The Elastic Modulus of Canine Aortic Valve Leaflets in Vivo and in Vitro

Transcription

1 792 The Elastic Mdulus f Canine rtic Valve Leaflets in Viv and in Vitr MNO THUBRIKR, WILLIM C. PIEPGRSS, L. PUL BOSHER, ND STNTON P. NOLN SUMMRY rtic valve leaflets underg extrardinary flexin due t the cmplete reversal f their curvature during billins f cardiac cycles. The flexin stresses in the leaflet depend n its elastic mdulus which we investigated in viv and in vitr. In six dgs, we placed radipaque markers n an artic leaflet. Leaflet length was calculated frm the marker psitins recrded flurscpically. rtic and ventricular pressures were recrded. Dgs were killed and leaflet stress-strain curves determined in vitr. Leaflet length in viv decreased 10.4 ± 4.7% frm diastle t systle in each cardiac cycle. Using the law f LaPlace, pressure gradients acrss the leaflets were cnverted int the stresses in the leaflets. The leaflets had an initial "elastic phase" f lw mdulus in systle fllwed by an "inelastic phase" f high mdulus in diastle. The elastic mdulus was 2.4 ± 0.7 x 10 6 dynes/cm 2 in systle and 5.2 ± 1.7 x 10 7 dynes/cm 2 in diastle. These results were similar t thse btained in vitr. Since flexin rigidity is prprtinal t (elastic mdulus) x (thickness) 3, the lwer mdulus in systle greatly reduces flexin stresses in the leaflet and increases leaflet lngevity. The higher elastic mdulus in diastle prevents excessive bulging r prlapse f the leaflet while it is subjected t the diastlic pressure gradient. We cnclude that a natural r prsthetic leaflet which is thickened r has a high elastic mdulus thrughut the cardiac cycle will have a greater flexin stress that culd cause early failure. Circ Res 47: , 1980 Dwnladed frm by n January 25, 2019 S the artic valve pens and clses, the valve leaflets underg cmplete reversal f their curvature in the circumferential directin. large amunt f flexin is assciated with this change f curvature. The leaflets must withstand this flexin during billins f cardiac cycles. The answer t hw a natural leaflet survives such a degree f flexin must lie in the elastic prperties f the leaflet and in the ability f the leaflet t regenerate itself t maintain thse elastic prperties. material having less stiffness (lwer elastic mdulus) is easier t bend than a material having greater stiffness (higher elastic mdulus). In vitr, stress-strain studies f fresh human (Clark, 1973; Wright and Ng, 1974; Yamada, 1970), prcine (Tan and Hlt, 1976; Rbel, 1972), and canine (Mundth et al., 1971) artic leaflets have shwn that the leaflets have a variable elastic mdulus with a lwer and a higher range. Hwever, it is nt knwn whether the leaflets functin at bth the lwer and the higher values f mduli in viv. If the reversal f leaflet curvature ccurs in viv at the lwer mdulus, flexin stresses in the leaflets wuld be greatly reduced. In the present study we investigated the in viv changes f the leaflet length f canine artic valves t determine their elastic mduli. Methds Six dgs (20-30 kg) were anesthetized with pentbarbital (25 mg/kg, iv) and were placed n car- Frm the Department f Surgery, University f Virginia Schl f Medicine, Charlttesville, Virginia. Supprted by Natinal Institutes f Health Grant HL ddress fr reprints: Man Thubrikar, Ph.D., Bx 263, Department f Surgery, University f Virginia Medical Center, Charlttesville, Virginia Received July 24, 1979; accepted fr publicatin June 6, dipulmnary bypass. Thrugh an arttmy, three radipaque markers (small platinum cylinders, 1 mm X 1 mm; 10 mg) were placed n the ladbearing prtin f the left crnary leaflet in the circumferential directin (Fig. 1). In three dgs, the markers were placed n the artic surface and, in the ther three, n the ventricular surface f the leaflet. One marker was placed in the ppsite cmmissure at the level f the tw lateral leaflet markers t establish a reference plane passing thrugh these three markers. n additinal marker was placed at the center f the free edge f the right crnary leaflet t help identify a clsed r pen valve. The dgs were allwed t recver and then were studied repeatedly ver several weeks. During each study the dgs were anesthetized lightly with ketamine (4-8 mg/kg/hr) and were psitined under an x-ray tube which culd be rtated. The mvement f the markers in the beating heart was recrded n videtape in tw prjectins sequentially: (1) with the x-ray beam perpendicular t the axis f the arta i.e., tw lateral markers n the leaflet and the cmmissure marker were prjected in a straight line (Fig. 2, side view) and (2) with the x-ray beam parallel t the axis f the arta i.e., the tw lateral markers n the leaflet and the cmmissure marker were prjected in a triangle (Fig. 2, tp view). These prjectins were btained separately fr diastle and fr systle because the alignment f the markers changed frm diastle t systle. Thus, fur prjectins were btained at a given systemic pressure. The dg then was rtated 180 degrees n its spinal axis and fur new prjectins were recrded. In all the prjectins, the magnificatin was determined by placing a steel ball f knwn diameter adjacent t the dg,

