Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

In vitro fluid dynamics of the Bjork-Shiley monostrust mitral disc valve using laser doppler anemometry Ma, Zhi-Yong 1993

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-ubc_1994-0037.pdf [ 2.53MB ]
Metadata
JSON: 831-1.0081038.json
JSON-LD: 831-1.0081038-ld.json
RDF/XML (Pretty): 831-1.0081038-rdf.xml
RDF/JSON: 831-1.0081038-rdf.json
Turtle: 831-1.0081038-turtle.txt
N-Triples: 831-1.0081038-rdf-ntriples.txt
Original Record: 831-1.0081038-source.json
Full Text
831-1.0081038-fulltext.txt
Citation
831-1.0081038.ris

Full Text

IN VITRO FLUID DYNAMICS OF THE BJORK-SHILEY MONOSTRUTMITRAL DISC VALVE USING LASER DOPPLER ANEMOMETRYbyZHI-YONG MAB.Eng., Wuhan Iron and Steel University (P.R. China), 1982M.Eng., Shanghai Institute of Mechanical Engineering (P.R. China), 1984A THESIS SUBMITTED IN PARTIAL FULFILMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESDepartment of Mechanical EngineeringWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIANovember, 1993© Ma Zhi-Yong, 1993In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of myDepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of Mechanical EngineeringThe University of British Columbia2324 Main MallVancouver, B.C.Canada V6T 1Z4Date_____________________ABSTRACTIIIn recent decades, several different types of prosthetic devices have beenintroduced in clinical practice to replace the diseased natural heart valves. In Canadaalone, around 10,000 operations aimed at treatment of valvular diseases are carriedout every year. Although evolution of prosthetic heart valves have, in general,succeeded in increasing the patient’s lifespan, scope exists in improvement of theirdesign as attested by failure of several commonly used heart valves. Successful designof prosthetic heart valves depends on thorough understanding of several aspectsincluding biocompatibility, structural integrity and complex fluid dynamics.Focus of the present thesis is on the fluid dynamical performance withemphasis on fundamental information of long range value which can serve asreference:(i)(ii)(iii)in assessing performance of prosthetic heart valves widely in use at present;in development of improved configurations of new designs;for government health agencies and manufacturers in formulating performancecriteria which must be met to protect the user community;(iv) for practising cardiac surgeons in selecting appropriate prostheses forimplantation.This thesis first introduces the basic knowledge about the heart, heart valvesand the laser Doppler anemometry (LDA) as the general background. This is followedby a description of the test methodology. One of the challenging aspects is the analysisand display of the vast amount of data obtained in a meaningful way. Computer codesdeveloped to this end thus form an important part of the thesis.Finally, the thesis focuses on the fluid dynamic results and their analysis withrespect to the Bjork-Shiley monostrut tilting disc valve, in mitral location, using a111sophisticated cardiac pulse duplicator in conjunction with a 3-beam, two-component,LDA system. Time histories of the velocity profile, turbulence intensity, Reynoldsstress, etc., are presented for both posterior and anterior orientations of the valve, forfive different pulse rates.Results suggest relatively favourable performance in the posterior position. Thestress level was found to be safe and would not present the danger of haemolysis. Ingeneral, the valve performance was found to be insensitive to the flow rate.ivTABLE OF CONTENTSABSTRACTLIST OF FIGURESPREFACE AND ACKNOWLEDGMENT1. INTRODUCTION 11.1 Concepts in Human Cardiovascular System and Heart Anatomy 21.2 Cardiac Output and Mitral Valve Disease 91.3 Overview of Prosthetic Mitral Valve Development1.4 Review of In Vitro Studies1.4.1 Typical Results for Representative Mitral Valves1.4.2 Application of the LDA1.5 Background to the Present Study1.6 Purpose and Scope of the Present Investigation2. TEST SYSTEM AND METHODOLOGY2.1 The Test Facility2.2 Instrumentation and Model2.2.1 Laser Doppler Anemometer2.2.2 Computers2.2.3 Mitral Valve2.2.4 Aortic Valve2.3 Methodologies2.3.1 LDA Measurement Techniques2.3.2 Data Acquisition and Reduction2.3.3 Data Analyses and Display25252828282829293134373. RESULTS AND DISCUSSIONS3.1 Posterior Orientation3.1.1 Mechanical Performance3.1.2 Fluid Dynamical Performance3.2 Anterior Orientation3911vix15181920232441415976V3.2.1 Mechanical Performance 773.2.2 Fluid Dynamical Performance 803.3 Performance Comparison of the Posterior and Anterior Orientations 814. CONCLUSIONS AND RECOMMENDATIONS 874.1 Concluding Remarks 874.2 Recommendations for Future Work 89REFERENCES 91APPENDIX-I: COMPUTER CODES 931.1 Programs for the Experiments 931.2 Programs for Data Analyses and Output 941.2.1 MAIN MENU Program 941.2.2 PREPARATION DATA Menu Program 961.2.3 SINGLE-PLOT Menu Program 961.2.4 FIVE-PLOT Menu Program 991.2.5 FIVE÷FIVE Menu Program 991.2.6 NINE-PLOT Menu Program 1061.2.7 TEN-PLOT Menu Program 1061.2.8 Common Options in the Programs 1111.2.9 Other Options in the Programs . . 1121.3 Other Programs 112APPENDIX-Il: SUMMARY OF MECHANICAL PERFORMANCE 113viLIST OF FIGURESFigure 1-1 The position of the heart within the thoracic cavity 3Figure 1-2 A schematic diagram of the structure of the heart (an internalview). Arrows represent direction of the blood flow 5Figure 1-3 A diagram showing relative positions of the valves and thesupporting fibrous connective tissue 6Figure 1-4 A schematic diagram of the circulatory system. Arrows indicatedirection of blood flow 8Figure 1-5 The pressure distribution inside the heart where: P = thepressure difference between the origin of the blood flow (meanpressure of about 100 mmHg in the aorta) and the end of thecircuit (zero mmHg in the vena cava); RA = right atrium; LA =left atrium; RV = right ventricle; and LV = left ventricle 11Figure 1-6 A schematic diagram of the left side of the heart 12Figure 1-7 A schematic diagram of a natural mitral valve 13Figure 1-8 The position of the natural mitral leaflets in the normal leftventricle. The anterior mitral leaflet (A) is continuous with theaortic wall; the posterior leaflet (P) attaches to the annulus andis primarily a continuation of the mural endocardium of theatrium. The two leaflets differ in shape but are approximatelyequal in area 14Figure 1-9 Diagrams of some commonly used prostheses: (a) Bjork-Shileymonostrut used in this study; (b) Bjork-Shiley c-c; (c) Bicer-Val;(d) St. Jude bileaflet; (e) Starr Edwards; (f) Mitroflow 16Figure 1-10 A schematic diagram of the TEM00 mode structure of the laser.22Figure 1-11 Fringe patten in the measurement region 22Figure 2-1 Schematic diagram of the test system and associatedinstrumentation 26Figure 2-2 Details of the test chamber showing the left atrium, aorta, anda section of the left ventricle with the mitral and aortic valvesin position 27Figure 2-3 Schematic diagram showing flow regions of the mitral valve(Bjork-Shiley monostrut, model 27XAMMB) used in theexperiments 30viiFigure 2-4 Plan and elevation views showing downstream measurementlocations 32Figure 2-5 Orientation and definition of velocity components within theventricle 35Figure 3-1 Schematic diagram showing three phases of interest in a cardiaccycle showing instances where measurements are emphasized.. 40Figure 3-2 Schematic diagram showing the mitral disc valve in theposterior orientation 42Figure 3-3 Time history of velocity and stress profiles for the posteriororientation of the mitral valve at the location X=100 mm,Z=0.4D (pulse rate=71 beats/mm,U0=14.03 cmls) 43Figure 3-4 Time history of velocity and stress profiles for the posteriororientation of the mitral valve at the location X=100 mm,Z=0.625D (pulse rate=71 beats/mm,U0=14.03 cmJs) 46Figure 3-5 Time history of velocity and stress profiles for the posteriororientation of the mitral valve at the location X=100 mm,Z=0.625D (pulse rate=84 beats/mm, U0=17.54 cmls) 49Figure 3-6 Time history of velocity and stress profiles for the posteriororientation of the mitral valve at the location XtlOO mm,Z=0.625D (pulse rate=78 beats/mm,U0=15.35 cmls) 52Figure 3-7 Time history of velocity and stress profiles for the posteriororientation of the mitral valve at the location X=100 mm,Z=0.625D (pulse rate=67 beats/mm,U0=12.28 cm/s) 55Figure 3-8 Time history of velocity and stress profiles for the posteriororientation of the mitral valve at the location X=100 mm,Z=0.625D (pulse rate=62 beats/mm,U0=10.96 cmls) 57Figure 3-9 Variation of velocity and stress profiles at five down streamlocations (X=100 mm) for the posterior orientation of the mitralvalve when the valve is fully open (pulse rate=71 beats/mm,U0=14.03 cnils) 62Figure 3-10 Variation of velocity and stress profiles at five down streamlocations (X=100 mm) for the posterior orientation of the mitralvalve when the aortic valve is fully open (pulse rate=71beats/mm,U0=14.03 cm/s) 63Figure 3-11 Variation of velocity and stress profiles at five down streamlocations (X=100 mm) for the posterior orientation of the mitralvalve at two different instants (T=100 ms, 300 ms)corresponding to acceleration and deceleration phases of the flow(pulse rate=71 beats/mm,U0=14.03 cmJs) 65v-luFigure 3-12 Variation of velocity and stress profiles at five down streamlocations (X=100 mm) for the posterior orientation of the mitralvalve at two different instants (T=450 ms, 550 ms) when theaortic valve is open (pulse rate=71 beats/mm,U=14.03 cmls).. 66Figure 3-13 Variation of velocity and stress profiles at five down streamlocations (X=96 mm, 92 mm) in the posterior orientation of thevalve at the instant T=0 ms representing beginning of the mitralvalve opening (pulse rate=71 beats/mm, U0=14.03 cmls) 67Figure 3-14 Variation of velocity and stress profiles at five down streamlocations (X=96 mm, 92 mm) in the posterior orientation of thevalve at the instant T=100 ms corresponding to the accelerationphase of the flow (pulse rate=71 beats/mm,U0=14.03 cmls). . . . 68Figure 3-15 Variation of velocity and stress profiles at five down streamlocations (X=96 mm, 92 mm) in the posterior orientation of thevalve at the instant T=200 ms corresponding to the peak phaseof the flow (pulse rate=71 beats/mm, U0=14.03 cmls) 69Figure 3-16 Variation of velocity and stress profiles at five down streamlocations (X=96 mm, 92 mm) in the posterior orientation of thevalve at the instant T=300 ms. The mitral valve is closing (pulserate=71 beats/mm,U0=14.03 cmls) 70Figure 3-17 Variation of velocity and stress profiles at five down streamlocations (X=96 mm, 92 mm) in the posterior orientation of thevalve at the instant T=450 ms while the aortic valve is opening(pulse rate=71 beats/mm,U=14.03 cmls) 71Figure 3-18 Variation of velocity and stress profiles at five down streamlocations (X=96 mm, 92 mm) in the posterior orientation of thevalve at the instant T=500 ms when the aortic valve is fullyopen (pulse rate=71 beats/mm,U0=14.03 cniJs) 72Figure 3-19 Variation of velocity and stress profiles at five down streamlocations (X=96 mm, 92 mm) in the posterior orientation of thevalve at the instant T=550 ms representing the aortic valveclosing (pulse rate=71 beats/mm,U0=14.03 cm/s) 73Figure 3-20 Schematic diagram showing the mitral disc valve in the anteriororientation 77Figure 3-21 Time history of velocity and stress profiles for the anteriororientation of the mitral valve at the location X=100 mm,Z=0.625D (pulse rate=71 beats/mm,U0=12.72 cmls) 78Figure 3-22 Variation of velocity and stress profiles at five down streamlocations (X=100 mm) for the anterior orientation of the mitralvalve at two different instants (T=50 ms, 100 ms). The mitralvalve is opening (pulse rate=71 beats/mm,U=12.72 cmls) 82ixFigure 3-23 Variation of velocity and stress profiles at five down streamlocations (X=100 mm) for the anterior orientation of the mitralvalve at two different instants (T=150 ms, 450 ms)corresponding to the mitral and aortic valves fully open (pulserate=71 beats/mm,U0=12.72 cmls) 83Figure 3-24 Comparison of the mitral valve orientations (posterior andanterior) showing variation of the maximum shear stress profilesat five down stream locations (pulse rate=71 beats/mm) 85Figure 1-1 Flow chart explaining the scheme adopted for collecting data. . 95Figure 1-2 Format of the MAIN program 97Figure 1-3 Scheme of the IMPORT program 98Figure 1-4 Flow chart for the P1MENU program 100Figure 1-5 Flow chart for the P5MENU program 102Figure 1-6 Scheme adopted in the P55MENU program 104Figure 1-7 Approach to the P9MENU program 107Figure 1-8 Framework of the P1OMENU program 109xPREFACE AND ACKNOWLEDGEMENTThis thesis is submitted in partial fulfilment of the requirements for the degreeof Master of Applied Science in the University of British Columbia. The thesisrepresents application of the fluid dynamic principles, in conjunction with carefullyplanned experiments and refined computer software, to study a problem in thebiomedical area. The research program aims at in vitro experiments on the mitral flowpast a prosthetic heart valve. There are several important aspects to the study,however, the major focus was on two areas: (i) development of computer codes forcontrolling the tests, date analysis and display; (ii) relative performance evaluationof the Bjork-Shiley monostrut valve in posterior and anterior orientations.I am greatly indebted to Professor V.J. Modi, my supervisor, for offering thisvaluable research opportunity and enthusiastic encouragement, and for reviewing andcorrecting the manuscript patiently and earnestly. His favours are ever at a premium.I am grateful to Dr. T. Akutsu and Ms. W.F. Bishop for their assistance anduseful discussions, which gave me a very helpful introduction to the research program.My appreciation also goes to my friends and colleagues who helped me during thestudy.I especially dedicate this thesis to my wife, Ying, and to my parents who arein my home country, whose love and encouragement have made living abroad aloneand finishing this study possible.11. INTRODUCTIONClinical introduction of the pump oxygenator in 1953 provided the means fordirect surgery on the mitral valve. The far advanced diseased state of most mitralvalves requiring operation, however, prevented satisfactory restoration of theirfunction. The surgical management of valvular heart diseases has progressedconsiderably since the first successful clinical implantation of a ball mitral valveprosthesis in 1960. Nowadays, around 10,000 operations or re-operations for heartvalve replacements are carried out every year in Canada. The replacement of thediseased heart valves with prothetic devices has improved and prolonged many lives.There are various models of artificial heart valve prostheses in use today. Ascan be expected, they have their respective advantages and disadvantages includingthe risk of unexpected complications. It is important to investigate mechanical andhydrodynamic performance of artificial heart valves in vitro and, if possible, in vivoto assist cardiac surgeons in the selection of the appropriate valve for a particularpatient. From an engineering point of view, the in vitro study has certain attractivefeatures:(a) it is safe and provides a starting point in determining relative merits ofdifferent prostheses at a relatively low cost;(b) valve related complications for patients with an artificial valve can be directlyrelated to the performance of the valve;(c) the performance of an artificial valve tested in vitro is similar to that obtainedthrough an in vivo study as long as the in vitro test system closely simulatesthe physiological function, the anatomical shape of the natural environmentand the circulation parameters;(d) with the application of the laser Doppler anemometry and other advance2experimental tools, it is possible to obtain quantitative measures of thehydrodynamic performance of artificial valves;(e) an artificial heart valve design may be improved based on the results of invitro tests.The objective here is to study fluid dynamical characteristics of the BjörkShiley monostrut valve (BS mono, 27XAMMB), occupying the mitral position; anddevelop appropriate codes required for the test operation, data analysis and displayof results.1.1 Concepts in Human Cardiovascular System and Heart AnatomyThe cardiovascular system consists of the heart and blood vessels. The heartis a hollow, four-chambered muscular organ, which is roughly the size of a clenchedfist and has an average weight of 255 grams in adult females and 310 grams in adultmales. It is estimated that the heart contracts, during a year, some 42 million times,ejects 3 million litres of blood and consumes 5.0 x i0 Joules of energy whichapproximately equals the work needed to raise an adult body with 50 kg of weight tothe height of 100 km. The small heart does a great deal of work.The heart is located within the thoracic cavity between the lungs in themediastinum, and about