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Effects of Leaflet Stiffness on In Vitro Dynamic BioprostheticHeart Valve Leaflet Shape

Hiroatsu Sugimoto1 and Michael S. Sacks2

1Center for Brand and Product Management, University of Wisconsin, Madison, WI, USA2Department of Biomedical Engineering, Institute for Computational Engineering and Sciences,University of Texas at Austin, 201 East 24th Street, ACES 5.438, 1 University Station, C0200,Austin, TX 78712-0027, USA

AbstractAdvances in the development of replacement heart valves require a deeper understanding of thevalve dynamics. In the present study, dynamic aortic valve (AV) leaflet geometries werequantified in vitro using a structured laser-light imaging system (Iyengar et al., ABME 29(11):963–973, 2001). Native AV leaflets were first imaged under simulated physiological flowconditions within a rigid glass conduit with simulated anatomic sinuses. Next, the valve/glassconduit combination was removed from the loop and immersed in a 0.625% aqueousglutaraldehyde solution at room temperature for 24 h to produce a bioprosthetic heart valve(BHV). The BHV leaflets were then re-imaged under identical flow conditions while kept in thesame position in the glass conduit to minimize artifacts associated with removal/reinsertion of thevalve. We observed that: (1) the native leaflet exhibited small, high frequency shifts in shape; (2)the BHV leaflet demonstrated a more stabile shape, as well as focal regions of prolonged, highcurvature; (3) the BHV leaflet opened and closed faster by ~10 ms compared to native leaflet; (4)in both the BHV and native states, the AV opened from basal region leading to free edge (5) whenclosing, both the native and BHV close with both free edge and circumferential together. The highbending observed in the BHV leaflet correlated with known locations of tissue deteriorationpreviously reported in our laboratory. Thus, in order to minimize leaflet tissue damage, methods ofchemical modification utilized in BHVs that maintain leaflet flexibility are necessary to minimizethe onset and progression of tissue damage. We conclude that leaflet stiffness can have aconsiderable effect on dynamic valve motion, and can induce deleterious bending behaviors thatmay be associated with tissue breakdown and valve failure. Moreover, these unique data canprovide much needed quantitative information for computational simulation of heart valve leafletstiffness on heart valve function.

KeywordsCardiac valve bioprostheses; Imaging; Aortic; Valve; Curvature; Geometry

© 2013 Biomedical Engineering Society

Address correspondence to Michael S. Sacks, Department of Biomedical Engineering, Institute for Computational Engineering andSciences, University of Texas at Austin, 201 East 24th Street, ACES 5.438, 1 University Station, C0200, Austin, TX 78712-0027,USA. [email protected].

CONFLICT OF INTERESTThe authors have no conflicts of interest.

NIH Public AccessAuthor ManuscriptCardiovasc Eng Technol. Author manuscript; available in PMC 2014 March 01.

Published in final edited form as:Cardiovasc Eng Technol. 2013 March ; 4(1): 2–15. doi:10.1007/s13239-013-0117-y.

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INTRODUCTIONBioprosthetic heart valves (BHV) fabricated from biologically derived heterograftbiomaterials continue to be the dominant replacement heart valve technology, either as aconventional prosthetic design or more recently utilizing percutaneous delivery.25,29,33

However, while extending the lives of thousands of patients worldwide, BHV are stilllargely based on empirical designs and involve extensive trial and error testing. Moreover,regardless of the specific design or delivery method, limited long-term fatigue resilienceremains major limitation in the durability of any device utilizing these biomaterials.

Leaflet mineralization, with or without leaflet tearing, 31–33 and mechanicalfatigue10,26,32,38,40 are two primary fatigue processes. Fatigue damage independent ofcalcification has been shown to be a cause of structural damage to the leaflets ofbioprostheses,27 indicating that tissue structural damage independent of calcification ismechanism of deterioration.9,21,26,27 Moreover, after chemical fixation the entireextracellular matrix is highly bonded, inducing a substantial increase in tissue stiffness in thelow strain range,6,15,25,38 as well as essentially eliminating the ability for tissue fiber to sliderelative to each other.