2 ELSTIC MODULUS OF ORTIC VLVE LEFLETS/Thubrikar et al. 793 Dwnladed frm by n January 25, 2019 FIGURE 1 line drawing f the artic valve. L, R, and N are the leaflets crrespnding t the left, right, and nncrnary artic sinuses, respectively. Three radipaque markers (, B, C) n the lad-bearing prtin f the leaflet in the circumferential directin and ne marker (D) in the ppsite cmmissure at the level f the tw lateral leaflet markers are shwn. marker n the right crnary leaflet is shwn by a vertical bar. Leaflet length is length f the segment BC. at the level f its artic valve. Since the level f the valve had t be judged frm the utside, the magnificatin factr culd be in errr and culd affect the abslute leaflet length. Hwever, this is nt critical, since the results are based upn the relative length, which is nt affected by the magnificatin factr. The videtape recrding f the marker mvement was made at a rate f 60 fields/sec, using a cntinuus peratin f the x-ray tube and the cnventinal mde f interlaced peratin f the Vidicn televisin camera. The pressures in the ascending arta and in the Side DISTOLE SYSTOLE FIGURE 2 schematic representatin f the artic valve shwing nly ne leaflet fr clarity., B, and C represent the three markers n the leaflet, and D represents the marker in the ppsite cmmissure, x is the distance f pint B frm the plane DC. B' is the prjectin fb n the plane DC; p is the perpendicular distance f pint B' frm the line C. Distances x,, fi, and p required t calculate the leaflet length are indicated (see ppendix I). left ventricle were recrded, using Sanbrn pressure transducers (mdel 267B) via 7F pigtail catheters. Fr the catheter-transducer system, the natural frequency was 91 Hz and the damping factr was determined by the methd described by McDnald (1974a). In diastle, the pressure gradient acrss the leaflet was calculated as the average difference between the artic and ventricular pressures. In systle, the pressure gradient acrss the leaflet was nt measured but was assumed t be in the range f 0-10 mm Hg. The ECG (lead II) als was recrded. The studies were repeated ver a wide range f systemic pressures which was achieved by infusing angitensin r nitrprusside. The videtape was synchrnized with the hemdynamic recrdings using a special circuit which triggered a slenid in the videfield and simultaneusly recrded an event marker n the hemdynamic recrding. The videtapes were analyzed as fllws. First, in a straight-line prjectin in diastle, a segment f 2-3 cardiac cycles was chsen at a given artic pressure. The segment was identified n the hemdynamic and videtape recrdings. In this segment, the videtape was displayed in a stp-mtin mde n a televisin screen and the marker psitins were transferred frm the screen nt transparent acetate paper. The videtape then was advanced field by field and the marker psitins were transferred in each field fr 2-3 diastles. Frm the marker psitins, distance x was measured in the straight-line prjectin in all the videfields (Fig. 2, side view in diastle; ppendix I). Secnd, in a triangular prjectin in diastle, a segment f 2-3 cardiac cycles was chsen at the same artic pressure as befre and was identified n the hemdynamic and videtape recrdings. The videtape was displayed n a televisin screen and the marker psitins were transferred n a transparent acetate paper field by field fr 2-3 diastles. The distances, 4, and p were measured in all the videfields (Fig. 2, tp view in diastle, and ppendix I). Frm these tw prjectins in diastle, the length f the marked segment BC f the leaflet (Fig. 1; ppendix I) was determined as fllws. Equal numbers f videfields frm the straight-line prjectin and frm the triangular prjectin were selected. The videfields at the beginning, middle, and end f diastle frm these tw prjectins were matched. The match was achieved with a lss f ne r n videfield frm any f the prjectins, because the heart rate was kept cnstant during the recrding. Fr each matched pair, the length f the leaflet segment was determined frm the distances x,, &, and p as explained in ppendix I. The calculatin als yields the radius f the segment f the leaflet, which was nt measured directly. The terms, leaflet length and radius, are used t describe the length and radius f the segment BC (ppendix I: radius R = NC). In systle, at the same systemic pressure as abve, the segments f 2-3 cardiac cycles were