two-third of it is placed left of the midline (Fig. 1-1). Itconsists of the upper atria (left atrium and right atrium) together with the lower rightand left ventricles. The atria contract and empty simultaneously into the ventricles.The atria are separated by a thick muscular membrane, while the ventricles by a thinone, called the septum. Atrioventricular valves (tricuspid and bicuspid) are locatedbetween the atria and ventricles, and semilunar valves (pulmonary and aortic) arepresent at the base of the two large vessels leaving the heart. The valves maintain the3PERICARDIUMRIGHT LUNGDIAPHRAGMHEARTAPEX OF HEARTFigure 1-1 The position of the heart within the thoracic cavity.4flow of blood in one direction (Fig. 1-2). The structure of the heart and the action ofits valves allow it to pump blood low in oxygen to the lungs and oxygen-rich blood tothe body.The right atrium receives systemic venous blood from the superior vena cava,which drains the upper portion of the body, and from the inferior vena cava, whichdrains the lower portion. Blood from the right atrium passes through the tricuspidvalve to fill the right ventricle. Ventricular contraction causes the tricuspid valve toclose and the blood to leave the right ventricle through the pulmonary semilunarvalve. The blood enters the lungs through the right and left pulmonary arteries. Aftergas exchange has occurred within the capillaries of the lungs, oxygenated blood istransported to the left atrium through four pulmonary veins, two from each lung. Theleft ventricle receives blood from the left atrium. These two chambers are separatedby the bicuspid or mitral valve. When the left ventricle is relaxed, the valve is openand allows blood to flow from the atrium to the ventricle; when the left ventriclecontracts, the valve closes. The appearance of the valves is shown in Figure 1-3, andtheir actions are summarized in Table 1-1.The blood vessels consist of arteries, arterioles, capillaries, venules and veins.It is estimated that there are 100,000 km of the blood vessels throughout the body ofan adult, which can go around the earth 4 times if connected in one line. The arteriesand veins transport blood from the heart to the capillaries and back to the heart. Thecapillaries exchange plasma fluid and dissolved molecules between the blood andsurrounding tissues. Blood leaving the heart passes through the vessels of arteries,arterioles and capillaries, which are of progressively smaller diameter, and bloodreturning to the heart from the capillaries passes through venules and veins, the laterwith larger diameters.The blood circulatory system is schematically shown in Figure 1-4. There are5Right atriumTricuspid valveRight ventricleFigure 1-2 A schematic diagram of the structure of the heart (an internal view).Arrows represent direction of the blood flow.archTO LUNGFROM LUNGarteriesTO LUNGPulmonary valveFROM LUNGvalveChordae tendineaeLeft ventricleIrrferior vena cavaPapillary muscleaorta6PULMONARY SEMILUNARVALVEAORTIC SEMILUNARVALVETRICUSPIDVALVEFigure 1-3 A diagram showing relative positions of the valves and the supportingfibrous connective tissue.two principal divisions of the circulatory blood flow. The pulmonary circulationconsists of the pulmonary trunk with its semilunar valve, the pulmonary arteries thattransport blood from the right ventricle to the lungs, the pulmonary capillaries withineach lung that oxygenate the blood, and four pulmonary veins that transportoxygenated blood back to the heart. The systemic circulation is composed of all theremaining vessels of the body including the aorta with its semilunar valve, all thebranches of the aorta, all capillaries other than those in the lungs, and all veins otherBICUSPID VALVEFIBROUS CONNECTIVE TISSUE7Table 1.1 Comments on the heart valves.Valve Location CommentsTricuspid valve Between right atrium Composed of three cusps thatand right ventricle, prevent a backflow of blood fromsurrounding right atrium during ventricularatrioventricular orifice contractionPulmonary Entrance to Composed of three half-moon-semilunar valve pulmonary trunk shaped flaps that prevent abackflow of blood from pulmonarytrunk into right ventricle duringventricular relaxationBicuspid (mitral) Between left atrium Composed of two cusps thatvalve and left ventricle, prevent a backflow of blood fromsurrounding left ventricle to left atrium duringatrioventricular orifice ventricular contractionAortic semilunar Entrance to ascending Composed of three half-moonvalve aorta shaped flaps that prevent abackflow of blood from aorta intoleft ventricle during ventricularrelaxation8A schematic diagram of the circulatory system. Arrows indicatedirection of blood flow.PULMONARYTRICUSPID VALVIORTIC VALVEH EARlKIDNEYTRUNKFigure 1-49than the pulmonary veins. The right atrium receives all the venous return of oxygen-depleted blood from the systemic veins.The cardiac cycle, which results from the electrical activity, refers to therepeating pattern of contraction and relaxation of the heart. The phase of contractionis called systole, and the phase of relaxation is referred to as diastole. These terms arenormally used to suggest contraction and relaxation of ventricles.The heart thus has a two-step pumping action. The right and left ventriclescontract almost simultaneously. During diastole, the venous return of blood fills theventricles. At the end of diastole, the amount of blood in the ventricles is referred toas the end-diastolic volume. Contraction ofventricles in systole ejects about two-thirdof the blood in the ventricles, leaving one-third of the initial amount as the end-systolic volume. The ventricles then fill with blood during the next cycle. In eachnormal cardiac cycle, five-eighth of the period is spent in diastole, and three-eighthin systole [1].1.2 Cardiac Output and Mitral Valve DiseaseThe normal cardiac output is around 4900 — 5600 ml of blood per minute at 70beats per minute (average resting cardiac rate) in an adult or 70 — 80 ml per beat foran average stroke volume. The total blood volume is equal to about 5 — 6 litres. Thismeans that it takes about a minute for a drop of blood to complete the pulmonary andsystemic circuits. Normally, ventricular contraction strength is sufficient to eject 70— 80 ml of blood out of a total end-diastolic volume of 110— 130 ml.Blood pressure is regulated by a variety of control mechanisms. When the heartis in systole, the maximum pressure is about 25 mmHg in the right ventricle and 120mmHg in the left ventricle and aorta. When in diastole, the lowest pressure is around108 mmHg in the right ventricle, 0 mmHg in the left ventricle, and 80 mmHg in theaorta. The blood pressure rises from the diastolic to systolic levels and provides thedriving force for blood flow. The average pressure is around 2 mmHg in the veins and100 mmHg in the aorta (Fig. 1-5). The low pressure is insufficient to return thevenous blood, which is almost 70% of the total blood volume, to the heart. Veins,however, pass between skeletal muscle groups that produce a massaging action asthey contract, which is often described as the skeletal muscle pump. There are twovenous valves in the part of the vein located in the skeletal muscle pump. When thepump operates, the venous valves keep one-way flow of blood to the heart.The average power produced by a normal heart is estimated at 1.5 watts: 1.3W is produced by the left side of the heart, and 0.2 W by the right side. The pressurechange in the left ventricle is about 120 mmHg which is much larger than that of 17mmHg in the right ventricle.Because of large differences between these parameters vital to the function ofthe heart, heart valve diseases normally relate to the left side, i.e. the mitralapparatus (Fig. 1-6). The mitral valve is commonly the predominant cardiac structureinvolved when the heart is a part of abnormalities or generalized disease processes[1,21.The mitral valve is a complex unit comprising an annulus, the leaflet or cuspveil, the chordae tendineae and the papillary muscles as shown in Figure 1-7. Theleaflet veil is attached to a fibromuscular ring, i.e. the annulus. The free margin of theleaflet veil is divided into anterior and posterior leaflets or cusps. The areas of the twoleaflets are nearly identical, but their shapes differ considerably and conform to theirfunctions (Fig. 1-8). The basal attachment of the anterior leaflet is comparativelyshort, since it is in direct continuity with the aortic wall, which serves as its fulcrum.The basal attachment of the posterior leaflet is comparatively long, since it attaches11Figure 1-5 The pressure distribution inside the heart where: LPtthe pressuredifference between the origin of the blood flow (mean pressure ofabout 100 mmHg in the aorta) and the end ofthe circuit (zero mmHgin the vena cava); RA=right atrium; LA=left atrium; RV=rightventricle; and LV=left ventricle.Pressure=0-4 mmHg( mean=2 mmHg )Pressure=0-120 mniHgPressure=80-120 mmHgmean=100 mmHg )Blood flow12I/—..-AORTAI/IAORTIC VALVE , / 4 / LE ATRIUM-// AI—I V/ p MITRAL VALVE7400 CHORDAE- TENDINEAEPAPILLARYMUSCLESLEFT VENTRICLEFigure 1-6 A schematic diagram of the ‘eft side of the heart.13ANNULUS, .ANTERIORCUSP_____POSTERIOR.•.••CUSP;L:L‘i{E,///////..a PAPILIy:/ .!: .. ,. :. MUSCLES•SFigure 1-7 A schematic diagram of a natural mitral valve.ICDCD-.—C-.o‘—a0CD‘—‘CD-I-fCD—CD,-..0(1)‘-.-,c+2P I-.,c-CD.0CDCD.CDCD-,-I+)I-foI—I-rJ2CDI—iCfCDCD1-4,1-.—CD15to the entire length of the annulus and is primarily a continuation of the muralendocardium of the left atrium. Proper closure of the leaflets represents an importantgoal of the mitral mechanism. Some heart diseases, typically rheumatic endocarditisand dystrophic valvular disease, cause the mitral valve stenosis and incompetencesuch as mitral regurgitation. It may lead to congestive cardiac failure and death.The diseased mitral valve is usually replaced with an artificial one. It must beemphasized that the mitral valve replacement is only a compromise, rather than acure. Even with extensive studies and progress towards an ideal valve substitute, theproblems associated with heart valve prostheses persist. As can be expected, certaincomplications that cause stenosis or incompetence are uniquely associated with aparticular prosthesis because of its design or structure.1.3 Overview of Prosthetic Mitral Valve DevelopmentThe history of mitral valve replacement with a prosthesis extends to more than30 years since the first successful clinical implantation of a ball mechanical device byStarr [31. The early protheses demonstrated the feasibility of mitral replacement withthe ball valve, but carried with it an unacceptable incidence of serious thromboemboliccomplications. The developments in configuration design, material and manufacturingtechnique have led to a wide variety of prostheses since then.Some of the major configurations introduced for clinical mitral replacement(Fig. 1-9) are listed bellow [2,4,5]:1960 Starr mechanical caged ball;1962 Starr-Edwards mechanical caged ball;1965 Kay-Shiley mechanical caged disc;1966 Lillehei mechanical pivoting disc;16(a)Cc)(e)(b)Figure 1-9 Diagrams of some commonly used prostheses: (a) Bjork-Shileymonostrut used in this study; (b) Bjork-Shiley c-c; (c) Bicer-Val; (d) St.Jude bileaflet; (e) Starr Edwards; (f) Mitroflow.(d)U)171967 Wada-Cutter mechanical titling cusp;1967 Beall-Surgitool mechanical caged disc;1968 Starr-Edwards mechanical caged disc;1969, Bjork-Shiley, mechanical tilting disc;1970 Hancock biological leaflets;1970 Lillehei-Kaster mechanical pivoting disc;1975 Carpentier-Edwards biological leaflets;1977 Hall-Kaster mechanical pivoting disc;1977 St. Jude mechanical pivoting double discs;1980 Bicer-val mechanical tilting disc;1982 Mitroflow biological cusps.Although there are a number of different designs of prosthetic mitral valve inuse, they can be classified into a few categories according to their material, structureand mechanical performance.Broadly speaking, based on the material used, there are two types ofprostheses, namely the mechanical and the biological valves. The bio-prostheses, likethe Mitroflow valve, are made of biological tissues. They are introduced in an attemptto imitate natural valves more closely, and thereby, improve hemodynamic functionand decrease thrombogenicity. The Honcock porcine bio-prosthesis, commerciallyavailable since 1970, is a representative of the first generation of successful biologicalvalves. The mechanical valves, like the Bjork-Shiley design [61, attempt to simplify thestructure of a natural valve. The use of an occiuder, in the form of a ball or a disc,results in the peripheral flow as against the central flow for the tissue valves.The mechanical valves are characterized by two distinctly different forms ofstructural elements: the high-profile caged ball; and the low-profile disc. The lowprofile disc valves are preferred in the mitral position, since they do not protrude into18the left ventricular cavity as the caged ball valves may. The protrusion may causearrhythmia due to interference with the ventricular septum and obstruction of the leftventricular outflow tract.As mentioned before, characteristics of the occiuders do vary. The centraloccluder obstructs the central forward flow, as in different types of ball valves or inthe Kay-Shiley disc valve [71. The tilting or pivoting disc occiuder permits a centralforward flow (together with the peripheral contribution) as in the Bjork-Shiley orLillehei-Kaster disc valves.The closing mechanism of the mechanical valves may be looked upon asoverlapping or non-overlapping. An overlapping occluder hits the valve seat on closureat every heart beat, as in the Starr-Edwards ball valve or the Lillehei-Kaster pivotingdisc valve. The non-overlapping occiuder fits within the valve ring but does not hit theseat on closure, as in the Smcloff-Cutter ball valve or the Bjork-Shiley tilting discvalve.1.4 Review of In Vitro StudiesThe objective of in vitro tests is to assess the performance of artificial valvesprior to implantation in the vital environment. These data are necessary to predictclinical performance as well as interpret the clinical observations and areas of failure.Moreover, in vivo assessment of prosthetic action has been limited by a number ofpractical and challenging considerations besides technical and ethical. Hence a vastbody of literature pertains to in vitro studies in laboratories aimed at understandingthe process of stenosis, hemolysis, incompetence, regurgitation, clotting, etc.. Effortshave been made to assess mechanical integrity through material properties andfatigue tests. On the other hand, hemodynamic performance has focused on pressure19change and recovery, flow rates and velocity profiles, stresses and energy losses, andothers.1.4.1 Typical Results for Representative Mitral ValvesTo have some appreciation of important parameter values, several typicalresults reported in the literature are quoted here.(i) Pressure drop across mitral valvesThe maximum pressure change across the Beall valve (centrally occlusivevalve) with 17.75 mm of orifice diameter was found to be 52.5 mmHg at a cardiacoutput of 12.4 1/mm [2,81. The Bjork-Shiley valve (c-c) with 22 mm of the orificediameter had the largest orifice and the smallest pressure drop, the maximum being12.0 mmHg at the same cardiac output [2,81. The Hancock valve (stunted heterograftthree-leaflet valve) with an 18 mm diameter of orifice had a thick muscular region atthe base of one cusp which prevented it from opening fully with consequent stenosiseven at high cardiac outputs, and had a maximum pressure change of 27.0 mmHg[2,81. The Starr-Edwards valve (caged ball valve) with a 17mm diameter of the orificeproduced a maximum pressure change of 21.0 mmHg [2,8].The pressure change across the mitral valves during diastole depends onvelocity at the mitral ring and orifice area, not on shape, except for the Beall valvewhose orifice is obstructed by the posterior wall of the left ventricle when implanted.(ii) Leak ratesA very high leak rate was found during the static test of the Bjork-Shiley valve(maximum 720 ml/min at the pressure difference of 180 mmHg) [2]. Relatively highleak rates were also observed in the Beall and Starr-Edwards valves (maximum 330and 355 mllmin at the same pressure difference, respectively) [21. The leakage through20these valves would, under unfavourable conditions, cause hemolysis [21. The Hancockvalve was found to have a smaller leak rate (182 mllmin maximum) [2].