We have utilized custom fatigue devices to subject circumferentially oriented porcine BHVtissue strips to controlled cyclic isolated flexural loading (i.e., without tensile loading).17

Results indicated that flexural rigidity was markedly reduced after only 10 × 106 cycles, andprogressively decayed at a lower rate with cycle number thereafter. Moreover, the against-curvature fatigue direction induced the most damage, suggesting that the ventricularis andfibrosa layers have low resistance to cyclic flexural compressive and tensile loads,respectively. These results underscored that porcine-derived heterograft biomaterials arevery sensitive to flexural fatigue, with delamination of the tissue layers the primaryunderlying mechanism. The delamination behavior was also similar to those found inaccelerated wear tested and in vivo explanted bio-prostheses.21,27,40

Ultimately, heterograft materials are non-viable and by definition have finite durability.However, novel chemical modifications, such as those that retain gly-cosaminoglycans mayhelp in extending durability by mitigating the flexural induced fatigue.6,15,16 While the exactnature of the role of GAGs in cross-linked BHV tissues remains to be elucidated, thesestudies underscore the need to understand flexural deformations that occur in BHV leafletsover the cardiac cycle.

Existing studies on the deformation and shape of the aortic valve leaflets have previouslyexamined closed valve geometry, either in the unloaded static state35,36 or under quasi-staticloading.1,7 Dynamic pericardial BHV strain and geometry have previously examined,13,37

and demonstrated complex deformations and changes in curvatures. We have performedextensive dynamic mitral valve leaflet and annular strain measurements in vivo and invitro.2,8,23,24 While others have performed extensive studies of the native aortic valve invitro,39,42 there are no corresponding studies of the effects of leaflet stiffness (either naturalor induced by chemical processing) on the dynamic flexure of the aortic heart valve over thecomplete leaflet surface. Further, the complex solid/fluid interactions complicates efforts atcomputational modeling, which continue to be limited by inadequate material models andthe requisite validation data.4,5,11,14,18–20,41

Our group has developed a structured light projection technique to quantify heart valvedynamic leaflet shape.13 The imaging system generates a matrix of small (~200 µmdiameter) laser dots projected onto leaflet surface without physical contact; all mounted in aphysiological flow apparatus. The rapidly changing, complex valve geometry justified theneed for a high temporal and spatial resolution approach. Further, the use of a non-

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contacting optical approach assured that there were no restrictions on valve motions andfacilitated imaging of the complete leaflet surface.

The goal of the present study was to investigate the flexural deformations that occur in theBHV leaflets over the cardiac cycle using a structured light imaging system13 over thecomplete cardiac cycle. The mechanical behavior of the component leaflet tissues plays animportant role in determining this response over valve function, especially during opening/closing phases. It is thus important to quantify the effects of leaflet mechanical behavior,especially stiffness. To investigate this effect, we developed a study design that allowedeach valve to be first imaged in the unmodified native state, chemically processed with anaqueous glutaraldehyde solution, then re-imaged under identical flow conditions. Thus, eachvalve acted as its own control. The resulting changes in leaflet motion and shape (using asensitive local surface patch technique to obtain the local surface curvatures) werequantified and implications to prosthetic valve function discussed.

METHODSPhysiological Flow Loop and Leaflet Visualization

A detailed description of the integrated flow loop imaging system, including the integratedcamera/boroscope imaging system, has been previously presented. 13 Briefly, a pulsatileflow loop was used capable of reproducing physiological aortic pressure wave-forms, withnormal saline used as the flow loop medium. Flow parameters were set to 60 beats perminute, systolic and diastolic pressures (140 and 80 mmHg, respectively), 5 L per minutesimulated cardiac output with a 150 mmH2O atrial reservoir as preload pressure (Fig. 1a).

