Support. By W. E. Rudzinski . . . . .37

Some Structural Aspects of a Western Cross Timbers Forest in North Central Texas.

By Glenn C. Kroh and James Nisbet . . . . . 41

Heavy Metal Pollution in El Paso During Selected Time

Periods. By Howard G. Applegate and Keith Redetzke . 47

The Commercial Production of Mudminnows ( Fundulus grandis ) for Live Bait: A Preliminary Economic Analysis. By Benita P. Waas,

Kirk Strawn, Michael Johns, and Wade Griffin . . . 51

Effects of a High Potassium Diet and Prostaglandin on Induced

Gastric Ulceration in Rats. By Marshall J. Mann and David P. Shepherd . 61

Biological Form Representation by Techniques Developed for

Airfoils. By W. M. Heffington and K. L. Eaves . . . 67

Circulating Corticosteroid and Leucocyte Dynamics in Channel Catfish during Net Confinement. By J. R. Tomasso, Bill A. Simco,

and Kenneth B. Davis . 83

Comparative Digestive Efficiency of White-tailed and Sika Deer.

By Christopher Wheaton and Robert D. Brown . . . . . 89

Summer Diet of Finfish from Nearshore Habitats of West Bay, Texas. By Steve K. Alexander .

93

THE TEXAS JOURNAL OF SCIENCE

Volume XXXV, No. 2 July 1983

CONTENTS

Instructions to Authors . . . . . . . .99

Observation of Episodic Sedimentation in a Tidal Inlet (Sabine Pass, Texas

and Louisiana). By George H. Ward, Jr . . . . . 101

Midwater Fishes of the Gulf of Mexico Collected from the

R/V Alaminos, 1965-1973. By Edward O. Murdy, Richard E. Matheson, Jr.,

Janice D. Fechhelm, and Michael J. McCoid . 109

In Vitro Analysis of Transfer Factor Activity in Guinea Pig Leukocyte Extracts by the Agarose Drop Assay. By Andrew Paquet, Jr.,

George B. Olson, and C. G. Drube . 129

Variation in Transplantable Tumor Growth-parameters Can Be Reduced.

By David G. Morrison, Mary Pat Moyer, Jay C. Daniel, Waid Rogers,

and Rex C. Moyer . HI

Paleoenvironmental Significance of a Nonmarine Pleistocene Molluscan Fauna

from Southern Texas. By Raymond W. Neck . H7

Caloric Value of the Liver Fluke, Fasciola hepatica.

By Jeremy M. Jay and Norman O. Dronen . 155

Status of Bighorn Sheep in Texas.

By Bruce D. Leopold and Paul R. Krausman . . . 167

Eggs and Young of Schott’s Whipsnake, Masticophis taeniatus schotti.

By Hugh K. McCrystal and James R. Dixon . 161

Observations on Host Selection by Lysathia ludoviciana (Chrysomelidae), a Beetle with Potential for Biological Control of Certain Aquatic Weeds.

By John M. Campbell and William J. Clark . 165

Characterization of Erythrocyte Esterases on Electrophoretic Gels.

By John P. Cherry . . . 169

THE TEXAS JOURNAL OF SCIENCE

Volume XXXV, No. 3 September 1983

CONTENTS

Instructions to Authors . 179

Geology’s Heritage and Promise. By Michel T. Halbouty . . 181

Translation of C Shell Scripts to C for Faster Execution of UNIX

Computer Programs. By Grady Early, Jane Gambill and Teresa Thomas . 189

Vegetational Analysis of a Post Oak-Black Hickory Community

in Eastern Texas. By K. L. Marietta and E. S. Nixon . 197

Woody, Streamside Vegetation of Prairie Creek in East Texas.

By E. S. Nixon, R. L. Ehrhart, S. A. Jasper, J. S. Neck and J. R. Ward . 205

Global Inverse Function Theorem. By John D. Miller . 215

New Records of Invertebrate Saprovores from Barn Owl Pellets.

By Kirk L. Hamilton and Annemarie B. Hamilton . . . 219

A New Edgeworth-type Expansion. By James G. Galloway and E. D. McCune . 221

Relationships of Sugar Maples (Acer saccharum and A. grandidentatum ) in Texas and Oklahoma with Special Reference to Relict Populations.

By Frederick R. Gehlbach and Robert C. Gardner . 231

Recent Population Trends of Cormorants (Aves: Pelicaniformes) in Texas.

By Michael L. Morrison, Brenda S. Hale and R. Douglas Slack . 239

Occurrence of the Caddisfly Atopsyche erigia in Texas’

Guadalupe River below Canyon Reservoir. By Robert A. Short . 243

Herpetofauna of the Pedro Armendariz Lava Field, New Mexico.

By Troy L. Best, Herman C. James, and Frank H. Best . 245

Taxonomic Status of the Brazilian Colubrid Snake,

Xenodon suspectus Cope. By James R. Dixon . 257

Viscometric Measurement of the Cellulase Activity of a

Soil Fungus. By J. Ortega and E. J. Baca . . . . . 261

New Records of the Freshwater Ectoproct Pectinatella magnifica

in Eastern Texas. By Raymond W. Neck and Richard W. Fullington . . .269

THE TEXAS JOURNAL OF SCIENCE

Volume XXXV, No. 4 January 1984

CONTENTS

Instructions to Authors . . . . . . .275

Toric Sections. By Ali R. Amir-Moez and Gregory A. Fredricks . 277

Use of Fissiogenic Stable Ruthenium Versus Xenon Isotopes in the Determination of Induced Fission in Uranium Ores.

By Moses Attrep, Jr., and Kung Hsing-Tung . 283

The Death Dip Among Ordinary Folks: A Study of the Dip/Peak Phenomenon for Texans Dying in 1979. By Rollo K. Newsom, Alvin P. Short,

Louis M. Tanner, and T. C. Borelli . . . 293

Cattle Egrets ( Ardeola ibis = Bubulcus ibis ) in Texas.

By Raymond C. Telfair II and Larry E. Marcy . . . 303

Swim Bladder Stress Syndrome in Largemouth Bass.

By Gary J. Carmichael and J. R. Tomasso . 315

Distributional Records and Notes for Nine Species of Mammals in Eastern

Texas. By Arthur G. Cleveland, John T. Baccus, and Earl G. Zimmerman . 323

Development of Tensile Strength in Compatible Autografts of Eggplant ( Solanum pennellii) and Tomato ( Lycopersicon esculentum).

By Mary T. McGarry and Randy Moore . . . 327

Abstracts of the Ninth North American Physarum Conference . 333

Index to Volume XXXV . . . 349

Reviewers

362

SECTION I

MATHEMATICAL SCIENCES Mathematics, Statistics, Operations Research

SECTION X AQUATIC SCIENCES

SECTION IX COMPUTER SCIENCES

The Texas Academy of

Science

SECTION II PHYSICS

SECTION III EARTH SCIENCES Geography Geology

SECTION VIII SCIENCE EDUCATION

SECTION VII CHEMISTRY

SECTION VI ENVIRONMENTAL SCIENCES

SECTION IV BIOLOGICAL SCIENCES Agriculture, Botany, Medical Science, Zoology

SECTION V SOCIAL SCIENCES Anthropology, Education, Economics, History, Psychology, Sociology

AFFILIATED ORGANIZATIONS Texas Section, American Association of Physics Teachers Texas Section, Mathematical Association of America Texas Section, National Association of Geology Teachers

GENERAL INFORMATION

MEMBERSHIP. Any person or group engaged in scientific work or interested in the pro¬ motion of science is eligible for membership in The Texas Academy of Science. Dues for members are $20.00 annually; student members, $12.00 annually; sustaining members, at least $30.00 in addition to annual dues; life members, at least $400.00 in one payment; patrons, at least $500.00 in one payment; corporate members, $250.00 annually; corporate life members, $2000.00 in one payment. Library subscription rate is $45.00 annually. Pay¬ ments should be sent to the Secretary-Treasurer, Box 2176, Huntsville, TX 77341.

The Journal is a quarterly publication of The Texas Academy of Science and is sent to all members and subscribers. Inquiries regarding back issues should be sent to Dr. Fred S. Hendricks, Dept. Wildlife 8c Fisheries Sciences, Texas A8cM University, College Station, TX 77843.

Manuscripts submitted for publication in the Journal should be sent to Dr. W. H. Neill, Dept. Wildlife 8c Fisheries Sci., Texas A8cM Univ., College Station, TX 77843.

The Texas Journal of Science (USPS 616740) is published quarterly at Huntsville, Texas U.S.A. (Second class postage paid at Post Office, Huntsville, TX 77341, and at additional mailing office at Lubbock, TX 79401.) Please send form 3579 and returned copies to Texas Tech Press, Box 4240, Lubbock, TX 79409.)

THE TEXAS JOURNAL OF SCIENCE

Volume XXXV, No. 1

March 1983

CONTENTS

Instructions to Authors . . . . . 3

Modeling Systolic Mitral Valve Motion: A Tool for Clarifying Mitral Valve Prolapse. By Jon F. Hunter, David P. Seaton, William M. Lively,

Gerald E. Miller, and David L. Stoner . 5

Thin Layer Chromatography of Nitrogen Heterocycles on a Modified

Silica Gel Support. By W. E. Rudzinski . 37

Some Structural Aspects of a Western Cross Timbers Forest in North Central Texas.

By Glenn C. Kroh and James Nisbet . . . . . 41

Heavy Metal Pollution in El Paso During Selected Time

Periods. By Howard G. Applegate and Keith Redetzke . . . 47

The Commercial Production of Mudminnows ( Fundulus grandis) for Live Bait: A Preliminary Economic Analysis. By Benita P. Waas,

Kirk Strawn, Michael Johns, and Wade Griffin . . . . . 51

Effects of a High Potassium Diet and Prostaglandin on Induced

Gastric Ulceration in Rats. By Marshall J. Mann and David P. Shepherd . 61

Biological Form Representation by Techniques Developed for

Airfoils. By W. M. Heffington and K. L. Eaves . . . . . 67

Circulating Corticosteroid and Leucocyte Dynamics in Channel Catfish During Net Confinement. By J. R. Tomasso, Bill A. Simco,

and Kenneth B. Davis . . . . . . . . . . . . 83

Comparative Digestive Efficiency of White-tailed and Sika Deer.

By Christopher Wheaton and Robert D. Brown . . . . . 89

Summer Diet of Finfish from Nearshore Habitats of West Bay,

Texas. By Steve K. Alexander . . . 93

\

\\

\r

NOTE: Authors with funds for page contributions are expected to make such payments. The contribution of $35.00 per page is encouraged to defray printing costs, and authors of articles exceeding ten printed pages are expected to make some contribution to the publication fund. How¬ ever, payment of printing costs is not a condition for publication in The Texas Journal of Science, and NO AUTHOR, WHO WOULD OTHER¬ WISE SUBMIT A MANUSCRIPT, SHOULD HESITATE TO DO SO BECAUSE OF LACK OF SUCH FUNDS. Members without funds may apply to the Texas Academy of Science for a grant to cover some or all costs of publication. This becomes effective January 23, 1982.

INSTRUCTIONS TO AUTHORS

Papers intended for publication in The Texas Journal of Science are to be submitted to Dr. William H. Neill, Dept. Wildlife & Fisheries Sciences, Texas A&M University, College Station, TX 77843.

The manuscript is not to have been published elsewhere. Triplicate typewritten copies (the original and 2 reproduced copies) must be sub¬ mitted. Typing of both text and references should be double-spaced with 2-3 cm margins on standard 8V2 X 11 -inch typing paper. The title of the article should be followed by the name and business or institutional address of the author(s). Be sure to include zip code with the address. If the paper has been presented at a meeting, a footnote giving the name of the society, date, and occasion should be included but should not be numbered. Include a brief ABSTRACT at the beginning of the text (abstracting services pick this up directly) followed by an INTRODUC¬ TION (understandable to any scientist) and then whatever paragraph headings are desired. The usual editorial customs, as exemplified in the most recent issue of the Journal, are to be followed as closely as possible.

In the text, cite all references by author and date in chronological order , i.e., Jones (1971); Jones (1971, 1972); (Jones 1971); (Jones 1971, 1972); Jones and Smith (1971); (Jones and Smith 1971); (Jones 1971; Smith 1972; Beacon 1973). If there are more than 2 authors, use: Jones et al. (1971); (Jones et al. 1971). References are then to be assembled, arranged ALPHABETICALLY, and placed at the end of the article under the heading LITERATURE CITED. For a PERIODICAL ARTICLE use: Jones, A. P., and R. J. Wilson. 1971. Effects of chlorinated hydrocarbons. J. Comp. Chem. 37:116-123. For a PAPER PRESENTED at a symposium, etc., use the form: Jones, A. P. 1971. Effects of chlorinated hydrocarbons. WMO Symposium on Organic Chemistry, New York, N.Y. For a PRINTED PAPER use: Jones, A. P. 1971. Effects of chlorinated hydrocar¬ bons. Univ. of Tex., Dallas, or Jones, A. P. 1971. Effects of chlorinated hydrocarbons. Univ. of Tex. Paper No. 14, 46 p. A MASTERS OR Ph D. THESIS should appear as: Jones, A. P. 1971. Effects of chlorinated hydro¬ carbons. M.S. Thesis, Tex. A&M Univ., College Station. For a BOOK, NO EDITORS, use: Jones, A. P. 1971. Effects of chlorinated hydrocarbons. Academic Press, New York, N.Y., 439 p. For a CHAPTER IN A BOOK WITH EDITORS: Jones, A. P. 1971. Structure of chlorinated hydrocarbons, p. 13-39. In A. P. Jones, B. R. Smith, Jr. and T. S. Gibbs (Eds.), Effects of chlorinated hydrocarbons. Academic Press, New York, N.Y. For a BOOK WITH EDITORS: Jones, A. P. 1971. Effects of chlorinated hydrocarbons. J. Doe (Ed.). Academic Press, New York, N.Y., p. 3-12. For an IN PRESS PERIODICAL reference, use: Jones, A. P. In Press. Effects of chlorinated hydrocarbons. J. Org. Chem. For an in PRESS BOOK reference, use: Jones,

4

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

A. P. In Press. Effects of chlorinated hydrocarbons. Academic Press, New York, N.Y. References must include article title and page numbers.

References such as unpublished data or personal communications should not be listed in the LITERATURE CITED section. However, within the text they should be presented as: (unpubl. data from C. J. Jones, Dept. Zoology, Univ. Texas, Austin) or (pers. comm, from R. C. Smith, P.O. Box 133, Mexia, TX).

All tables are to be typed with a carbon ribbon, free of error, without handwritten notations, and ready for photographic reproduction. Tables should be placed on separate sheets with a marginal notation on the manuscript to indicate preferred locations. Tables must have a text refer¬ ence, i.e., Table 2 shows. . .or (Table 2).

Figures are to be original inked drawings or glossy photographs no larger than 6% X 4% inches and mounted on standard 8% X 11-inch paper. Legends for figures are to be typed separately. Figures must have a text reference, i.e., Figure 3 illustrates. . .or (Fig. 3).

All photographs, line drawings, and tables are to be provided with self-explanatory titles or legends. Each illustration should be marked on the back with the name of the principle author, the figure number, and the title of the manuscript of which it is a part.

Authors will receive galley proofs plus the original typescript along with information concerning reprints and page charges. Proofs must be corrected (using ink) and returned to the Editor within 3 days. Payment (check or purchase voucher) for page charges (or the publication grant request) must accompany the return of the corrected proofs or a delay in the printing of the manuscript could occur. Reprint orders should be returned directly to Texas Tech Press, Box 4240, Lubbock, TX 79409

NOTICE: IF YOUR ADDRESS OR TELEPHONE NUMBER CHANGES, NOTIFY US IMMEDIATELY SO WE CAN SEND YOUR GALLEY PROOFS TO YOU WITH¬ OUT LOSS OR DELAY.

MODELING SYSTOLIC MITRAL VALVE MOTION:

A TOOL FOR CLARIFYING MITRAL VALVE PROLAPSE'

by JON F. HUNTER/" DAVID P. SEATON/

WILLIAM M. LIVELY/ GERALD E. MILLER," and DAVID L. STONER"

1 Department of Veterinary Physiology and Pharmacology, b Bioengineering Program, and c Computing Science Division Texas A&M University College Station, TX 77843

ABSTRACT

A dynamic model of the human heart’s mitral valve motion during systole is presented. This model includes a description of the geometrical interrelationships between compo¬ nents of the mitral apparatus, namely mitral valve leaflets, annulus, chordae tendineae, papillary muscles, and left ventricle. The biomechanical properties of the mitral valve leaflets and chordae tendineae and the contractile nature of the annulus, papillary mus¬ cles and left ventricle are considered. Mitral valve profile/position is described for selected properties of model components.

INTRODUCTION

Mitral valve prolapse (also referred to as floppy or billowing mitral valve, systolic-click/late-systolic-murmur syndrome, Barlow’s or Reid- Barlow’s syndrome, or idiopathic mitral valve prolapse) has been des¬ cribed as the most common cardiac valve disorder (Jeresaty 1979). The exact prevalence of mitral valve prolapse is unknown, but results of various surveys indicate that approximately 4% of the general popula¬ tion may be affected (Brown et al. 1975; Procacci et al. 1976; Jeresaty 1979). Numerous articles describing this syndrome have been published during the past fifteen years and recent advances in ultrasound instru¬ mentation have greatly aided in its detection. However, considerable controversy still remains regarding the etiology, criteria for diagnosis, and significance of mitral valve prolapse.

Normal function of the mitral apparatus depends upon the coordi¬ nated interaction of mitral valve leaflets, annulus, chordae tendineae, papillary muscles, the left ventricle, and the left atrium (Devereux et al. 1976). Mitral valve prolapse has been associated with alterations in all of these components except the left atrium. This model is a computer simulation of the anatomical and physiological interrelationships of

•This investigation was supported under United States Air Force Contract F33615-78-D- 0629.

The Texas Journal of Science, Vol. XXXV, No. 1, March 1983

6

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

those components of the mitral apparatus which have been implicated as contributing to prolapse. It is based on published anatomical and physiological data and is limited, as are other models of the mitral valve, by the assumption of quasi-static forces in the system (Burch and DePasquale 1965; Burch and Giles 1972; Ghista and Rao 1972; Clark and Sutera 1973).

Large excursions of the mitral valve occur during five phases of the cardiac cycle — (1) rapid ventricular filling, (2) slow ventricular filling, (3) atrial systole, (4) isovolumetric systole (aortic valve closed), and (5) ventricular ejection (aortic valve open) (Karas and Elkins 1970). Valve motion during diastole is particularly complex. It is influenced by pressure differences across the mitral valve, geometry of the mitral opening and surrounding structures, transient vortices adjacent to the valve, and possibly active contraction of the muscle fibers in the leaflets (Zaky et al. 1969; Priola et al. 1970; Bellhouse 1972a, b; Hwang 1977). Diastolic valve motion has been excluded from this model due to the lack of quantitative information on the effects of pressure, flow, and active contraction during diastole.

The effects of flow through the mitral valve opening can be neg¬ lected during systole provided regurgitation is not occurring. This sim¬ plifies the mathematical description of valve motion and since the intent of this model is to provide a better understanding of mitral valve prolapse, a systolic event, it seems logical to concentrate on this phase of the cardiac cycle.