(iii) Turbulent shear stressesThe maximum value of the mean turbulent shear stress measured during peakof systole was 1200 dynes/cm2for the Starr-Edwards caged ball valve, 1600 dynes/cm2for the Bjork-Shiley tilting disc valve, and 1050 dynes/cm2for the St. Jude bileafletvalve [2,9,10,111. The corresponding values during the deceleration phase were around800, 600, and 800 dynes/cm2,respectively. These results indicated that the prostheticvalve geometries created large intensity turbulent flow fields with regions of flowseparation, stagnation and high turbulent shear stresses.For biological prostheses, the maximum turbulent shear stress was found tobe much lower, around of 500 dynes/cm2,which may not cause damage to bloodelements [2,11,121.1.4.2 Application of the LDALaser Doppler anemometry (LDA), a versatile procedure, has been widely usedin flow measurements since it does not affect the flow field, being a non-contactsensor. It uses the Doppler shift (Christan Doppler, 1842) of light scattered by movingparticles to determine their velocity and hence of the fluid field. Dual beamanemometer was the first to appear commercially and is still popular although 3-beamtwo components and other more sophisticated devices are slowly gaining ground.Of course, laser is the most important element of an LDA system. It providesmonochromatic and coherent beams, and has an extremely high frequency stability.At the exit of a laser, the mode structure of light in a plane perpendicular to thedirection of propagation (TEMoo, Transverse Electromagnetic Mode), is circularly21symmetric with a Gaussian intensity profile (Fig. 1-10). Two Gaussian beams crossingat their waist (the narrowest part of the laser beam) in space generate an evenlyspaced fringe pattern. The spatial frequency ? of the fringe is given, approximately,by1 = 2nsin(O/2)where ? is the laser wavelength; 8, the crossing angle; and n, the index of refractionof the medium (Fig. 1-11). If the interference plane is put in the probe volume, aparticle moving in the direction perpendicular to the interference plane at a speed v,will generate the frequency expressed byf = V = 2vnsin(O/2)A simpler explanation would be that the light scattered by a moving particle fromeach beam has a Doppler shift proportional to its velocity. The difference in Dopplershifts between the two beams is given byf 1 ). 2vnsin(O/2)1 2 -_________where k1, k2 are the propagation vectors of the two laser beams (k=2ic/?) and V is thevelocity vector. The dot product of the two vectors means that an LDA is only sensitiveto the component of velocity normal to the fringe plane. One can set withconsiderable precision leading to an accurate method of measuring particle velocityin the intersection region.By means of the LDA, it is possible to measure local instantaneous velocitycomponents of the downstream flow across a mitral prosthetic valve. Some researchershave reported measurements of fluid dynamical parameters associated with artificialheart valves using an LDA system [5,9,10,12,131. The research group at UBC hasadopted a three-beam LDA system measuring two orthogonal velocity componentsinside a cardiac duplicator of the left ventricle [5,141.22Figure 1-10 A schematic diagram of the TEMoomode structure of the laser.k1Vk2Interference planeFigure 1-11 Fringe pattern in the measurement region.231.5 Background to the Present StudyThe bioengineering group in the Department of Mechanical Engineering atU.B.C. has designed, constructed and instrumented a complex cardiac simulator [51.It closely duplicates the physiological function as well as the anatomical shape of thevital left side of the heart and its circulation system to evaluate hemodynamicperformance of heart valves. A three-beam LDA system is used, which enablesresearchers to obtain, accurately, two components of velocity distribution inside theleft ventricle. The computer control test methodology with 3-D scanning of the leftventricle permits efficient collection of data including pressure change across themitral and aortic valves, two components of instantaneous velocity and theirdistribution, flow rate and pulse rate. The versatile character of the system permitsselection of the pressure wave form of the pulse, flow rate, pulse rate, stroke volume,etc.. It also allows for both steady and pulsatile flow experiments.Over the years tests have been carried out using both mechanical and tissuevalves [5,121. They include Starr-Edwards, Bjork-Shiley (c-c), St. Jude and Bicer-val(mechanical) as well as Hancock I and Carpentier-Edwards SAV (tissue, porcine).Some experiments have also been conducted with Bjork-Shiley (mono) having 27 mmof annulus diameter and 21.9mm of orifice diameter. The results have been presentedin terms of nondimensional similarity parameters as this would eliminate thedependency on individual valve size, test fluid viscosity and density. The results werepresented in several different forms to help appreciate complex behaviour of fluiddynamical parameters and the overall valve performance.241.6 Purpose and Scope of the Present InvestigationIt is apparent that the bioengineering group has developed a unique system fortesting fluid dynamical performance of prosthetic heart valves. However, as can beexpected, there is always scope for improvement. In the present case, there was a needfor improvement in the software used for the control of experiments as well asacquisition, analysis and display of data. This would not only facilitate conduct of theexperiments but also improve analyses and accuracy of results.As shown by earlier studies, the Bjork-Shiley (mono) tilting disc valve had arelatively better fluid dynamical performance as a mitral valve compared to othermechanical valves [6,141. The next logical step is to assess the effect of valveorientation and beat rate, corresponding to rest and exercise conditions, on theperformance.To that end, the study attempts to gain better quantitative understanding ofthe velocity and turbulent shear stress fields in the immediate vicinity of the mitralvalve, under simulated conditions of physiological pulsatile flow, as affected by thepulse rate as well as posterior and anterior positions of the valve. The results arefundamental to the understanding of the complex fluid dynamics involved, leading toimproved valve design as well as establishment of criteria for its manufacture.252. TEST SYSTEM AND METHODOLOGY2.1 The Test FacilityThe test system is schematically shown in Figure 2-1. The system has a closedloop and permits hydrodynamic performance assessment of mitral and aorticprosthetic valves during steady or pulsatile flow experiments.The test chamber consists of the atrium and aorta, a thin flexible transparentpolyurethane ventricle, which attempts to simulate the natural left ventricle, and asurrounding plexiglas box. These are held in place by a support block as shown inFigure 2-2. The cavities containing the mitral and aortic valves are also made ofplexiglas in accordance with the anatomical information. The transparency of theventricle and plexiglas box is essential for the LDA measurements. The space betweenthe ventricle and the box is filled with distilled water.Controlled reciprocating motion of the piston generates a fluctuating pressurecondition in the plexiglas box at a desired frequency which, in turn, leads to thecontraction and expansion of the polyurethane left ventricle, simulating the systolicand diastolic phases of a typical cardiac cycle. The rhythmic ‘cardiac’ operation leadsto the flow from the left atrium to the aorta and the rest of the simulatedcardiovascular system with the fluid finally returning to the left atrium reservoir (Fig.2-1).The traverse mechanism allows the probe volume of the LDA to be placed atalmost any desired location inside the ventricle with three degrees of freedom. Motionin the horizontal x-y plane is controlled by the main computer via two stepping niotorswith an accuracy of 0.001 mm in the x direction and 0.005 mm in the y direction. Thethird degree of freedom (z-direction) is controlled through a scissor screw jack thatDATATRANSLATIONACQUISITIONBOARDCHARACTER1STICRESISTANCE&COMPLIANCEPERIPHERALRESISTANCELOAORIFICEMETERSTEPPINGMOTORCONTROLVALVEIISIGNALI[3owMET]I ELECTRONIC’PROCESSOR____________LMANOMETERIIIIFigure2-1Schematicdiagramofthetestsystemandassociatedinstrumentation.t3‘SUPPORTBLOCKFigure2-2Detailsof thetestchambershowingtheleftatrium,aorta,andasectionoftheleftventriclewiththemitralandaorticvalvesinposition.LEFTflTRIUMLEFTVENTRICLE28raises and lowers the laser platform manually with an accuracy of around 0.5 mm.2.2 Instrumentation and Model2.2.1 Laser Doppler AnemometerMeasurement of velocity and turbulence intensity distribution in the ventricleis carried out using a three-beam, two-colour, forward scatter LDA system. It consistsof an Argon Ion Laser (Model 549OACWC) made by Ion Laser Technology, U.S.A.; agroup of Dantec optics; and a Dantec signal processor frequency tracker (Model55N20). The Argon Ion Laser is used to supply a polarized monochromatic beam inTEMoo mode, which may be tuned in the range of 457 nm to 514.5 nm. The LDAtransmitting system splits the laser beam into two optically shifted beams of a blue(488 nm) and a green (514.5 nm), and a non-shifted beam of mixed colours (blue andgreen). The non-shifted beam is used as a reference while the shifted beams measuretwo instantaneous orthogonal velocity components.2.2.2 ComputersTwo computers are responsible for the running of the cardiac pulse duplicatorsystem. Data acquisition and processing are accomplished with an IBM compatible386/33 MHz personal computer. The movement of the LDA system in the x, ydirections is also controlled by this computer. The driver unit is controlled through aNova Turbo PC/XT.2.2.3 Mitral Valve29As mentioned earlier, disc valves of several different design have beendeveloped over the years and are widely used in practice. The Bjork-Shiley monostrut(BS mono) is one such mechanical disc valve. In the present study, a BS mono valve(Model XAMMB) with the annulus diameter of 27 mm and the orifice diameter of 21.9mm was used at the mitral location (Fig. 2-3).The BS mono valve consists of a free floating convexo-concave pyrolytic carbondisc suspended between two eccentrically situated struts. The major orifice strut isperpendicular to the minor orifice. The pyrolytic disc tilts open to a maximum of 700.The housing and struts are made from a single piece of Haynes 25, a cobalt alloy, thusavoiding any welding points which may cause mechanical failure. The design attemptsto overcome the strut fracture complications of earlier models by making the strutsintegral parts of the valve ring.2.2.4 Aortic ValveA Starr-Edwards (Model 2M6120) caged ball mechanical valve was used in theaortic position for all experiments. Among the mechanical valves, the caged ball valveshave the lowest rate of regurgitation (3-7%) compared to tilting disc valves (10-13%)and bileaflet (10%) valves [2,41. Therefore, for the purpose of this study, the StarrEdwards valve is ideal in the aortic position as the small amount of regurgitation hasa minimal effect on the flow development in the left ventricle.2.3 MethodologiesExperiments were focused at measurement of instantaneous velocitydistribution and turbulent stresses downstream of the mitral valve. Effects of the30Figure 2-3 Schematic diagram showing flow regions of the mitral valve (BjörkShiley monostrut, model 27XAMMB) used in the experiments.FLOWMAJORORIFICEVENTRICLESIDE OF VALVEMINORORIFICEATRIUMSIDE OF VALVEFLOW31valve orientation and pulse rate on the fluid dynamical parameters were also ofinterest. All experiments were conducted under a pulsatile flow condition similar tothe natural cardiac cycle. The pressure change in the aorta during all the tests wasmaintained approximately at 120/80 mmHg, the normal vital cardiac pressure drop.The cardiac output ranged from 2.5 to 4.0 1/mm at 62 — 84 beats per minute, whichwas smaller than the average natural cardiac output.Data for velocity distribution were collected at 6 downstream locations: 0.4D;0.5D; 0.625D; 0.75D; 0.875D and 1.OD as shown in Figure 2-4. Here D represents thediameter of the upstream inlet tube just before the mitral valve. The closestdownstream location was limited to 0.4D since the laser beams were blocked beyondthat location. This limitation produced a gap in the velocity profile and valuableinformation in close proximity to the valve was unobtainable. The fluid dynamicparameters in the region beyond the 1.OD location, being far away from the mitralvalve, were not important and hence not measured. At each downstream location, i.e.z = constant, data were collected across the x-y plane. At the centre line (x=100 mm)of the x-y plane, several different pulse rates were used (84, 78, 71, 67 and 62 beatsper minute). The experiments were carried out using two different valve settings, theanterior position (major orifice of the tilting disc valve anteriorly located towards theaortic orifice) and the posterior orientation (major orifice posteriorly located away fromthe aortic orifice). The ranges of the measuring positions in the ventricle are listed inTable 2-1.2.3.1 LDA Measurement TechniquesTwo components of the instantaneous velocity at any point inside the ventriclecan be obtained using the three-beam, two-component LDA system. These orthogonal32AORTICFigure 2-4 Plan and elevation views showing downstream measurement locations.33Table 2-1 Ranges of the measuring positions in the ventricle.Z X Ymin Ymax zWmax(mm) (mm) (mm) (mm)100 71 12996 71 1290.4D 5892 73 12788 77 12384 82 118100 72 12896 73 127 560.5D 92 75 12588 78 12284 84 116100 74 12696 75 1250.625D 5292 78 12288 82 11884 87 113100 75 12596 76 1240.75D 5092 78 12288 83 11784 92 108100 77 12396 78 122 460.875D92 81 11988 87 113100 79 12196 80 1201.OD 4292 83 11788 90 110Note: D=50 mm is the diameter of the upstreaminlet tube. The center of a measuring plane isat X=100 mm,Y= 100 mm.34components, directly acquired by the LDA system, are located on the y-z plane witha ±45° angle to the z-axial direction as shown in Figure 2-5, where the v componentis anteriorly oriented and the w is in the posterior direction.The centre of the ventricle (x=100 mm, y=100 mm) is determined by firstfocusing the laser beams on one of the side walls of the ventricle in the y-direction,and then traversing to the opposite wall. The mid-point of the travel is then taken asthe centre location in the y-direction (y=lOO mm). A similar procedure is followed forthe x-direction. However, because of the refraction, the movement of the measuringvolume inside the ventricle does not correspond to the movement scaled in the xdirection. So the centre in the x-direction (x=100 mm) is corrected.For that reason, measurements are carried out at different points (x, y, z) alonga horizontal line in the y-direction. Desired movement of the probe volume of the laserbeams is controlled by the main computer. There is a 2 mm interval between themeasuring points in the y-direction from one side of the ventricle wall to the anotherside while collecting the data. On completion, the computer moves the laser 4 mm inthe x-direction to conduct another y-direction sweep. This continues over the desiredrange to construct a three dimensional map of the two-component velocity distribution.2.3.2 Data Acquisition and ReductionAt a given instant in the cardiac cycle, at each physical point, the computer cancollect up to 8 different parametric values including two velocity components of theLDA system, pressures in the atrium, ventricle and aorta, and the flow rate. For eachparameter, the rate of collecting data is 500 times per second. This allows a profile tobe constructed every 2 ms. The measurements of a batch of instantaneous data startfrom the clock signal which is generated at the onset of systole (the piston moving35Left AtriumDValveAorticValveVentricleAxisFigure 2-5 Orientation and definition of velocity components within the ventricle.36forward) by the computer controlling the driver unit. Every measuring period takes1.2 seconds to collect a batch of 600 data points, over a normal cardiac cycle of 0.85s. Each data point represents the average over 20 measuring periods. This insuresstatistically valid and reliable results. In this way, up to 4800 data points are collectedat one measurement location. Obviously, for the entire experiment, to evaluate thevalve performance, enormous amount of information is recorded.The turbulent stresses are calculated from the instantaneous velocitymeasurements. The instantaneous velocity U(t) in a turbulent flow can be decomposedinto a mean flow component U(t) and a fluctuating component U’(t) which is definedbyU’(t) = U(t) - 1.3(t).Since only two instantaneous components, (t) and (t), are measured by the LDAsystem, the fluctuating velocities, v’(t) and w’(t), are obtained from:v’(t) = (t) - v(t);and w’(t) r(t) - w(t);where v(t) stands for the mean component in the v direction and w(t) for the meancomponent in the w direction. Then, the turbulent shear stress or the Reynolds stressis expressed asRN(t) = —p v’(t) w’(t) ,and the normal stresses as=—p [v’(t) ]2=—p [w’(t) ]2in v and w directions, respectively. Here p is the density of the fluid.The approach taken for determination of the Reynolds stress involvesmeasurement of the instantaneous velocity following the clock