Attached to the flow loop was a structured light projection/dual camera imaging system to3D reconstruct valve leaflet surface geometry. The system consisted of a 10 mW diode laseroutfitted with an optical pattern generator head which illuminated leaflet surfaces for aperiod of 500 µs using a 19 × 19 dot matrix pattern (dot diameter ≤0.2 mm, Fig. 1b). Thetwo CCD cameras, with 60 degrees angle line of sight with respect to each other, createdtwo simultaneous images of the leaflet surface (Fig. 2a). Twenty-four such images wereacquired for each valve at different times of the cardiac cycle, with higher densityacquisition during open/closing phases (Table 1; Fig. 1a). Each image had an average of 140laser dots visible on the leaflet, ranging from 90 to 190 since the leaflet area change over thecardiac cycle (Fig. 2). Note that the cameras acquired one frame (at 30 Hz) at a time, startedjust before the laser was switched on. The net effect was to obtain a 500 µs image (since therest of the time the flow loop was completely dark) of the valve at the specified offset time,which was observed to be sufficiently short to capture valve motion as evidenced by a lackof blurring of the laser dots.

Valve PreparationA total of five porcine aortic heart valves were tested, all 25 ± 1 mm in diameter. Uponarrival from the abattoir, each aortic root was trimmed to leave only the necessary aortictissue to maintain the valvular structure to allow for maximum leaflet visibility. A metalstent used in medical grade replacement heart valves (Carpentier valve, Edwards Lifesciences) was then gently slipped over the aortic wall remnant. The commissure regions ofthe stent were sutured with 3-0 silk suture (Ethicon, USA) aligned with the commissure ofthe valve. The base of valve was then secured to the metal stent with sutures. The preparedvalve was then secured onto a plastic ring made out of Tygon tubing, which fits inside thePyrex aortic sinus. Each valve was oriented so that its non-coronary leaflet was vertical inthe view chamber and completely visible by both cameras and imaged, due to its largestarea.

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After the native valve was imaged over the complete cardiac cycle, the valve together withthe viewing chamber was removed intact from the rest of the flow loop. Each valve was thenimmersed in 0.625% glutaraldehyde aqueous solution while statically pressurized at ~4mmHg for a period of 24 h. Pressurization was achieved by maintain a water column of 10cm in height above the valve. Care was taken not to move or distort the position of the valvewithin the viewing chamber. After chemical treatment, the viewing chamber was replacedback onto the flow loop and the identical imaging protocol was repeated to acquire 3Dsurfaces at identical time points and flow conditions as for the native valve state. Note thatcomparison of native and BHV valve pressure and flow waveforms indicated that both werenearly identical (Fig. 1a).

3D Reconstruction and Surface Meshing, and Leaflet Dimensional ChangesThe 3D spatial positions of each laser dot were recovered using Direct LinearTransformation from the corresponding 2D coordinates, which were digitized from thestereo image pairs (Fig. 2a).13 The resulting 3D spatial positions were used to construct asurface mesh using custom software developed by Shimada et al.34 to construct a contiguoustriangular mesh using the laser dots as the vertices(Fig. 2b). The resulting 3D triangularmesh thus completely defined the surface of the leaflet at each acquisition point in thecardiac cycle. The non-coronary leaflets from a total of five porcine aortic valves weretested. Next, to facilitate basic comparisons in leaflet shape, we examined key changes inleaflet dimensions, including change in commissural angle and leaflet excursion fromopened to closed, were quantified. Note that leaflet excursion was estimated as the distancethe center of the leaflet travels from fully opened to fully closed.

Surface Curvature CalculationsA major focus of this study was quantification of the time-course surface geometric eventsof the leaflets during over the cardiac cycle. This requires knowledge of the leaflet surfacecurvatures over entire leaflet surface. While we have previously utilized sophisticatedsurface fitting techniques for heart valve motion,37 in pilot tests we found that a localsurface patch technique22 approach proved to be more sensitive in detecting subtle changesin local curvature.