3 794 CIRCULTION RESERCH VOL. 47, N. 5, NOVEMBER 1980 Dwnladed frm by n January 25, 2019 chsen in the straight-line prjectin and in the triangular prjectin. Frm these tw prjectins, several matched pairs f videfields were btained as described abve. Fr each pair, distance x was measured in the straight-line prjectin (Fig. 2, side view in systle), and distances 4, 4, and p were measured in the triangular prjectin (Fig. 2, tp view in systle). Fr each pair f videfields, the length and radius f the leaflet were determined frm the distances x,, < >, and p (ppendix I). t a given systemic pressure, therefre, tw prjec tins were used fr the leaflet length in systle, and tw prjectins were used fr the leaflet length in diastle. The leaflet length and radius were crrected fr magnificatin by the magnificatin factr that was cnstant fr diastle and systle. s was mentined earlier, the cnstant magnificatin factr may prduce errr in the abslute length f the leaflet, but it prduces n errr in the change in the leaflet length frm diastle t systle. It is wrth nting that the artic valve mves as the heart cntinues t functin and the markers d nt stay aligned in a straight-line prjectin thrughut diastle r systle. Therefre, nly thse videfields were analyzed which shwed perfect marker alignment. Figure 3 is a typical graphic representatin f (1) leaflet length, (2) leaflet radius, (3) artic pressure, and (4) left ventricular pressure. Since diastlic and systlic leaflet lengths are btained frm fur different prjectins, the artic and ventricular pressures shwn are schematic. t anther systemic pressure, the leaflet length and radius in diastle and systle were btained frm fur mre prjectins at that pressure. The amunt f shrtening in the leaflet length frm diastle t systle was calculated as [ (Ld-L s )/ L d ] X 100%, where Ld and L s were the mean leaflet lengths in diastle and systle, respectively. Each value f Ld r L s was btained by averaging the leaflet Length Leaflet Radius (mm) Pressure (mm Hg),* "*! FIGURE 3 plt f leaflet length in the circumferential directin, leaflet radius, artic pressure, and ventricular pressure vs. time. rtic and ventricular pressures are schematic. The leaflet length in diastle was greater than that in systle. The leaflet radius in diastle was smaller than that in systle. ~i leaflet lengths frm pairs f videfields in diastle r in systle in 2-3 cardiac cycles and reprted as mean ± SD at a given pressure. Over a wide range f pressure, multiple values f Ld and L s were btained in a given dg. T see whether Ld was significantly different frm L s, the difference between their means was tested by a paired data analysis. Similarly, t see whether the leaflet shrtening measured with the artic markers was significantly different frm that measured with the ventricular markers, the fllwing was dne: fr all the dgs, at all systemic pressures, the values f the leaflet shrtening btained frm the artic markers and thse btained frm the ventricular markers were put in tw separate grups. The difference between the means f these tw grups was tested fr significance by Student's Mest. The accuracy f the measurement was determined with a plastic mdel f the artic valve, in which the leaflets were curved in the circumferential directin. Radipaque markers were placed in psitins similar t thse in viv. The straight-line prjectins and the triangular prjectins were recrded with the mdel leaflet in the pen and clsed psitins. The distances x,, 4, and p were measured in these prjectins, and the length f the segment f the mdel leaflet was determined (ppendix I). The actual length f the segment was measured with a magnifying eyepiece micrmeter with the mdel leaflet in a flat psitin. The difference between the calculated length and the measured length was 2%. In viv, the analysis f the leaflet length was perfrmed independently by each f three bservrs. The methd is accurate (2% errr) fr determining the leaflet length in a single study. Hwever, additinal errr is intrduced, especially frm the magnificatin factr, when the data frm multiple studies f the same dg are cmbined. The magnitude f this errr was estimated t be anther 2%. This results in an verall errr f 4% when multiple studies are cnsidered tgether. Each dg was studied three times with the first study 1 week after the peratin, and the subsequent studies 3-5 weeks apart. ll the