A computer program has been developed that accepts clinically obtained data, data based on published reports, and/or modeling assumptions and predicts mitral valve position/profile during systole. This approach was taken so that model verification and possibly diag¬ nostic screening could easily be achieved without major alteration of the program. Thus, input parameters were selected so that clinical measurements could be obtained using non-invasive instrumentation — electrocardiography, apexcardiography, carotid pulse pressures, indirect blood pressure, and cardiac imaging techniques (cineangiography or real-time ultrasound).

DESCRIPTION OF THE MODEL Coordinate System

Understanding the geometry of the mitral apparatus is essential for appreciating the interrelationships that exist between the various com¬ ponents of this model. An orthogonal coordinate system was devised to simplify the three dimensional description of the anatomy and dynamic motion associated with the various cardiac structures. This coordinate system is formed by the intersection of three planes (Fig. 1): (1) an x-y

MODELING MITRAL VALVE MOTION

7

Figure 1. Coordinate system for the mitral apparatus. The origin is located at the cen¬ ter of attachment of the anterior leaflet to the annulus.

plane that contains the mitral valve annulus and remains perpendicu¬ lar to the long axis of the ventricle throughout the cardiac cycle (Tsaki- ris et al. 1971), (2) an x-z plane that passes perpendicular to a line of coaptation and through the middle portions of the anterior and poste¬ rior mitral valve leaflets, and (3) a y-z plane passing through the ante¬ rior leaflet-annulus attachment.

8

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

Pressure and Timing Considerations

Systole has been classically defined as the period of ventricular con¬ traction beginning with the rise of the left ventricular pressure and ending at the time of the incisural notch of the aortic pressure pulse (Wiggers 1921). For purposes of this simulation, ventricular systole is considered to be the interval between the Q-wave of the electrocardio¬ gram and the incisural notch. To assist in properly sequencing the var¬ ious active contractions and pressure related events that are described in this model, systole is subdivided into three time periods— (1) electrome¬ chanical delay time (EDT), (2) isovolumetric contraction time (IVCT), and (3) ejection time (ET). The duration of these various phases of sys¬ tole is influenced by a number of factors, including stroke volume, aor¬ tic pressure, heart rate, and end diastolic volume (Wiggers 1921; Braunwald et al. 1958; Wallace et al. 1963).

Electromechanical delay time (EDT) is the interval between electrical stimulation and mechanical contraction of the myocardium. It proba¬ bly represents the delay associated with the excitation-contraction cou¬ pling of individual muscle fibers (Spodick and Kumar 1968a). This phase of ventricular systole begins with the onset of the Q-wave of the EGG; however, the exact time of termination of this phase is poorly defined. Some researchers consider the mitral component of the first heart sound as defining the end of EDT (Frank and Kinlaw 1962). Other investigators believe that the kinetocardiograph provides an accurate indication of the termination of EDT (Harrison et al. 1964). Spodick and Kumar (1968a) report that the endpoint of EDT more appropriately corresponds to a distinctive portion of the apexcardio- gram, the apexcardiogram upstroke (ACGU). They have shown that ACGU coincides with the onset of intramural myocardial tension and therefore appears to be the best indicator of the initiation of ventricular contraction.

Model assumptions:

1. During the period corresponding to the electromechanical delay time (EDT), the only component of the mitral apparatus that is actively contracting is the annulus (Tsakiris et al. 1971).

2. The mitral valves are in equilibrium and the leaflets are coapted during EDT. (This assumption is contradictory to published reports that valve closure does not occur until ventricular pressure rises, approximately 20 msec following the end of the EDT phase (Kostis et al. 1969; Fabian et al. 1972); however, this assumption is defensible based upon the fact that valve motion is negligible immediately following closure and therefore previous movements will have minimal influence on subsequent valve positions (Upton et al. 1976).)

MODELING MITRAL VALVE MOTION

9

100

Transvalvular Pressure 50 (Hypothetical)

0

Carotid Pressure Profile

Apexcardiogram

Electrocardiogram

M-IVCTHh - ET - H

EOT

i i i i i i

Time (msec) 0 100 200 300 400 500

Figure 2. Diagrammatic representation of pressure and timing events during systole — electromechanical delay (EDT), isovolumetric contraction time (IVCT), ejection time (ET), apexcardiogram upstroke (ACGU), pulse transmission delay (PTT), carotid pulse upstroke (CARU), and carotid pulse incisura (GARIN).

Input data (Fig. 2):

Hypothetical— Electromechanical delay time (EDT) equals 22 msec (Spodick and Kumar 1968a).

Clinical-Electromechanical delay time (EDT) as determined by measuring the interval between the onset of the Q-wave and the upstroke of the apexcardiogram (EDT = QWAVE— ACGU). Isovolumetric contraction time (IVCT) is the period of the caardiac cycle extending from the end of EDT to the opening of the aortic valve. IVCT changes from beat to beat and has been shown to be affected by heart rate, contractile state of the myocardium, ventricular end-diastolic volume, aortic diastolic pressure, and stroke volume (Wallace et ah 1963; Harrison et al. 1964; Kumar and Spodick 1970; Fabian et al. 1972; Hirschfeld et al. 1976). For purposes of this model the onset of this

10

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

phase is associated with the upstroke of the apexcardiogram (ACGU). The three most commonly used indicators for the end of IVCT are (1) the carotid pulse upstroke (CARU), (2) the carotid pulse upstroke cor¬ rected for pulse transmission delay (CARUC), and (3) the E point of the apexcardiogram (Spodick and Kumar 1968b; Kumar and Spodick 1970; Oreshkov 1972; Fabian et al. 1972). For purposes of this model, the carotid pulse upstroke corrected for pulse transmission delay is the most accurate timing index. Pulse transmission delay (PTT) may be determined by simultaneously recording carotid pulse profile and pho- nocardiograms; the time between the aortic component of the second heart sound and the nadir of the carotid incisura provides an accurate estimate of PTT. The average PTT for the right carotid artery is approximately 23 msec (Fabian et al. 1972).

Model assumptions:

1. Left ventricular wall and papillary muscle contractions begin with the onset of IVCT (Spodick and Kumar 1968b; Hirakawa et al. 1977).

2. Transvalvular pressure increases linearly during this phase of the cardiac cycle.

Input data (Fig. 2):

Hypothetical — Isovolumetric contraction time (IVCT) equals 71 msec (Kumar and Spodick 1970). Transvalvular pressure (TP) at the end of IVCT equals 80 mm Hg.

Clinical — Isovolumetric contraction time (IVCT) as determined from apexcardiogram and carotic pulse recordings corrected for pulse transmission delay (IVCT = ACGU— CARUC). Transvalvu¬ lar pressure (TP) at the time of aortic valve opening may be esti¬ mated using standard indirect sphygmomanometric techniques to determine peripheral diastolic pressures (Krausman 1975).

Ejection time (ET) is defined as the period between the onset of the aortic pressure rise and the incisural notch. This can be clinically mea¬ sured from the beginning of the carotid pulse upstroke (CARU) to the nadir of the carotid pulse incisura (CARIN) (Fabian et al. 1972). Close agreement exists between ET measured in this manner and direct mea¬ surements obtained within the aorta (Weissler et al. 1961; Van de Werf et al. 1975). Kumar and Spodick (1970) and Fabian et al. (1972) have experimentally derived equations relating heart rate to ET; however, other parameters that affect ET, namely stroke volume, aortic pressure, and myocardial contractility, have not been mathematically character¬ ized.

During ejection the carotid pulse profile is closely related to the aor¬ tic pressure waveform (Robinson 1963) and thus may serve as an approximation of transvalvular pressure profile.

MODELING MITRAL VALVE MOTION

11

Model assumptions:

1. Annulus, left ventricular wall, and papillary muscle contractions continue throughout this phase of systole.

Input data (Fig. 2):

Hypothetical— Ejection time (ET) equals 292 msec (Kumar and Spodick 1970). Transvalvular pressure (mm Hg) is expressed by the following equation:

TP = 80 + 40 • sin(K • ETT) (1)

where ETT (msec) is the time measured from the start of the ejec¬ tion phase and K is a constant (0.009) selected so that peak trans¬ valvular pressure occurs at approximately 175 msec.

Clinical— Ejection time (ET) as determined by carotid pulse recordings (ET = CARU— CARIN) (Fabian et al. 1972; Van de Werf et al. 1975) or by echocardiography (Hirschfeld et al. 1975). Transvalvular pressure throughout the ejection phase may be estimated from carotid pulse recordings and peripheral systolic and diastolic blood pressure determinations using sphygmoman- ometric techniques (Krausman 1975).

Mitral Valve Leaflets

The mitral valve has been described by Chiechi et al. (1956) as a con¬ tinuous veil of tissue attached around the entire circumference of the mitral orifice. The valve consists of fibrous, elastic, and muscular ele¬ ments covered by an endocardial coat. The muscular elements are con¬ centrated in the basal portion of the valve and appear to be anatomi¬ cally and possibly functionally continuous with the left atrium (Fenoglio et al. 1972; Wit et al. 1973). Collagen fibers extend from the annulus through the leaflet to form chordae tendineae and thus form a continuous fibrous tissue from the annulus to the papillary muscles (Fenoglio et al. 1972).

The free edge of the veil of tissue is interrupted by indentations which divide the valvular tissue into two major leaflets (Fig. 3). The anterior leaflet (also referred to as the aortic, septal, greater, or ante¬ romedial leaflet) has been described as semicircular or triangular in shape (Fig. 4) (Chiechi et al. 1956; Ranganathan et al. 1976). The pos¬ terior leaflet is rectangular in shape (Fig. 4). Indentations along the free edge of the posterior leaflet give it a scalloped appearance. In 92% of the normal human hearts studied by Ranganathan et al. (1976), the posterior leaflet was triscalloped with a large middle scallop.

Along the free edge of both leaflets is a zone of tissue that appears roughened (Fig. 4). This opaque portion of the mitral valve receives the insertion of chordae tendineae on its ventricular surface. This rough

12

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

y

(top view of closed valve)

Figure 3. Anatomy of the mitral valve. Infinitesimal strip of leaflet extending along the x-axis represents the mitral valve position and profile (modified from Davila and Palmer 1962).

zone has been described as an area of coaptation for leaflet apposition (Carpender et al. 1976; Ranganathan et al. 1976). The ratio of rough zone to smooth leaflet tissue in the anterior leaflet is 0.6 and for the posterior leaflet 1.4 (Ranganathan et al. 1976). Based on these ratios and anatomical data for leaflet heights (Table 1), the leaflets would contact each other along a strip approximately 0.8 cm wide at the cen¬ ter of the leaflets. However, this is not compatible with measurements of annulus dimensions since the portions of the leaflets that are not opposed would not physically reach from the anterior to the posterior

MODELING MITRAL VALVE MOTION

13

Anterior Leaflet Posterior Leaflet

Figure 4. Schematic representation of mitral valve leaflets illustrating the shape of the

leaflets and extent of the rough zone (modified from Ranganathan et al. 1970).

The mechanical properties of mitral valve leaflets have been studied by several investigators (Clark and Butterworth 1971; Ghista and Rao 1972; Clark 1973). There is an initial stretching of the leaflet at very low (pre-transition) stresses (Fig. 5A). With additional stress, the modu¬ lus of elasticity changes abruptly at the transition stress (Fig. 5B) to a larger post-transition modulus of elasticity characteristic of a stiffer material (Fig. 5C). Typical values for pre- and post-transition moduli, transition stress, and transition strain are listed in Table 2. The strain at transition is approximately 15% of the original unstretched leaflet height. From this curve and values for the elastic moduli, it is apparent edge of the annulus. The extent of coaptation probably varies from a single line to a plane of coaptation depending upon the degree of annulus narrowing, leaflet dimensions, and positions of the leaflets rel¬ ative to the annulus.

Table 1. Selected anatomical data for mitral valve leaflets (from autopsy of normal human subjects).

Parameter	Average Value	Number Subjects	Sex	Reference
Anterior Leaflet Height	23 mm	50	?	Carpentier et al. 1976
Anterior Leaflet Height	24 mm	26	M	Ranganathan et al. 1970
Anterior Leaflet Height	22 mm	24	F	Ranganathan et al. 1970
Anterior Leaflet Height	24 mm	60	M	Chiechi et al. 1956
Anterior Leaflet Height	22 mm	45	F	Chiechi et al. 1956
Anterior Leaflet Height	23 mm	25	M	Rusted et al. 1952
Anterior Leaflet Height	21 mm	25	F	Rusted et al. 1952
Posterior Leaflet Height	14 mm	50	p	Carpentier et al. 1976
Posterior Leaflet Height	14 mm	26	M	Ranganathan et al. 1970
Posterior Leaflet Height	12 mm	24	F	Ranganathan et al. 1970
Posterior Leaflet Height	14 mm	60	M	Chiechi et al. 1956
Posterior Leaflet Height	12 mm	45	F	Chiechi et al. 1956
Posterior Leaflet Height	13 mm	25	M	Rusted et al. 1952
Posterior Leaflet Height	12 mm	25	F	Rusted et al. 1952

14

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

Figure 5. Typical stress-strain characteristics of mitral valve leaflets. Pre-transition (A), transition (B), and post-transition (C) properties.

that most of the total leaflet stretch is associated with the relative elastic properties of the leaflet prior to reaching transition.

Based on studies of Ghista and Rao (1972) and Miller et al. (1981), transition for the leaflets is reached at low transvalvular pressure (between 2 and 13 mm Hg). Lack of apparent leaflet stretch in angio¬ graphic and ultrasound imaging studies support the conclusion of Rushmer et al. (1956) and Miller et al. (1981) that the valve leaflets and chordae tendineae are normally under tension throughout the cardiac cycle and that this tension is sufficient to cause the leaflets to operate in the post-transitional region at all times.

Model assumptions:

1. The presystolic leaflet heights, which represent pre-stressed dimen¬ sions, are anterior leaflet height (AMVIL) = 2.4 cm, and posterior leaflet height (PMVIL) = 1.4 cm.

Table 2. Biomechanical properties of mitral valve leaflets ex situ.

Pre-Transition Modulus dyne /cm2-	Post-Transition Modulus dyne /cm2	Transition Stress dyne /cm2	Transition Strain %	Reference
1 • 105	5 • 107	3 • 104		Ghista and Rao 1972
1.1 • 105	2.9’ 107	3.4- 104	14.3	Clark 1973
NO oo	8.3 • 107	3.8- 104	15.0	Clark and Butterworth 1971

MODELING MITRAL VALVE MOTION

15

Anterior Leaflet

Figure 6. Elliptically shaped leaflets. Major axes drawn between annulus attachment and leaflet free edges.

2. The leaflets are uniform, thin membranes which are only capable of supporting internal stress in tension (Clark and Sutera 1973).

3. An infinitesimal strip of leaflet selected from the middle portion of each leaflet will represent the position and profile of the mitral leaflets and that this leaflet strip can only move in the x-z plane (Clark and Sutera 1973) (Fig. 3).

4. The leaflet assumes an elliptical shape which has as its major axis an imaginary line joining the free edge of the leaflet to the point of attachment of the leaflet to the annulus (Fig. 6).

5. The extent of coaptation is determined by the natural intersection of elliptical segments drawn to represent the anterior and poste¬ rior leaflets (Fig. 7).

6. The forces exerted by the chordae tendineae on the free edges of the leaflets can be represented as a distributed tension along the entire free edges (Clark and Sutera 1973).

7. The attachments between the annulus and the leaflets and between the chordae tendineae and the leaflets can be regarded as ideal hinges which offer no resistance to rotation (Clark and Sutera 1973).

16

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

z

Figure 7. Zone of leaflet coaptation as determined by the natural intersection of ellip- tically shaped leaflets.

8. The inertial forces are neglected throughout the analysis and the mechanical forces generated by transvalvular pressure are treated in a quasi-static manner.

9. The mitral valve leaflets are pre-stressed and can be characterized by their post-transition modulus (MVE = 5 • 107 dyne/cm2) (Ghista and Rao 1972).

10. The tension or stress in the leaflet (MVT) can be calculated by the following equation (Miller et al. 1981):

MVT = 666 • TP • ANL ^2)

HL

where MVT is leaflet tension (dyne/cm2), TP is transvalvular pres¬ sure (mm Hg), ANL is annulus diameter measured along x-axis (cm), and HL is leaflet thickness (assumed to be 0.05 cm).

11. The strain of the leaflets (MVSTR) is:

MVSTR = MVT (3)

MVE

12. The height of each leaflet is:

AMVL = AMVIL • (1 + MVSTR), (4)

where AMVL is the anterior mitral valve leaflet height (cm), and AMVIL is the anterior mitral valve leaflet height initially (assumed to be 2.4 cm). A similar expression applies for calculat¬ ing the height of the posterior mitral valve:

MODELING MITRAL VALVE MOTION

17

Z Z

Figure 8. Diagrammatic representation of the initial geometry of the mitral apparatus. Point Q is located at the leaflet free edges. A is the angle between the chordae tendi- neae and a line parallel to the z-axis.

PM VL = PMVIL • ( 1 + MVSTR). (5)

Input data:

Hypothetical — The initial position (Figs. 8A and B) of the leaflet free edges (Q) is QX = 2.0, QY = 0.0, and QZ = —0.9.

Clinical — The initial position of the leaflets may be determined using real-time, two-dimensional ultrasound imaging techniques; however, translation of axes from a transducer-centered coordinate system to that used in this model must be performed to insure appropriateness of the data.

Mitral Valve Annulus

The annulus consists of dense collagenous tissue with scattered thin elastic fibers and serves as a framework for attachment of the mitral valve leaflets (Davila and Palmer 1962). Viewed from above with the atria removed (Fig. 9), the annulus consists of (1) a fibrous trigone sit¬ uated between the anterior leaflet and the aortic and tricuspid valves,

18

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

Left Fibrous Trigone

Figure 9. Anatomy of the mitral valve annulus (modified from Silverman and Hurst

1968).

and (2) a rather poorly defined band of fibroelastic tissue which forms the attachment site for the posterior leaflet (Silverman and Hurst 1968).

Besides serving as a base for leaflet attachment, the annulus may be involved in insuring competence of the mitral valve (Perloff 1976). Tsakiris et al. (1971) have demonstrated, using anesthetized dogs, that the annulus undergoes active contraction. After reaching a maximum size in late diastole, the area of the annulus decreases by 19 to 34% dur¬ ing atrial and ventricular systole. One-half to two-thirds of this decrease in area apparently occurs during atrial contraction. This nar¬ rowing of the annulus is eccentric: The portion of the annulus forming the attachment for the posterior leaflet moves toward a relatively fixed site of anterior leaflet attachment, the fibrous trigone. The degree of

Table 3. Selected anatomical data for mitral annulus (from autopsy of normal human subjects).

Parameter	Average Number of Value Subjects Sex	Reference
Circumference	9 cm	24	11M, 13F Bulkley and Roberts 1975
Circumference	11.6 cm	60	p	Carpentier et al. 1976
Circumference	9 cm	26	M	Ranganathan et al. 1970
Circumference	7.5 cm	24	F	Ranganathan et al. 1970
Circumference	10.0 cm	60	M	Chiechi et al. 1956
Circumference	9.0 cm	45	F	Chiechi et al. 1956
Circumference	9.9 cm	25	M	Rusted et al. 1952
Circumference	8.5 cm	25	F	Rusted et al. 1952
Intercommissural Diameter	2.5 cm	25	M	Rusted et al. 1952
Intercommissural Diameter	2.1 cm	25	F	Rusted et al. 1952
Area of Annulus	7.93 cm2	8	M	Chiechi et al. 1956
Area of Annulus	6.42 cm2	8	F	Chiechi et al. 1956

MODELING MITRAL VALVE MOTION

19

narrowing of the annulus is a function of several factors, including duration of the P-R interval, duration of the ventricular systole, ven¬ tricular volume during diastole, and degree of emptying during systole. Table 3 is a compilation of published reports regarding dimensions of the human mitral valve annulus.