To accomplish this, the local surface was parameterized using surface patch methoddescribed in Sacks et al.22 from the reconstructed mesh at each time point. The methodutilizes a bi-quadric surface defined in a local neighborhood about each mesh point,parameterized in terms of the local tangent plane coordinates xα, α = 1, 2. The positionvector r is parameterized using

(1)

A search radius of 2 mm was used resulting in a surface patch size of 10–40 nodes (mean 25nodes), with the constants a, b, and c determined for each node using standard regressionmethods.22 Using standard formulae,12 the metric g and curvature b tensors can bedetermined for each local surface using

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(2)

where

The resulting physical components of the curvatures along normal sections aligned to thecoordinate directions are given by

(3)

The principal curvature magnitudes were determined at the center of each surface patch (i.e.,

at the current node) using . It should be noted that we chose aninward directed normal (i.e., directed towards the aortic side) to allow for positive signedvalues for bI and bII when the valve was fully closed. The corresponding principal curvatureunit vector directions eI and eII were determined at the center of each surface patch using

(4)

where eI,II were initially referenced to the local tangent plane coordinates then mapped backto the valve leaflet (or laboratory) coordinate system.

RESULTSOverall Surface Geometric Characteristics

3D reconstruction results demonstrated high fidelity from cycle-to-cycle, as evidenced byvirtually identical reconstructions form one cycle to the next (Fig. 3). Of particular note wasthe ability to recover the entire aortic-side surface at both end-diastolic and full systolic flowstates (Fig. 3a and 3b), even with the large leaflet deformations present. Positional stabilitywas also confirmed by both the consistent 3D locations of the commissures and end-

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diastolic surfaces (Fig. 3c). We also noted the presence of pronounced bends in the leafletwere accurately recovered by the present method (Fig. 3b).

The resultant 3D reconstructed surfaces also demonstrated complex shape changes over thecomplete cardiac cycle (Fig. 4). The native valve opened earlier and closed later whencompared to BHV valve. Native leaflets also continuously shifted in shape, whereas theBHV leaflet opens and maintains the same shape until closure. Of particular note was thatwhile in the closed configuration all leaflet surfaces were smooth, BHV leaflets exhibitedregions of significant bending. Moreover, these regions of bending persisted between t = 360and 630 ms; a 270 ms period. Of particular note was the tendency for the BHV valves to“snap” shut within a time period of ~10 ms, a behavior not observed in the native valves(Fig. 4, rightmost column, time 630–640 ms). We also noted that the measured change incommissural angle was ~80° and the total leaflet excursion ~10 mm for both native andBHV states, with negligible differences between the two states (Table 2). No statisticaldifferences were observed between any group (p <0.05). Thus, chemical fixation does notaffect the starting and ending geometry of the aortic valve leaflet.

Since the time-course changes in 3D leaflet surfaces are complex, we also examined theleaflet along the free edge (Fig. 4).While the native leaflets opened in an overall smooth andorderly fashion, their closing behavior was more complex. In contrast, BHV leaflets openedsuddenly, in a snap-like manner, as well as demonstrating focal regions of high curvature,whereas the native leaflet opened more symmetrically.

Surface CurvatureAs noted in Fig. 4, native leaflets tended to open in an approximately symmetric manner,whereas as the BHV leaflet often exhibited focal regions of high curvature (arrow, Fig. 5).We noted that both the native and BHV leaflets experienced an approximately 0.33 mm−1

total change in circumferential curvature that did not exhibit any statistical differences (p <0.05, Table 2).

Overall, the surface shape changes were best characterized by the minor curvature bII (Fig.6). Overall, the leaflets exhibited an expected change in sign of bII as the valve opened. Ofparticular note, portions of the BHV leaflet with severe bending consistently have bendingin the circumferential direction (Fig. 6, arrows). The native valve has uniform minorcurvature and direction of bending shifts as the cycle progresses. Generally, while the nativeleaflet experienced localized bending, the intervals were short and not isolated to singlelocation during the cardiac cycle. In contrast, for the BHV leaflet locations of high bendingwere consistently on one side of the valve during fully opened phase. This area of highbending was typically at least 10% in area and continued for ~200 ms.