dgs were killed and the marked leaflets were remved. Frm each leaflet, a rectangular strip (apprximately 12 mm lng and 3 mm wide) was cut incrprating the marked segment in the circumferential directin. Fr these strips, the stress-strain curves were determined, in vitr, using an Instrn tensile-testing machine (strain rate f 5 mm/min). Results In viv, the length f the leaflet in the circumferential directin varied during a cardiac cycle (Fig. 3). In a given cardiac cycle, the leaflet length remained cnstant during diastle. During systle, the leaflet length remained cnstant in sme cardiac cycles but decreased in thers as systle prgressed. The leaflet length always was greater in diastle

4 ELSTIC MODULUS OF ORTIC VLVE LEFLETS/Thubrikar et al. 795 Dwnladed frm by n January 25, 2019 than in systle. The radius f curvature f the leaflet was cnstant during diastle but usually increased during systle as systle prgressed. The mean radius always was smaller in diastle than in systle. These bservatins were true in any single cardiac cycle, at any systemic pressure, in all six dgs. In each dg, the amunt f leaflet shrtening frm diastle t systle neither increased nr decreased as the systemic pressure increased (e.g., Table 1, fr dg 2). The measurements ver a wide range f pressure were btained frm multiple studies n a given dg. s was mentined in Methds, this leads t an verall errr f 4% in the leaflet length. Cnsequently, the leaflet lengths in diastle and in systle shw a significant scatter ver a wide range f pressure (Table 1). Hwever, the difference between the diastlic and the systlic length f the leaflet was highly significant (P < ). Fr all f the dgs, the amunt f leaflet shrtening did nt vary with the artic diastlic pressure (Fig. 4). The mean (±SD) change in the leaflet length was 6.4 ± 3% with the markers n the artic side and 14.9 ± 4% with the markers n the ventricular side f the leaflet (Fig. 4). This difference in the leaflet shrtening was highly significant (P < ). This result is imprtant because it indicates the mechanisms with which the change in the leaflet curvature frm diastle t systle can be achieved, and it will be cnsidered again in the Discussin. The average shrtening f the leaflet was 10.6% n the surface lcated in the middle f the artic surface and the ventricular surface. In six dgs, the mean (±SD) radius f curvature f the leaflet was 9 ± 1 mm in diastle and 10 ± 2 mm in systle. When the leaflet length was pltted against the pressure gradient acrss the leaflet, a characteristic behavir was bserved (e.g., Fig. 5, fr dg 5). The plts btained frm all six dgs shwed similar behavir. In systle, there was a large change in the leaflet length fr a small change in the pressure gradient and, in diastle, there was a small change in the leaflet length fr a large change in the pres- E M I u FOR six 0 DOGS t 1 1 * I 1» rtic Diastlic Pressure (mm Hg) O Vvntriculai rtic FIGURE 4 Decrease in the leaflet length vs. artic diastlic pressure. Fr three dgs with the markers n the ventricular side, the average decrease was 14.9 ± 4%, and fr three dgs with the markers n the artic side, the average decrease was 6.4 ± 3%. sure gradient (Fig. 5). The leaflets had an initial "elastic phase" (less stiffness in systle) fllwed by an "inelastic phase" (mre stiffness in diastle). In systle, the relatinship between the leaflet length and the pressure gradient is s sensitive t the pressure gradient that a highly accurate measurement f the pressure gradient (perhaps f the rder f 1 mm Hg) is required t establish the relatinship quantitaively. In systle, the pressure gradients were nt measured. Hwever, this sensitive dependence was evident in several cardiac cycles in which the leaflet length decreased during systle, as systle prgressed, presumably as the systlic pressure gradient decreased (Fig. 3). Similarly, in diastle, the relatinship between the leaflet length and the pressure gradient is s sensitive t the leaflet length that a highly accurate measurement f the leaflet length (perhaps <1% errr) is required t establish the relatinship quantitatively. Since such a high degree f accuracy, in viv, is impssible t achieve with the present technique, any small decrease in TBLE 1 Change in the Leaflet Length as a Functin f rtic Pressure fr a Single Dg rtic pressure (mm Hg) 102/70 110/85 120/95 125/96 144/ / / / /170 Leaflet length in diastle (mm) 18.9 ± ± ± ± ± ± ± ± ± 0.6 Leaflet length in systle (mm) 17.2 ± ± ± ± ± ± ± ± ± 0.8 Decrease in leaflet length (%) Mean 9.2 ± 2.2 Leaflet length is reprted as mean ± SD fr n = Decrease in leaflet length is reprted as mean ± SD.