Model assumptions:

1. The annulus remains at right angles to the long axis of the ven¬ tricle during systole (Tsakiris et al. 1971).

2. The annulus does not rotate relative to the ventricle during systole (Tsakiris et al. 1971).

3. The orthogonal coordinate system used in this simulation is cen¬ tered at the annular attachment of the mid-point of the anterior leaflet (Fig. 1).

4. The annulus narrows at a constant rate throughout systole.

Input data:

Hypothetical — Annulus diameter (ANEDL) at the start of systole — 2.90 cm. Annulus diameter (ANESL) at the end of ventricular ejection = 2.73 cm. (These dimensions are based on assuming a circular annulus with a maximal diastolic circumference — 10 cm, a total reduction in annulus area of 26.5% which corresponds to a decrease in diameter of 14.3%, and contraction during atrial systole accounting for 63% of the total narrowing.)

Clinical— Annulus measurements, obtained using cineangio¬ graphy or ultrasound imaging, may be substituted for hypotheti¬ cal data.

Chordae Tendineae

Chordae tendineae radiate from the tips of both papillary muscles to attach to the ventricular border of the mitral valve leaflets (Fig. 10). Chordae arising from the anterolateral papillary muscle connect to the anterolateral commissure and the adjoining halves of the anterior and posterior leaflets. Similarly, chordae arising from the posteromedial papillary muscle pass to the respective commissure and portions of the leaflets (Davila and Palmer 1962; Silverman and Hurst 1968).

Ranganathan et al. (1976) have categorized chordae tendineae on the basis of their size and location of attachment to the mitral valve. Chor¬ dae attaching to the anterior leaflet are classified as either (1) rough- zone chordae which branch before inserting on or near the free edge of the leaflet, or (2) strut chordae which are relatively large chordae and insert directly on the edge of the leaflet near its mid-portion. Posterior leaflet chordae are either (1) rough-zone chordae, (2) cleft chordae which attach between leaflet scallops, or (3) basal chordae which attach near the annulus and may arise directly from the wall of the left ventri¬ cle. An average of 25 primary chordae tendineae is associated with the

20

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

z

Figure 10. Anatomy of the chordae tendineae (modified from Davila and Palmer 1962).

mitral valve; 9 attach to the anterior leaflet (7 rough-zone and 2 strut types), 14 attach to the posterior leaflet (10 rough-zone, 2 cleft, and 2 basal), and 2 attach to the commissures separating the anterior and pos¬ terior leaflets (Lam et al. 1970; Ranganathan et al. 1976). The lengths of chordae attaching to the leaflets are summarized in Table 4.

Chordae tendineae are composed of three layers— (1) an outer layer of endocardial cells, (2) an intermediate layer of loosely meshed collagen and elastic fibers, and (3) an inner core of dense collagen (Fenoglio et al. 1972; Lim and Boughner 1977). The mechanical properties of chor¬ dae are similar to those of the mitral valve leaflets, in that these struc¬ tures exhibit a non-linear stress-strain characteristic (Fig. 11) (Lim and Boughner 1975). Salisbury et al. (1963) measured tension along chordae tendineae throughout the cardiac cycle and reported that (1) presystolic chordae tendineae tension can be as high as 12 g; (2) during the isovo- lumetric contraction phase, tension in the chordae tendineae rises simultaneously with left ventricular pressure; and (3) during ejection, tension either drops or levels off and does not appear to be directly related to left ventricular pressure.

Model Assumptions:

1. Chordae tendineae insert on the free edges of the mitral valve leaf¬ lets.

2. Chordae tendineae are freely hinged at the sites of attachment to the leaflets and papillary muscles.

MODELING MITRAL VALVE MOTION

21

Table 4. Selected anatomical data for chordae tendineae (from autopsy of normal human subjects).

Parameter	Average Number of Value Subjects	Sex	Reference
Chordae Tendineae Length Anterolateral P.M. to Anterior Leaflet	1.5 cm	50	?	Carpentier et al. 1976
Chordae Tendineae Length Posteromedial P.M. to Anterior Leaflet	1.7 cm	50	p	Carpemier et al. 1976
Chordae Tendineae Length Anterior Leaflet	1.75 cm	50	27M, 23F	Lam et al. 1970
Chordae Tendineae Length Posterior Leaflet	1.4 cm	50	?	Carpentier et al. 1976
Posterior Leaflet	1.4 cm	50	27M, 23F	Lam et al. 1970

STRAIN (%)

Figure 11. Biomechanical properties of the chordae tendineae. Cross-sectional area = 0.004 - 0.006 cm2; strain-rate = 12.7 cm /min (from Lim and Boughner 1975).

22

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

3. Chordae tendineae operate in a pre-stressed condition at the start of systole (Salisbury et al. 1963) and thus may be characterized by their post-transition elastic modulus throughout systole (CTE = 2 • 109 dyne/cm2) (Lim and Boughner 1975).

4. Chordae tendineae lengths reported in Table 4 represent pre¬ stressed measurements. The initial length for all chordae (CTIL) equals 1.5 cm.

5. Chordae tendineae tension (CTT) is a function of two parameters — transvalvular pressure (TP) and ventricular geometry. The chordae exert tension on the free edges of the leaflets to res¬ train their atrial-ward movement. Ventricular geometry influences the angle that the chordae make with respect to the z-axis and thus the tension within the chordae counteracting atrial-ward movement of the leaflets (Fig. 8D). Based on a study by Salisbury et al. (1963) and considerations for ventricular geometry, an empirical formula relating CTT to TP has been derived:

CTT = 650 • _ _ (6)

COSA • CTA

where CTT is chordae tendineae tension (dyne/cm2), TP is trans¬ valvular pressure (mm Hg), COSA is the cosine of angle A, and CTA is the area of an average chordae tendineae (assumed to be .004 cm2).

6. Chordae tendineae strain (CTSTR) may be calculated as follows:

CTSTR = CTT ; (7)

CTE

and the length of the chordae tendineae may be expressed by the following equation:

CTL = CTIL ( 1 + CTSTR) (8)

where CTL is the chordae length (cm), and CTIL is the initial chordae length (assumed to be 1.5 cm).

Papillary Muscles

The two groups of papillary muscles, the anterolateral and poste¬ romedial, are located immediately below the respective commissures of the leaflets. The antereolateral papillary muscle usually has a single muscle belly and is continuous with the ventricle along the anterolat¬ eral free wall; the posteromedial papillary muscle typically consists of two or three distinct muscle bellies and is located at the junction of the

MODELING MITRAL VALVE MOTION

23

posterior free wall and the ventricular septum (Rusted et al. 1952; Chie- chi et al. 1956; Estes et al. 1966; Silverman and Hurst 1968; Roberts and Cohen 1972). Papillary muscles may also be classified on the basis of their morphology as follows: (1) Completely tethered, the papillary muscle is fully adherent to the ventricular myocardium; (2) Free and fingerlike, with one-third or more of the papillary muscle protruding freely into the ventricular cavity; and (3) Mixed or intermediate, with considerable trabecular attachments and tethering between the papillary muscle and ventricular wall (Ranganathan and Burch 1969).

The papillary muscles normally arise from the left ventricular wall at the apical and middle thirds (Silverman and Hurst 1968; Perloff 1976). They are oriented parallel to the left ventricular wall to which they are attached. The attachment usually extends almost the full length of the muscle and consists of crossing muscle bundles and threadlike bands (Estes et al. 1966; Silverman and Hurst 1968).

There is considerable disagreement among investigators regarding the timing and extent of papillary muscle contraction. Cronin et al. (1969) indicate that ventricular wall contraction precedes papillary muscle contraction. According to Semafuko and Bowie (1975), the anterolateral papillary muscle lengthens during isovolumetric contrac¬ tion and the early ejection phase of the cardiac cycle. This study sug¬ gests that papillary muscle shortening may occur only when the force of muscle contraction exceeds the forces that tend to elongate the papil¬ lary muscle, i.e. chordae tendineae tension resisting atrial-ward leaflet excursion. Other investigators report that the papillary muscles shorten throughout systole (Burch and DePasquale 1965; Hirakawa et al. 1977). The total shortening, measured in dogs, varies in published data from 10% to 22.8% of the total length (Grimm et al. 1975; Hirakawa et al. 1977; Huntsman et al. 1977).

Model assumptions:

1. The papillary muscles are symmetrically oriented relative to the x- z plane and attach to the ventricular wall at points two-thirds of the distance from the annulus to the apex (Fig. 8D).

2. The papillary muscles are tethered along their entire lengths to the ventricular wall and maintain a longitudinal orientation, parallel to the x-axis, throughout systole.

3. The presystolic lengths of the papillary muscles are determined from geometric considerations following specifications of the pre¬ systolic position of the mitral valve, chordae tendineae lengths, and left ventricular dimensions.

4. A total contraction of 16.4% of the presystolic papillary muscle length occurs linearly with respect to time during the isovolumet¬ ric contraction and ejection phases of systole.

24

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

Table 5. Selected anatomical data for the left ventricle (normal human subjects).

Average Number of

Parameter Value Subjects Sex Method3 Reference

Annulus to Apex Length at

End-Diastole (AAEDL)	7.0 cm	24	11M, 13F	A	Bulkley and Roberts 1975
AAEDL	7.3 cm	25	M	A	Rusted et al. 1952
AAEDL	6.7 cm	25	F	A	Rusted et al. 1952
Minor Axis Length at End-Diastole
(MAEDL)	5.0 cm	10	?	E	Fortuin et al. 1972
MAEDL	4.40 cm	20	11M, 9F	E	McDonald et al. 1972
MAEDL	5.18 cm	37	M	E	Gerstenblith et al. 1977
Minor Axis Length at End-Systole
(MAESL)	3.8 cm	10	p	E	Fortuin et al. 1972
MAESL	2.83 cm	20	1 1M,9F	E	McDonald et al. 1972
MAESL	3.44 cm	37	M	E	Gerstenblith et al. 1977

aA — autopsy; E = echocardiography

Left Ventricle

Cardiac performance traditionally has been defined according to hemodynamic determinants and only recently have attemps been made to correlate these with muscle function and geometric considerations (Liedtke et al. 1972). The left ventricle has a particularly important role in the anatomy and physiology of the mitral apparatus. Ventricular shape and contraction patterns influence value motion directly through changes in transvalular pressure and indirectly through alternations in geometric relationships between the papillary muscles and the valve leaflets.

Major dimensional changes of the left ventricle are associated with the ejection phase of systole. During ejection, there is marked contrac¬ tion of the left ventricle which results in continuous repositioning of the papillary muscles relative to the leaflets /annulus. Altered left ven¬ tricular shape will affect the overall operation of the mitral apparatus due to the complex geometric interrelationships among components of the mitral apparatus.

Table 5 summarizes published data regarding ventricular dimensions. Table 6 lists results of various studies that have attemped to measure the extent of ventricular contraction.

Model assumptions:

1. The left ventricle is a truncated ellipsoid of revolution (Koushan- pour and Codings 1966; Hutchins et al. 1978) that both shortens and contracts symmetrically about its major axis throughout the ejection phase of systole (McDonald 1970).

MODELING MITRAL VALVE MOTION

25

Table 6. Selected physiological data for the left ventricle.

Parameter	Average Value	Subjects	Number of Subjects	Sex	Method3 Reference
Annulus to Apex % Shortening	6.9-8. 1%	Canine	5	?	S	Hirakawa et al. 1977
Annulus to Apex % Shortening	8%	Canine	5	p	c	Liedtke et al. 1972
Annulus to Apex % Shorteing	4.6%	Canine	13	?	A	Ross et al. 1967
Minor Axis Length % Shortening	25%	Human	?	?	R	Daughters et al. 1977
Minor Axis Length % Shortening	35.5%	Human	20	11M	E	McDonald et al. 1972
Minor Axis Length % Shortening	61%	Canine	5	9F ?	C	Liedtke et al. 1972
Minor Axis Length % Shortening	26%	Canine	13	?	A	Ross et al. 1967
Minor Axis Length % Shortening	34%	Human	37	M	E	Gerstenblith et al. 1977
Minor Axis Length % Shortening	24%b	Human	10	p	E	Fortuin et al. 1972

aA = autopsy (special fixation); C = cineangiocardiography;

E = echocardiography; R = radiopaque markers; S = sonomicrometry. b Computed from anatomical data.

2. The contractions along the major and minor axes are linear func¬ tions of time (i.e. constant rate of contraction) (Bishop et al. 1969; Hinds et al. 1969; Bishop and Horwitz 1970).

Input data:

Hypothetical — Mitral annulus to apex dimensions (AAL) are end- diastole (AAEDL) — 7.30 cm, and end-systole (AAESL) = 6.75 cm — resulting in an overall 7.5% shortening. Minor axis dimen¬ sions (MAL) are end-diastole (MAEDL) = 4.86 cm, and end-systole (MAESL) = 3.34 cm — resulting in an overall 31% shortening. Extent of truncation (TRUNC): The annulus is located at 60% of the total eliptical major axis; major axis end-diastole = 12.17 cm, and major axis end-systole = 1 1.25 cm.

Clinical — Actual dimensional measurements of annulus-to-apex and minor axis may be obtained using cineangiography or ultra¬ sound imaging and degree of truncation estimated from these measurements.

MODEL OPERATION

Mitral value motion is predicted by a computer program that de¬ scribes the dynamic alterations in the various components of the mitral

26

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

Table 7. Input values for the model.

Abbreviation	i Parameter	Assumed Value
EDT	Electromechanical Delay Time	22 msec
IVCT	Isovolumetric Contraction Time	71 msec
ET	Ejection Time	292 msec
TP	Transvalvular Pressure	(Refer to Fig. 2)
AMVIL	Anterior Leaflet Height (Initial)	2.4 cm
PMVIL	Posterior Leaflet Height (Initial)	1.4 cm
MVE	Mitral Valve Leaflet Elastic Modulus	5 • 107 dyne/ cm2
QX	X — Coordinate of Leaflet Free Edge (Initial)	2.0 cm
QY	Y — Coordinate of Leaflet Free Edge (Initial)	0.0 cm
Qz	Z — Coordinate of Leaflet Free Edge (Initial)	—0.9 cm
ANEDL	Annulus Diameter at End-Diastole	2.70 cm
ANESL	Annulus Diameter at End- Systole	2.56 cm
CTIL	Chordae Tendineae Length (Initial)	1.5 cm
CTE	Chordae Tendineae Elastic Modulus	2 • 109 dyne /cm2
PMPER	Papillary Muscles-Percent Shortening	16.4%
AAEDL	Annulus to Apex — End-Diastolic Length	7.3 cm
AAESL	Annulus to Apex — End-Systolic Length	6.75 cm
MAEDL	Minor Axis — End-Diastolic Length	4.86 cm
MAESL	Minor Axis — End-Systolic Length	3.34 cm
TRUNC	Truncation — Percent (annulus to apex /major axis
	length)	60%
GAPIL	Distance Between the Point of Annular Attachment of
	the Posterior Leaflet and the Ventricular Wall (Initial)	0.0 cm
INCRT	Time Increment to Step Through Program	10 msec

apparatus. Following input of clinically obtained and/or hypothetical data (Table 7), the computer program initializes the geometry of the model using the coordinate system previously described (Fig. 1). The anterior portion of the annulus is located at x=0, y=0, and z=0 (Fig. 8A). The leaflets are represented by elliptical segments in the x-z plane, extending from the annulus to the point of coaptation (Q) at the leaflet free edges (Fig. 8A). In a y-z plane (x=Qx), the leaflets are represented as single point, Q (Fig. 8B). As previously described, a truncated ellipse is used to model the left ventricle. Its major axis is parallel to the z-axis and located within the x-z plane; the minor axis is parallel to the x-y plane and separated from this plane by a distance specified by the extent of truncation (Fig. 8C). The ellipse representing the ventricle is assumed to pass through the posterior portion of the annulus (x= ANEDL, y=0, z=0), but can be positioned anywhere along the x-axis by specifying a separation between the annulus and ventricle wall (GAPIL) as an input condition. The papillary muscles are represented as straight lines oriented parallel to the z-axis in a y-z plane (x=Qx), and attaching to the ventricular wall at a point two-thrids the distance from annulus to apex. The lengths of the papillary muscles are deter¬ mined by geometric considerations — specifically, the intersection of

MODELING MITRAL VALVE MOTION

27

lines representing chordae tendineae with vertical lines projecting from the papillary muscle attachment sites toward the annulus (Fig. 8D). The computer program is designed so that this initial geometry can be easily altered to describe a wide range of clinical or hypothetical con¬ figurations of the mitral apparatus.

The model is “set in motion” by performing a series of subroutines that describe the dynamic alterations in the various components of the mitral apparatus. These alterations include (1) contractility of the annulus, papillary muscles, and the left ventricle (linear functions of time); (2) mechanical deformation of the mitral value leaflets (linearly related to transvalvular pressure); and, (3) lengthening of the chordae tendinease (a function of transvalvular pressure and ventricular geome¬ try).

Calculations are performed to describe the geometry of the mitral apparatus at specific time intervals (INCRT) throughout systole. Sub¬ routines are executed in the following sequence: (1) annulus contrac¬ tion; (2) ventricular contraction (determines the x,y, and z coordinates of the sites for attachment of papillary muscles); (3) papillary muscle contraction (specifies the z coordinate of the papillary muscles-chordae tendineae junctions); (4) chordae tendineae length, Eq. (8) (determines point Q); and , (5) mitral value leaflet heights, Eqs. (4) and (5).

Note: During the electromechanical delay (EDT) phase of systole, only the annulus contraction subroutine is utilized; during the isovolumetric contraction (IVCT) phase, all subroutines except ventricular contrac¬ tion are performed.

The output of the program is a time-series description of the mitral value components throughout systole. The following numerical output is listed at time intervals (INCRT) specified in the input data set: (1) anterior and posterior coordinates of the annular ring, (2) annulus to apex distance, (3) ventricular minor axis length, (4) papillary muscle length, (5) chordae tendineae length, (6) coordinates of point Q, (7) anterior and posterior leaflet heights, (8) major and minor axes for leaf¬ let ellipses, and (9) maximum leaflet deflection in the z-direction for each leaflet.

RESULTS Normal Model

The output of this model, using the hypothetical input data indicated in Table 7, is summarized in Fig. 12. Point Q moves slightly down¬ ward (0.02 cm) from its initial position during the isovolumetric con¬ traction phase and then moves upward approximately 0.1 cm during the ejection phase. The anterior leaflet elongates approximately 0.05 cm and the posterior leaflet elongates approximately 0.02 cm. The

28

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

Z

Figure 12. Mitral valve position /profile at selected times during systole. Input data as specified in Table 7. AA is the anterior portion of the annulus, AP is the posterior portion of the annulus, and point Q is located at the leaflet free edges.

maximum leaflet deflection in the z-direction is less than 0.1 cm above the plane of the annulus. Fig. 12 illustrates, in a graphical way, the motion of the leaflets and demonstrates the relatively small displace¬ ments throughout systole.