While informative, since the observed spatial and temporal changes in surface curvaturewere complex, computation of a mean changes in curvature does not fully capture theresulting shape (Table 3). We thus extended our statistical analysis to determine frequencyhistograms of the principal curvatures over the leaflet surface (Fig. 7). For bI, most of thevalve was positively curved, with a skew towards positive direction, and for bI the exactopposite occurred. As the native valves opened the major curvature shifted from positive tonear neutral value, indicating the leaflets tend to flatten out, whereas for BHV valves it didnot. In terms of minor curvature, native valve exhibited a more curved surface when open,and BHV valve shows a complete reversal in curvature as it opens. The BHV leaflets showtwice the amount of change in peak frequency. Furthermore, when the BHV valve opens, theminor curvature plot flattens out, thus indicating the broad range of bending that occurs on asingle leaflet.

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DISCUSSIONDespite the knowledge that leaflet motion plays a fundamental part of any investigation ofnative and prosthetic heart-valve mechanics, there have been relatively few studies toquantify aortic valve shape due to practical limitations. While current high-speed video(operating at > 1000 frames/s) or strobe photography are usually sufficient to detect obviousdesign flaws such as leaflet contact with other valve components, more sophisticatedtechniques are necessary to resolve subtler aspects such as bending and wrinkling. Given thecomplexities reported herein of the observed valve motion, the present study underscores theneed for additional experimental investigations of heart valve dynamics. This is especiallytrue considering that current computational approaches directed towards understandingvalve dynamics clearly will require such information for problem definition and modelvalidation.

Key FindingsThe current experimental design allowed us to compare the effects of chemical fixation onvalve leaflet kinematics under controlled simulated hemodynamic conditions. We observedseveral key differences in the dynamic behavior of the native and BHV leaflets. Whilenative leaflets opened in a spatially and temporally complex but overall smooth manner,BHV leaflets tended to stay open and maintain the same overall shape until it rapidly closed(Figs. 4, 5, 6). The increase in tissue rigidity also limited fluttering often observed in thenative valve. BHV leaflets also demonstrated significant bending on one side of the leafletwhile the middle and other side of the valve stayed flat. Native leaflets would experiencesimilar severe bending, but the location would shift during cardiac cycle. While period ofvalve opening was the same, the action time to transition from open to close and vice versawas shorter. Specifically, it took 60 and 40 ms for the native valve to open and close,respectively, and for the BHV valve 40 and 30 ms, respectively. Note that both valves wouldopen beginning from the basal region of valve leading to the free edge.

Implications for Valve DurabilityIn two previous studies, we quantified collagen fiber disruption in porcine BHVs subjectedto either in vitro accelerated wear testing (AWT)28 or explanted from patients after severalyears of in vivo function for non valve related problems27 (Figs. 8a and 8b). Collagen fiberdisruption was quantified as an increase in the skew of the collagen fiber distribution, due toshearing of the fibers (Figs. 8c and 8d).17 When compared to in vitro AWT and humanexplanted leaflets, the locations of persistent bending were located in similar regions of theleaflet (Figs. 8e and 8f). Note that the regions of high curvature experienced by the leafletexperiences were quantified by the minor curvature bII, since this region of the leafletsurface bends away from the inward directed surface normal and is thus negative (i.e., lessthan the major curvature bI).

The similarity in location to observed patterns of tissue damage in both in vitro acceleratedwear tested and human explants suggests that the pronounced stiffening of the valve leaflettissue is a significant source of leaflet tissue damage. While the exact mechanisms have tobe worked out, we have noted similar sensitivity to flexural (i.e., bending) induced damagein vitro.17 While not definitive, the results of the present study suggest that the substantiallyhigher flexural rigidity induces the abnormal leaflet dynamics, which may contribute toregions of focal flexural fatigue. This hypothesis is supported by our recent study whereinporcine-derived aortic valve heterograft biomaterials were found to be very sensitive toflexural fatigue,17 with delamination of the tissue layers the primary underlying mechanism.This appears to be in contrast to pericardial BHV, wherein high tensile stresses areconsidered to be the major cause of structural failure.