signal and calculationof the mean flow velocity. To obtain the local instantaneous mean values, the37instantaneous velocity signals in each batch of data are smoothed using a forwardaveraging technique including five neighbouring points. The smoothing process isrepeated 10 times to provide a curve which approximately stands for the mean valueprofile in that period. The fluctuating velocity components are now obtained bysubtracting the forward averaged data from the measured data. At each local point,a total of 20 measuring periods are averaged to obtain the final results for theturbulent velocities and stresses.2.3.3 Data Analyses and DisplayIn the present study, the amount of data obtained is literally enormous. Theresults represent the fluid dynamic performance of the mitral valve. It is importantto adopt an appropriate method to present this comprehensive information concisely.The investigation focuses on the time histories of velocity and stress distributions inthe left ventricle. The maximum as well as minimum values are useful in theevaluation of the mitral valve performance. Suitable graphical representationappeared to be appropriate to show the time-history of the turbulent flow and itsdistribution inside the ventricle. The velocity distribution plotted in vector form clearlypresents the profile changes during a cardiac cycle. On a monitor, the flow was clearlyanimated through the display of spatially distributed time dependent velocity vectors.In order to compare experimental results obtained under different experimentalconditions, the best way was to present them in the non-dimensional form. In somecases, it was difficult to include all related fluid dynamic variables on a single chart.In that case, a tabular form proved to be helpful.To facilitate conduct of experiments in a desired regulated fashion and dataanalyses, it was necessary to develop a set of computer programs. They can make the38test procedure more flexible, relatively easy to implement and more accurate.Furthermore, data acquisition, analysis and display can be carried out quickly,efficiently and with a degree of versatility. Original programs were written by Akutsu[5,14], however, there was scope for improvement. The new algorithms are describedin Appendix-I.393. RESULTS AND DISCUSSIONSUsing the test facility and instrumentation introduced in Chapter 2, bothsteady and pulsatile flow experiments can be conducted. Steady state experimentshelp understand fluid dynamic characteristics of prosthetic heart valves under thefully open condition. Such studies are particularly useful during the developmentalstages of a prosthesis as an indication of acceptability. Akutsu [51 has reported steadyperformance (besides pulsatile flow characteristics) of several mechanical prostheticheart valves. Of course, the steady flow condition may be obtained quite easily by asimpler test system instead of this elaborate design, which is mainly aimed atunsteady (pulsatile) tests.The flow through a ventricle experiences 3 distinct phases during each cardiaccycle: acceleration, peak flow and deceleration as shown in Figure 3-1. Steady stateexperiments model only the peak flow condition which closely corresponds to the fullyopen condition of the heart valves. They do not reveal information about the valveperformance during the acceleration and deceleration phases of the cycle. Since onlythe peak flow condition is simulated during the steady state test, the results are timeindependent which is different from the clinical situation. Focus here is on thepulsatile flow test.As pointed out before, the tests were carried out with the Bjork-Shileymonostrut disc valve occupying the mitral position. The focus is on the time historiesof the velocity and turbulent stresses within the left ventricle during a cardiac cycle.The results are presented in the nondimensional form. Effects of the valve orientationas well as the frequency (of opening and closing of the valves, beats per minute) arealso assessed. The nondimensionalizing parameters are the orifice velocity U0 and theradius of the ventricle at Z = O.4D station._4-. c).—I Figure3-1Schematicdiagramshowingthreephasesofinterestinacardiaccycleshowinginstanceswheremeasurementsareemphasized.PEAK12-6 0•ACCELERATIONOpensValveDECELERATIONValveCloses0100200300400Time(ms)C41In each figure, the velocity is presented in the vector form by solid lines, theReynolds shear stress by a solid line with cross symbols, one of the turbulent normalstresses by a dotted line and the other by a solid line with b symbols.Measurements were carried out at six downstream locations as defined inChapter 2. The amount of information obtained through systematic scanning ofvariables is rather enormous, hence presentation of the comprehensive results in ameaningful way becomes a challenging task. The format used help assess spatialdistribution of the important parameters simultaneously at selected instantsdistributed over the entire cardiac cycle.For the given valve orientations (posterior and anterior), periods of systolic anddiastolic phases as affected by opening and closing characteristics of the disc(mechanical performance) are discussed first followed by the analysis of the fluiddynamic parameters. Finally, the relative performance of the valve in the twoorientations is compared.3.1 Posterior OrientationA mitral disc valve in the posterior orientation has the minor orifice locatedcloser to the aortic valve (Fig. 3-2). The disc of the valve is perpendicular to the planeformed by the axes of the left atrium and the aorta.3.1.1 Mechanical PerformanceThe mechanical performance refers to the open period of the heart valve andthe duration of systolic as well as diastolic phases. These are the main parameters,associated with mechanical operation of the valve, needed in understanding the fluid42Figure 3-2 Schematic diagram showing the mitral disc valve in posteriororientation.dynamics of the mitral valve. Using the time history of velocity as given by theprogram P9MENU, it is easy to evaluate the mechanical performance under a givenexperimental condition. The following results correspond to the constant pulsepressure (120 I 80 mmHg) and five different pulse rates.Time is counted from the opening of the mitral valve. Hence, the negative timeimplies that the data were recorded prior to the mitral valve opening.(i) Reference pulse rate of 71 beats per minuteFigures 3-3 and 3-4 show a series of timehistory plots at the 0.4D and 0.625Dz stations, respectively. Striking variations of the velocity vector profiles with time andthe spatial y coordinate is apparent in both the figures. At T=0, i.e. the beginning ofthe mitral valve opening, the number of data location is 256. When T=200 ms, the(IDLUC,)Ua:I—Cl)-JiCE0z-443COOCl)UIIFC,)UI(0180.0 0.5—1C’)LULJCDCI)LUCEI—(I)-JiCE0z2—1T-5OO(msec)1.0 Y / D4T = -450 C msec—1COUCEFCl)CELUICO2>-I00-JLU>-40>-FC)48VELOCITY: 0.0— 2U = U / U’)-4SHEAR STRESS:tRNV’W’/UOx >0 0 0F-NORMAL STRESSES: Cl)Ui2 Itv=v’v /Uo 4 01ztw= IUo2A 8 2 20.0 1.0 Y/D4T = -300 ( msec ) T = -250 C msec( cont’d)Note: Pressure drop = 120 / 80 mmHg; D4 means the distance along the Y direction at thevertical position Z = O.4D inside the left ventricle; negative T values imply that the data aremeasured prior to the mitral valve opening. Throughout the abscissa is Y/D4 and its scaleremains the same.Figure 3-3 Time history of velocity and stress profiles for the posteriororientation of the mitral valve at the location X=100 mm, Z=O.4D(pulse rate=71 beats/mm, Uo=14.03 cmJs).0.5 1.0 Y/D4T -400 C msec ) T = -350 C msec2—10.544T = -50 ( rnsec T 0 ( msec) -r * 50 (-4>-00-JU>0480.0T = 100 ( rnsec) T = 150 ( msec(contd)CoLUCoCoUa:FCo0z0I = 200 ( msecNote: Pressure drop = 120 / 80 mmHg; D4 means the distance along the V direction at the vertical position Z = 0.4Dinside the left ventricle; negative T values imply that the data are measured prior to the mitral valve opening.Throughout the abscissa is YID4 and its scale remains the same.Figure 3-3 (cont’d) Time history ofvelocity and stress profiles for the posteriororientation of the mitral valve at the location X=100 mm,Z=O.4D (pulse rate=71 beats/mm, Uo=14.03 cm/s).-404iI4Içaid1 Co°a:I—Co-J0z2>-I—00-JU-I>>-I—00.5T = -200 ( msec10—1CooCoUJa:I—C/)a:UICol2—1CoOCoLUa:I—Coa:wICol28—0.0-4 —48—0.0‘1’ / D4T = -100 ( msec—1Y / D4T=-150(msec)1.0C/)UiCoCOLUa:I-CO-Ja:905 Y / D42Y / D4—1CoOCoUJa:I—Coa:UiIujl20.5 1.0 Y/D4 V / D445>-I00-JuJ>>-I00-j00-JLii>T = 550 ( mseccoOa:ICoa:wcolCDUiCDa:I-CD-Ja:10z2Y / D4T = 650 (msec)Note: Pressure drop = 120/80 mmHg; D4 means the distance along the Y direction at the vertical position Z = 0.4Dinside the left ventricle; negative T values imply that the data are measured prior to the mitral valve opening.Throughout the abscissa is Y/D4 and its scale remains the same.Figure 3-3 (cont’d) Time history ofvelocity and stress profiles for the posteriororientation of the mitral valve at the location X=100 mm,Z=O.4D (pulse rate=71 beats/mm, Uo=14.03 cmls).-4 —1 —1280.0 0.5 1.0 V / D4T = 250 (msec T = 300 C msec—12V / D4T = 350 (mseccoOC)wa:I-CDUiIcolC/)Lii(IDCDwCD-Ja:0zT 400 (msec)2-4V / 04T = 450 ( msec2V / D4T- 500 C msec—1CDUiC)CD(I)-ja:0zT = 600 C msec)CowCoUa:I—Co-jia:0zCoU‘-‘COCoUia:I—Co-Ja:0z46—1-4480.0 0.5 1.0T -50 (mc-4>00-JUJ>>-I—00-J—1CoOCoUia:I—Coa:UiICol2—1CoOCoUa:I—Coa:UICol2Y / D40 C msec2—1°r48—0.0 0.5 1.02T 100 ( msec—1 —10VELOCITY:—2 T=50(rnsec)U = U / Uo-4SHEAR STRESS:TRN=VW’/UO 0NORMAL STRESSES: 9tv=vv/Uo2 4‘tw=W /uo2A A 80.0T=150(msec) T200(msec)( contd)Note: Pressure drop = 120/80 mmHg; D4 means the distance along the Y direction at thevertical position Z = 0.4D inside the left ventricle; negative T values imply that the data aremeasured prior to the mitral valve opening. Throughout the abscissa is Y/D4 and its scaleremains the same.Figure 3-4 Time history of velocity and stress profiles for the posteriororientation of the mitral valve at the location X=100 mm,Z=O.625D (pulse rate=71 beats/mm, Uo14.O3 cmJs).CoIii‘-‘Coa:COa:0z20.5 1.0 Y/D42Note: Pressure drop = 120/80 mmHg; D4 means the distance along theY direction at the vertical position Z = 0.4Dinside the left ventricle; negative T values imply that the data are measured prior to the mitral valve opening.Throughout the abscissa is Y/D4 and its scale remains the same.Figure 3-4 (cont’d) Time history ofvelocity and stress profiles for the posteriororientation of the mitral valve at the location X=100 mm,Z=O.625D (pulse rate=71 beats/mm, Uo=14.03 cmJs).47U)uJU)a:uJIcOlU)LuU)a:U).49T 250 C msec2T 300 C rnsec2j//LV / D4T = 350 (msec>-F—00-jLu>0>-F—0Ui>48—0.0-40>-F—00-JUi>48—0.0—1U)0U)Lua:F-U)a:.4LuIU)12U)LuU)U)Lua:F--U)-J.4z0.5T 400 ( msec)1.0 V / D4T = 450 ( n,sec2—1V / D4T 500 (msec—1U)0U)Lua:F—U)a:.4LuIcolU)LuU)U)Lua:F—U)a:10z20.5 1.0 Y/D42T 550 C msec ) 1 600 C msec ) 1 550 ( msecV / 0448mitral valve reaches the fully open condition. At the time of 300 ms, the left ventriclestarts contracting and the systolic phase begins. Almost at the same time, the mitralvalve starts closing. The left ventricle continues to contract and the mitral valveprogressively closes until it is completely shut at T=400 ms. The aortic valve beginsto open as soon as the mitral valve is completely closed. The aortic valve is fully openat around 500 ms. At the instant corresponding to 650 ms or —200 ms, the aortic valveis completely closed. Now the left ventricle starts to expand, i,e. the diastolic phasebegins. The diastolic phase continues until the left ventricle begins to contract atT=300 ms.Thus, the cardiac cycle takes 850 ms which is consistent with the pulse rateof 71 beats per minute. The systolic and diastolic phase periods are 350 ms and 500ms, i.e. 41 percent and 59 percent of the cardiac cycle, respectively. This is very closeto the normal vital cardiac situation mentioned in Section 1.1. Thus during a cardiaccycle, for 400 ms or 47 percent of the period the mitral valve is open, and for 250 msor 29 percent of the period the aortic valve remains open. In the mitral valve openperiod of 400 ms, three-fourth is spent inside the diastole, covering 60 percent of thediastolic phase, and one-fourth inside the systole, representing 29 percent of thesystolic phase. The aortic valve open period of 250 ms represents 71 percent of thesystolic phase.(ii) Pulse rate of 84 beats per minuteFrom the velocity profiles in Figure 3-5, the mitral valve open period, whichbegins at T=0, ends at 350 ms, and the valve is fully open at around 200 ms. At thebeginning of the mitral valve opening, the number of data location is 206. The aorticvalve starts opening at 350 ms, is fully open at 400 ms, and is completely closed at550 ms. At the instant of 250 ms, the left ventricle starts contracting and at 550 msc/IUIJ(I)C,)LUa:I—(I)-jza)UI‘JC,)a)LUa)-Ja:CzCl)UI‘Ci)a)LUa:Cl)la:0z49—1—1r2-40480-40) 0.5 tOT-50 (msecY / D4T 0 C msec—12—1>-09UI>>-I—09>08UI>r4coOCoUIa:I—a)a:UIIa)8—0.0 0.5T = 50 (msec2-41.0 Y/D4T 100 C msec—102—1VELOCITY:i=ui Uc?SHEAR STRESS:tRN =VW’ I UoNORMAL STRESSES:tv=7 iuc?tw= iuc?A A AFigure 3-5cooCoUIa:CoUIIiC/)80.020.5 1.0 Y/042T 150(msec) T=200(msec)( contd)Note: Pressure drop = 120/80 mmHg; D4 means the distance along the V direction at thevertical position Z = 0.4D inside the left ventricle; negative T values imply that the data aremeasured prior to the mitral valve opening. Throughout the abscissa is Y/D4 and its scaleremains the same.Time history of velocity and stress profiles for the posteriororientation of the mitral valve at the location X=100 mm,Z=O.625D (pulse rate=84 beats/mm, Uo=17.54 cm/s).Note: Pressure drop = 120/80 mmHg; D4 means the distance along the V direction at the vertical position Z = 0.4Dinside the left ventricle; negative T values imply that the data are measured prior to the mitral valve opening.Throughout the abscissa is YID4 and its scale remains the same.Figure 3-5 (cont’d) Time history ofvelocity and stress profiles for the posteriororientation of the mitral valve at the location X=100 mm,Z=O.625D (pulse rate=84 beats/mm, Uo=17.54 cm!s).—150coOCl)u-iFC,)LUICl)LUC,)Cl)LU‘IFCo-J0z2‘i’ / D4T = 250 ( msec2-4T=300(msec) T=35Q(msec)>-F00-JuJ>>-F00-J>-I0uJ>—1COOFC/)CliICl)0Cl)LUI—CO-J0z04800-40420.5 1.0 Y/D4T = 400 ( msec ) T = 450 C rnsec—1 ...-..-- —12V / D4T = 500 (rnsec)CoOCOLUFCOLUIcol2-80.0 05 1.0COLI-iC))FCl)-J0z2V / D4T=55Q(msec) T—600(msec) T=650(msec)V / D451it starts dilating. The cardiac cycle is 714 ms long corresponding.to the pulse rate of84 beats per minute. The systolic phase, the period corresponding to the left ventricle’scontraction, takes 300 ms. The diastolic phase representing the period of relaxationtakes around 414 ms.Thus in the present cardiac cycle, 42 percent of the period is spent in thesystole and 58 percent in the diastole. For 350 ms or 49 percent of the cardiac cyclethe mitral valve remains open; and for 200 ms or 28 percent of the cycle the aorticvalve is open. Of the mitral valve open period, five-seventh is spent inside the diastole,which is 60 percent of the diastolic phase, and two-seventh inside the systole, whichis 33 percent of the systolic phase. The entire aortic valve’s open period of 200 ms isinside the systolic phase, which is 67 percent of the phase.(iii) Pulse rate of 78 beats per minuteFrom the time history of the velocity profiles in Figure 3-6, the mitral valveremains open for 350 ms, and the valve is fully open at around 200 ms. At thebeginning of the mitral valve opening, the number of data location is 231. The aorticvalve starts opening at 350 ms, is fully open at 400 ms, and completely closed at 600ms. At T=250 ms, the left ventricle starts contracting and at 600 ms it starts relaxing.The cardiac cycle of 769 ms corresponds to the pulse rate of 78 beats per minute. Thesystolic phase period takes 350 ms and the diastolic phase period is 419 ms induration.In this cardiac cycle, 46 percent of the period is spent in the systole and 54percent in the diastole. For 350 ms, i.e. 46 percent of the cardiac cycle, the mitralvalve remains open; and for 250 ms the aortic valve remains open. Of the mitral valveopen period, five-seventh is spent inside the diastole, which is 59 percent of thediastolic phase, and two-seventh within the systole, representing 29 percent of thecontd)CouJCou-ia:I—Co0zNote: Pressure drop = 120 / 80 mmHg; D4 means the distance along the Y direction at thevertical position Z = 0.4D inside the left ventricle; negative T values imply that the data aremeasured prbr to the mitral valve opening. Throughout the abscissa is Y/D4 and its scaleremains the same.Figure 3-6 Time history of velocity and stress profiles for the posteriororientation of the mitral valve at the location X=100 mm,Z=O.625D (pulse rate78 beats/mm, Uo15.35 cmls).520.5T = -50 (msecY / D4T— 0 C msec—1CoOCoLI-ia:I—CiDa:ICol2—1CoCo°wa:I—Coa:wCo12—1-480.0-480.0-4SHEAR STRESS:tRN =V’W /Uo2x i x 0>-NORMAL STRESSES:2tv=v’v IUo 4tw=W Iuo2. A 80.0—1CowJCoCowa:I-Cl)-J0z2—1Cou-iCoCouJa:I—Co-J0z2—1VELOCITY:— 2U=UI Uo0.5 1.0T = 50 ( msecY / D4T = 100 ( msecu-ia:I—Coa:I-iJICD20.5 1.0T — 150 C msecY / D42T = 200 C msec )>-00-JLi-i>>-I—00-JuJ>coOCi)IJJccI—C’)cc4:Li-iI0)1(‘Jo(0u-iccI—Cou-iICoOg3ccI—CI)-J4:cc10z(0wCl)CouJI—Co-J4:ccl0zNote: Pressure drop = 120/80 mmHg; D4 means the distance along the Y direction at the vertical position Z = 0.40inside the left ventricle; negative T values imply that the data are measured prior to the mitral valve opening.Throughout the abscissa is YID4 and its scale remains the same.Figure 3-6 (cont’d) Time history ofvelocity and stress profiles for the posteriororientation of the mitral valve at the location X= 100 mm,Z=0.625D (pulse rate=78 beats/mm, Uo=15.35 cmJs).