Sensitivity Analysis

Perturbation of the model may be performed by altering any of the input parameters. In terms of mitral valve prolapse, the model is insen¬ sitive to changes in the annulus diameter, chordae tendineae length, time of onset of papillary muscle contraction, time of onset of ventricu¬ lar contraction, ventricular minor axis dimension, and annulus to apex distance. The model is moderately sensitive to changes in the percent of papillary muscle contraction and changes in the papillary muscle att¬ achment point. The model is extremely sensitive to change in leaflet and chordae tendineae properties.

Three selected perturbations are illustrated in Figs. 13-15. Increasing the elasticity of the leaflets (MVE = 5T06 dyne/cm2, —1/10 the stiff¬ ness of normal valvular tissue) produces a rapid ballooning of the ante¬ rior leaflet (Fig. 13). Increasing the elasticity of the chordae tendineae (CTE = 1 TO8 dyne/cm2, —1/20 the stiffness of normal chordae tendi¬ neae) results in an early prolapse of both leaflets (Fig. 14). Eliminating

MODELING MITRAL VALVE MOTION

29

Figure 13. Mitral valve position /profile at selected times during systole. Input data as specified in Table 7, except the leaflets have increased elasticity (MVE = 5 • 106 dyne/cm2). AA is the anterior portion of the annulus, AP is the posterior portion of the annulus, and point Q is located at the leaflet free edges.

papillary muscle contraction produces a late prolapse, which is most noticeable in the posterior leaflet (Fig. 15).

DISCUSSION

Biological models are, by necessity, limited in scope and subjective in nature (Yates 1978). They represent an attempt to mathematically express anatomical, physiological, and/or pathological concepts that quite often, are not fully defined. Despite these inherent limitations in biological models, they are extremely useful tools for (1) identifying the essential components of a system, (2) quantifying information about a subject, (3) exposing contradictions or incompleteness in data sets, (4) examining major implications regarding a system, and (5) determining the effects of selected perturbations upon the performance of a system (Yates 1978).

This model will hopefully provide a better overall understanding of the functioning of the mitral value and associated structures in relation to prolapse. The model has established that the basic components that must be included in any model of the mitral valve prolapse are mitral value leaflets, annulus, chordae tendineae, papillary muscles, and the left ventricle. Alteration in the physical dimensions, mechanical prop-

30

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

Figure 14. Mitral valve position /profile at selected times during systole. Input data as specified in Table 7, except the chordae tendineae have increased elasticity (CTE = 1 • 108 dyne/cm2). AA is the anteior portion of the annulus, AP is the posterior portion of the annulus, and Q is located at the leaflet free edges.

erties, or contractile properties of these elements can markedly influ¬ ence the performance of the mitral value itself.

Construction of this model represents a compilation of published anatomical and physiological information regarding the mitral appara¬ tus. Review of the literature indicates that an adequate, quantitiative description of dynamic cardiac anatomy and physiology does not exist. Published data regarding the mitral apparatus are fragmentary and occasionally contradictory. Unfortunately, this rather tenuous data base has been used to support various hypotheses for mitral valve prolapse.

The primary abnormalities producing mitral valve prolapse still elude description. Prolapse has been associated with (1) myxomatous degeneration of the valve leaflets (Read et al. 1965; Pomerance 1969; Kern and Tucker 1972; Marshall and Shappell 1974; Silver 1976), (2) anomalous arrangement of chordae tendineae (Edward 1971; Silver 1976), (2) anomalous arrangement of chordae tendineae (Edwards 1971; Silver 1976), (3) coronary artery disease (Aranda et al. 1976), (4) left ven¬ tricular asynergies (Pisano et al. 1977), (5) annulus dilatation (Bulkley and Roberts 1975), (6) papillary muscle dysfunction (Nutter et al. 1975; Cobb's and King 1977), and (7) postural changes in left ventricular geometry (Fontana et al. 1975). Results of this modeling effort support the belief of Barlow et al. (1968), who claim that there is obviously more than one etiology for mitral valve prolapse.

MODELING MITRAL VALVE MOTION

31

Figure 15. Mitral valve position /profile at selected times during systole. Input data as specified in Table 7, except the papillary muscles are non-contractile (PMPER = 0%). AA is the anterior position of the annulus, AP is the posterior portion of the annulus, and point Q is located at the leaflet free edges.

Perhaps the greatest value of this model is in predicting mitral valve profile /position under various conditions. Perturbation studies indi¬ cate that prolapse can either result from or be accentuated by (1) reduc¬ ing the degree of annulus contraction (annular calcification), (2) increasing the elasticity of the leaflets (myxomatous degeneration), (3) increasing the elasticity of the chordae tendineae, (4) decreasing the contractility of the papillary muscles (coronary artery disease), (5) decreasing end-systolic ventricular volume, and (6) increasing preload /afterload. Particularly dramatic changes occur with alterations in either leaflet properties, chordae tendineae properties, or papillary muscle contractility.

One exciting potential application of this model is its use as a clini¬ cal tool in determining the underlying pathological alteration(s) con¬ tributing to a particular pattern of mitral valve prolapse. Mitral valve profiles obtained in patients using either biplane cineagiography or ultrasound imaging could be compared to profiles based on selected model perturbations and therby establish relationships between mitral valve profiles and specific pathological conditions. It is apparent in Figures 13-15 that a particular perturbation may result in a distinctive time sequence of mitral profiles. This potentially provides the cardiol¬ ogist with an extremely valuable diagnostic and prognostic tool.

32

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

Final conclusions regarding the possible value of this model await validation studies to determine the accuracy of simulation in predicting mitral valve performance in the normal subject and in those persons exhibiting mitral valve prolapse.

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THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

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THIN LAYER CHROMATOGRAPHY OF NITROGEN HETEROCYCLES ON A MODIFIED SILICA GEL SUPPORT

by W. E. RUDZINSKI

Department of Chemistry

Southwest Texas State University

San Marcos , TX 78666

ABSTRACT

Square planar dialkylphosphorodithioate complexes of nickel have been sorbed onto a silica gel surface, and the extent of adduct formation with nitrogen heterocyclic bases has been evaluated and explained in terms of steric hindrance between the nickel complex and associating base.

INTRODUCTION

The neutral square planar dialkylphosphorodithioate complexes of nickel have a tendency to form tetragonal adducts in the presence of Lewis bases (Coucouvanis 1979). If the Lewis base is a heterocyclic ni¬ trogen compound, the structure of the heterocycle plays a dominant role in the extent of adduct formation (Rudzinski 1977). In order to study the coordination chemistry of bis(0,0’-dimethylphosphoro- dithioate) nickel (II), Ni (DMPDT>2, the nickel complexes are sorbed onto a silica gel plate forming a surface available for adduct formation. Nitrogen heterocyclic bases then are spotted on the plate and their affinity for the surface evaluated. Bulky or sterically-hindered bases are not expected to have a high retentivity on the surface. If the dialkyl¬ phosphorodithioate ligand had large alkoxy groups bonded to the phosphorus, then these also will affect the extent of adduct formation.

MATERIALS AND METHODS

Bis(0,0’-dimethylphosphorodithioate) nickel (II) was synthesized as described elsewhere (Rudzinski et al. 1977). Bis(0,0’-diethylphos- phorodithioate) nickel (II) was synthesized in the same manner as above by using ethanol instead of methanol.

The chelate was dissovlved in reagent grade benzene, and the solution was sprayed on a thin layer silica gel plate (Eastman Chromagram Sheet 6061) using a dichlorofluoromethane aerosol. Three coats were sufficient to cover the silica gel plate. The plates then were allowed to air dry for ten minutes.

The Texas Journal of Science, Vol. XXXV, No. 1, March 1983

38

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

Table 1. Thin layer chromatography results.

Heterocycle	# of Samples	Rr	Standard Deviation
isoquinoline	Ni(DEPDT)2 with 1-propanol as 9	the solvent .83	2 X 10"2
quinoline	3	.76	2 X 10~2
8-aminoquinoline	3	.75	3 X 10"2
6-methoxyquinoline	3	.77	5 X 10“2
aridine	Ni(DMPDT)2 with 2-propanol as 4	the solvent .68	6.2 X 10~2
isoquinoline	4	.33	1.7 X 10~2
isoquinoline	Ni(DMPDT)2 with 1 -propanol as the solvent 10 .04	1.2 X 10"2
pridine	7	0	0
1 , 1 0-phenanthroline	2	.005
quinoline	12	.74	7.1 X 10“2
2-methoxyquinoline	3	.65	9.1 X 10“2

The nitrogen heterocycles used for the study were the following: (1) pyridine (Mallinckrodt), (2) quinoline (Aldrich Chemical Co.), (3) iso¬ quinoline (J. T. Baker Chemical Co.), (4) 2-methoxy quinoline (Aldrich Chemical Co.), (5) 6-methoxyquinoline (K and K Laboratories), (6) 8- aminoquinoline (G. Frederick Smith Chemical Co.), (7) acridine (Aldrich Chemical Co.), (8) phenazine (Aldrich Chemical Co.), and (9) 1,10-phenanthroline (J. T. Baker Chemical Co.). Isoquinoline, quino¬ line, and pyridine were redistilled. The remaining compounds were used as received from the manufacturer.

The developing solvents (ethanol, 1 -propanol, 2-propanol) were redis¬ tilled. Liquid samples were spotted at one end of the plate and then developed by an ascending technique in a closed container saturated with developer vapor. The plate then was dried and the Rf values mea¬ sured. No reagent was needed for the detection of the components since they were self-indicating. Solids were dissolved in the minimum amount of developing solvent, and then spotted and developed as above.

RESULTS AND DISCUSSION

The results of the thin layer chromatography are summarized in Table 1. The Rf values obtained with Ni(DEPDT)2 as the stationary phase and 1 -propanol as the mobile phase indicate that there is little variation in the Rf value with a variation in heterocycle. This is ascribed to the steric hindrance provided by the ethoxy group bonded to the phosphorus atom. In this case, the alkyl group of the phosphorodi- thioate is the primary regulator in adduct formation. The silica gel support does not seem to influence significantly the retention of the

CHROMATOGRAPHY OF NITROGEN HETEROCYCLES

39

heterocycles (all Rf > 0.75). When Ni (DMPDTJa is the stationary phase and 1 -propanol is the solvent, the nature of the heterocyclic base is a primary regulator in adduct formation. As an example, quinoline has an Rf value of 0.74 while isoquinoline essentially does not move (Rf = 0.04). This is attributed to the fact that quinoline is sterically hindered in aligning itself for proper coordination:

x\ /K /N /

/ Ks/NVs/P\;

X = -0CH3, ^ 0CH2CH3

Isoquinoline on the other hand can coordinate with a minimum of steric interaction:

X = -0CH3, - 0CH2CH3

The adducts of pyridine (Ooi and Fernando 1967), and 1,10- phenanthroline (Shetty and Fernando 1970) with dialkylphosphorodi- thioate nickel (II) are known to exist and have been characterized by single crystal X-ray structure determinations, and the low Rf values support the interpretation of adduct formation.

Finally, there appears to be a correlation between the solvent and the extent of adduct formation. The longer the carbon chain in the alkyl group of the developing solvent the stronger the adduct formed between the nigrogen heterocycle and Ni(DMPDT)2. In analyzing the compara¬ tive Rf values of quinoline and isoquinoline in ethanol, 2-propanol, and 1 -propanol, quinoline retains essentially the same Rf value, while

40

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

that of isoquinoline decreases (Rf = 0.59 in ethanol, Rf = 0.33 in 2- propanol, Rf = 0.04 in 1 -propanol). This decrease in Rf with develop¬ ing solvent correlates well with the solvent strength of the alcohols (Snyder and Kirdland 1979).

LITERATURE CITED

Coucouvanis, D. 1979. The chemistry of the dithioacid and 1,1-dithiolate complexes, 1968-1977, p. 301-469. In S. J. Lippard (Ed.), Progress in Inorganic Chemistry, v. 26. John Wiley and Sons, New York, NY.

Ooi, S., and Fernando, Q. 1967. The crystal and molecular structure of the adduct of bis(0,0’-diethyldithiophosphato) nickel (II) with pyridine. Inorg. Chem. 6:1558-1562. Rudzinski, W.E. 1977. Stability of transition metal complexes of 0,0’-dialkyldithiophos- phates and their adducts. Ph.D. Dissertion, University of Arizona, Tucson, AZ. Rudzinski, W.E., Behnke, G.T., and Fernando, Q. 1977. A normal coordinate analysis of bis(0,0’-dialkyldithiophosphate) nickel (II) complexes. Inorg. Chem. 16:1206-1210. Shetty, P.S., and Fernando, Q. 1970. Structures of five and six-coordinated mixed- ligand chelates of nickel (II) containing sulfur and nitrogen donor atoms. J. Am. Chem. Soc. 92:3964-3969.

Snyder, L. R., and Kirkland, J. J. 1979. Introduction to Modern Liquid Chromato¬ graphy, 2 Ed. John Wiley and Sons, Inc., New York, NY., 246-268.

SOME STRUCTURAL ASPECTS OF A WESTERN CROSS TIMBERS FOREST IN NORTH CENTRAL TEXAS1

by GLENN C. KROH and JAMES NISBET

Department of Biology

Texas Christian University

Fort Worth, TX 16129

ABSTRACT

Structural aspects of a north-central Texas tract of the cross timbers forest were deter¬ mined. The one-hectare study area was located within the Fort Worth, Texas, Nature Center and Refuge. Specifically, average basal area, frequency distribution of height and size classes, diversity, importance values and taxonomic composition of the forest were determined. Mean basal area by species indicated post oak ( Quercus stellata) is dominant (80%), followed by blackjack oak ( Quercus marilandica) (9%). Mean basal area for all tree species combined was 24.6 m2/ha, indicating that the forest is mature. Tree diversity, cal¬ culated by the Shannon- Weiner method, is 1.03.

INTRODUCTION

The cross timbers, as described by Dyksterhuis (1948), occurs from the Arkansas River in Oklahoma to approximately 150 miles south of the Red River. At the Red River, the forest splits into two bands, the western cross timbers and eastern cross timbers. Rice and Penfound (1955) evaluated different methods of sampling upland oak forests based on the cross timbers of Oklahoma, and later (Rice and Penfound 1959) did a descriptive study of the area. Risser and Rice (1971a) used an ordination technique to determine upland tree species associations of the Oklahoma cross timbers and then (Risser and Rice 1971b) com¬ pared diversity indices with the mixed mesophytic and oak hickory forest in the southern Appalachian region. The oak upland forest was significantly less diverse than those in the eastern United States. The objectives of the present study were to determine structural parameters of a north Texas post-oak forest and contrast some aspects of this community with similar oak forest communities in Oklahoma.

STUDY AREA

The study area is located in the western cross timbers community at the Fort Worth, Texas, Nature Center and Refuge. Principal trees in the undisturbed forest are Quercus stellata (post oak), Quercus mari¬ landica (blackjack oak), Celtis laevigata (hackberry) and Ulmus crassi-

1 Funded by Texas Christian University Research Foundation Grant #B7986. Presented at the 1978 Texas Academy of Science Meeting At Texas Tech University, Lubbock, TX.

The Texas Journal of Science, Vol. XXXV, No. 1, March 1983

42

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

NO. OF 100 m2 samples

Figure 1. Performance curve. Only trees greater than 2.5 cm in diameter were considered. Vertical bars represent ± two standard errors.

folia (cedar elm). The climate is humid subtropical with hot summers. It is also continential, characterized by a wide range in annual tempera¬ ture extremes. Precipitation averages about 81 cm annually, but varies considerably from year to year, ranging from less than 51 to more than 127 cm. Greatest amount of rain occurs during April and May. The soil is a yellow-brown podsolic derived from Cretaceous strata. The study area was selected within the forest on the basis of accessibility and gen¬ eral representativeness of the stand.

Table 1. Density, dominance, frequency, and importance of woody species with DBH of 2.5 cm or greater.3

Species	Relative Density %	Relative Dominance %	Relative Frequency %	Importance Value5
Post Oak	54	80.0	82.0	216.0
Blackjack Oak	24	9.0	13.0	46.0
Hackberry	14	7.0	4.0	25.0
Cedar Elm	5	3.0	1.0	9.0
Red Mulberry	3	0.4	0.06	3.46
TOTAL	100	99.4	100.06	299.46

aWoody species with DBH less than 2.5 cm were Acer negundo, Bumelia lanuginosa, Cornus drummondii, Crataegus sp., Forestiera acuminata, Fraxinus pennsylvanica, Gleditsia tria- canthos, Ilex decidua, Viburnum rufidulum.

bImportance value is the sum of relative density, relative dominance and relative frequency.

CROSS TIMBERS FOREST STRUCTURE

43

DIAMETER CLASSES

CD

OtC

DBH CLASS CM

Figure 2. Frequency distribution of post oak and blackjack oak by diameter at breast height (DBH).

MATERIALS AND METHODS

A 1-ha area was measured and ten 100-m transects, 10 m apart, were established with permanent numbered stakes placed at 25-m intervals. Sampling sites were randomly selected with the aid of a random numbers table. A circular sample of 100 m2 was taken at each site. The number of sites sampled was determined with a performance curve

44

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

15

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l

10

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~r~

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Figure 3. Frequency distribution of trees by height. Only trees with DBH greater than 2.5 cm were considered.

(Greig-Smith 1957), with total basal area used as the criterion (Fig. 1). Twenty sites were sampled.

Only trees with diameters at breast height (DBH) greater than 2.5 cm were measured. Heights were determined using a Haga altimeter. Total basal area, basal area per species, density, frequency, tree diversity using the Shannon-Weiner index (H’ = — T plog2pi; Cox 1980), size and height class frequencies were determined.

RESULTS AND DISCUSSION

A total of 14 species of trees was noted at the study site (Table 1). The four dominant trees were post oak, blackjack oak, hackberry, and cedar elm. Post oak had the greatest importance value (Cox 1980), fol¬ lowed by blackjack oak, hackberry, cedar elm and red mulberry ( Moms rubra). Importance values have been used as a measure of niche size (Whittaker 1970) and may indicate the proportion of site resources used by each species (Kroh and Stephenson 1980).

CROSS TIMBERS FOREST STRUCTURE

45

Post oak and blackjack oak together account for approximately 70% of the total basal area in the upland forests of Oklahoma (Rice and Penfound 1959). In our forest, 80% of the basal area was comprised by post oak and 9% by blackjack oak. Rice and Penfound (1959) indicated that upland forest stands rarely exceed a total basal area of 25 m2/ha. The oak stand in which Johnson and Risser (1974) measured biomass and net primary production had a basal area of 18 m2 /ha. With a mean basal area of 24.6 m2/ha (Fig. 1), the forest we studied seems cer¬ tain to be an old-growth forest and is quite possibly a climax commun¬ ity. The Shannon- Weiner index was 1.03, a value similar to that (0.94) found by Risser and Rice (1971a) in Oklahoma upland forest areas.

Frequency distributions of size classes (Fig. 2) show that blackjack oak may be declining in the study area; its replacement rate seems to be less than one. Post oak, however, appears to be maintaining its popula¬ tion. There may be a dynamic equilibrium between post oak and black¬ jack oak as a function of the availiability of moisture and nutrients. Johnson and Risser (1974) showed that post oak required a higher level of moisture and nutrients than blackjack oak. Replacement rates may decrease in post oak populations during years of drought, releasing blackjack oak seedlings from competition.