5 UlUl) 796 CIRCULTION RESERCH VOL. 47, N. 5, NOVEMBER 1980 Dwnladed frm by n January 25, 2019 > adient Elastic Mdulus E,= 2x)0 6 (max) Stress Strain S l/l dynes cm 2 dynes Leaflet Length (mm) FIGURE 5 Leaflet length vs. pressure acrss the leaflet in viv. The circles represent measured leaflet length and measured pressure gradient in diastle. Vertical bars represent measured leaflet length and an assumed pressure gradient f 0-10 mm Hg in systle. The elastic mdulus in diastle was btained frm the slpe f the line thrugh the measurements in diastle. The elastic mdulus in systle was btained frm the line f maximum slpe thrugh the measurements in systle. The leaflet had an initial "elastic phase" f lw mdulus in systle fllwed by an "inelastic phase" f high mdulus in diastle. the leaflet length that might have ccurred as a result f decreasing pressure gradient during a single diastlic perid wuld nt be detected (Fig. 3). In viv, the pressure gradient acrss the leaflet represents stress n the leaflet and the change in the leaflet length represents the strain. Therefre, Figure 5 defines the segments f the stress-strain curve f the leaflet, in which the leaflet functins during diastle and during systle under physilgical cnditins. lthugh the present technique did nt have the accuracy required t establish a precise quantitative relatinship between the stress and the strain, an attempt was made t estimate the rder f magnitude f elastic mduli f the leaflet. line f maximum slpe was drawn thrugh the bars in systle (Fig. 5). The slpe f this line gives the maximum elastic mdulus f the leaflet in systle. nther line was drawn thrugh the pints in diastle, s that a smth transitin was achieved between this line and the line in systle (Fig. 5). Justificatin fr drawing such a line is that the resulting stress-strain curve resembles the bserved stress-strain curve f that leaflet in vitr. linear regressin line thrugh the pints in diastle was cnsidered unsuitable because it had a pr crrelatin cefficient as a result f significant scatter in the leaflet length. Frm the slpes f these lines, the incremental elastic mduli f the leaflet in diastle and in systle were calculated using the methd described by McDnald (1974b) (see ppendix II). The incremental elastic mdulus in diastle (ED) was calculated using (1) the measured pressure gradient, (2) the measured radius f the leaflet, and (3) an assumed leaflet thickness f 0.5 mm. leaflet thickness f 0.4 t 0.5 mm has been measured by us, at a later time, n cmparable dgs. The incremental elastic mdulus in systle (Es) was calculated using (1) the assumed pressure gradient f 0-10 mm Hg, (2) the measured radius f the leaflet, and (3) an assumed leaflet thickness f 0.5 mm. The ED and Es f the leaflet fr each dg are listed in Table 2, where dgs 1, 4, and 5 had markers n the ventricular side f the leaflet, and dgs 2, 3, and 6 had markers n the artic side f the leaflet. In vitr, the stress-strain curves fr each marked leaflet were determined in the circumferential directin after the dgs were killed. ll the stressstrain curves shwed a characteristic nnlinear behavir (e.g., Fig. 6, fr dg 5). Fr each leaflet, the stresses in diastle and in systle were calculated frm the in viv measurements (as explained in ppendix II), and were pltted n the in vitr stress-strain curve. This defines the diastlic and systlic segments f the in vitr stress-strain curve crrespnding t the similar segments f the in viv stress-strain curve. Frm these segments, the incremental elastic mduli in diastle and in systle were calculated (Table 2). The elastic mduli calculated frm bth the in viv and the in vitr measurements were quite cmparable (Table 2). The mean (±SD) elastic mdulus in diastle was 5.2 ± 1.7 X 10 7 dynes/cm 2 and in systle was 2.4 ± 0.7 X 10 6 dynes/ cm 2. Discussin Cyclic Changes in the Leaflet Length during a Cardiac Cycle In each cardiac cycle, the leaflet was lnger in diastle than in systle, indicating that the leaflet is elastic and stretches with increased lading (Fig. 3). In diastle, the leaflet is under a greater lad (greater pressure gradient) than in systle (smaller pressure gradient). In any single diastlic perid, the leaflet length did nt change, indicating that the leaflet is in an "inelastic phase" and that the small changes in the pressure gradient during diastle have little effect n leaflet length. This is als evident frm Figure 5 which shws that, in diastle, a large change in the pressure gradient causes a small change in the leaflet length. In a single systle, the leaflet length was cnstant in sme cardiac cycles and decreased in thers (Fig. 3). This result is difficult t interpret since the pressure gradient acrss the leaflet was nt measured. The measurements f the pressure gradients by thers (Mc- Dnald, 1974c; Driscl and Eckstein, 1965) have indicated that the gradient is maximum at the beginning f systle and decreases during systle.