—153—1CowCl)ccICo-J4:cc0zT 250 ( msec-42—12Y/D4 Y/D4T = 300 ( msec)>-T = 350 C msec0.5 1.020480.0-40480.0T = 400 C msec ) T 450 C msecV / D4—12—1V / D4T = 500 (msec)COO(I)uJccICOcc4:LuICoV / D40.5 1.02T550(rnsec) T=500(msec) T=650(msec)2V / D454systolic phase. The aortic valve open period of 250 ms occupies 71 percent of thesystolic phase.(iv) Pulse rate of 67 beats per minuteNow the cardiac cycle period is around 900 ms (Fig. 3-7). The mitral valveopens at T = 0 and closes at 400 ms. At T=0, the number of the data location is 281.The aortic valve opens at 400 ms and remains open for 300 ms. The left ventriclebegins to contract at 300 ms and the phase lasts for 400 ms. Thus, the systolic phasetakes 400 ms which is 44 percent of the cardiac cycle and the diastolic phase takes500 ms, i.e. 56 percent of the cycle. Of the mitral valve open period, three-fourth isspent inside the diastole, which is 60 percent of the diastolic phase, and one-fourthinside the systole, corresponding to 25 percent of the systolic phase. The aortic valveopen period occupies 75 percent of the systolic phase.(v) Pulse rate of 62 beats per minuteThe time histories of velocity profiles presented in Figure 3-8 indicate thechanges during the cardiac cycle, which has a period of around 0.968 second at therate of 62 beats per minute. The mitral valve opens at T = 0 and closes at 500 ms. AtT = 0, the number of the data location is around 306. The aortic valve opens at 500ms and remains open for 300 ms. The left ventricle begins to contract at 400 ms andthe contraction phase extends for around 400 ms. Therefore, the systolic and diastolicphases take 41% and 59% of the cardiac cycle, respectively. During the mitral valveopen period, four-fifth is spent inside the diastole, which is 70 percent of the diastolicphase, and one-fifth within the systole, which is 25 percent of the systolic phase. Theaortic valve open period occupies 75 percent of the systolic phase.The mechanical performance data are summarized in Appendix-IT in a tabularGOw“GOGOwcrI—GO-J0z—155—1GOw‘Coa:GO-J1z2—1wa:I—GOa:wI(012—10.5T = -100 ( msec1.0 V / D4T— -50 ( msecGO°a:GOa:LuIGO2T=0(msec) T=50(msec)-40>-I.03uJ>480.0-40F—0948VELOCITY: 00— 2U = U I Uo-4SHEAR STRESS:tRN VW /Uox x x 0>-NORMAL STRESSES:2 >tv=vv IUo 4tw= IUo2I 8 20.0T 100(msec) (contd) T= 150(msec)Note: Pressure drop = 120 / 80 mmHg; D4 means the distance along the Y direction at thevertical position Z = 0.4D inside the left ventricle; negative T values imply that the data are —measured prior to the mitral valve opening. Throughout the abscissa is Y/D4 and its scaleremains the same.Figure 3-7 Time history of velocity and stress profiles for the posteriororientation of the mitral valve at the location X=100 mm,ZO.625D (pulse rate=67 beats/mm, Uo12.28 cm/s).05 1.0 V / D42GOuJGOGOa:F-GO-J0z(‘DO(I)uJa:F--GOLuIGOl0.5 1.0 V / D42>-I—00-JU>Figure 3-7 (cont’d)coOCoUa:I—CoUIcolC,)uJCoCOuJa:I—Co-J.4a:10zTime history ofvelocity and stress profiles for the posteriororientation of the mitral valve at the location X=100 mm,Z=O.625D (pulse rate=67 beats/mm, Uo=12.28 cm/s).56—1coOCoUa:I—Coa:.4UiI010UiCoCOUa:I—CO-J.4a:10z>-00-JUJ>>-I00.5T 200 C msec1.02 2—1Y/D4 Y/D4T— 250 C msec T = 300 (msec—1-40480.0-40480.0-40480.020.5 1.0 Y/D4T=35Q(msec) T400(rnsec)Y / D4T = 450 (mseccoOCoUa:I—Coa:4UICo2[20.5 1.0 Y/D4T=500(msec) T—550(msec)2V / D4T = 600 (msec)Note: Pressure drop = 120 / 80 mml-Ig; D4 means the distance along the Y direction at the vertical position Z = O.4Dinside the left ventricle; negative T values imply that the data are measured prior to the mitral valve opening.Throughout the abscissa is YID4 and its scale remains the same.>-0Sw>>.I—00-jw>0000a:0a:uJI010U00a:I—0-J0000a:Cl)-J-457—1oOa:I-0a:uJI2-4Y / D4T=-100(msec) T—50(msec)—102—1>-I—0S480.0 0.5 1.0-r = 0 ( msec2-4V / D41 50 C msec)0VELOCITY:U=ui uc?SHEAR STRESS:tRN VW I UoNORMAL STRESSES:‘tv=VV /uctw=W /ucA AFigure 3-80a:I-00I012C,)uJ‘JO0I—0I2T = 100 ( rnsec ) T = 150 ( rnsec( contd)Note: Pressure drop = 120 / 80 mmHg; D4 means the distance along the Y direction at thevertical position Z = 0.4D inside the left ventricle; negative T values imply that the data aremeasured prior to the mitral valve opening. Throughout the abscissa is Y/D4 and its scaleremains the same.Time history of velocity and stress profiles for the posteriororientation of the mitral valve at the location X=100 mm,Z=O.625D (pulse rate=62 beats/mm, Uo=1O.96 cmls).80.020.5 1,0 Y/D4coOg3a:IC’)a:wICOlCOOCOuJa:I—COa:uJI01COU]CO(I)U]a:ICO-J2a:19COuJCOCOU]a:I—CO-J2a:19Note: Pressure drop = 120/80 mmHg; D4 means the distance along the Y direction at the vertical position Z = 0.4Dinside the left ventricle; negative T values imply that the data are measured prior to the mitral valve opening.Throughout the abscissa is YID4 and its scale remains the same.Figure 3-8 (cont’d) Time history ofvelocity and stress profiles for the posteriororientation of the mitral valve at the location X=100 mm,Z=O.625D (pulse rate=62 beats/mm, Uo=1O.96cmJs).—158—1T = 200 ( msec2T = 250 ( rrisec2T = 300 C msec>-I>-I—0>—1COOCOU]a:I—COa:U]ICOl2COLI]COCOU]a:I—CO-J2a:02-40480.0-40480.00.5 1.0 Y/D4T 350 (rnsec ) 1 400 C msec—1V / D4T 450 C msec—10.5 10 Y/D42T=500(msec) T=550(msec) T=600(msec)2V / D459form to facilitate comparison.3.1.2 Fluid Dynamical PerformanceThe fluid dynamical performance of an artificial heart valve includes pressuredrop, velocity profile, and stress distribution across the valve as well as in the wakedownstream. The present study focused on the velocity and stress distributions in theleft ventricle. The measurement plane closest to the valve is at Z = O.4D. As shownin the previous figures in this chapter, the flow regime in the left ventricle is highlydependent on time during a cardiac cycle. There are a number of variables whichaffect the flow profiles which include cardiac rate, measurement position, valve type,size and orientation, ventricle volume and shape, stroke volume, wave form of thepressure, etc.. To get some understanding of the complex flow field the emphasis hereis on the effect of valve orientation and pulse rate with other variables held fixed. Ingeneral, the effect of ventricle volume and geometry, stroke volume, pressure waveform, etc. is expected to be small. Nondimensional presentation of the data also helpsin minimizing their influence.(i) Effect of the time changePlots presented earlier (Figs. 3-3 to 3-8) clearly suggested significant variationof the flow parameters during a cardiac cycle. A velocity vector presents bothmagnitude and direction of the fluid speed at a point for a specified instant.In the diastolic phase, when the mitral valve is not open, the fluid moves atrelatively low speeds and the changes in velocity are small (Fig. 3-3 from T = —150 mstoO ). During the period, the ventricle is relaxing (expanding) and the pressure withinthe flow field is reduced. When the pressure is below 20 mmHg, the mitral valve60begins to open. At the initiation of the mitral valve opening, there is a jet like flow ina small region in the ventricle closer to the mitral valve (Fig. 3-3, T = 50 ms). As themitral valve opens further, the direction of the jet changes and becomes moreperpendicular to the orifice plane together with the increase in velocity (Fig. 3-3, T =100 ms). This forms the acceleration phase of the mitral flow.In the peak flow phase, the mitral valve is fully open. The fluid speed reachesmaximum values on the mitral valve side but the velocities are rather low (almostzero) on the aortic valve side (Fig. 3-3, T = 200 ms) as the ventricle is still expanding(dilating). So the acceleration and peak phases of the flow are inside the diastolicphase. When the ventricle contracts, the incoming flow from the atrium decelerates.The deceleration continues until the mitral valve is closed (Fig. 3-3, from T = 250 msto 400 ms). Note, the deceleration period is in the systolic phase.In general, during the deceleration, the flow region can be divided in two parts:region towards the mitral valve where the velocity decreases in the downstreamdirection; and the one closer to the aortic side where the velocity vectors show reversalin the flow direction. The increase in velocity is rather modest (compared to thedecrease in velocity on the mitral side) because the aortic valve has not opened yet.The pressure in the ventricle increases during this phase. Once the pressure reachesthe value of around 20 mmHg, which is enough to close the mitral valve, the fluid flowon the aortic side slows down and velocity is low throughout (Fig. 3-3, T = 400 ms).Note, the mitral flow rate is nearly zero, and there is a quick increase in pressure.Once the pressure reaches 80 mmHg, the aortic valve begins to open. Now thefluid on the aortic side begins to accelerate. With the ventricular contraction, thepressure continues to increase. When the pressure reaches the peak value of 120mmHg, the aortic valve is fully open. As the fluid continues to flow into the aorta andthe ventricle stops contracting (end of the systolic phase), the pressure decreases from61its maximum value. When it drops below 80 mmHg, the aortic valve is completelyclosed. Meanwhile, the ventricle starts to expand (beginning of the diastolic phase)and the pressure continues to drop. Once the pressure inside the ventricle falls to 20mmHg, the mitral valve begins to open again, and a new cycle begins.The velocities on the mitral valve side are near zero while the aortic valve isopening. So the mitral flow remains zero from the time of the mitral valve closure tothe instant when it opens.The figures also display the two components of the normal stresses as well asthe shear stress. Normally, the more organized the velocity profiles, the lower andsmoother are the stress profiles. When both the mitral and aortic valves are not open,all the stresses are near zero everywhere as the mitral flow is near zero (Fig. 3-3, T= —200 ms to 0). At other instants, the shear stress is much lower than the normalstresses. The shear stress profiles do show bursts of larger values during opening ofthe mitral and aortic valves, and around closure of the aortic valve. This can beexpected as then the flow is highly disturbed. The normal stresses also show similartrends but with much higher values.(ii) Effect of the z-positions (downstream locations)Figures 3-9 and 3-10, obtained using the program P5MENU, present variationof the velocity, normal stresses and shear stress at the five downstream locations ofZ = 0.4D, 0.5D, 0.625D, 0.75D and 0.875D (X = 100 mm) at two instants when themitral or the aortic valve is fully open. It is apparent that the fluid velocities andstresses are larger, at all the z stations, when the mitral valve is fully open comparedto the similar condition of the aortic valve. This means that the fluid field is highlyturbulent at the central plane of the ventricle (X = 100 mm) during the peak flowphase. The major orifice being on the mitral side creates a counter-clockwise62Note: Pressure drop = 120/80 mmHg; D4 means the distance along theY direction at the vertical positionZ = 0.4D inside the left ventricle.Figure 3-9 Variation of the velocity and stress profiles at five down stream locations(X= 100 mm) for the posterior orientation ofthe mitral valve when the valveis fully open (pulse rate=71 beats/mm, Uo=14.03 cm/s).04- 0.50.6250.750-40LU>48VELOCITY:— 2U = U I UoNCl)C’)0Cl)ILIJIC/)2SHEAR STRESS:t RN =VV / ucx )( xCOLUCl)C/)0 LUixHC/)-J1 <a:0z2NORMAL STRESSES:0.87500 0.5tv=vv IY / D4T = 200 ( msec )tw=ww /Uc• A1.0.-L- --Z\ \CowCoCo0 wccI—Co-J<‘I0z2T = 500 (msec )Note: Pressure drop = 120 / 80 mmHg; D4 means the distance along theY direction at the vertical positionZ = 0.4D inside the left ventricle.Figure 3-10 Variation of the velocity and stress profiles at five down stream locations(X= 100 mm) for the posterior orientation ofthe mitral valve when the aorticvalve is fully open (pulse rate=71 beats/mm, Uo=14.03 cmls).63CoCoCoccwICo2SHEAR STRESS:t RN =V IN X K-400-JuJ>8VELOCITY:= U I UJN0.40.50.625-07500.8750.0NORMAL STRESSES:tv=R / uctw=W /uo20.5 1.0 AY / D464circulation in the lower region downstream (Z = 0.75D, 0.875D). When the aortic valveis fully open, the fluid directly enters the aortic valve. In the mitral side region, thevelocities are quite small and directed downstream suggesting that the mitral valvehas closed properly and there is no reverse flow of fluid back into the left atrium.Figure 3-11, plotted by the program P55MENU, shows velocity and stressvariation during the acceleration (T = 100 ms) and deceleration (T = 300 ms) phasesof the flow, at five downstream locations in the ventricle. The pulse rate equals 71beats per minute. It is obvious that the flow is more turbulent and stresses are higherduring the acceleration phase (due to the ejection). The large stresses appear in thecorresponding flow field.Figure 3-12 shows variation of the profiles when the aortic valve is opening (T= 450 ms) and closing (T = 550 ms). The profiles are similar at different z stations.The stresses are larger at the instant of the aortic valve closure. Relatively largerstresses appear in the region near the aortic valve side.Figures 3-13 to 3-19 are plotted using the program P1OMENU. Here variationsat two x-positions (X = 92 mm, 96 mm) are shown at seven typical moments (T = 0,100 ms, 200 ms, 300 ms, 450 ms, 500 ms and 550 ms). Combining Figures 3-11 and3-12, the history of the flow performance inside the entire ventricle can be observedand analyzed although the profiles are presented at only three x-positions. At the startof the mitral valve opening (T = 0), it is easy to understand why the fluid fieldexhibits very small level of turbulence stresses everywhere (Fig. 3-13). Note, thevelocities are near zero throughout the field. As observed in Figure 3-11, the flow inthe ventricle is strongly disturbed on the mitral valve side. Of course, the stressprofiles are not steady and fluctuate in the disturbed region.Together with Figure 3-11, that showed the flow variation at the centralposition, it is clear that the variation is higher at X = 96 mm position. This isCl) C’)0I. Cl)w I Cl)28Cl)w (1) (I) I Cl) -J < 0 z‘ii0.5Y/D4T=300(msecNote:Pressuredrop=120/80mmHg;D4meansthedistancealongtheYdirectionattheverticalpositionZ=0.4Dinsidetheleftventricle.Figure3-11Variationofthevelocityandstressprofilesatfivedownstreamlocations(X=100mm)fortheposteriororientationofthemitralvalveattwodifferentinstants(T=100ms,300ms)correspondingtoaccelerationanddecelerationphasesoftheflow(pulserate=71beats/mm,Uot14.03cmls).N0.40.5\.11iJJJ—1-4 0 40.625>- I 0 0 -J w >N0.7500.50.6250.7500.875w1I/-0.875VELOCITY:—2U=U/ UoSHEARSTRESS:2‘tRN=vw/UoKKXNORMALSTRESSES:tv=vv/Uo2tw=ww/Uo2V/D4T100Cmsec0.01.0cnNote:Pressuredrop=120/80mmHg;D4meansthedistancealongtheYdirectionat theverticalpositionZ=0.4Dinsidetheleftventricle.Figure3-12Variationof thevelocityandstressprofilesatfivedownstreamlocations(X=100mm)fortheposteriororientationofthemitralvalveattwodifferent instants(T=450ms,550ms)whentheaorticvalveisopen(pulserate=71beats/mm,Uo=14.03cmls).-40.4N0.50.6250.7500,875C!)Cl)0I--C/)aj1I Cl)28dLLI AI0.00.51.0V/D4T450CmsecVELOCITY:—2U=UI UoSHEARSTRESS:—1 0 2U) w /1) U) w a: I- Cl) -J a: 0 z0.6250.7500.875tRN=vwIUø2xxxNORMALSTRESSES:2‘tv=vVIUo2tw=w’wIUoV/D4T=550Cmsec)NORMALSTRESSES:/Y/D4(X96mm)T0CmsecV/D4(X=92mm)T=0CmsecNote:Pressuredrop=120/80mmHg;D4meansthedistancealongtheYdirectionattheverticalpositionZ=0.4DInsidetheleftventricle.Figure3-13Variationofthevelocityandstressprofiles atfivedownstreamlocationsandtwox-positions(X=96mm,92mm)intheposteriororientationofthevalveattheinstantT=0representingbeginningofthemitralvalveopening(pulserate71beats/min,Uottl4.03cmls).NasfçI_K.n.rM-.-IUI-Aa=0.4 0.5-7w=70.625.—a=-0.750•-.._._a.La_a_a.