Height-class frequency distributions show that about 50% of the trees sampled were between 5 and 10 m tall, with only 14% taller than 10 m (Fig. 3). Red mulberry was restricted to the lower understory; cedar elm was not greater than 10 m tall; and post oak, blackjack oak, and hack- berry were found in all three layers.

LITERATURE CITED

Cox, G. 1980. Laboratory Manual of General Ecology. 4th ed. W. C. Brown Co., Dubuque, Iowa.

Dyksterhuis, E. J. 1948. The vegetation of the western cross timbers. Ecol. Monogr. 18:325-376.

Greig-Smith, P. 1957. Quantitative Plant Ecology. Butterworths, London.

Johnson, F. L., and P. G. Risser. 1974. Biomass, annual net primary production, and dynamics of six mineral elements in a post oak-blackjack oak forest. Ecology 55:1246- 1258.

Kroh, G. C., and S. N. Stephenson. 1980. Effects of diversity and pattern on relative yields of four Michigan first-year fallow-field plant species. Oecologia 45:366-371.

Rice, E.L., and W.T. Penfound. 1955. An evaluation of the variable-radius and paired- tree methods in the blackjack- post oak forest. Ecology 36:315-320.

Rice, E. L., and W. T. Penfound. 1959. The upland forests of Oklahoma. Ecology 40:593-608.

Risser, P. G., and E. L. Rice. 1971a. Diversity in tree species in Oklahoma upland forest. Ecology 52:876-880.

Risser, P. G., and E. L. Rice. 1971b. Phytosociological analysis of Oklahoma upland forest species. Ecology 52:940-945.

Whittaker, R. H. 1970. Communities and Ecosystems. Macmillan, London.

HEAVY METAL POLLUTION IN EL PASO DURING SELECTED TIME PERIODS

by HOWARD G. APPLEGATE

Center for Inter-American and Border Studies

University of Texas at El Paso

El Paso, TX 79968

and KEITH REDETZKE

Department of Biology

University of Texas at El Paso

El Paso, TX 79968

ABSTRACT

Ambient concentrations of lead, zinc, cadmium and arsenic were measured in El Paso, Texas. Data collected before, during and after strike periods at a local copper smelter were compared. Lowest values were obtained during the strike period. This suggests the smelter was a source of a portion of the heavy metals.

INTRODUCTION

A previous article in this journal detailed the use of a scanning elec¬ tron microscope and ion-probe to identify sources of particulates in ambient air (Gray et al. 1980). By means of morphology and chemical composition, individual particles were related to processing steps at a local smelter. This equipment is not available to all investigators inter¬ ested in identifying point sources of particulates. Another way to iden¬ tify these sources is to monitor the atmosphere when the suspected source is and is not in operation. This is difficult to do if the plant operates 24-hours a day, seven days a week. In such a case, one way to gather data is when the plant is on strike.

METHODS

Suspended particulates were collected by the El Paso City-County Air Polllution Control Unit using hi-vol samplers according to Environ¬ mental Protection Agency-approved methodology (40 CFR 50.1, 1978). The samples were analyzed by atomic absorption spectroscopy for lead, zinc, cadmium and arsenic (Hubert et al. 1980). Sampling sites were shown in a previous publication (Hubert et al 1981a).

The Texas Journal of Science, Vol. XXXV, No. 1, March 1983

48

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

RESULTS AND DISCUSSION

Data are presented in Table 1. Pre-and post-strike data were collected for the same length of time as the duration of the strike. Exceptional operating conditions can be expected when a plant is preparing to shut down prior to a strike and again when the plant is starting up produc¬ tion subsequent to the strike. Accordingly, data for the last week prior to the shut down and the first week of the start up are shown separ¬ ately. Each time period thus has five sets of data: normal pre-strike emissions, shutting-down emissions, strike emissions, starting-up emis¬ sions and normal post-strike emissions.

These data were analyzed statistically using a t-test. A one-tailed test was used with a probability value of 0.05, since lowered ambient levels were expected during the strike period. Each metal was tested separ¬ ately, pairing strike levels versus normal levels by site and year. Normal operating levels were calculated as the average of pre- and post-strike emissions. Ambient levels of lead, cadmium, and arsenic were signifi¬ cantly reduced (P = 0.05) during the strike periods, and the reduction in zinc levels was nearly significant (P = 0.1).

These results indicate that the smelter is a significant source of lead, cadmium and arsenic. Zinc showed consistent declines during strike periods, but the relationship is less certain and may involve other sour¬ ces.

Only for cadmium and arsenic were zero amounts recorded during strikes. This probably reflects the low concentrations of these two com¬ pounds during normal pre- and post-strike conditions. Usually, they are found in concentrations of less than one microgram per cubic meter of air. Several times during the abnormal conditions associated with shutting down and starting up, concentrations of cadmium and arsenic were found to be greater than one microgram per cubic meter of air.

The relatively high concentrations of lead and zinc in ambient air even during the longest strike (5 months) are probably due to blowing residual dust. Also, ores are stockpiled in the open. Particulates blown from these stocks could be deposited on hi-vol filters and thus detected in atomic-absorption spectroscopic analysis. Cadmium and arsenic were not present in the ores in high enough concentrations to be detected on a routine basis during strikes.

Abnormal ambient concentrations of the metal can be expected in the process of shutting down and staring up an industry. A comparison was made between the values found the week prior to and the week fol¬ lowing the strike with their respective “normal” values. A greater per¬ centage of abnormally high ambient concentrations was found prior to the strike than following the strike— -i.e., 58 percent vs 37 percent in 1974; 75 percent vs 17 percent in 1977; 31 precent vs zero percent in

Table 1. Ambient concentrations of heavy metals in the atmosphere of El Paso, Texas, before, during, and after smelter strikes. All values are micrograms per cubic meter of air. ND indicates no data.

HEAVY METAL POLLUTION IN EL PASO

49

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50

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

1980. This suggests the process of shutting down is inherently more dirty than the processes involved in starting up.

Thermal inversions start in the fall, peak during the winter and are least during the summer in El Paso. These affect the quantities of heavy metals measured in the area (Hubert et al. 1981a, b). Compari¬ sons cannot be made among the three data sets for 1974, 1977 and 1980 since they cover different time spans and different inversion conditions.

Meteorological conditions at the smelter are not known. Official meteorological data from the El Paso International Airport were com¬ pared with data from the Cd. Juarez Airport and two continuous air monitoring stations. Wind speeds and directions at the four stations could not be correlated. None of the stations was near the smelter.

LITERATURE CITED

40 CFR 50.1. 1978. Code of Federal Regulations: “Protection of the Environment.” Parts 50-59.

Gray, R. W., H. G. Applegate and W. R. Roser. 1980. Analysis of particulates by scan¬ ning electron microscopy and ion probe. Texas J. Sci. 32 (3): 259-264.

Hubert, J. S., R. M. Candelaria and H. G. Applegate. 1980. Determination of lead, zinc, cadmium and arsenic in environmental samples. Atomic Spectroscopy, 1 (4):90-93. Hubert, J. S., R. M. Candelaria, B. F. Rosenblum and H. G. Applegate. 1981a. A survey of ambient air levels of lead in El Paso, Texas, from 1972-1979. Air Pollution Control Association Jour. 3 1 (3):259-261 .

Hubert, J. S., R. M. Candelaria, B. F. Rosenblum, R. Munoz and H. G. Applegate. 1981b. A survey of ambient air levels of arsenic and cadmium in El Paso, Texas, from 1972-1979. Air Pollution Control Association Jour. 31(3):262-263.

THE COMMERCIAL PRODUCTION OF MUDMINNOWS (. FUNDULUS GRANDIS) FOR LIVE BAIT:

A PRELIMINARY ECONOMIC ANALYSIS

by BENITA P. WAAS and KIRK STRAWN

Department of Wildlife and Fisheries Sciences

Texas A&M University

College Station, TX 77843

and MICHAEL JOHNS and WADE GRIFFIN

Department of Agricultural Economics

Texas A&M University

College Station, TX 77843

ABSTRACT

The economic feasibiltiy of operating a commercial mudminnow farm was determined using the Generalized Budget Simulation Model for Aquaculture developed at Texas A&M University. A 10-yr planning horizon was used for the study. Initial investment costs, annual budgets and cash flows were estimated to determine cost, returns and profit. Economic profit, break-even analysis and net present value were used to evaluate the eco¬ nomic feasibility. Based on a grow-out stocking density of 400,000 /ha, 85% projected sur¬ vival, 2 crops per year and achieved production at 80% of capacity, the 24-ha facility showed an economic profit of $41,160 for the 6th year of operation. The break-even price of $0.40 /dozen was $0.25 less than the market price of $0.65. The break-even production of 278,705 dozen /yr is 174,629 dozen less than the assumed annual production of 453,334 dozen.

INTRODUCTION

In recent years there has been an increased interest not only in devel¬ oping biological and technological aspects of aquaculture systems but also in looking into their economic relationships. Economic, investi- ment and feasibility studies have been undertaken for a number of aquacultural systems including catfish (Griffin and Lacewell 1978; Ekstrom 1979), penaeid shrimp (Anderson and Tabb 1970; Williams 1973; Aquacop 1975; Adams et al. 1979; Johns et al. 1981a, b), fresh¬ water prawn (Gibson and Wang 1977; Shang and Fujimura 1977; Roberts and Baur 1978) pompano (Cuevas 1978) and oysters (Im et al. 1976; Lipschultz and Krantz 1978, 1980). Although commercial baitfish farming has proved to be a rapidly growing, high-profit business, very few economic studies on baitfish production have been documented in scientific literture (Shang and Iversen 1971; Herrick and Baldwin 1975).

The Texas Journal of Science, Vol. XXXV, No. 1, March 1983

52

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

Fundulus grandis (Cyprinodontidae), regionally called “bullmin- now”, “chub”, “mudfish” or “mudminnow”, is in popular demand as live bait for sport fishes such as southern flounder, spotted seatrout and red drum along the coastal Gulf of Mexico and South Atlantic states. Local suppliers of mudminnows rely exclusively on catches from the wild. Fish are either seined from tidal marshes or trapped using min¬ now traps baited with cracked crabs. Since these methods are not relia¬ ble, supply is irregular and has continued to fall short of demand since 1970. As a result, there is much interest in raising this fish as a com¬ mercial enterprise.

Initial research efforts on the culture of mudminnows were con¬ ducted at Claude Peteet Mariculture Center in Alabama. Studies focused on the maintenance, spawning and harvesting techniques of broodstock and young, and rearing of juveniles to bait size utilizing commercial feeds (Tatum and Helton 1977; Tatum et al. 1979). Mcll- wain (1977) reared mudminnows in a closed system and concluded that it would not be a commercially feasible venture because of the high cost of rearing systems. Our studies at Houston Lighting 8c Power Company’s Cedar Bayou Generating Station research facility east of Baytown, Texas, have shown positive technological feasibility for mudminnow farming along the Texas Gulf coast (Waas 1982). How¬ ever, commercial baitfish production is a highly specialized industry due to the nature of transportation and sales facilities needed, the res¬ tricted areas in which production can occur economically, and the sea¬ sonal nature of the market. Thus, it is important not only to know the biological and technological aspects of production but also to be able to establish and demonstrate the economic feasibility of such an opera¬ tion before prospective investors commit substantial resources to pro¬ duction.

METHODS AND DATA

The economic feasibility of a mudminnow hatchery /grow-out opera¬ tion was examined using the Generalized Budget Simulation Model for Aquaculture developed at the Department of Agricultural Economics, Texas A8cM University (Griffin et al. 1980). The model is designed to produce itemized fixed and variable costs, annual and monthly budge¬ tary outputs, cash flows, break-even quantities and prices for a specified aquaculture system. These values are then presented to reveal produc¬ tion and net revenue for a venture.

The proposed 24-ha (60 acre) facility would consist of a system of 40 0.2-ha spawning/hatching ponds and 10 1.0-ha grow-out ponds cover¬ ing a total area of 18 hectares. The facility design (Fig. 1) is based on data relative to growth and reproductive biology of mudminnows

ECONOMICS OF MUDMINNOW PRODUCTION

53

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food silos storaqe office* - J oo 3 3

Figure 1. Design of the proposed 3-phase pond production facility (spawning/hatching/ grow-out) for mudminnow farming. Ponds marked X are equipped with wooden piers.

obtained from studies at Cedar Bayou as well as from previous work in Alabama (Tatum et al. 1979; Trimble et al. unpubl. data). Several bio¬ logical parameters, discussed below, are assumed to be of importance for optimal production of mudminnows.

54

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

Climatic Conditions

The designed facility can be adapted for production anywhere along the Texas Gulf coast where a sufficient water supply is available and outdoor temperatures are suitable for continued spawning (approxi¬ mately 22-28°C) from March to October (Fivizzani 1977; Waas 1982).

Production of Fry

During the spawning season 20 0.2-ha ponds would function as spawning ponds while the other 20 would function as hatching ponds. Eggs laid on spawing mats will be hatched in the latter and the fry grown to an average size of 0.5 g (28-30 mm). Stocked at 65,000 brood fish /ha, production for each spawning pond is assumed to be 400,000 fry (at 75% survival from egg to fry) during the spawning season (late February to October). Fry produced from late February to May and May to August would be raised as crops I and II, respectively. Fry resulting from spawning activities after August would be overwintered and used for broodstock the following year. The recommended size for spaw¬ ning/hatching ponds is 0.2 ha as it would be necessary to keep them small to facilitate efficient egg collection and fry harvest. Two of the 0.2 ha ponds would be equipped with wooden piers and would serve as holding facilities for fish during harvest (Fig. 1). Fish would be held in large net cages and sold to bait dealers at the facility.

Grow-out Ponds

The 10 1.0-ha grow-out ponds would be stocked at a density of 400,000 fish /ha. Fry would be graded prior to stocking to ensure size uniformity. Although this stocking density has not been tested, work in Alabama has demonstrated that fish stocked at 370,000 /ha grew only a little slower than those stocked at 250,000 /ha (Trimble et al. 1981). Current studies show sufficient growth rates can be maintained at stocking densities as high as 500,000 /ha (P. Perschbacher, pers. comm.). A grow-out season of 55-65 days and 85% survival is based on Cedar Bayou and Alabama data (Tatum et al. 1979).

Food and Feeding

Fish would be fed commercial minnow feed (33% protein; particle size 0.5 mm) at the rate of 3% of body weight /day for brood fish. Food comsumption values for grow-out fish were based on an average food conversion ratio of 2.0. Average weight of brood fish and of fish sold is considered to be 7 and 3 g, respectively.

RESULTS OF ECONOMIC ANALYSIS

The analysis first calculates capital investment for the designed facil¬ ity followed by yearly gross revenue and operating costs. It also pro-

ECONOMICS OF MUDMINNOW PRODUCTION

55

Table 1. Estimate of capital cost for year 6 in the 10-year planning horizon of the mud- minnow hatchery /grow-out operation, 1982.

1.	Land (60 acres @ $2,000 /acre)	$120,000
2.	Pond Construction
	a.	Levees: excavation, caliche, grass seed	$101,768
	b.	Pipes, Drains, Water Supply System	28,646
	Subtotal	$130,414
3.	Buildings
	a.	Storage and Shop (1,800 sq. ft.)	$36,000
	b.	Office Building (750 sq. ft.)	15,000
	c.	Architecture and Engineering Fee	13,457
	Subtotal	$64,457
4.	Machinery and Equipment
	a.	Pumps	$1,100
	b.	Stand Pipe Screen, Filter Bags	755
	c.	Transport Tank and Agitators	1,060
	d.	Feed Blower /Trailer	3,610
	e.	Feed Silos (2)	8,000
	f.	Spawning Mats (2,400 @ $5.00 per mat)	12,000
	g-	Minnow Graders, Holding Baskets, Seines etc.	2,146
	h.	Refrigerator	950
	i.	Miscellaneous Lab Equipment
		(microscope, scale, refractometer, etc.)	4,031
	j-	Shop Tools	1,290
	k.	Office Equipment	1,518
	Subtotal	$36,460
5.	Vehicles
	a.	Tractor	$8,762
	b.	Pick-up	10,000
	Subtotal	$18,762
6.	Broodstock Establishment (21,666 doz. @ $0.85 /doz.)	$18,417
		TOTAL CAPITAL COSTS	$388,510

vides a detailed annual budget for the sixth year of operation. All input and output prices are assumed to remain constant over the planning horizon. Break-even analysis, economic profit and net present value are then examined to evaluate the feasibility of the facility. Revenue and cost are in 1982 dollars.

Capital Investment

Included in this category are funds initially committed to the project (Table 1). All equipment and construction prices were obtained during the spring of 1982 and are representative of the upper Texas coastal area. A 10-yr planning horizon is used for the facility. The total capital cost (CC) of the facility is $388,510. Pond construction and land value are the two major expenses, accounting for 33.6 and 30.9% of the total investment. Building cost constitutes 16.6% of CC; buildings consist of

56

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

Table 2. Schedule of activities for a 2-crop mudminnow farming enterprise.

Total

Spawning Hatching to Grow-out Grow-out

Phase Juveniles Phase Harvest Days

Crop I Feb. 15-Apr. 30 Feb. 22-May 25 June 1-Aug. 5 Aug. 5-Aug. 20 65

Crop II Mayl-July30 May 8-Aug. 20 Sept. 1 -Nov. 5 Nov. 5-Nov. 20 65

Aug. 1-Oct. 10 Fry resulting from this spawning activity would be raised, wintered and used for broodstock the following year.

a storage facility for spawning mats and equipment and an office. Cost of machinery and equipment is 9.4%. The useful life of all facilities is estimated at 10 years, and salvage value of buildings and pond facility are estimated by the straight-line depreciation method. Adult brood- stock would be initially purchased from trappers for 85 C per dozen, which amounts to only 4.7% of CC.

Annual Production and Revenue

A suggested schedule of activities for the 2-crop operation is pre¬ sented in Table 2. This operation is based on a production rate of 80% of the total capacity of the facility, allowing for problems such as occa¬ sional outbreaks of disease, equipment failures, adverse weather condi¬ tions, bird predation, or other production problems. Also, based on the stocking density of 400,000 /ha and projected survival of 85%, a total of 453,333 dozen mudminnows would be produced on an 8-9 month pro¬ duction schedule (crop I in August; crop II in November). At $0.65 per dozen of baitfish, sales would generate an annual revenue of $294,667 (Table 3).

Operating Costs

Estimated annual operating costs (OC) (Table 4) are considered in two categories, variable costs (VC) and fixed costs (FC). Feed is the

Table 3. Summarized annual budget for year 6 in 10-year planning horizon for baitfish hatchery /grow-out operation.

Gross revenue from baitfish production	$294,667.00
Total variable cost (VC)	$ 31,795.00
Total fixed cost (FC)	$149,363.00
Total cost (FC + VC)	$181,158.00
Net revenue	$113,509.00
Income tax	$ 52,214.00
Net after-tax revenue	$ 61,295.00
Required return to equity capital	$ 20,135.00
Economic profit	$ 41,160.00
Break-even price	$ .40
Break-even quantity	278,705 dozen
Total capital investment	$388,510.00
Net present value based on 25% initial investment in capital costs	$341,866.00

ECONOMICS OF MUDMINNOW PRODUCTION

57

Table 4. Estimated annual opeating costs for year 6 in the 10-year planning horizon of the mudminnow hatchery /grow-out opeation, 1982.