6 ELSTIC MODULUS OF ORTIC VLVE LEFLETS/Thubrikar et al. 797 The decrease in the leaflet length during a single systlic perid, bserved in sme cardiac cycles, culd be due t decreasing pressure gradient. This wuld suggest that in systle the leaflet is in an "elastic phase" and is sensitive t small pressure changes acrss it. This wuld als suggest that, in Figure 5, the scatter in the leaflet length in systle prbably represents a true variatin in the leaflet length due t variatin in the pressure gradient. The radius f the leaflet was cnstant during diastle and increased during systle (Fig. 3). This bservatin is cnsistent with the previus bservatin (Thubrikar et al., 1977, 1979) that the amunt f leaflet pening decreases during systle. (i) VENTRICULR MO3 (ii) ORTIC S D ^97 Effect f Systemic Pressure n the munt f Leaflet Shrtening The amunt f leaflet shrtening frm diastle t systle was cnstant ver a wide range f pressure (Table 1). This interesting bservatin may be imprtant fr nrmal valvular functin. (iii) Dwnladed frm by n January 25, 2019 Effect f Leaflet Cnfiguratin n the munt f Leaflet Shrtening The amunt f leaflet shrtening was 14.9 ± 4% when measured with the markers n the ventricular surface and 6.4 ± 3% when measured with the markers n the artic surface (Fig. 4). This bservatin can be explained in tw ways. (1) When the markers were n the ventricular surface, the "imaginary" segment indicated by the markers was lnger in diastle and shrter in systle than the actual segment f the leaflet (Fig. 7i), thus exaggerating the amunt f true shrtening. The markers n the artic surface have the ppsite effect; i.e., the Lad (Gms) 120 i Increase in Leaflet Length (mm) * FIGURE 6 Increase in leaflet length vs. lad n the leaflet in vitr. The lads crrespnding t the diastlic pressures f 80 and 120 mm Hg are indicated. The dtted lines indicate the slpes f tw segments which crrespnd t systle and diastle. The stress-strain curve is nnlinear, indicating that the leaflet has a variable mdulus with a lwer and a higher range. FIGURE 7 Schematic representatin f the leaflet in diastle (D) and in systle (S). (i) The markers are n the ventricular surface f the leaflet. If the leaflet length changes frm 90 t 100 mm (slid lines), then the "imaginary" segment (dtted lines) represented by the markers changes frm 88 t 103 mm (r x 15%). (ii) The markers are n the artic surface. The "imaginary" segment (dtted lines) changes frm 92 t 97 mm (r x 5%). (iii) If the straight leaflet is 90 mm lng in systle and 100 mm lng in diastle, and if the leaflet changes cnfiguratin by bending, then the length f the ventricular (V) side f the leaflet wuld change frm 88 t 103 mm (r x 15%), and the length f the artic () side f the leaflet wuld change frm 92 t 97 mm (r ~ 5%). leaflet nw appears shrter in diastle and lnger in systle than its true length (Fig. 7ii), thus diminishing the amunt f true shrtening. (2) s the leaflets mve frm diastlic psitin t systlic psitin, they change cnfiguratin by bending and/ r shear defrmatin within the leaflet. In the case f bending, in diastle, the ventricular surface expands and the artic surface shrinks (Fig. 7iii). Similarly, in systle, the ventricular surface shrinks and the artic surface expands. This wuld als result in a smaller change in the artic surface and a greater change in the ventricular surface. Thus, if the behavir f the markers n a particular surface truly represents the behavir f that surface, then the difference in the leaflet shrtening indicates that the leaflet changes cnfiguratin by the mechanism f bending. This is imprtant because it determines the stresses t which the leaflet wuld be subjected. The stresses in the leaflet due t bending defrmatin are the subject f a cmpanin paper (Thubrikar, 1980).