——U0.8750.40.50,6250.7500.875-0.1-40.00aj0,14I ci)028C,)w Cl)C’)0I— C,)-j1< a: 0 z2-VELOCITY:—2U=UIUoSHEARSTRESS:‘URN=vw/U3t)tX0.00.51.00.00.52‘Uw=w’w’/Uo1.00.40.4Y/04(X=96mm)7100CmsecY/04(X=92mm)T=100(msecNote:Pressuredrop=120/80mmHg;D4meansthedistancealongtheYdirectionattheverticalpositionZ=0.4Dinsidetheleftventricle.Figure3-14Variationofthevelocityandstressprofilesatfivedownstreamlocationsandtwox-positions (X=96mm,92mm)intheposteriororientationofthevalveattheinstantT=100mscorrespondingtotheaccelerationphaseoftheflow(pulserate=71beats/min,Uo=14.03cmls).0.5I 0 0 -J w >-4 0 4 8N0.50.6250.7500.875-0.1C/)C/)0.0H C’)0.1I Cl)02C’)U Cl)Cl)0H C/)-J1< ii 0 z0.6250.7502VELOCITY:—2U=UI UoSHEARSTRESS:tRN=vwIKKKNORMALSTRESSES:tv=vv/ Uo2tw=ww/Uo0.8751.00.40.4Y/D4(X=96mm)T200(msec)0.00.5Y/D4(X=92mm)T=200(msec1.0Note:Pressuredrop=120/80mmHg;D4meansthedistancealongtheVdirectionattheverticalpositionZ=0.4Dinsidetheleftventricle.Figure3-15Variationofthevelocityandstressprofilesatfivedownstreamlocationsandtwox-positions (X=96mm,92mm)intheposteriororientationofthevalveattheinstantT=200mscorrespondingtothepeakphaseof theflow(pulserate=71beats/min,Uo=14.03cmls).0.5>- 0 0 -J w >-4 0 4 BN0.50.6250.7500.875-0.1U)U)0.0U)0.1I U)02C,)w U)U) :10.6250.7502VELOCITY:—2U=U/ UoSHEARSTRESS:tRNKKKNORMALSTRESSES:tv=’i2tw=ww/UoAA0.875N0.4__0.40.50.5vLl0.14I C’)0.6250280.625SHEARSTRESS:tRN=VW/Uo—1IcIcX0.75000.7501NORMALSTRESSES:2tV=V’VIUo08750.8750.00.51.0000.51.0Y/04(X96mm)Y/D4(X=92mm)T=300(msec)T300(msec)Note:Pressuredrop=120/80mmHg;D4meansthedistancealongtheYdirectionattheverticalpositionZ=O.4Dinsidetheleftventricle.Figure3-16Variationofthevelocityandstressprofiles atfive downstreamlocationsandtwox-positions (X=96mm,92mm)intheposteriororientationof thevalveattheinstantT=300ms.Themitralvalveisclosing(pulse rate=71beats/min,Uo=14.03cmls)._>\__(I) w U) Cl) w a: I— U) -J 0 zNote:Pressuredrop=120/80mmHg;D4meansthedistancealongtheVdirectionattheverticalpositionZ=0.40insidetheleft ventricle.Figure3-17Variationofthevelocityandstressprofiles atfive downstreamlocationsandtwox-positions (X=96mm,92mm)intheposterior orientationof themitralvalveattheinstant T=450mswhiletheaorticvalveisopening(pulse rate=71beats/min,Uo=14.03cmls).0.40.4N0.50.6250.7500.8750.5‘I(/f/[/0.625-0.1-4Ci)U)0.00I——U) a:0.14I Cl)0280 2\\\\\\\\‘-0.750“TTiRVELOCITY:—2U=U/ UoSHEARSTRESS:‘URN=vw/Uo2xitxNORMALSTRESSES:tv=R/u2‘Uw=w’W/UoAAA0.875Y/04(X=OOmm)T450(msec0.00.51.00.00.57XY/D4(X=92mm>T=450Cmsec1.0-0.1-4U) C,)0.0C,)cc0.1I ()02804SHEARSTRESS:tRN=77iuxxxNORMALSTRESSES:‘tv=vRIuoAANote:Pressuredrop=120180mmHg;04meansthedistancealongtheYdirectionattheverticalpositionZ=0.40insidetheleftventricle.Figure3-18Variationof thevelocityandstressprofiles at fivedownstreamlocationsandtwox-positions(X=96mm,92mm)intheposteriororientationof themitralvalveat theinstantT=500mswhentheaorticvalveisfullyopen(pulserate=71beats/min,Uo=14.03cmls).>- 0 0 -J w >0 40.4N0.5.-----0.625...:0.7500.875VELOCITY:—2U=U/ Uo0,50.6250.7500.875i.-:Cl)w C/)C/)I- C’)-J 4 Cr 0 z20.00.51.00.0Y/04(X96mm)T500CmsecV\U2‘Cw=WwIUo0.5Y/04(X=92mm)T=500(msec)1.0--0.1C,) Cl)0.0H Cl)a:0.1I Cl)0.2NORMALSTRESSES:‘Cv=R/UoNote:Pressuredrop=120/80mmHg;D4meansthedistancealongtheVdirectionattheverticalpositionZ=0.4Dinsidetheleftventricle.Figure3-19Variationofthevelocityandstressprofilesatfivedownstreamlocationsandtwox-positions (X=96mm,92mm)intheposteriororientationofthemitralvalveattheinstantT=550msrepresentingtheaorticvalveclosing(pulse rate=71beats/min,Uo=14.03cmls).0.4>- H 0 0 -J w >-4 0 4 8N0.50.6250.7500.8750.40.50.6250.7500.875VELOCITY:—2U=U/ UoSHEARSTRESS:tRN=vwIUo2xxx—1 0 2Cl)uJ (I) Cl) w a: H Co -J a: 0 z0.00.51.00.0Y/04(X96mm)T=550Cmsec0.52‘Cw=WWIUoA.1.0Y/D4(X=92mm)T550Cmsec)74governed by the geometry of the valve (Fig. 2-3), which has two flow orifices. Thevalve’s monostrut is located at the centre of the minor orifice. It may be pointed outthat the directions of the flow at X = 100 mm and X = 96 mm are slightly different.Interference caused by the fluid streams from two orifices appears to be stronger atX 96 mm. The two fluid streams meet at around Z = 0.75D station, interact andmove together almost horizontally towards the opposite wall of the ventricle. Thisresults in a counter-clockwise flow inside the ventricle. But at the early stage of theacceleration phase, the ventricle is still relaxing, so the circulation does not result ina vortex. This can be discerned from Figures 3-11 and 3-14 where the velocity vectorsare mainly aimed towards the downstream direction at T 100 ms.When the mitral valve is fully open, the flow is in the peak phase. At X = 96mm, there are larger stresses compared to other x positions as shown in Figures 3-15,3-3 and 3-4. Also the turbulence intensity is slightly reduced compared to that for theflow in the acceleration phase (Fig. 3-14). But the flow pattern indicates that thecirculatory flow is developed at Z = 0.75D (Fig. 3-15). However, it does not extend tothe whole region inside the ventricle because the ventricle contracts just after themitral valve is fully open. The circulation is limited and forced to move towards theupper region with a decrease in velocity (Figs. 3-16, 3-17 and 3-18) due to the onsetof systole and closure of the mitral valve.In the central plane (X = 100 mm), the maximum velocity of 92.7 cm/s wasmeasured at Z = 0.4D; the maximum shear stress of 377.4 dynes/cm2at Z = 0.625D;and the maximum normal stress of 464.2 dynes/cm at Z = 0.75D. In the plane of X= 96 mm, the maximum velocity of 93.56 cm/s was found at Z = 0.4D; the maximumshear stress of 354.3 dynes/cm2at Z = 0.625D; and the maximum normal stress of523.6 dynes/cm2 at Z 0.4D. Similarly, in the plane of X = 92 mm, the maximumvelocity of 83.85 cm/s occurred at Z = 0.4D; the maximum shear stress of 190.875dynes/cm2at Z 0.625D; and the maximum normal stress of 289.7 dynes/cm2at Z =0.625D. In the entire left ventricle, the peak velocity was observed at X = 96 mm andZ = 0.4D; the maximum shear stress at X = 100 mm and Z = 0.625D; and themaximum normal stress at X = 96 mm and Z = 0.4D.(iii) Effect of the pulse ratesThe time histories of the profiles for five different pulse rates at X = 100 mmand Z = 0.625D were presented in Figure 3-4 to 3-8. As discussed before, themechanical performance of the valves is affected by the pulse rate. This is consistentwith the observed physiological behaviour. For all the pulse rates studied, the systolicphase covers around 40% of the cardiac cycle and the diastolic phase extends over theremaining 60% of the cycle. This means that the cardiac cycle created by the pulsesimulator is close to the natural one. During systole, around 70% of the phase iscovered by the aortic valve opening at all the pulse rates studied. The time taken toopen the mitral valve occupies a larger portion of the diastole as the pulse ratereduces. The longer time spent in the diastole would reduce the turbulence caused bythe opening of the mitral valve.So far as the fluid dynamical performance is concerned, the effect of the pulserate is minimal except for the durations of the three mitral flow phases. This wouldcorrespond to the periods of the valve mechanical performance. Distributions of thevelocity and stresses in a cardiac cycle are similar at the same stage of the cycle. Asdiscussed before, for the pulse rate of 71 beats per minute, the jet type ejecting flowat the onset of the mitral valve opening is also present at other pulse rates. Suddenbursts in the shear stress magnitude generally appear during the periods of the mitralvalve opening and the aortic valve closing. The highest velocity appears during thepeak flow phase; the highest shear stress usually in the deceleration phase; and the76highest normal stress near the closure of the aortic valve.The mitral flow rates have the values of 4, 3.5, 3.2, 2.8 and 2.5 litres perminute corresponding to the pulse rates of 84, 78, 71, 67, and 62 beats per minute,respectively, under the same pressure change of 120/80 mmHg. The correspondingReynold’s numbers based on the orifice diameter of the mitral valve are 3.84 x i04,3.36 x 10, 3.07 x i04, 2.69 x and 2.40 x respectively.At Z = 0.625D position, correspondingly, the maximum velocities are equal to86.97, 80.28, 73.02, 69.88, and 68.57 cmls, respectively for the different pules rates.The associated maximum normal stresses are 425, 385.4, 380.2, 324.1 and 237.9dynes/cm2.The maximum shear stresses values are 167.7, 113.2, 377.4, 291.4 and 71.3dynes/cm2at Z = 0.625D. Reduction in the peak velocity with a reduction in the pulserate is as expected. Similarly, the maximum normal stress also reduces as the pulserate reduces. But for the shear stress, the highest value (377.4 dynes/cm2)appears atthe rate of 71 beats/mm; it is extremely low (71.3 dynes/cm2)at the lowest rate of 62beats/mm; and continues to be lower at the higher pulse rates (84 beats/mm and 78beats/mm) used in the study.3.2 Anterior OrientationThe mitral disc valve in the anterior orientation means that the major orificeof the valve is located on the side nearer to the aortic valve and the disc is tiltedtowards the aorta (Fig. 3-20). The disc of the valve is perpendicular to the planeformed by the axes of the left atrium and aorta.An earlier study had indicated inferior performance of the valve in thisorientation [14]. Hence, the results presented here are only for 71 BPM.77Figure 3-20 Schematic diagram showing the mitral disc valve in the anteriororientation.3.2.1 Mechanical PerformanceFigure 3-21 shows the time-history of velocity and stress profiles at X = 100mm and Z = 0.625D position. From the changes in the velocity profiles, the openingand closing characteristics of the mitral valve can be discerned. As mentioned before,T =0 corresponds to the beginning of the mitral valve opening, and to the number 325of the data location. At T = 150 ms, the mitral valve is fully open; while at T 350ms, it is completely closed. The aortic valve starts opening at the instant T = 400 ms,is fully open at 450 ms, and completely closed at 600 ms. Thus the aortic valve is openfor 250 ms. The ventricle starts contracting at 200 ms and diastole sets in at 600 ms.(0w‘-‘CoCoUCo-J0zI ri rC/Jo(0uJa:Coa:UI(0/7f///[ )c COuJ‘-‘C/)(I)Ua:I—(0I1cr0z05T = -200 C rnsec1.02-4048—0.0-4 —:8—00V / D4T = -150 (msec2—1 —1CooCOUa:I—COa:LUI(017800-JU>>I—00-J2VELOCITY:U=ui uSHEAR STRESS:2 (0tRN=VW IUoX ) K CO>- Ua:NORMAL STRESSES: 3-JU>2 la:t=r1 i_______________2T = 50 ( msec( contd)Note: Pressure drop = 120/80 mmHg; D4 means the distance along the Y direction at thevertical position Z = 0.4D inside the left ventricle; negative T values imply that the data aremeasured prior to the mitral valve opening. Throughout the abscissa is Y/D4 and its scaleremains the same.Figure 3-21 Time history of velocity and stress profiles for the anteriororientation of the mitral valve at the location X=100 mm,Z=O.625D (pulse rate=71 beats/mm, Uo=12.72 cmls).0.521.0 Y/D4T=-100(msec) T=-50(msec)—1C/)U-’a:COa:LUICO2T = 0 ( msecV / D4>-I—00-JuJ>cc00)wa:I—0)a:UI(/31Cl)0)wa:I—Cl)a:i0zNote: Pressure drop = 120/80 mmHg; D4 means the distance along the Y direction at the vertical position Z = 0.4Dinside the left ventricle; negative T values imply that the data are measured prior to the mitral valve opening.Throughout the abscissa is Y/D4 and its scale remains the same.Figure 3-21 (cont’d) Time history ofvelocity and stress profiles for the anteriororientation of the mitral valve at the location X=100 mm,Z=O.625D (pulse rate=71 beats/mm, Uo=12.72 cm’s).79>-I—00-JuJ>>-I—0uJ>-40480.0-4048-0.0T = 100 ( rnsec T 150 C msec—1(00C/)wa:I.Cl)a:LuI012—1coOCl)wa:I—0)LuIcol2—1‘1’ / D4T = 200 C msec—1C,)Lu((CcLua:I—Co-J0z2—1Cl)0)Ua:I—(0-J0z2—10.5 1.0T 250 ( msec-4r9y / Q4V / D4T 300 C msec T = 350 (msecT 400 ( msec2V / 04T — 450 C msec)2V / D4T = 500 (msec)80This means that the systolic phase of the cardiac cycle extends over 400 ms. Onecardiac output cycle takes around 850 ms at the pulse rate of 71 beats per minute. Sothe diastolic phase takes 450 ms.Thus, 47 percent of the cardiac cycle is spent in the systole, and 53 percent inthe diastolic phase. For the mitral valve open period, two-seventh is in the diastole,which represents 24 percent of the diastolic phase. The remaining five-seventh is inthe systole covering 38 percent of the diastole phase. The entire open period of theaortic valve occupies 63 percent of the systolic phase.3.2.2 Fluid Dynamical PerformanceIn the velocity profiles shown in Figure 3-2 1, there is an initial flow field beforethe mitral valve opens (T = —100 ms and T = —50 ms). Furthermore, there is a flowtowards the orifice in a small region near the valve in the systolic phase when theaortic valve is not yet open. This suggests that the mitral valve cannot closecompletely in the anterior orientation. This, in turn, would cause a reversed flow, i.e.regurgitation. Once the mitral valve begins to open, almost all the positionsdownstream are disturbed, and two flow regimes corresponding to the major andminor orifices are formed (T = 50 ms, 100 ms). The major orifice flow on the aorticside has a higher velocity. Higher stresses occur in the region where the two flowfields interact, particularly when the mitral valve is fully open. When the aortic valveis fully open, the flow inside the ventricle is in the clockwise sense (T = 450 ms, 500ms). The clockwise circulation results from differential velocity of the two flow fieldsas well as incomplete closure of the mitral valve. The change in direction required toenter the aorta results in larger energy losses. The peak velocity occurs near theventricle wall on the mitral valve side. As the ventricle wall is pulsating, the large81velocity near the wall results in higher turbulence intensity and larger stresses.Figures 3-22 and 3-23 present variation of the velocity and stresses at fivedownstream locations at four typical moments. In the acceleration phase of the mitralflow, the fluid inside the ventricle is moving downstream almost everywhere. As canbe expected, the velocities are different at a given station on the mitral and aorticsides. The stress profiles have larger bursts at the cross region of the two flow fieldsas mentioned before. When the mitral valve is fully open, the difference in the velocityfield is reduced and the normal stress profiles are smoother but continue to have largevalues. When the aortic valve is open, the main flow appears on the mitral valve side,and normal stresses are reduced. At all the z stations, the shear stress is smaller andmore stable than the normal stresses. The character of the fluid dynamic performanceis quite similar at the different z stations.Considering the entire ventricle, the maximum velocity of 78.63 cmJs appearsat X = 100 mm and Z = 0.4D; the maximum shear stress of 268.4 dynes/cm2at X =100 mm and Z = 0.5D; and the maximum normal stress of 520.1 dynes/cm2at X = 92mm and Z = 0.625D.3.3 Performance Comparison of the Posterior and Anterior OrientationsThe character of the cardiac cycle for the two orientations is different even forthe same experimental conditions. For the posterior orientation, at 71 beats perminute, the systolic phase takes 41 percent of the cardiac cycle and the diastolic phasethe remaining 59 percent. On the other hand, for the anterior orientation, 47 percentand 53 percent correspond to the systolic and diastolic phases, respectively. The longerthe systolic phase, the smaller are the stresses in the anterior orientation because theventricle contracts more slowly and the flow is less disturbed. As pointed out before,0.40.4U) U) I— U) < w I (I)28(I) w U) U)0H C)) -J‘I< cc 0 z2-1-4N0.50,6250.7500 0 -j0.50.6250.7500.8750.875VELOCITY:—2U=UIUoSHEARSTRESS:tRN=vw/U,txxNORMALSTRESSES:tv=v’v/Uo22tw=ww/UoAAA0.00.51.00.00.5Figure3-221.0Y/D4Y/D4T=50Cmsec)T=100CmsecNote:Pressuredrop=120/80mmHg;D4meansthedistancealongtheYdirectionattheverticalpositionZ0.4Dinsidetheleftventricle.Variationofthevelocityandstressprofilesatfivedownstreamlocations(X=100mm)fortheanteriororientationofthemitralvalveattwodifferentinstants(T=50ms,100ms).Themitralvalveisopening(pulserate=71bçats/min,Uo=12.72cmls).t’31iIJiI-//IIU) U) (0 < w I U)28(I) uJ U) (I)oI— U) -J < 0 z2Y/D4T=150(msecV/D4T=450(msecNote:Pressuredrop=120/80mmHg;04impliesthedistancealongtheYdirectionattheverticalpositionZ=0.4Dinsidetheleftventricle.Figure3-23Variationofthevelocityandstressprofilesatfivedownstreamlocations(X=100mm)fortheanteriororientationofthemitralvalveattwodifferentinstants(T=150ms,450ms)correspondingtothemitralandaorticvalvesfullyopen(pulseratet7lbeats/mm, Uo=12.72cmls).0.4-1-40.5I C) 0 -J w >0 4N0.50.6250.7500.875iiiIi0.6250.7500.875VELOCITY:—2U=U/ UoSHEARSTRESS:tRN=vW/Uo2xxxNORMALSTRESSES:tv=vR/ uo2tw=wW/UoA.A0.00.51.00.00.51.084the cardiac cycle in the posterior orientation is close to the natural one. Only one-fourth of the mitral valve’s open period is spent in the systole phase for the posteriororientation while as much as five-seventh for the anterior orientation. This meansthat the mitral valve cannot close properly and efficiently in the anterior orientation.As explained earlier, this may cause regurgitation which is an important parametersin assessing the valve performance.Figure 3-24 shows variation of the maximum shear stress for the twoorientations at 71 beats per minute of the pulse rate. For both the orientations, themaximum shear stresses appear in the X = 100 mm plane which crosses the centresof the mitral valve, aortic