Variable Costs

1. Feed (52.6 metric tons) $12,185

2. Fuel $ 2,134

3. Part-time labor $ 9,240

4. Utilities

a. Electricity $ 4,898

b. Telephone $ 600

c. Water $ 400

5. Repair and Maintenance

a. Equipment $ 232

b. Machinery $ 663

6. Payroll taxes $ 1,443

Total Variable Costs $31,795

Fixed Costs

1. Salary — full time personnel $60,000

2. Interest $32,999

3. Depreciation $42,016

4. Taxes $ 6,126

5. Insurance $ 8,222

Total of Fixed Costs $149,363

TOTAL OPERATION COSTS $181,158

major VC item, representing 38.3%. Feed costs are calculated at 10.232/ kg. Part-time labor is 29.1% of VC. This labor would be utilized during harvest of fry for stocking and adults for marketing. Salaries of full-time personnel (manager and 6 laborers) represent 40.2% of FC. Depreciation is 28.1% of FC. Interest calculated at 21% per year is the third highest FC item (22.1%). Total annual operating cost of the facil¬ ity is $181,158.

The annual budget for year 6 of the planning horizon is given in Table 3. Net revenue above total OC is $113,509. Income tax calculated on a corporate basis is $52,214, resulting in a net after-tax return of $61,295.

Break-even Analysis

Break-even analysis is useful in studying the relationship between FC, VC, and profit. Break-even price (BEP) and break-even production (BEQ) are considered in the analysis (Table 3). BEP of $0.40 represents the lease price required for the yield to equal OC for year 6 of opera¬ tion assuming the projected yearly production rate of 453,334 dozen baitfish. This is $0.25 less than the market price of $0.65 /doz. BEQ of 278,705 dozen at the current unit price of $0.65 indicates the lowest level of production needed to prevent losses. This BEQ is 61% of the production capacity assumed in the analysis.

58

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

Economic Profit

Economic profit helps to evaluate the investment potential of the baitfish operation as opposed to an alternative investment. This is done by estimating returns the owner can expect for his equity capital from the alternative investment. Equity capital is taken as 25% down pay¬ ment of the total investment of the facility. The alternative investment in this study is taken as corporate bonds which have a return rate of 15.73% per year, with an added 5% per year as adjustment for risk and uncertainty associated with the baitfish operation. That is, mudmin- now farming, being a new venture, can be considered a high risk in comparison to corporate bonds. Changes in demand for baitfish, deple¬ tion of sportfish stocks, discovery of additional or alternative bait sour¬ ces are some additional factors that contribute to the risk. The required return to equity capital (Table 3) is $20,135 and economic profit is $41,160. Positive value of economic profit implies that investment of equity capital in the baitfish operation results in higher returns than the next best alternative.

Net Present Value

By taking into account the time value of expenditures and earnings, the net present value (NPV) method allows one to make a realistic comparison of future returns with initial expenditures. This is done by discounting the expected future returns by an appropriate discount rate over the planning horizon of the project. Discount rate used for the analysis is 19.75%. A NPV value greater than zero means the investment is economically profitable. In the present analysis NPV was estimated considering the owner’s investment as 25% of the capital investment and remaining 75% financed at 17% interest rate for the life of the investment. A net present value of $341,866 (Table 3) indicates the investor would receive a rate of return greater than 21.7%.

CONCLUSION

Based on the assumptions incorporated into the framework of the model, a commercial mudminnow operation of the assumed design, located along the Texas coast would be economically profitable. Some of the assumptions that have major impact on its feasibility are fry production levels, stocking densities in grow-out ponds, timing of the production cycle to take advantage of peak periods, and a ready market. As previously mentioned, biological assumptions are based on experi¬ mental data and work is presently being carried out to further optimize stocking densities and increase fry production. Use of a higher ratio of females in spawning ponds has been shown to increase fry production (Waas unpubl. data). Timing of crop harvest with peak demand peri¬ ods may be the key element in success of the operation, as demand for mudminnows is seasonal. Along the Texas coast demand is low during

ECONOMICS OF MUDMINNOW PRODUCTION

59

the first 6 months of the year. It increases steadily from late July to a November peak during the flounder season. Even if all possible steps are taken to market the crop during high-demand periods, oversupply or shortages of baitfish are not always forseeable. Climatic conditions that curtail fishing can cause a temporary decline in sales of bait.

Since mudminnows have not been raised commercially, a thorough market survey is necessary before large-scale production is undertaken. Prospective producers should visit fish camps and other bait selling areas and determine the scope of the market. Although there will be initial competition from the wild catch, bait dealers have clearly shown a preference for pond raised mudminnows because of their higher qual¬ ity, uniform size, and most of all, because of the assurance of a reliable and adequate supply during high-demand periods. Supply of fish for bio-assay work and the sale of fingerlings as food for predatory aqua¬ rium fish are additional marketing channels that should be explored.

Economies of size were not investigated in this study. It would be useful to determine the facility size that captures most of the available economies, as it aids in the reduction of fixed costs per unit of output. Since production of mudminnows for bait is a relatively new venture it would be wise initially to start with a smaller-sized production facility. Possibly 4-6 hectares (10-15 acres) in a one-man or family operation would help minimize investment per unit.

ACKNOWLEDGEMENTS

This research was funded by the Houston Lighting 8c Power Com¬ pany through the Department of Wildlife and fisheries Sciences and Texas Agricultural Experiment Station Project 6462-3790. We thank Ron Biever, Mark Byford, Mark Hardin, Pete Perschbacher, Celeste Rees and Dr. Larry Wiesepape for their help in data collection. The economic analysis was supported through a research project sponsored (in part) by the Texas A8cM University Sea Grant College Program, supported by the National Oceanic and Atmospheric Administration’s Office of Sea Grant, Department of Commerce, under grant number NA81AA-D-00092.

This paper represents contribution number TA- 18031 of the Texas Agricultural Experiment Station.

LITERATURE CITED

Adams, C. M., W. L. Griffin, J. P. Nichols, and R. W. Brick. 1979. Bioengineering- economic-model for shrimp mariculture systems, 1979. TAMU-SG-80-203, Texas A&M University, College Station, TX.

Anderson, L. G., and D. C. Tabb. 1970. Some economic aspects of pink shrimp farming. Gulf Carr. Fish Ins. 23:113-124.

Aquacop. 1975. Maturation and spawning in captivity of penaeid shrimp Penaeus mer- guiensis de Man, Penaeus japonicus Bate, Penaeus aztecus Ives, Metapenaeus ensis de Hann, and Penaeus semisulcatus de Hann. Proc. World Mar. Soc. 6:123-132.

60

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

Cuevas, H. Jr. 1978. Economic feasibility study of Florida pompano ( Trachinotus caro- linus) and rainbow trout ( Salmo gairdneri ) production in brackish water ponds. M.S. Thesis, Auburn Univ., Auburn, AL.

Ekstrom, J. P. 1979. A computerized budget simulator for use in catfish farming. M.S. Thesis, Texas A8cM University, College Station, TX.

Fivizzani, A. J., Jr. 1977. Environmental and hormonal regulation of seasonal conditions of the Gulf killifish ( Fundulus grandis). Ph.D. Dissertation, Louisiana State Univer¬ sity, Baton Rouge, LA.

Gibson, R. T., and J. Wang. 1977. An alternative prawn production system design in Hawaii. UNIHI-Sea Grant TR-77-05. HAES J. Ser. paper no. 2142.

Griffin, W. L., and R. D. Lacewell. 1978. Estimated cost of producting catfish in Texas, 1977-1978. Proc. 1978 Fish Farm. Conf., Ann. Conv. Fish Farmers TX. p. 35-61.

Griffin, W. L., C. M. Adams, and L. A. Jensen. 1980. A generalized simulation model for aquaculture. Texas A&M University, Sea Grant Programs. Sea Grant 04-8- Mol- 133.

Herrick, S. F., and W. J. Baldwin. 1975. The commercial production of top minnows — A preliminary economic analysis. Sea Grant Advisory Report. Unviersity of Hawaii. UNIHI-SG-AR-75-02. HIMB Contirb. no. 464.

Im, K. H., R. H. Johnson, and R. D. Langmo. 1976. The economics of hatchery produc¬ tion of Pacific oyster seed — a research report. Proc. Nat. Shellfish Assoc. 66:81-94.

Johns, M., W. Griffin, A. Lawrence, and D. Hutchins. 1981a. Budget analysis of shrimp maturation facility. J. World Mar. Soc. 12:104-109.

Johns, M., W. Griffin, A. Lawrence, D. Hutchins, and J. Fox. 1981b. Budget analysis of shrimp hatchery facilities. J. World Mar. Soc. 12(2). In press.

Lipschultz, F., and G. E. Krantz. 1978. An analysis of oyster hatchery production of cultched and cultchless oysters utilizing linear programming techniques. Proc. Nat. Shellfish. Assoc. 68:5-10.

Lipschultz, F., and G. E. Krantz. 1980. Production optimization and economic analysis of an oyster ( Crassostrea virginica) hatchery in the Chesapeake Bay, Maryland, USA. Proc. World Mar. Soc. 11:580-591.

Mcllwain, T. D. 1977. Bait fish rearing. Project GR-76-005, Mississippi Mar. Res. Coun¬ cil., Long Beach, MS.

Roberts, K. J., and L. C. Bauer. 1978. Costs and returns for Macrobrachium grow-out in South Carolina, USA. Aquaculture 15:383-390.

Shang, Y. C., and T. Fujimura. 1977. Production economics of fresh water prawn (Macrobrachium rosenbergii ) farming in Hawaii. Aquaculture 11:99-110.

Shang, Y. C., and R. T. B. Iversen. 1971. The production of threadfin shad as live bait for Hawaii’s skipjack tuna fishery: an economic feasibility study. Economic Research Center, Univ. of Hawaii, Honolulu, HI.

Tatum, W. M., and R. F. Helton, Jr. 1977. Preliminary results of experiments on the feasibility of producing bullminnows (Fundulus grandis ) for the live bait industry. Proc. World Mar. Soc. 8:49-54.

Tatum, W. M., W. C. Trimble, and R. F. Helton, Jr. 1979. Production of Gulf killfish in brackish water ponds. Proc. An. Conf. Southeast. Assoc. Fish. Wildlife Agencies 32:502-508.

Trimble, W. C., W. M. Tatum, and S. A. Styron. 1981. Pond studies on Gulf killifish (Fundulus grandis) mariculture. J. World Mar. Soc. 12(2). In press.

Waas, P. B. 1982. Development and evaluation of a culture system suitable for the pro¬ duction of Gulf killifish (Fundulus grandis Baird and Girard) for live bait in the thermal effluent of a power plant. Ph.D. Dissertation, Texas A&M University, College Station, TX.

Williams, R. J. 1973. Economic feasibility of commercial shrimp farming in Texas. M. S. Thesis, Texas A&M Unviersity, College Station, TX.

EFFECTS OF A HIGH POTASSIUM DIET AND PROSTAGLANDIN ON INDUCED GASTRIC ULCERATION IN RATS1

by MARSHALL J. MANN and DAVID P. SHEPHERD

Department of Biology

Southeastern Louisiana University

P.O. Box 791

Hammond, LA 70402

ABSTRACT

Forty (40) Sprague-Dawley rats were placed on a high potassium (K), low sodium diet for 23 days while another 40 received standard rat chow. All animals received an IP injec¬ tion of 20mg/kg indomethacin to induce gastric ulcers. Twenty (20) animals from each of the above groups received a 0. 15mg/kg oral dose of prostaglandin (PGE2).. The high K diet alone reduced the number and severity of indomethacin-induced gastric ulcers and it enhanced the anti-ulcer effect of PGE2.

INTRODUCTION

Prostaglandin E2 (PGE2) has been shown to have a cytoprotective effect upon the gastric mucosa of rats exposed to various ulcer-inducing compounds, including the drug indomethacin (Lippman 1974; Robert 1976). Shepherd et al. (1973) reported that 65% of rats they fed a special diet high in potassium survived exposure to 1000R whole-body gamma irradiation. This amount of radiation typically results in the death of all animals, and the primary cause of death is damage to the gastroin¬ testinal tract (Quastler 1956; Casarett 1968). Therefore, a high- potassium diet may protect the gastrointestinal tract from radiation damage.

The purpose of this study was to evaluate potassium as a potential protecting agent for the gastric mucosa of rats given the ulcer-inducing compound indomethacin. The approach was to use a high-potassium diet and standard laboratory chow to form two experimental groups. Half of each experimental group was given oral doses of PGE2. All animals were injected with indomethacin.

MATERIALS AND METHODS

Eighty (80) Sprague-Dawley rats, mixed sexes and weighing 100-125 g each, were divided into equal groups (A and B). Group A was placed

Paper presented at 84th Annual Meeting of the Texas Academy of Science, Austin, TX, March 1981.

The Texas Journal of Science, Vol. XXXV, No. 1, March 1983

62

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

on a standard laboratory chow (Purina Rat Chow), while Group B as given a special diet high in potassium (0.73%) and low in sodium (0.019%) (ICN Life Science Group, Cleveland, Ohio). This is half the sodium and four times more potassium than the minimum require¬ ments of these ions. Other data related to consumption of the high- potassium diet — including food intake, duration of the diet, weight gain and serum Na and K levels — have been previously reported (She¬ pherd et al. 1973). Animals of Group B were maintained on the diet for 23 days. All animals received distilled water ad libitum.

After 23 days, Groups A and B were subdivided into groups of twenty animals each (Al, A2, Bl, B2). All animals were fasted 24 h with dis¬ tilled water ad libitum. Then, groups A2 and B2 were given Prosta¬ glandin E2 (PGE2) (Sigma Chemical Company, St. Louis, Mo.) orally at a dose of 0.15mg/kg (Main and Whittle 1975). PGE2 was combined with absolute ethanol (0. lml/mg) and added to 1% methyl cellulose and mixed five minutes with a magnetic stirrer. Oral administration of PGE2 was accomplished via a 76-mm intubation needle. Immediately following oral PGE2, all animals were injected (IP) with 20mg/kg indomethacin (Djahanguiri 1969). Preparation of the indomethacin fol¬ lowed the method of Main and Whittle (1975). Five hours later (Lip- pman 1974) all animals were etherized; the stomach was removed and opened along the greater curvature. The stomach was inverted on the index finger, washed under tap water and examined by an observer to whom the treatment was not known. The necrohemmorrhagic areas were counted, and graded on a severity scale of one to three (1 = less than 1mm; 2 = l-2mm; 3 = greater than 3mm) (Main and Whittle 1975).

RESULTS

The effects of a high potassium diet and synthetic prostaglandin (PGE2) on the incidence of indomethacin-induced acute gastric ulcers are indicated in Table 1. The most striking datum in Table 1 is the 80% reduction in the number of animals experiencing ulcers in the experimental group B2. These animals were on the high potassium diet and received oral PGE2 before indomethacin injection. The 80% reduc¬ tion is by comparison with group Bl. Group A2 which was on stand¬ ard lab chow also received oral PGE2 but only had a 30% reduction in incidence of ulcers, compared with Al.

The difference in incidence of ulcers between groups Al and Bl was not significant, but there was a significant difference in the total number of ulcers (Table 2). The data from Table 2 demonstrates that diet was significantly involved in reducing the total number of indomethacin-induced ulcers. Group Bl, on the high-potassium diet,

GASTRIC ULCERS IN RATS

63

Table 1. Effect of high-potassium diet and PGE2 on incidence of gastric ulcers in rats.

Group3	Diet	Dose of pge2	# of Animals with Ulcers per group (20)	% Incidence	% Reduction15
Al	Lab Chow		18/20	90%
A2	Lab Chow	0.15mg/kg	12/20	60%	30%
Bl	High K+		20/20	100%
B2	High K+	0.15mg/kg	4/20	20%	80%c

a All groups received 20mg/kg indoemthacin. b Reduction is based on comparison of A2 to A1 and B2 to Bl.

Significant at 0.005 probability level.

had 184 ulcers as compared to 328 ulcers for the lab-chow Group Al. Those animals that were on the high-potassium diet and given PGE2 (Group B2) had only 5 ulcers as compared to those animals on lab chow and receiving PGE2 (Group A2), which had 73 ulcers.

Both prostaglandin treatment and the high potassium diet, when used alone, reduced the total number of ulcers; however, when used together, not only was the total number of ulcers reduced but also the severity was reduced (Table 3). Because ulcers of severity 3 had areas ranging from (2mm)2 to approximately total glandular surface, it is very significant that all the ulcers in Group B2 were less than 1mm. Of the four B2 animals with ulcers, three had only one (#1 severity) and the fourth had two (#1 severity). The sole difference between this group (B2) and Group A2 was the high potassium diet. Therefore, the syner¬ gism of PGE2 and a high potassium diet resulted in a smaller surface area of the stomach having necrohemmorrhagic lesions.

DISCUSSION

The fact that potassium is an essential requirement for protein syn¬ thesis and growth is well established (Eagle 1955; Lubin 1964, 1967; Ledbetter and Lubin 1977). When cells are damaged by irradiation, potassium moves out of the cells (Ting and Zirkle 1940; Harrison et al. 1958; Portela et al. 1963); but when animals are provided with optimal availability of potassium in the diet, they are somewhat protected from

Table 2. Effect of high-potassium diet and PGE2 on the number of gastric ulcers in rats.

Group3	Diet	Dose of pge2	Total # Ulcers	Average # Per Rat
Al	Lab Chow		328	16.4
A2	Lab Chow	0. 15mg/kg	73	3.6
Bl	High K+		184	9.2
Bw	High K+	0.15mg/kg	5	0.25

a All groups received 20mg/kg indoemthacin.

64

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

Table 3. Effect of high-potassium diet and PGE2 on the severity of gastric ulcers in rats.

		Dose of	Number of Ulcers with Severity =
Group2	Diet	pge2	1	2	3
Al	Lab Chow		267	48	13
A2	Lab Chow	0.15mg/kg	57	12	4
B1	High K+		158 (85.8%)	20 (10.8%)	6 (3.2%)
B2	High K+	0.15mg/kg	5 (100%)	0	0

a All groups received 20mg/kg indoemthacin.

the radiation as shown by a reduction in the number of deaths (She¬ pherd et al 1973). Therefore, the primary objective of the present inves¬ tigation was to determine whether optimal availability of potassium would protect gastrointestinal cells from a potentially damaging agent, indomethacin.

The results show that rats placed on a diet high in potassium and low in sodium enjoyed some degree of protection: the total number of experimental ulcers was reduced by almost half. But when oral admin¬ istration of prostaglandin (PGE2) accompanied the special diet, the effects were synergistic. PGE2 treatment alone resulted in a 30% reduc¬ tion in animals with ulcers. When PGE2 was combined with the high potassium diet, there was an 80% reduction in animals with ulcers.

Most evidence suggests that the initial action of some damaging agents on the gastric mucosa is the inhibition of active ion transport (Kuo et al. 1974; Sernka et al. 1974; Kuo and Shanbour 1976a, b). Specif¬ ically, studies have shown that indomethacin inhibits active transport of sodium (Chaudhury and Jacobson 1978) while prostaglandin stimu¬ lates active transport of sodium (Bowen et al. 1975), and these results have been used to postulate a mechanism of PGE2 cytoprotection (Chaudhury and Jacobson 1978). There are no significant data concern¬ ing potassium in relation to this phenomenon.