7 798 CIRCULTION RESERCH VOL. 47, N. 5, NOVEMBER 1980 Dwnladed frm by n January 25, 2019 The Elastic Mdulus f the Leaflet in Systle and Diastle The elastic mdulus is defined as the rati f stress ver strain, and it is variable fr the leaflet (Fig. 6). In the present study, therefre, the "incremental elastic mdulus" (McDnald, 1974b), which is an verall rati f stress ver strain fr a given segment, was calculated. In calculating the incremental elastic mdulus, a leaflet thickness f 0.5 was assumed. Clark and Finke (1974) measured the thickness at the center f the leaflet as 0.5 mm in humans. This thickness was cnsidered t be clse enugh t that f canine leaflets fr an apprximate estimate f elastic mdulus. leaflet thickness f mm has been measured by us, at a later time, n cmparable dgs. Fr calculating the elastic mdulus in viv, it was assumed that, in systle, the bserved range f leaflet lengths ccurred ver a pressure gradient f 0-10 mm Hg. Driscl and Eckstein (1965) measured the average maximum pressure gradient in dgs as 9.4 mm Hg in early systle, and believed that the gradient decreased during systle. If the elastic mdulus in systle is calculated fr a pressure gradient f 5.0 mm Hg, its value wuld be half f that shwn in Table 2. In calculating the stresses frm the pressure gradient, the leaflet was cnsidered t be cylindrical, as has been bserved by the authrs (Thubrikar, et al., 1977, 1979) and thers (Swansn and Clark, 1974). The values f elastic mduli calculated frm the in viv measurements are apprximate since the calculatin invlves assumptins abut the leaflet thickness and systlic pressure gradient. The present study is intended nly t shw that the leaflet is, in fact, in the lw mdulus regin in systle, and in the high mdulus regin in diastle. The magnitudes f elastic mduli shuld be btained frm the stress-strain curves carried ut carefully in vitr. Fr calculating the elastic mdulus in vitr, similar assumptins were made. The elastic mduli calculated frm in viv and in vitr measurements were cmparable (Table 2). The elastic mdulus in diastle was similar t that calculated by Clark (1973) fr human artic leaflets. The elastic mdulus in systle was times lwer than that in diastle. Mundth et al. (1971) bserved that the mdulus in the initial phase was 10 times less and TBLE 2 Elastic Mdulus f rtic Leaflets (dynes/ cm 2 ) In viv In vitr Dg Diastlic 2.8 X 10' 3.4 X 10' 4.2 x 10' 6.2 x 10' 6.7 x 10' 7.2 x 10' E,, = 5.2 ± 1.7 x E~ = 2.4 ± 0.7 x Systlic 2.7 X 10" 2.0 X 10" 1.9 X 10" 2.1 X X 10" 2.7 x 10" Diastlic 2.7 X 10' 6.0 X 10' 4.6 X 10' 7.1 X 10' 6.5 X 10' Systlic 1.6 X 10" 2.4 X X 10" 3.4 X 10" 3.7 X 10" Clark (1973) bserved that it was 300 times less than the mdulus in the later phase. The Relatinship f Elastic Mdulus t Flexin Stress The present study cnfirms that the artic leaflet has an initial "elastic phase" f lw mdulus fllwed by an "inelastic phase" f high mdulus. It further indicates that in viv the leaflet is, in fact, in an elastic phase in systle and in an inelastic phase in diastle. The transitin between the tw phases may r may nt ccur alng the line jining them (Figs. 5 and 6), since the mdulus during transitin depends n the rate at which the leaflets pen and clse. The higher elastic mdulus in diastle is imprtant because it prevents excessive bulging r prlapse f the leaflet under nrmtensin r hypertensin. Even mre imprtant is the lwer mdulus in systle. Since the leaflets, in rder t pen and clse, must underg cmplete reversal f their curvature, it is imprtant that the flexin stresses assciated with the change f curvature be minimal. Flexin rigidity is directly prprtinal t (elastic mdulus) X (thickness) 3 (Harvey, 1974). The lwer elastic mdulus in systle reduces flexin rigidity, thereby reducing the flexin stresses in the leaflet. The thinness f the leaflet als suggests that reductin f flexin stress is imprtant. Leaflet lngevity undubtedly is enhanced by its lw elastic mdulus in systle. natural r prsthetic leaflet which is thickened r has a high elastic mdulus thrughut the cardiac cycle will have greater flexin stress, which culd cause early failure. The leaflet cmes t a lwer elastic mdulus regin by changing its length, which culd be detrimental, as the length change may induce fatigue in the leaflet. Hwever, the gain in reducing the flexin stresses due t lw elastic mdulus must be mre than the lss due t increased fatigue. This suggests that the leaflets may be prne t flexin failure mre than fatigue failure. ppendix I Calculatin f arc length and radius f the leaflet segment encmpassed by the markers: Suppse BC dentes the markers n the leaflet and D the marker in the cmmissure. Then, the length and radius f the segment f the leaflet is, respectively, the length and radius f the arc BC. In a straightline prjectin, measure x. x = distance f pint B frm the plane DC. In a triangular prjectin measure, \, 2, and p, p being the perpendicular distance f pint B' frm the line C. B' is the prjectin f B n the plane DC. B = V4 2 + x 2, BC = V 2 + x 2, OB = Vp 2 + x 2 Say a = <BC = <BO + <OBC. Then,OB.OB