valve and left ventricle. In the posterior orientation, peakshear stresses at every z station occur at T = —490 ms, i.e. at the late stage of thedeceleration phase but prior to the opening of the aortic valve. In the anteriororientation, the corresponding instant is —628 ms which is in the same phase andstage as in the posterior case. This means that the maximum shear stress inside theventricle depends on the performance of the mitral and not the aortic valve.The maximum shear stresses are larger at most z stations in the posteriororientation. Furthermore, the shear stress also changes more frequently in theposterior orientation. The large magnitude stresses and high frequency would inflictmore damage to the blood cells. The peak shear stress is 377.4 dynes/cm2 in theposterior orientation which is below the threshold value for destruction of the redblood cells [15,161. Now the stresses and their variations occur close to the aorticvalve, while in the anterior orientation they are near the mitral valve. Large stressesclose to the mitral valve imply higher turbulence intensity.The problem of improper closure and regurgitation was already pointed outbefore. For the same experimental conditions, the mitral flow rate is 2.9 mI/mm in theanterior orientation and 3.2 mllmin is in the posterior orientation. The incomplete0.40.40.0Y/04(X=lQOmrn)(a)posterior orientation(T=-490ms)C!) (00I (I),,U I U)U)U U) U)0I- U)-j < 0 z> I— 0 0 -j U >0.0Y/D4(X100mm)(b)anteriororientation(T=-628ms)Note:Pressuredrop=120/80mmHg;04meansthedistancealongtheYdirectionattheverticalpositionZ=0.40insidetheleftventricle.NegativeTvaluesimplythedatameasuredprior tothemitralvalveopening.Figure3-24Comparisonof themitralvalveorientations(posteriorandanterior)showingvariationofthemaximumshearstressprofilesatfivedownstreamlocations(pulse rate=71beats/mm).cx C)i-20.5-4 0 4 8N0.50.6250.7500.87540,6250.7502VELOCITY:—2U=U/ UoSHEARSTRESS:tRNNXNORMALSTRESSES:‘tv=’VIuo2tw=w!w/UoAAA0.8750.51.086closing of the mitral valve in the anterior orientation reduces the mitral flow by 9%.The regurgitation caused by the incomplete closing of the valve represents one of themajor complications for patients with the artificial valves as mentioned in theintroduction. On the other hand, the mitral valve in the posterior orientation createsthe counter-clockwise circulation inside the ventricle. This corresponds to the workingof the natural left ventricle as indicated in Figure 1-8. In contrast, the clockwise flowin the anterior orientation demands more energy as explained earlier.Therefore, based on the above results, the posterior orientation is recommendedfor implantation of the Bjork-Shiley monostrut mechanical valves.874. CONCLUSIONS AND RECOMMENDATIONS4.1 Concluding RemarksThe primary objective of the project has been to assess fluid dynamicalperformance of Bjork-Shiley monostrut mitral valve as affected by orientation andpulse rate. This involved extensive test-program using a sophisticated cardiac pulseduplicator in conjunction with a 3-beam, 2-component LDA system. This also requireddevelopment of computer codes for efficient operation of the test facility as well asdata acquisition, analysis and display. The thesis reports on significant progress madein achieving these goals.Several programs were developed either in QuickEASIC or the language usedby the SYSTAT MACRO. As they can be executed from one menu, the process becomeseasy, efficient and readily implementable. The quality of output on a laser printershowed considerable improvement. The programs made conducting the research moreprecise and efficient.With the program P9MENU, the results can be plotted sequentially, on onepage, at up to nine distinct moments. These plots helped evaluate temporal evolutionof the flow in the ventricle. The program P5MENU can plot time history of the flowparameters, at five downstream positions, on a single page at a given instant.Similarly, P55MENU can display the same information on a page at two instants. Theflow properties in two vertical planes can be plotted on one page by the programP1OMUNE to facilitate comparison.The test-program was aimed at measurements of spatial as well as timevariations of velocity, turbulence intensities, and normal and Reynolds stresses in theleft ventricle. The amount of information obtained through a carefully planned study88is literally enormous. Only some typical data useful in establishing trends arepresented in the thesis. Based on the results following general conclusions can bemade:(i) As can be expected, the mechanical performance of the valve is governed by thecardiac simulator. Different cardiac cycles or pulse rates lead to differentopening and closing behaviours. Of course, this in turn affects the fluiddynamical performance of the valve. The peak velocity and stress valuesdepend on open and closed periods of the mitral valve.(ii) Performance of the Bjork-Shiley monostrut mitral valve is sensitive toorientation. The posterior orientation is recommended for implantation due tosafe stress levels and reduced possibility of damage to red blood cells.(iii) A distinct flow pattern is established in the ventricle, depending on the valveorientation in the later stage of the deceleration phase prior to opening of theaortic valve. In the posterior orientation the flow circulates counter-clockwise;while in the anterior orientation the pattern is clockwise. The latter dissipatesmore energy while entering aorta due to changes in direction of the flow.(iv) In the anterior orientation, the Bjork-Shiley monostrut mitral valve fails toclose completely. This leads to regurgitation and incompetence of the valve. Theincomplete closing of the valve reduced the mitral flow by 9%.(v) In the posterior orientation, the cardiac cycle is closer to the natural one. Inthe anterior orientation, the systolic phase was longer compared to thephysiological one, and the aortic valve opens later in the cycle.(vi) The major and minor orifices of the Bjork-Shiley valve form two distinctstreams which meet above the central plane of the ventricle and undergoturbulent mixing downstream during the acceleration phase. Althoughdisturbance to the flow field is stronger in the posterior orientation, the peak89shear stress is not high enough to cause destruction of red blood cells.(vii) For both the orientations, the maximum shear stress occurs in the centralvertical plane of the ventricle and at the late stage of the deceleration phasebut prior to the opening of the aortic valve.(viii) Fluid dynamical performance of the valve is relatively insensitive to the pulserate.4.2 Recommendations for Future WorkThis research program is still in the early stage of development. There areseveral complex and challenging aspects which need to be investigated. Moreimportant ones needing urgent attention are listed below:(a) Modification of the test facility should be undertaken to eliminate obstructionto the laser beam in the region Z <O.4D. It will enable acquisition of importantinformation close to the valve. This would require redesign of the test-chamber.The ventricle should also be increased in size to bring the stroke volume closerto the natural one.(b) The program which controls the movement of the piston should be modified tosimulate different cardiac cycles with different pressure waves. The movementof the piston in the simulator is the power source that regulates the ventricularaction and the resulting cardiac circulation. Also a program for calibration ofthe instrumentation should be organized and integrated with the existingsoftware to make conduct of the experiments more automatic and accurate.(c) Further tests should be conducted to assess the effects of the stroke-volume,and cardiac cycle profile.(d) Nondimensional presentation of the information should be explored further.90(e) There is scope for undertaking a flow visualization study within the ventricleto get better physical appreciation of the complex flow field.91REFERENCES1. Graaff, K.M.V., and Fox, 5.1., Concepts of Human Anatomy and Physiology,Wm.C. Brown Publishers, Iowa, Second Edition, 1990, pp. 612-921.2. Kalmanson, D., The Mitral Valve: a Piuridisciplinary Approach, PublishingSciences Group, Inc., Acton, Massachusetts, USA, 1976.3. Starr, A., and Edwards, M.L., “Mitral Replacement: The Shielded Ball ValveProsthesis,” J. Thoracic Cardiovascular Surgery, Vol. 42, 1961, pp. 673-677.4. Chandran, K.B., “Prosthetic Heart Valves,” Mechanical Engineering, Vol. 108,No. 1, 1986, pp. 53-58.5. Akutsu, T., Hydrodynamic Performance ofMechanical Prosthetic Heart Valves,Ph.D. Thesis, The University of British Columbia, 1985.6. Björk, V., and Lindblom, D., “The Monostrut Bjork-Shiley Heart Valve,” JAmCoil Cardiol, Vol. 6, 1985, pp. 1142-1148.7. Köhler, J., “An Artificial Heart Valve with a Curved Disc”, Conference Digest,1st International Conference on Mechanics in Medicine and Biology, Aachen,Germany, ASME, 1978, pp. 340-343.8. Bruss, K.H., Reul, H., Gilse, J., and Knott, E., “Pressure Drop and VelocityFields of Four Mechanical Heart Valve Prostheses: Bjork-Shiley Standard,Bjork-Shiley C-C, Hall-Kaster and St. Jude Medical,” Life Support Systems,Vol. 1, 1983, pp. 3-22.9. Woo, Y-R, Yoganathan, A.P., et al., “In Vitro Pulsatile Flow Measurements inthe Vicinity of Mechanical Heart Valves in the Mitral Flow Chamber,” LifeSupport Systems, Vol. 4, 1986, pp. 63-85.10. Yoganathan, A.P., Sung, H-W, et al., “In Vitro Velocity and TurbulentMeasurements in the Vicinity of 3 New Mechanical Aortic Heart Valve92Prostheses,” J. Thoracic Cardiovascular Surgery, Vol. 95, 1988, pp. 929-939.11. Tillmann, W., “In Vitro Wall Shear Stress Measurements at Artificial HeartValves: a Comparative Study”, Conference Digest, 1st International Conferenceon Mechanics in Medicine and Biology, Aachen, Germany, ASME, 1978, pp.344-348.12. Rabago, G., Martinell, J., et al., “Comparison of Mechanical and BiologicalProstheses,” Heart Valve Replacement: Current Status and Future Trends,”Future Publishing Co. Ltd., Mount Kisco, N.Y., 1987.13. Yoganathan, A.P., Cardiovascular Fluid Dynamics ofFrosthetic Aortic Valves,Ph.D. Thesis, California Institute of Technology, U.S.A., 1978.14. Bishop, W.F., Hydrodynamic Performance of Mechanical and BiologicalProsthetic Heart Valves, M.A.Sc. Thesis, The University of British Columbia,1990.15. McDonald, D.A., Blood Flow in Arteries, The Camelot Press Ltd., Southampton,Second Edition, 1974.16. Bergel, D.H., Cardiovascular Fluid Dynamics, Academic Press Inc., London,Volume 1, 1972.-. 93APPENT)IX-I: COMPUTER CODES1.1 Programs for the ExperimentsThe modified programs include one for a computer to control the movement ofthe piston pump in the driver unit, i.e. to generate a desired pulse rate and a pressurewave form inside the ventricle. The other program controls movements of the LDAtraverse mechanism.The sinusoidal wave-form was chosen for the cardiac pressure time history. Theamplitude and period can be adjusted to a specified value by selecting differentparameter constants in the program. For example, in the present case, thedisplacement constant of 200 was used to represent amplitude of the pressure wave.The delay constant values of 4, 5, 6, 7 and 8 correspond to 84, 78, 71, 67 and 62 beatsper minute of pulse rate, respectively.The computer code for controlling the movements of the laser beams waswritten in QuickBASIC language. Before using the program, data from theinstruments must be recorded when the fluid inside the ventricle is static. The resultsare used to calibrate zero readings of the instruments. On setting a cardiac pulse rate,pressure change and the starting point of measurements, one is ready to implementthe program. During the execution, the program conducts the experiments as specifiedas well as collects, reduces and records fluid dynamical information described inChapter 2. Typically, the two components of mean turbulent velocity and threeturbulent stresses are recorded. At each measuring point, 600 samples of informationfor each variable are recorded. The information represents average performance of themitral flow during 1.2 seconds. Once the scan along the y direction is completed, theflow is animated to show the vectors of mean velocity at the scanned point on the94screen of a monitor. This provides a visual check of the measured data for grossdiscrepancies. All the data were recorded in the binary code and analyzed usingprograms described later. A flow chart for the program is schematically shown inFigure 1-1.1.2 Programs for Data Analyses and OutputThe data analysis is carried out by invoking SYSTAT software (1990, SYSTAT,Inc.). A set of programs were written in the language specified by SYSTAT andexecuted in the Macro mode of SYSTAT. Using the programs, it is convenient toperform complex data transformations and print out interactive outputs in one figureon a laser printer. These codes make it possible to reduce and display a large amountof experimental data efficiently. It is now possible, with a personal computer, to plottime histories of velocity vectors at a point in the left ventricle and overlay thecorresponding turbulent stresses. There are several options for the format such asnature of the graph (plot), size, position, overlap, colour, etc.. The options are listedin a menu or conversational command lines on the computer screen. Following theseprompts, in the menu or command lines, it is easy to set the specifics for a plot usingan available software. Some other options can also be specified by modifring theprograms because the language used is simple and user-friendly.1.2.1 MAIN MENU ProgramThis program creates a so-called MAIN MENU on the screen which acts as asource and has access to the sub-menus of EXPERIMENTS, PREPARATION-DATA,SINGLE-PLOT, FIVE-PLOTS, FIVE+FIVE, NINE-PLOTS and TEN-PLOTS. The95IRUNI4jInput and check data of zero reading41Input some specific information‘ISet A/D (D/A) board ready for converting data signalsby invoking PCLAB programMove the probe volume of LDA systemto the start point of measurementCollect total 4800 signals for 8 channels in the following order:Collect 600 signals per 1.2 seconds for each channel;2. Smooth the signals of the instantaneous velocitycomponents by using 10 times, 5 points average to getlocal mean values;3. Calculate local turbulent stresses;4. Repeat step 1 to step 3 up to 20 times;5. Calculate the average of 20 cycles;6. Recording data onto a computer disc.Yes C Check the last measuring point )JNoMove the probe to next measuring point along y direction_________Animate the flow in the period of 1.2 secondsby showing the velocity vectors on screenCheck the measuring dataWrongCorrectContinue testing No stopYesMove the laser beams to the next x positionFigure 1-1 Flow chart explaining the scheme adopted for collecting data.96program is run by typing in SUBMIT PLOT or MAIN in the Macro mode of SYSTAT.The associated scheme is shown in Figure 1-2.1.2.2 PREPARATION DATA Menu ProgramThis program imports the data from the experimental records and convertsthem into the SYSTAT style files. It contains two, choices for access: theARRANGEMENT ORIGINAL DATA and RE-ARRANGEMENT DATA (Fig. 1-3).The first access to the original data is achieved through the EXPDATAprogram which is written in the QuickBASIC language. It converts the selectedexperimental data, including velocity components and stresses, from the binary codeinto the ASCII format. The velocity data are stored in a file with the name extensionV’EL and the stress data are with the extension STR. The program can also searchmaximum values of the selected data. The maximum velocity is recorded in a file*VJ4) and the maximum stresses are stored in a file *5Jj (here symbol *represents any other valid letters of the files).Another access, the RE-ARRANGEMENT DATA, to run the IMPORT program(Fig. 1-3) is through introduction of the data in ASCII code into the SYSTAT format.The program, IMPORT, provides the choice of velocity data and stress data imports.The velocity data are stored in a file named with the initial letter V and an extensionSYS. The stress data file is designated with the initial letter S and an extension SYS.For access to this menu, one has to choose IMPORT from the MAIN MENU (Fig. 1-2)or directly enter SUBMIT IMPORT in the Macro mode.1.2.3 SINGLE-PLOT Menu Program97-RUN MAIN (Access to Sub-menus) IMAIN MENU (EXPRIMENTS, IMPORT DATA, SINGLE-PLOT, FIVE-PLOT,FrVE÷F1VE, NINE-PLOT, TEN-PLOT, QUIT)—EXPERIMENTS (Go to carry out experiments and collect data, Figure 14)— IMPORT DATA(Go to PREPARATION DATA menu, Figure 1-4, to runEXPDATA and IMPORT for data import)—SINGLE-PLOT (Go to run P1MENU, Figure 1-4, for single ploton one page)—FiVE-PLOT (Go to run P5MENU, Figure 1-5, to plot in the x-yplane, at up to five z-loeations in one graph)—F1VE÷F1VE (Go to run P55MENU, Figure 1-6, for double FIVE-PLOT on one page)—NINE-PLOT (Go to run P9MENU, Figure 1-7, for up to nine plotson one page)— TEN-PLOT (Go to run P1OMENU, Figure 1-8, to plot on two x-yplanes, at up to five z-locations per page)— QUIT (Stop running the program and return to the Macromodel of SYSTAT)Figure 1-2 Format of the MAIN program.98RUN EXPDATA AND IMPORT (Convert Data and Store the Datainto SYSTAT Data Files)PREPARATION DATA (ARRANGEMENT ORIGINAL DATA,RE-ARRANGEMENT DATA, QUIT)ARRANGEMENT ORIGINAL DATA (Go to execute EXPDATA)Velocity Data (Create a velocity data file: * VEL)Stress Data (Create a stress data file: * . STR)Maximum Data (Search maximum values of the data)Maximum velocity (Recorded in the file: * V. MAX)Maximum stresses (Recorded in the file: * S . MAX)Quit (Automatically back to PREPARATION DATA menu)RE-ARRANGEMENT DATA (Go to run IMPORT)VELOCITY-DATA (Create a velocity data file: V * SYS)STRESS-DATA (Create a stress data file: S * 55)QUIT (Return to PREPARATION DATA menu)QUIT (Return to MAIN MENU, Figure 1-2)Note: symbol * implies any other valid letters of the files.Figure 1-3 Scheme of the IMPORT program.99The program, P1MENU, is written for a single plot or a graph in one x-y planeand at one z-location. The menu has the choice of plotting velocity vectors, normal andshear stresses, and overlaying them. Variables in a plot can be dimensional or non-dimensional. Output can be printed through a laser printer, stored as a postscript file,or displayed on the screen. The access to the execution of this program can beobtained from the MAIN MENU (Fig. 1-2) or by directly loading the P1MENU in theMacro made of the SYSTAT. The procedure scheme is shown in Figure 1-4.1.2.4 FWE-PLOT Menu ProgramThe program named as P5MENU is for plotting velocity distributions at up tofive z-locations in one figure. Such plots are useful to get an overview of the entireflow field in the y-z plane inside the ventricle. The menu provides the choice ofplotting velocity vectors, normal and shear stresses, and overlaying them. Variablesin a plot can be dimensional or non-dimensional as before. Output can be printed ona laser printer, stored into a file, or shown on the screen. To access menu, one selectsthe FIVE-PLOT from the MAIN MENU (Fig. 1-2) or just enters SUBMIT P5MENUin the Macro mode of SYSTAT. The program scheme is shown in Figure 1-5.1.2.5 FIVE-i-FIVE Menu ProgramFigure 1-6 shows the algorithm for the program P55MENU which is fordisplaying five-plots at two different instants on one page. Similar to the FIVE-PLOTmenu, one can plot velocity vectors, normal and shear stresses, and overlay them withvariables in dimensional or non-dimensional form. Output can be tackled in three100RUN P1MENU (One Plot on One Page) jSINGLE-PLOT Menu (COMMON-SET, VELOCITY, NORMAL-STRESS,SHEAR-STRESS, OVERLAY,QUIT, STOP)COMMON-SET Menu (DATA, PLOTS, NON-DIMENSION, PRINT-OFPION, QUIT)DATA (Choose and arrange data)Velocity Data (Two components in the y and z directions)Dimension (Dimensional variables)Non-dimension (Non-dimensional variables)_____Stress Data (Three stresses)Normal Stresses (In the y and z directions)Normal Stress 1 (In the y direction)Dimension (Dimensional variables)Non-dimension (Non-dimensional variables)Normal Stress 2 (In the z direction)Dimension (Dimensional variables)Non-dimension (Non-dimensional variables)Shear stress (In the y-z plane)Dimension (Dimensional variables)Non-dimension (Non-dimensional variables)PLOTS (Choose total number of plots for data distributions at the same zlocation but at different instants in a cardiac cycle)(cont’d)Figure 1-4 Flow chart for the P1MENU program.101(cont’d, Figure 1-4)NON-DIMENSION (Choose variable dimensions)Dimension (Dimensional variable output)Non-dimension (Non-dimension variable output)PRINT-OPTION Menu (PRINTER, PAGE, TITLE, NOTE, QUIT)PRINTER (Choose the destination of outputs)Laser (Output on a laser printer)Screen (Output on a screen)____File (Output into a ifie)PAGE (Write page numbers)TITLE (Write titles)NOTE (Write notes)QUIT (Back to COMMON-SET menu)QUIT (Return to SINGLE-PLOT menu)VELOCITY (Plot velocity vectors)NORMAL STRESS (Plot normal stresses)SHEAR STRESS (Plot shear stress)OVERLAY Menu (COMMON-SET, VEL+REYNOLDS÷STRESSES,SHEAR+NORMALS, QUIT)COMMON-SET (Go to COMMON-SET Menu)VEL+REYNOLDS-STRESSES (Overlay velocity proffle and threeturbulent stresses)SHEATh-NORMALS (Overlay shear stress and two normal stresses)QUIT (Back to SINGLE-PLOT Menu)QUIT (Return to MAIN MENU, Figure 1-2, switch to other sub-menu)STOP (Stop and quit plotting, back to the Macro mode of SYSTAT)Figure 1-4 (cont’d) Flow chart for the P1MENU program.102RUN P5MENTJ (Plots up to Five z-Locations on One Page)FIVE-PLOT Menu (COMMON-SET, VELOCITY, NORMAL-STRESS,SHEAR-STRESS, OVERLAY,QUIT, STOP)COMMON-SET Menu (DATA, PLOTS, NON-DIMENSION, PRINT-OPTION, QUIT)DATA (Choose up to five data files and arrange data)Velocity Data (Two components in the y and z directions)Dimension (Dimensional variables)Non-dimension (Non-dimensional variables)Stress Data (Three stresses)_____NormalStresses (In the y and z directions)Normal Stress 1 (In the y direction)Dimension (Dimensional variables)Non-dimension (Non-dimensional variables)Normal Stress 2 (In the z direction)Dimension (Dimensional variables)L Non-dimension (Non-dimensional variables)Shear stress (In the y-z plane)Dimension (Dimensional variables)Non-dimension (Non-dimensional variables)PLOTS (Choose total number of plots for the data distributionat different instants in a cardiac cycle. One page presentsprofiles at a specified monment.)(cont’d)Figure 1-5 Flow chart for the P5MENU program.103(cont’d, Figure 1-5)NON-DIMENSION (Choose variable dimensions)Dimension (Dimensional variable output)Non-dimension (Non-dimensional variable output)PRINT-OPTION Menu (PRINTER, PAGE, TITLE, NOTE, QUIT)PRINTER (Choose the destination of outputs)Laser (Output on a laser printer)(Output on a screen)File (Output into a ifie)PAGE (Write page numbers)TITLE (Write a title)NOTE (Write notes)QUIT (Back to the COMMON-SET menu)QUIT (Return to FiVE-PLOT menu)VELOCITY (Plot velocity vectors)NORMAL STRESS (Plot normal stresses)SHEAR STRESS (Plot shear stress)OVERLAY (Overlay velocity profile and three turbulent stresses)QUIT (Return to MAIN MENU, Figure 1-2, and switch to other sub-menus)STOP (Stop and quit plotting, back to the Macro mode of SYSTAT)Figure 1-5 (cont’d) Flow chart for the P5MEN(J program.104RUN P55MENU (Double Five Plots up to Five z-Locations on One Page)F1VE+FJVE Menu (COMMON-SET, VELOCITY, NORMAL-STRESS,SHEAR-STRESS, OVERLAY, QUIT)COMMON-SET Menu (DATA, PLOTS, NON-DIMENSION, PRINT-OPTION, QUIT)DATA (Choose up to five data files and arrange data)Velocity Data (Two components, in the y and z directions)Dimension (Dimensional variables)Non-dimension (Non-dimensional variables)Stress Data (Three stresses)Normal Stresses (In the y and z directions)Normal Stress 1 (In the y direction)Dimension (Dimensional variables)Non-dimension (Non-dimensional variables)Normal Stress 2 (In the z direction)Dimension (Dimensional variables)Non-dimension (Non-dimensional variables)Shear stress (In the y-z plane)Dimension (Dimensional variables)Non-dimension (Non-dimensional variables)PLOTS (Choose total number of plots for the data distribution atdifferent instants in a cardiac cycle. One page presents twoprofiles at two specified moments.)(cont’d)Figure 1-6 Scheme adopted in the P55MENU program.105(cont’d, Figure 1-6)NON-DIMENSION (Choose variable dimensions)Dimension (Dimensional variable output)Non-dimension (Non-dimension variable output)PRINT-OPTION Menu (PRINTER, PAGE, TITLE, NOTE, QUIT)PRINTER (Choose the destination of outputs)Laser (Output on a laser printer)Screen (Output on a screen)File (Output into a file)PAGE (Write page numbers)TITLE (Write titles)NOTE (Write notes)QUIT (Back to the COMMON-SET menu)QUIT (Return to FIVE+FIVE menu)VELOCITY (Plot velocity vectors)NORMAL STRESS (Plot normal stresses)SHEAR STRESS (Plot shear stress)OVERLAY (Overlay velocity profile and three turbulent stresses)QUIT (Return to MAIN MENU, Figure 1-2, and switch to other sub-menu)Figure 1-6 (cont’d) Scheme adopted in the P55MENU program.106different forms as pointed out before. To access the menu, one selects FIVE+F1VEfrom the MAIN MENU (Fig. 1-2) or just enters SUBMIT P55MENU in the Macromode of the SYSTAT.1.2.6 NINE-PLOT Menu ProgramThe P9MENU program is for plotting up to nine graphs showing time historiesof variables at different instants during one cardiac cycle for the same x, y, z positionson a single page. Such plots help towards better understanding of the flow character.As before choices include velocity vectors, normal and shear stresses, and their overlaywith dimensional or non-dimensional variables, and three forms of output. To accessthe menu, one chooses the P9MENU from the MAIN MENU (Fig. 1-2) or just entersSUBMIT P9MENU in the Macro mode of the SYSTAT. This procedure is shown inFigure 1-7.1.2.7 TEN-PLOT Menu ProgramThe P1OMENU uses the same graphic face as the program P55MENU. Theplots present flow fields at two different y-z planes but at the same moment. It ishelpful to look at changes in the flow conditions along the x direction. The programalso creates a menu to access functions described in the other programs. To access thismenu, it is only required to type SUBMIT P1OMENU and press the ENTER key inthe Macro mode of the SYSTAT or choose the TEN-PLOT from the MAIN MENU (Fig.1-2). Figure 1-8 explains the sequence of operations involved.107RUN P9MENU (Up to Nine Plots Per Page)LipLoT Menu (COMMON-SET, VELOCITY, NORMAL-STRESS,SHEAR-STRESS, OVERLAY,QUIT, STOP)COMMON-SET Menu (DATA, PLOTS, NON-DIMENSION, PRINT-OPTION, QUIT)DATA (Choose and arrange data)Velocity Data (Two components in the y and z directions)Dimension (Dimensional variables)Non-dimension (Non-dimensional variables)Stress Data (Three stresses)Normal Stresses (In the y and z directions)Normal Stress 1 (In the y direction)Dimension (Dimensional variables)Non-dimension (Non-dimensional variables)Normal Stress 2 (In the z direction)Dimension (Dimensional variables)Non-dimension (Non-dimensional variables)Shear stress (In the y-z plane)Dimension (Dimensional variables)Non-dimension (Non-dimensional variables)PLOTS (Choose total number ofplots for data distribution at the samez-location but at different instants in a cardiac cycle)(cont’d)Figure 1-7 Approach to the P9MENU program.108(cont’d, Figure 1-7)NON-DIMENSION (Choose variable dimensions)Dimension (Dimensional variable output)Non-dimension (Non-dimensional variable output)PRINT-OPTION Menu (PRINTER, PAGE, TITLE, NOTE, QUIT)PRINTER (Choose the destination of outputs)Laser (Output on a laser printer)(Output on a screen)File (Output into a ifie)PAGE (Write page numbers)TITLE (Write titles)NOTE (Write notes)QUIT (Back to the COMMON-SET menu)QUIT (Return to the NINE-PLOT menu)VELOCITY (Plot velocity vectors)NORMAL STRESS (Plot normal stresses)SHEAR STRESS (Plot shear stress)OVERLAY (Overlap plots)QUIT (Return to MAIN MENU, Figure 1-2, and switch to other sub-menu)STOP (Stop and quit plotting, back to the Macro mode of SYSTAT)Figure 1-7 (contd) Approach to the P9MENU program.109L I RUN P1OMENU(Plots at up to Two x-y Planes, Five z-Locations on One Page)TEN-PLOT Menu (COMMON-SET, VELOCITY, NORMAL-STRESS,SHEAR-STRESS, OVERLAY, QUIT)COMMON-SET Menu (DATA, PLOTS, NON-DIMENSION, PRINT-OPTION, QUIT)DATA (Choose up to five data ifies and arrange data)Velocity Data (Two components in the y and z directions)Dimension (Dimensional variables)Non-dimension (Non-dimensional variables)Stress Data (Three stresses)Normal Stresses (In the y and z directions)Normal Stress 1 (In the y direction)L Dimension (Dimensional variables)Non-dimension (Non-dimensional variables)Normal Stress 2 (In the z direction)Dimension (Dimensional variables)Non-dimension (Non-dimensional variables)Shear stress (In the y-z plane)Dimension (Dimensional variables)Non-dimension (Non-dimensional variables)PLOTS (Choose total number of plots for the data distributionat different instants in a cardiac cycle. One page presentsproffles at a chosen instant.)(cont’d)Figure 1-8 Framework of the P1OMENU program.110(cont’d, Figure 1-8)NON-DIMENSION (Choose variable dimensions)Dimension (Dimensional variable output)Non-dimension (Non-dimension variable output)PRINT-OPTION Menu (PRINTER, PAGE, TITLE, NOTE, QUIT)PRINTER (Choose the destination of outputs)Laser (Output on a laser printer)Screen (Output on a screen)File (Output into a file)PAGE (Write page numbers)TITLE (Write titles)NOTE (Write notes)QUIT (Back to COMMON-SET menu)QUIT (Return to TEN-PLOT menu)VELOCITY (Plot velocity vectors)NORMAL STRESS (Plot normal stresses)SHEAR STRESS (Plot shear stress)OVERLAY (Overlay velocity proffle and three turbulent stresses)QUIT (Return to MAIN MENU, Figure 1-2, and switch to other sub-menu)Figure 1-8 (cont’d) Framework of the P1OMENU program.1111.2.8 Common Options in the ProgramsTo use the programs, one must provide necessary information by respondingto the questions, one by one, in the COMMON MENU. The questions appear on thecomputer screen once the choice is made from the COMMON MENU. In theCOMMON MENU, there are four choices: DATA; PLOTS; NON-DIMENSION; andPRINT-OPTIONS. To access the COMMON MENU, select COMMON SETS from thesub-menu. In fact, the COMMON SETS will be chosen automatically and theCOMMON MENU will appear on the screen when one asks the programs to plot.When the DATA are selected from the COMMON MENU, the name of the datafile, the start locations of the variables, and the step of locations between the databeing plotted must be provided by following the prompts on the screen. Here thelocation means the number of data counted from 1 to 599 which stand for the timevariable and are assigned by the programs for the experiments described in AppendixI. All the data at these locations, from the start to 599 with the given step of the datalocation, will be analyzed, sequentially renumbered (starting from 1), stored in thecomputer memory and is ready for plotting. Through PLOTS one selects the totalnumber of charts to be plotted, the start data number and the step of the datanumbers. Here the numbers correspond to those of the data reassigned. The NON-DIMENSION gives two choices: plots with dimensional or non-dimensional variables.The default mode is dimensional. The last necessary choice of the PRINT-OPTIONSin the COMMON MENU provides other alternatives which include PRINTER, PAGE,TITLE and NOTES. The PRINTER decides the form of the plot outputs. As explainedearlier, graphs can be displayed on the computer screen, plotted by a laser printer orstored in a postscript file for printing later. If one does not want the plots, the answeris simply ‘no’ to questions: ‘Do you want to print plots ?‘; and ‘Do you want to view112plots ?‘. This implies that one just wants to analyze the experimental data. The choiceof PAGE, TITLE and NOTES are for writing page numbers, titles and notes onto theoutput of plots, respectively. The failure to answer the question means ‘no’. Beforeexiting the OPTIONS menu, the choice of PRINTER has to be made. Prior to leavingthe COMMON MENU, one must respond to the DATA, PLOTS and PRINT-OPTIONSinquiry.1.2.9 Other Options in the ProgramsThere are some other options during plotting, such as scale, location, line style,colour, writing notes or legends, etc.. These functions can be implemented bymodifying the commands or parameters in the program.1.3 Other ProgramsThe code named XY is used for positioning the cross of the laser beams. Theprogram is particularly useful while adjusting test instruments during preparation foran experiment.The program called ZERO records zero readings of the instruments. Theinformation is for calibration.Yet another program displays time histories of the velocity vectors in twodimensions, at a given z-station on the screen. It shows clearly variation of the mitral-flow during a cardiac cycle. It may be extended to animate, simultaneously, the flowconditions at several downstream stations.APPENDIX-IT:SUMMARYOFMECHANICALPERFORMANCEDuration,msBPMCardiacSystole*Diastole*ValveOpen***MitralValveOpenWithinCycleMitralAorticDiastoleSystole62968400,41%568,59%500,52%300,31%;400,70%100,25%75%ofthesystole67900400,44%500,56%400,44%300,33%;300,60%100,25%75%ofthesystole71850350,41%500,59%400,47%250,29%;300,60%100,29%71%ofthesystole78769350,46%419,54%350,46%250,33%;250,59%100,29%71%ofthesystole84714300,42%414,58%350,49%200,28%;250,60%100,33%67%of thesystoleNotes:T=0correspondstotheonsetofthemitralvalveopening.*%basedondurationofthecardiaccycle;**%basedondurationof thephaseunderwhichthenumberappears._________________________Instant,msBPM/CardiacFullyOpenFully_ClosedBeginClosingBeginOpeningBeginCycle,msMitralAorticMitralAorticMitralAorticDiastoleSystole62/96835055050080040050080040067/90025045040070030040070030071/850200500400650or—20030040065030078/76920040035060025035060025084/714200400350550250350550250

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0081038/manifest

Comment

Related Items