There is some evidence to suggest that there may exist a separate transfer mechanism resonsible for accumulating intracellular potassium and that this mechanism is not directly coupled to active sodium trans¬ port (Delong and Civan 1978). This could provide the basis for potas¬ sium acting as an independent protecting agent against the number and severity of indomethacin-induced ulcers. This could also explain why potassium acts synergistically with, or independent of, PGE2 in protecting the mucosa against indomethacin.

Consistent with potassium being involved in cellular protection is the hypothesis that intracellular potassium controls the rate of macro- molecular synthesis. The latter hypothesis is based on the observation that when cells are induced to leak potassium, there is a parallel

GASTRIC ULCERS IN RATS

65

depression in the rate of protein and DNA synthesis. When the potas¬ sium level in the medium around the cells is increased, near normal levels of cellular K can be sustained and macromolecular synthesis con¬ tinues (Ledbetter and Lubin 1977). This implies the possibility that a high-potassium medium may provide the cell with a means of “recov¬ ery” from various damaging agents. The specific role of dietary potas¬ sium in the apparent protection of the gastric mucosa against damag¬ ing agents such as indomethacin and radiation needs further investigation.

LITERATURE CITED v

Bowen, J. C., Y-J. Kuo, W. Pawlik, D. Williams, L. L. Shanbour, E. D. Jacobson. 1975. Electrophysiological effects of burimamide and 16, 16-dimethyl prostaglandin E2 on the canine gastric mucosa. Gastroenterology 68: 1480-1484.

Casarett, A. P. 1978. Radiation Biology. Prentice-Hall, Englewood Cliffs, NJ.

Chaudhury, T. K., and E. D. Jacobson. 1978. Prostaglandin cytoprotection of gastric mucosa. Gastroenterology 74:59-64.

DeLong, J. and M.M. Civan. 1978. Dissociation of cellular K^~ accumulation from net Na-^ transport by toad urinary bladder. J. Membr. Biol. 42:19-31.

Djahanguiri, B. 1969. The production of acute gastric ulceration by indomethacin in the rat. Scand. J. Gastroent. 4:265-268.

Eagle, H. 1955. Nutrition needs of mammalian cells in tissue culture. Science 122:501- 502.

Harrison, A. P., A. K. Bruce, and G. E. Stapleton. 1958. Influence of X-irradiation on potassium retentivity by Escherichia coli. Proc. Soc. Exp. Biol. Med. 98:740-746.

Kuo, Y-J., L. L. Shanbour, and T. J. Sernka. 1974. Effect of ethanol on permeability and ion transport in the isolated dog stomach. Am. J. Dig. Dis. 19:818-819.

Kuo, Y-J., and L. L. Shanbour. 1976a. Mechanism of action of aspirin on canine gastric mucosa. Am. J. Physiol. 230:762-768.

Kuo, Y-J., and L. L. Shanbour. 1976b. Inhibition of ion transport by bile salts in canine gastric mucosa. Am. J. Physiol. 231:1433-1436.

Leadbetter, M. L. S., and M. Lubin. 1977. Control of protein synthesis in human fibro¬ blasts in intracellular potassium. Exp. Cell Res. 105:223-227.

Lippman, W. 1974. Inhibition of indomethancin induced gastric ulceration in the rat by perorally administered synthetic and natural prostaglandin analogues. Prostaglandins 7:1010-1023.

Lubin, M. 1964. Intracellular potassium and control of protein synthesis. Fed. Proc. 23:994-999.

Lubin, M. 1967. Intracellular potassium and macromolecular synthesis in mammalian cells. Nature (Lond.) 213:451-458.

Main, I. H. M., and B. J. R. Whittle. 1975. Investigation of the vasodialator and antise- cretory role of prostaglandins in the rat gastric mucosa by use of non-steroidal anti¬ inflammatory drugs. Br. J. Pharmac. 53:217-226.

Portela, A., J. C. Perez, P. Stewart, M. Hines, and V. Reddy. 1963. Radiation damage in muscle cell membranes and regulation of cell metabolism. Exp. Cell Res. 29:527-531. Quastler, H. 1956. The nature of intestinal radiation death. Radiat. Res. 4:303-307.

Robert, A. 1976. Antisecretory, antiulcer, cytoprotective and diarrheogenic properties of prostglandins. Advances in Prostaglandin and Thromboxane Research 2:507-516. Sernka, T. J., C. W. Gilleland, and L. L. Shanbour. 1974. Effect of ethanol on active transport in the dog stomach. Am. J. Physiol. 226:397-399.

66

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

Shepherd, D. P., S. O. Brown, G. M. Krise, and H. R. Crookshank. 1973. Dietary protec¬ tion against ionizing radiation. Radiat. Res. 56:282-289.

Ting, T. P., and R. C. Zirkle. 1940. The kinetics of the diffusion of salts into and out of X-irradiated erythrocytes. J. Cell Comp. Physiol. 16:197-201.

BIOLOGICAL FORM REPRESENTATION BY TECHNIQUES DEVELOPED FOR AIRFOILS1

by W. M. HEFFINGTON

Department of Mechanical Engineering Texas A&M University College Station, TX 77843

and K. L. EAVES

Department of Biochemistry Texas A&M University College Station, TX 77843

ABSTRACT

Representation of biological forms that are approximately teardrop-shaped is possible by use of systems developed for describing airfoils. Such approaches include the Jou- kowski transformation (a conformal transformation which changes a circle in one com¬ plex plane into a teardrop shape in another complex plane) and the empirical NACA four-digit system. Both techniques require little data to represent the original object, unlike anthropological and biological methods which use large numbers of linear mea¬ surements and descriptive terms to describe shapes. Length, thickness and curvature angle are the only data required to represent a teardrop shape using the Joukowski transforma¬ tion, and four digits and the length are all that are required when using the NACA four¬ digit system. In this work, both the Joukowski tranformation and the NACA four-digit system are applied to incisors of olive baboons ( Papio cynocephalus anubis ), and the resulting shapes are compared to outlines of the original teeth. Shapes symmetrical about a central axis and unsymmetrical shapes are treated. Other transformations are discussed, and the use of microcomputers for obtaining outline drawings from photographs of bio¬ logical specimens is described. Possible uses and applications of these techniques are dis¬ cussed.

INTRODUCTION

Biological forms such as teeth are presently described in anthropo¬ logical and biological literature by photographs, drawings, or a series of linear measurements such as labial and lingual height and breadth, anterior-posterior crown length, and breadth of each molar cusp (Ash¬ ton and Zuckerman 1950). Descriptive terms used include biscuspid, sectorial, molariform, D-Y-5 cusp pattern, and bunodont-cusped (Zeisz and Nuckolls 1949; Krogman 1969). Problems with popular tooth- description methods are due in part to the quantity of data required to accurately describe a tooth.

'Presented at the Eighty-fourth Annual Meeting of the Texas Academy of Science, Austin, Texas, March, 1981.

The Texas Journal of Science, Vol. XXXV, No. 1, March 1983

68

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

Acquisition of a completely faithful quantitative representation of a biological form would require storage and manipulation of a infinite number of data points. Even to reproduce a two-dimensional outline of a tooth as viewed from a particular aspect (buccal or distal, for instance) would require an infinite number of data points for complete fidelity. In order to avoid this complexity, resort is made to approxi¬ mate systems in which the forms are represented by a finite number of points, and the features near the points are obtained by interpolation or extrapolation. As many as seventy points may be used to represent an object as simple as a tooth (Ashton and Zuckerman 1950). Another way of circumventing this difficulty is to provide a likeness of the original specimen such as a physical model, x-ray film, or a photograph (Zeisz and Nuckolls 1949).

Lacking sufficient quantitative data from which an outline shape may be obtained, sources report only selected data deemed to be impor¬ tant. Often little data is required to represent individual shapes. Simply giving the length and thickness of the buccal aspect of an olive bab- boon’s ( Papio cynocephalus anubis) lateral incisor may be sufficient data for an anthropologist to construct a suitable representation for the task at hand.

Since subsonic airfoils and some teardrop-shaped biological forms have similar outlines, systems developed by aerodynamicists for describ¬ ing these airfoil shapes should apply to teardrop-shaped teeth. Two such systems, the Joukowski conformal transformation and the NACA2 four-digit series, are used here to describe incisors from an olive baboon.

Transformations of biological shapes into related biological shapes often have been accomplished by reliance upon empirical formulations of the type used by Thompson (1917). Later works, such as those by Bookstein (1977) and Rosen (1978), have attempted more mathematically-based transformations; or, as Bookstein (1977) observed, they have used methods less geometrically precise than those of Thompson but more arithmetically tractable. The present effort belongs to the latter category.

Aerodynamicists have long known of conformal transformations using complex variables which transform simple circles into teardrop¬ shaped forms similar to the shapes of symmetrical and unsymmetrical subsonic airfoils. Many older text books — including those by Piercy (1937), von Karman and Burgers (1943), von Mises (1945), Pope (1951), and Rauscher (1953) — deal with this subject. These tranformations are perhaps less valuable to aerodynamicists for the shapes they transform

2NACA is an acronym for National Advisory Committee for Aeronautics, which has been replaced by NASA (National Aeronautics and Space Administration).

BIOLOGICAL FORM REPRESENTATION

69

than for the characteristics of the related fluid-flow fields about the cylinders and airfoils. Advantages of applying shape transformations of this type to those biological shapes which may be transformed from circles include, for example, representation of relatively complicated shapes at different stages of growth by circles that differ progressively in radii and center coordinates. The amount of data required to des¬ cribe a shape can be reduced to the Cartesian coordinates of the center and the radius of the circle.

Ad hoc methods for describing airfoils also were developed during the first half of this century. One such simple method is the NACA four-digit series, which can also be applied to teardrop-shaped biologi¬ cal forms.

Microcomputers, coupled with digitizer boards, provide a precise and quick method of obtaining the digital coordinates necessary for plot¬ ting and drawing the outline shape of physical specimens. In this study, coordinates were taken (digitized) from specimen photographs selected to provide data for the construction of the circles and whose shapes were used subsequently for comparison with the transformed circles.

MATERIALS AND METHODS

As an example of these techniques we apply the Joukowski trans¬ formation to circles for which size and location were determined from measurements of the length, thickness, and curvature of the two differ¬ ent teeth pictured in Plate 1. We also calculated the NACA 4-digit ser¬ ies that best describes these teeth. Both specimens are isolated lateral incisors from adult olive baboons. A line drawn equidistant from the upper and lower portions of the profile of tooth (A) shown in Plate 1 would be approximately straight (curvature approximately zero). Bio¬ logical forms lacking curvature are referred to as symmetrical. The other tooth shown in Plate 1 has significant curvature of a line equi¬ distant between the upper and lower portions of its profile, and provides data for the unsymmetrical example to be discussed.

In Plate 1 the boundaries of the teeth were visually aligned in an object plane and photographed at an object distance of about 116 mm with a 55 mm lens-equipped camera. The aspects forming the bound¬ aries of the forms were estimated to be within 3 mm of the object plane (plane of focus) which leads to a maximum error in relative distance between points on the boundaries of the teeth shown in Plate 1 of less than 3%. Error of this type resulting from photographic technique decreases linearly with increasing object distance. The photographs were printed at a magnification of approximately four times actual tooth size. During early phases of this study, coordinates of points on

70

THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

Plate 1. Photographs of lateral incisors showing (A) symmetrical tooth (buccal aspect), and (b) unsymmetrical tooth (distal aspect).

the boundaries of the teeth were digitized using a TALOS model 611 digitizer board with an advertised accuracy of less than ±0.13 mm for coordinate location. The digitizer board was interfaced with a Hewlett- Packard System 9815A desk-top microcomputer which provided a dig¬ ital display of the coordinate values. As many as seventy locations were digitized per tooth, and the overall accuracy of any location digitized was estimated to be less than 3% of the length of the tooth, with most of the possible error due to the photographic phase. The coordinates were then plotted on graph paper and connected by curved segments in order to obtain outline drawings of the teeth. In an alternative method, the outline drawings were traced from the photographs. All measure¬ ments were made directly on the resulting drawings and are about four times greater than corresponding measurements made on the actual teeth due to the photographic magnification factor.

Many microcomputer systems have the capability to provide the drawings directly, either by plotting and connecting the digitized points or by printing closely spaced dots.

BIOLOGICAL FORM REPRESENTATION

71

THE JOUKOWSKI TRANSFORMATION

A simple transformation that transforms certain circles in the z-plane to teardrop shapes in the w-plane is the Joukowski transformation3 (Pope 1951),

w=z + if. (1)

z

where z and w can both be expressed in complex notation as z = x + iy and w = u + iv, and b is a real constant. Not all circles in the z-plane are transformed into teardrop shapes; for instance, a circle of radius b centered at the origin of the z-plane will be transformed into a straight line between the points (— 2b, 0) and (2b, 0), in the w-plane. A problem in working with some conformal transformations is the lack of general analytical solutions that give information such as the resulting length and thickness. For the Joukowski transformation an approximate ana¬ lytical solution exists, valid when the thickness T is approximately small compared to the length L, and it yields for the symmetrical trans¬ formation (Pope 1951)

Xc=T/3\/3 (2)

and

b= L/4 (3)

where Xc is the x-coordinate of the center of the circle and — b is the intersection of the circle and the negative real axis. The y-coordinate of the center of the circle for the symmetrical transformation is, of course, equal to zero, and the circle radius is equal to the sum of Xc and b.

Figure 1 is a profile drawing of the symmetrical tooth from Plate 1. The measurements required to obtain the thickness and length for use in Eqs. (2) and (3) are indicated in relation to the outline drawing of the specimen. Substituting the thickness T = 24.5 mm and the length L = 122 mm into Eqs. (2) and (3), respectively, yields Xc = 4.7 mm and b = 31 mm. The circle in the z-plane resulting from these values has radius 36 mm and is shown in Fig. 1. The w-plane containing the Joukowski profile (transformed circle) according to Eq. (1) is superim¬ posed on the z-plane in Fig. 1 also, and shows the teardrop shaped transformation compared to the outline drawing of the actual tooth.

3The Joukowski transformation is sometimes referred to as the Kutta-Joukowski trans¬ formation, after Kutta and Joukowski who worked independently in Germany and Rus¬ sia, respectively, and who both advanced the transformation about 1910.

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THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

Figure 1. Diagram of (A) the outline of the symmetrical tooth in Plate 1 showing the thickness T = 24.5 mm and the length L = 122 mm, (B) the circle in the z-plane, and (C) the Joukowski profile in the w-plane.

The Joukowski profile is about 2% longer and about 10% thinner than the actual tooth due to the approximations involved in obtaining the analytical solutions for thickness and length.

For the unsymmetrical transformation (Piercy 1937) Xc and b are given by Eqs. (2) and (3), and the y-coordinate of the center of the circle is given approximately by

yc-(b+Xc)/3 (4)

where /3 is a curvature parameter which must be appropriately small in order to obtain Eq. (4). For the unsymmetrical Joukowski transforma¬ tion, J3 is equal to one-half the acute angle formed by the cusp and the x-axis. For the unsymmetrical tooth shown in Plate 1 and drawn in Fig. 2, P = 14 degrees was estimated to be one-half the angle formed between an imaginary curvature line and the x-axis when the tooth was graphically extended to form a point at the narrow end, approximately the shape of mature teeth from certain specimens (Taylor 1978). For the curved tooth shown in Fig. 2, application of Eqs. (2) - (4) to a thickness of 25 mm, an extended length of 113 mm, and P = 14 degrees yields Xc = 4.8 mm, b = 28 mm, and yc = 7.9 mm. The resulting circle (shown in Fig. 2) has a radius (equal to the distance from the center to — b) of 34 mm. The w-plane with the transformation of the z-plane circle in

BIOLOGICAL FORM REPRESENTATION

73

Figure 2. Diagram of the (A) outline of unsymmetrical tooth shown in Plate 1 showing the thickness T = 25 mm, (B) the graphically extended root to yield an overall length L = 113 mm, (C) the circle in the z-plane, and (D) the Joukowski profile in the w- plane.

Fig. 2 shows the Joukowski profile for comparison, which in this case is about 2% longer and 10% thinner than the tooth from which it was derived.

Both Joukowski profiles in Figs. 1 and 2 end in cusps at the narrow ends of the teeth. The cusps are a result of the singular point — b lying on the circumference of each circle. Equation (1) is also not conformal at +b, but this point causes no problem because it lies within both cir¬ cles. For reasons having to do with the air flow about the shape, aero- dynamicists have usually required the desired circles to pass through one singularity and enclose the other (Pope 1951). In working with shapes alone these requirements are not necessary. If the radius of each circle is increased slightly so that the point — b is enclosed, both singu¬ larities are enclosed, and transformation is possible in a manner that is everywhere conformal. The cusps in Figs. 1 and 2 then could be replaced by rounded shapes more suitable for biological forms.

In obtaining the approximate Eqs. (1) - (4), Xc/b and fi have been assumed to be small (Piercy 1937; Pope 1951). Requiring Xc/b to be small in equivalent to requiring the thickness T to be small compared to the length L, because dividing Eq. (2) by Eq. (3) yields xc/b = 0.77T/L. Additional results of the approximate method used here to solve Eq. (1) are that the maximum thickness of the Joukowski profile

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THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

occurs at about one-fourth the length, near the rounded end, and that the line of curvature is the arc of a circle (Pope 1951). These results obviously should influence the choice of biological shapes to which the Joukowski transformation may be applied.

OTHER CONFORMAL TRANSFORMATIONS

The Joukowski transformation described by Eq. (1) is a special case of the general transformation (known as the von Mises transformation)

w = z +£L + SL +...+ if. (5)

2 n

z z z

where the cn are constants (von Mises 1945). For the Joukowski trans¬ formation, ci = b2 and the remainder of the constants are zero. Increas¬ ing the number of terms used in a transformation results in better representation and greater analytical difficulty. Application of Eq. (5) is discussed in von Karman and Burgers (1943), von Mises (1945) and Rauscher (1953).

Another simple transformation of interest is the Karman-Trefftz transformation (Von Karman and Burgers 1943)

w — mb _ /z - b \ m ^

w + mb \ z + b /

where m = 2 — (k/7r) and k is the tail angle. This transformation is similar to the Joukowski transformation, but rather than yielding a cusp, produces a finite angle, k (for k greater than zero), at the trans¬ formation of the point where the circle passes through the singularity in Figures 1 and 2. For k = 0, the Joukowski transformation [Eq. (1)] is obtained from Eq. (6), and for k not equal to zero, Eq. (6) can be shown to correspond to an infinite series (von Karman and Burgers 1943).

NACA FOUR-DIGIT SERIES

This method of characterizing airfoils has corresponding designa¬ tions used in reference to teeth. The chord of an airfoil finds its corol¬ lary in the length of a tooth, and the camber of an airfoil is designated curvature (Fig. 3) when applied to a tooth (von Mises 1945). The chord and the length are generally the largest physical measurements that can be made on an airfoil profile and a tooth, respectively.