8 ELSTIC MODULUS OF ORTIC VLVE LEFLETS/Thubrikar et al. 799 k i Thus, we knw 0\ and Then, R = ^ / Sin e _l and Rc BC = 2 / where R = radius f the segment f the leaflet = NC; rc BC = length f the circumferential segment f the leaflet. Fr example, in diastle, Measured x = 8.9 mm, = 9.9 mm, <f 2 = 19.9 mm, p = 0.7 mm Calculated R = 16.3 mm, rc length = 37.6 mm Crrected fr magnificatin f 2: R = 8.2 mm; arc length = 18.8 mm. ppendix II T calculate stress and elastic mdulus: Incremental elastic mdulus E = (stress/strain) = (S/ L/L) fr Figure 5. Cnsidering the leaflet as a thin cylindrical shell, frm the law f LaPlace, Dwnladed frm by n January 25, 2019 If pints BC lie n an arc f radius R (R = NC), then Sin- 0i B - D - & B C RSin- = ;R Sl n-=_ B Simplifying, we get r & Sin (180 - a) - -^2 Sin, Cs a B stress = PR t where P = pressure gradient acrss the leaflet, R = radius, and t = thickness which is assumed t be 0.5 mm fr the leaflet. In Viv In Diastle Stress Sd = P d x R d Pd = difference between the highest and the lwest pressure gradients in diastle fr a given graph (e.g., Fig. 5) X Pd(mm Hg) X 0.9 (cm) dynes S d = 0.05 (cm) cm Strain L/L O is directly measured: Thus, elastic mdulus in diastle (Ed) can be calculated. In Systle ssuming P S = 10 mm Hg X 10 (mm Hg) X 1 (cm) dynes Stress S S = 0.05 (cm) cm Strain is directly measured and elastic mdulus in systle (E s ) can be calculated. In Vitr In diastle, using the law f LaPlace, stresses at the highest and lwest diastlic pressure gradients were calculated. Similarly, in systle, the stresses fr 10 and 0 mm Hg systlic pressure gradients were calculated. These stresses were pltted n the stressstrain curve t btain the strains and elastic mduli. cknwledgments We are greatly indebted t Dr. G. Wilkins Hubbard and Dr. Kenneth Cherry fr their valuable assistance during peratins.

9 800 CIRCULTION RESERCH VOL. 47, N. 5, NOVEMBER 1980 We are als grateful t the staff members f the Vivarium fr their help. References Clark RE (1973) Stress-strain characteristics f fresh and frzen human artic and mitral leaflets and chrdae tendinae: Implicatins fr clinical use. J Thrac Cardivasc Surg 66: Clark RE, Finke EH (1974) Scanning and light micrscpy f human artic leaflets in stressed and relaxed states. J Thrac Cardivasc Surg 67: Driscl TE, Eckstein RW (1965) Systlic pressure gradients acrss the artic valve and in the ascending arta. m J Physil 209: Harvey JF (1974) Thery and Design f Mdern Pressure Vessels. New Yrk, Van Nstrand Reinhld, p 95 McDnald (1974a) Bld Flw in rteries. Baltimre, Williams & Wilkins, p 199 McDnald (1974b) Bld Flw in rteries. Baltimre, Williams & Wilkins, p 262 McDnald (1974c) Bld Flw in rteries. Baltimre, Williams & Wilkins, p 121 Mundth ED, Wright JEC, usten WG (1971) Develpment f a methd fr stress-strain analysis f cardiac valvular tissue. Curr Tpics Surg Res 3: Rbel SB (1972) Structural mechanics f artic valve, Prsthetic Replacement f the rtic Valve, edited by LR Sauvage. Springfield, 111., Charles C Thmas, p 31 Swansn WM, Clark RE (1974) Dimensins and gemetric relatinships f the human artic valve as a functin f pressure. Circ Res 35: Tan JK, Hlt DL (1976) The effects f sterilizatin and strage treatments n the stress-strain behavir f artic leaflets. nn Thrac Surg 22: Thubrikar M, Harry RR, Nlan SP (1977) Nrmal artic valve functin in dgs. m J Cardil 40: Thubrikar M, Bsher LP, Nlan SP (1979) The mechanism f pening f the artic valve. J Thrac Cardivasc Surg 77: Thubrikar M, Piepgrass WC, Deck JD, Nlan SP (1980) Stresses f natural vs. prsthetic artic valve leaflets in viv. nn Thrac Surg 30: Wright JEC, Ng YL (1974) Elasticity f human artic valve cusps. Cardivasc Res 8: Yamada H (1970) Strength f Bilgical Materials. Baltimre, Williams & Wilkins, p i l l Dwnladed frm by n January 25, 2019