The mean camber line may be defined as a curved line generated by the locus of centers of the line segments drawn across the airfoil section perpendicular to the chord. The mean curvature line of a tooth is used here in a similar fashion. Other definitions of camber are possible, and

BIOLOGICAL FORM REPRESENTATION

75

Figure 3. Drawing of a cambered airfoil in an orthogonal x-y coordinate system showing the ordinate of maximum camber, ymax; the abcissa of maximum camber, xmax; the chord, c; mean camber line; and thickness t at location x given by the thickness func¬ tion (Eq.ll). Note that the thickness is measured normal to the mean camber line. For a tooth the chord would be designated length and the mean camber line as mean cur¬ vature line. Thickness is defined the same for both airfoil and tooth.

usually are approximately equivalent (von Mises 1945). The maximum thickness may be defined in various ways (von Mises 1945). Here we define it as the length of a line segment, locally perpendicular to the mean camber line across the airfoil section or tooth, in accordance with the NACA definition (Jacobs et al. 1933). Generally, the length or chord is oriented parallel to an axis in an orthogonal coordinate system when constructing a graphic representation.

The NACA four-digit specification (Jacobs et al. 1933; Jacobs and Pinkerton 1935; Jacobs et al. 1937) for an airfoil shape contains four digits and is often specified as NACA ABCD where the A, B, C, and D are digits. The first two digits determine the form of the mean camber line (graphically indicated in Fig. 3). The first digit indicates the ordi¬ nate ymax (see Fig. 3) of the maximum camber in percent of chord (and thus its utility in this form is limited to airfoils of maximum camber less than 10% of the chord length). For a NACA ABCD airfoil, the digit A = 10 ymax/c, where c is the chord. Applied to a tooth,

A = 100 ymax /L (7)

where L is the tooth length. The second digit, B, is the abcissa of the location xmax of maximum camber in tenths of the chord length, or B =

10 Xmax / c. For a tooth,

B = 10 Xmax/L.

(8)

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THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

For a symmetrical airfoil (one having a straight camber line) the A and B are identically zero, e.g., NACA OOCD.

The last two digits CD give the relative thickness of the airfoil in percent of chord, CD = 100 T/c, where T is the maximum airfoil thickness measured normal to the mean camber line (see Fig. 3). Notice two digits are used to represent the thickness. For a tooth,

CD = 100 T/L, (9)

and T here is the maximum tooth thickness measured normal to the curvature line. From the information given in the first two digits of the profile, obviously the x- and y- coordinates of the maximum camber location for unsymmetrical teeth can be derived from Eqs. (7) and (8); e.g., ymax — AL/100 and xmax = BL/10. The mean camber line then can be constructed from the following equations of parabolic arcs (von Mises 1945):

— Ymax (2xmax ~ x)x for 0 < X < Xmax

( Xmax )

(10a)

and

y = _ YHZ _ _(L - x) (L - x - 2xmax) (10b)

(L Xmax)

for Xmax < x < c. Once the camber line is known, the thickness function t, given by

t = ±t[ 1.4845 \/*— 0.6300£ - 1.7580(^)2

+ 1.4215(^)3 - 0.5075(^)4], (11)

can be used to determine the actual profile. At the abcissa x on the mean camber line, t is measured above and below (along a line normal to) the mean camber line to determine points on the profile (Fig. 3).

The length and thickness of the distal aspect of a curved tooth have been measured as L = 25.4 mm and T = 7 mm. The location of the y-coordinate of the maximum curvature was calculated to be ymax — 2.3 mm from measurements indicated in Fig. 4, according to

ymax = (yi + yi)/2. (12)

Values of yi and y2 and the value xmax — 12.8 mm were estimated directly from the tooth profile in the manner described in Fig. 4.

BIOLOGICAL FORM REPRESENTATION

77

Figure 4. Diagram of measurements to be made in order to estimate xmax and ymax. The measurements may be made on the actual specimen, or a photograph or other like¬ ness.

Application of Eqs. (7)-(9) resulted in a designation of NACA 9528. Once the profile designation and the length were available, a represen¬ tation of the tooth could be constructed by applying Eqs. (7) and (8) to determine xmax and ymax (had they not been known already, as in this case) and Eq. (9) to determine T. From Eq. (10) the mean camber line was drawn (Fig. 5), and from Eq. (11) the upper and lower portions of the profile were determined (Fig. 5).

The NACA 9528 shape fit the profile of the 25.4 mm long tooth rea¬ sonably well (Fig. 5). However, this airfoil profile resulted in a fairly sharp4 end at the root of the tooth. An arbitrary length extension of 10% (thickness still 7mm) improved fit near the root (Fig. 6). This length extension gave, by Eq. (7), a two digit A value of 11 and the complete profile could be written NACA U525.5 The tooth and profile are compared in Fig. 6. Estimated values of ymax and xmax were 3.2 mm and 14 mm respectively, for the lengthened profile.

The thickness function for airfoils (Eq. 11) was developed from a polynomial relation with five adjustable constants (Jacobs et al. 1933), which were chosen to yield desirable airfoil characteristics (such as nose shape, location of maximum thickness, and trailing-edge angle). At this time representational similarities between shapes of airfoils and teeth may be regarded as fortuitous and the method ad hoc. The method of development of the airfoil representation does suggest that perhaps an even better fit to teardrop-shaped biological forms may be obtained by

4The airfoil thickness function (Eq. 11) yields 0.10105T at the trailing edge (narrow end) rather than zero as might be expected.

5 A bar is here introduced under the first two digits to show that they represent one item (ordinate of maximum camber, ymax). In particular, this designation should not be con¬ fused with the NACA five-digit series.

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THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

D

Figure 5. Schematic of (A) NACA 9528 profile, (B) tracing of the photograph of a tooth, and (C) mean curvature line.

further adjustment to an appropriate thickness function such as that used by Jacobs et al. (1933) to fit data taken from average biological forms rather than desirable airfoil characteristics.

CONCLUSIONS

The Joukowski transformation shown in Eq. (1) yields a reasonable fit to the shapes of the selected unicuspid teeth. Collection, storage, and manipulation of length, thickness, and curvature angle are all that are required to relate the teeth to the simple geometric shape of a circle from which teardrop shapes similar to the original profiles can be gen¬ erated. Alternatively, the data representing a given shape may be stored and manipulated as the center coordinates (xc, yc) and the radius (or the parameter b) for a circle. Different circles may be used to represent dif¬ ferent stages of growth or species. Both distal and buccal aspects of appropriate teeth may be represented.

The approximate solution to the Joukowski transformation is valid only for small values of the parameters Xc/b and p. Significant errors (about 10% for the thicknesses in Figs. 1 and 2) in the thickness and length of the Joukowski profiles were introduced here by using speci¬ mens with only marginally small values of Xc/b and p. However, the results are appropriate as an example of the technique. The error introduced by using relatively large values of Xc/b and P rapidly decreases as the sizes of these parameters become smaller.

The alignment of the outlines of the actual teeth for comparison with the derived profiles is somewhat arbitrary, and the graphical extension of the length of the tooth in Fig. 2 in order to measure the curvature parameter P is also arbitrary. Other alignments and changes (one is not restricted to length extensions alone) are possible; however, they should be biologically defensible in some manner. In this case the

BIOLOGICAL FORM REPRESENTATION

79

Figure 6. Schematics of (A) NACA JJ525 profile, (B) tracing of the photograph of a tooth, (C) mean curvature line, and (D) graphical length extension (the bottom por¬ tion of the graphical extension coincides with the NACA J_1525 profile).

sharper point added to Fig. 2 is somewhat characteristic of certain mature specimens (Taylor 1978). A similar extension would have improved the transformed profile in Fig. 1. The fit of the NACA four¬ digit profiles in Figs. 5 and 6 to the selected tooth seems to be very good. The profile in each case results from application of Eq. (7) -(11) to the data stored in the digits of the profiles and the length (the extended length in Fig. 6). Storage and manipulation of the profile designated and the length are obviously easier than storage of photo¬ graphs, models, or several coordinate points to be used in plotting the tooth, and are compatible with modern computational techniques involving electronic computers.

Obvious improvements can be made in the system to improve accu¬ racy and versatility, such as allowing A to be two digits as shown here. A further improvement of the NACA four-digit system useful in aero¬ nautics was the NACA five-digit system, which allowed for improved aerodynamic performance. In this system the mean camber line is either an arc of a cubic parabola and a straight line, or portions of two cubic parabolas (von Mises 1945) and might find applicability to a teardrop shaped biological form with an S-shaped curvature line. Original doc¬ uments dealing with the NACA five-digit series are studies by Jacobs and Pinkerton (1935) and Jacobs et al. (1937).

This paper deals only with permanent unicuspid teeth. However, premolars and molars may be described as a collection of fused tear¬ drop shapes which can each be described as either a transformed circle or by a NACA 4-digit profile (Taylor 1978). Also human tooth buds develop from a spherical form to the final shape through a series of shapes which may be approximated by transformed circles (Langman 1975). It also might be possible to calculate the NACA series for an

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THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

entire developmental sequence of teeth and show how tooth shape changes through time. Also, fossil teeth can be characterized by a NACA four-digit number which could be used as part of the published description of each find. This would enable other investigators to reconstruct outlines of the teeth.

Other biological shapes could also be described by the Joukowski transformation and by NACA 4-digit series. Potentially describable objects include leaves, fish, and wings — any teardrop-shaped object of small thickness-to-length ratio (small Xc/b), small curvature approxi¬ mating that of a circular arc, and possessing maximum thickness at about 25% of the length, near the rounded end. A possible use for the simpler description of teardrop-shaped biological forms is in taxon¬ omy. Brief descriptions generated by the method discussed here may be easier to deal with than those given in standard taxonomic keys.

The Joukowski transformation and the NACA 4-digit series are two parsimonious descriptive methods that can adequately represent certain teardrop biological shapes such as teeth.

ACKNOWLEDGEMENTS

The authors wish to thank Dr. Ordean J. Oyen for supplying the specimens and for helpful discussions about the manuscript. We are also grateful to Dr. Robert S. Rice and Dr. John T. Demel for helpful comments, and to Mr. John Purcell for photographic work.

LITERATURE CITED

Ashton, E. H., and S. Zuckerman. 1950. Some quantitative dental characteristics of the chimpanzee, gorilla, and orangutan. Phil. Trans. Roy. Soc. (London), Series B. 234:471-484.

Bookstein, F. L. 1977. The study of shape transformation after D’Arcy Thompson. Math. Biosci. 34:177-219.

Jacobs, E. N., and R. M. Pinkerton. 1935. Tests in the variable-density wind tunnel of related airfoils having the maximum camber unusually far forward, p. 521-529. In NACA Technical Report 537, 21st Annual Report. Government Printing Office, Washington.

Jacobs, E. N., R. M. Pinkerton, and H. Greenberg. 1937. Tests of related forward camber airfoils in the variable-density wind tunnel, p. 697-731. In NACA Technical Report 610, 23rd Annual Reprot. Government Printing Office, Washington.

Jacobs, E. N., K. E. Ward, and R. M. Pinkerton. 1933. The characteristics of 78 related airfoil sections from tests in the variable density wind tunnel, p. 299-354. In NACA Technical Report 460, 19th Annual Report. Government Printing Office, Washing¬ ton.

Von Karman, Th., and J. M. Burgers. 1943. General aerodynamic theory: perfect fluids, p. 1-367. In W. F. Durnat (Ed.), Aerodynamic Theory. Verlag Julius Springer, Berlin. Krogman, W. M. 1969. Growth changes in skull, face, jaws, and teeth of the chimpanzee, p. 104-164. In The Chimpanzee, vol. 1. Karger Press, Basel, Switzerland.

BIOLOGICAL FORM REPRESENTATION

81

Langman, J. 1975. Medical Embryology, 3rd ed. The Williams and Wilkins Co., Balti¬ more, MD.

Von Mises, R. 1945. Theory of Flight. McGraw Hill, New York, NY.

Piercy, N. A. V. 1937. Aerodynamics. D. van Nostrand, New York, NY.

Pope, A. 1951. Basic Wing and Airfoil Theory. McGraw Hill, New York, NY.

Rauscher, M. 1953. Introduction to Aeronautical Dynamics. John Wiley, New York, NY. Rosen, R. 1978. Dynamical similarity and the theory of bilogical transfomations. Bull. Math. Biol. 40:549-579.

Taylor, R. M. S. 1978. Variation in Morphology of Teeth: Anthropologic and Forensic Aspects. Charles C. Thomas, Springfield, IL.

Thompson, D. W. 1917. On Growth and Form. Cambridge Unviersity Press, Cambridge, MA.

Zeisz, R. C., and J. Nuckolls. 1949. Dental Anatomy. C. V. Mosby. St. Louis, MO.

CIRCULATING CORTICOSTEROID AND LEUCOCYTE DYNAMICS IN CHANNEL CATFISH DURING NET CONFINEMENT

by J. R. TOMASSO1, BILL A. SIMCO, and KENNETH B. DAVIS

Department of Biology Memphis State University Memphis, TN 38152

ABSTRACT

Channel catfish ( Ictalurus punctatus ) were stressed by close confinement in a net for periods up to 24 h. Plasma corticosteroid concentrations increased from 0.8 ± 0.3 jug/100 ml (mean ± S.E.) to a peak of 5.7 ± 0.6 pg/lOO ml after 6 h, then declined by 24 h. Leucocrit decreased during the first 6 h, owing to a decline in lymphocyte numbers, then increased by 12 h. Hematocrit did not vary significantly during the 24-h period.

INTRODUCTION

Increases in circulating corticosteroid concentrations have been dem¬ onstrated in many species of fishes in response to a variety of stressors (Strange et al. 1977; Leach and Taylor 1980; Tomasso et al. 1981). Cor¬ ticosteroids (cortisol, cortisone, corticosterone) are released from the interrenal tissue (Wedemeyer 1970). A detrimental effect of increased corticosteroid release is immunosuppression (Grant 1967). One immu¬ nosuppressive effect identified in fishes is the corticosteroid-mediated decrease in circulating leucocytes (Weinreb 1958; Pickford et al. 1971; McLeay 1973). This study was conducted to determine the effect of stress-induced elevation of circulating corticosteroids on abundance and types of circulating leucocytes in the channel catfish (Ictalurus puncta¬ tus).

MATERIALS AND METHODS

Channel catfish were obtained from the Southeastern Fish Cultural Laboratory (Marion, Alabama) and maintained in large indoor recircu¬ lating systems (20-22 C) for at least 2 months prior to use. Fish were fed a commercial diet equivalent to approximately 1% of their body wieght per day. Feeding was suspended 48 hours prior to experiments.

Blood was obtained from the caudal peduncle by the use of a hepa¬ rinized syringe after the fish were anesthetized in a 0.02% solution of

1 Present address: Department of Biology, Southwest Texas State University, San Marcos, TX 78666.

The Texas Journal of Science, Vol. XXXV, No. 1, March 1983

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THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

MS-222. A portion of the blood was then immediately transferred to hematocrit tubes and centrifuged for 5 minutes at 13,000 x g. The remaining blood was also centrifuged and the plasma frozen until used for corticosteroid analysis.

Total blood volume and total packed cell volume in the hematocrit tubes were measured with dial calipers (± 0.01 mm) and packed white cells were measured using an ocular micrometer. The hematocrit and leucocrit (McLeay and Gordon 1977) were then determined by dividing the total packed cell volume and packed white cell volume, respec¬ tively, by the total blood volume. All measurements were taken within one hour of sampling. Total plasma corticosteriod concentrations were determined by competitive protein binding (Murphy 1967), as modified by Fagerlund (1970) using chicken serum as a transcortin source.

To determine the effect of net confinement on leucocrit and plasma corticosteroid levels, 10 fish (9-15 cm standard length) were netted from the holding system and immediately bled. Thirty more fish were then captured and confined in a dip net suspended in the tank in a way that allowed the fish to be underwater but severely crowded. Some of the confined fish were then bled after 6, 12, and 24 hours of confinement. The initial sampling (time 0) and the sampling after 6 hours of con¬ finement were repeated three times and, the replicate data from each bleeding time being similar, were pooled for further analysis. In all cases, each fish was sampled only once.

To determine changes, if any, in types of circulating leucocytes dur¬ ing the confinement, three fish (30-40 cm standard length) were cap¬ tured and immediately bled. Each was fin clipped for further identifica¬ tion, and confined in a net suspended in the holding tank as previously described. After 6 and 12 hours each fish was bled again. Following each bleeding, blood smears were made, stained, and relative numbers of cell types determined.

One-way analysis of variance followed by Duncan’s multiple range test was used to compare changes in leucocrits, hematocrits, and corti¬ costeroids during the course of the experiment. A probability level of < 0.05 was considered significant.

RESULTS AND DISCUSSION

Plasma corticosteroid concentrations increased from baseline levels (0.8 ± 0.3 /Jg / 1 00 ml, mean ± S.E.) to a peak of 5.7 ± 0.6 fJg / 1 00 ml after 6 hours of confinement (Fig. 1). A slight decrease in plasma corti¬ costeroid levels was apparent after 24 hours although the animals were still confined. This decrease, while fish are sill confined, has been observed in channel catfish elsewhere (Davis and Parker, unpublished data) and in chinook salmon (Strange and Schreck 1978) and may

CORTICOSTEROIDS AND LEUCOCYTES IN CATFISH

85

8

Figure 1. Leucocrit, hematocrit and plasma corticosteroid dynamics in channel catfish confined in a net for up to 24 hours. Dots with vertical lines represent mean + S.E. Numbers of fish measured are given directly above the x-axis. Sampling periods with statistically similar means share a common line.

represent the beginning of adaptation to the stressor (Selye 1950). Boehlke et al. (1966) reported higher resting corticosteroid concentra¬ tions in channel catfish (about 10 /rg/100 ml) than reported here and elsewhere (Strange 1980). It has been suggested that this discrepancy may be due to the use of fluorimetric assay by Boehlke and his coworkers in contrast to the competitive protein binding assay (Strange 1980).

Leucocrits decreased significantly from baseline levels (1.42 ±0.05) during the first 6 hours of confinement, but by 12 hours of confine¬ ment leucocrits were significantly higher than baseline levels (Fig. 1). An increase in the leucocrit of eels during social stress was explained by changes in the ratio of lymphocytes to granulocytes (Peters et al.

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THE TEXAS JOURNAL OF SCIENCE— VOL. XXXV, NO. 1, 1983

Figure 2. Circulating leucocyte dynamics in three channel catfish serially sampled dur¬ ing 12 hours of net confinement. Each individual fish is represented by an asterisk, dot or square (gran = granulocytes, lym = lymphocytes, leu = leucocytes, b. c. = total blood cells).

1980). While the total white cell count of the eel decreased due to a decreased number of circulating lymphocytes, the number of granulo¬ cytes actually increased. The increase in number of the larger granulo¬ cytes was apparently more than enough, in terms of volume, to offset the decrease in the small lymphocytes, resulting in an increased leuco- crit. Similar decreases in lymphocyte counts and increases in granulo¬ cyte counts have been described in largemouth bass (Esch and Hazen 1980) and coho salmon (McLeay 1973). However, it should be noted that while granulocyte counts increased in response to stress, numbers of circulating granulocytes are not corticosteriod mediated (Dougherty and White 1944).

The decrease in leucocrit observed after 6 hours of confinement in a net may be attributed to different temporal responses of lymphocytes and granulocytes to stress. Figure 2 shows the relationship of circulat¬ ing lymphocytes and granulocytes to confinement time. In all three fish examined, lymphocytes/ 100 cells had decreased