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LimitationsThe optical measurement system utilized in this study used non-fixed laser points to quantifyleaflet surface geometries, and thus cannot measure strain. It should be noted that due to thegeometry of the aortic valve root, a region of ~1 mm in height at the basal attachment of theleaflet was not always visible when the valve was fully closed. This had minimal impact onthe curvature studies as the area accounted for less than 2%of total leaflet. We should alsonote that a key difference was that the valve roots were imaged using a Pyrex aortic root,which was not distensible. Since the focus of the present study was on bioprosthetic valvedynamics, this will not directly affect our results. However, the results for the native leafletsshould not be taken as what occurs physiologically. Rather, they represent the upper boundof leaflet deformation that can occur when the surrounding root deformations are fullyrestricted. It should be noted that most of the radial stretch likely occurs in the coaptationregion, between the nodulus of Arantii and the free edge, which has been shown to be morehighly compliant in radial direction compared to the rest of the leaflet.3 Finally, we note thatthe present study will have to be confirmed in vivo with 3D ultrasound or related imagingtechnologies to verify these results in implanted BHV.

SummaryIn the present study, AV leaflet 3D geometry was quantified using a non-contacting imagingsystem over the complete cardiac cycle. We observed that: (1) the native leaflet exhibitedsmall, high frequency shifts in shape; (2) the treated leaflet demonstrated a more stabileshape, characterized by focal regions of prolonged, high curvature; (3) the BHV leafletopens and closes faster by ~10 ms compared to native leaflet; (4) for both untreated andtreated states, the aortic valve opened from basal region leading to free edge, and (5) duringclosing, both the untreated and treated tissues close with both free edge and mid-bellyregions in approximate synchrony. We conclude that leaflet stiffness has a considerableeffect on dynamic valve motion, and induces deleterious bending behaviors that may beassociated with tissue breakdown and valve failure.

These findings point towards the need for the development of chemical fixation technologiesthat minimize flexure induced damage to extend porcine heterograft biomaterial durability.These results clearly indicated that increased leaflet stiffness might induce flexural modefailures in the leaflet tissue. This result has implications for current efforts to improveporcine bioprosthetic valves. Clearly, efforts aimed in developing novel chemical fixationtechnologies should not only be focused on reducing mineralization, but also in minimizingleaflet stiffness.15,16,30

AcknowledgmentsThis research was supported by NIH grants HL-063026, HL-070969, and HL-108330.

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38. Vyavahare N, Ogle M, Schoen FJ, Zand R, Gloeckner DC, Sacks MS, et al. Mechanisms ofbioprosthetic heart valve failure: fatigue causes collagen denaturation and glycosaminoglycan loss.J. Biomed. Mater. Res. 1999; 46:44–50. [PubMed: 10357134]

39. Weiler M, Yap CH, Balachandran K, Padala M, Yoganathan AP. Regional analysis of dynamicdeformation characteristics of native aortic valve leaflets. J. Biomech. 2011; 44(8):1459–1465.Epub 2011/04/05. [PubMed: 21458817]

40. Wells SM, Sellaro T, Sacks MS. Cyclic loading response of bioprosthetic heart valves: effects offixation stress state on the collagen fiber architecture. Biomaterials. 2005; 26(15):2611–2619.[PubMed: 15585264]

41. Wipperman F. On the fluid dynamics of the aortic valve. J. Fluid Mech. 1985; 159:487–501.

42. Yap CH, Kim HS, Balachandran K, Weiler M, Haj-Ali R, Yoganathan AP. Dynamic deformationcharacteristics of porcine aortic valve leaflet under normal and hypertensive conditions. Am. J.Physiol. Heart Circ. Physiol. 2010; 298(2):H395–H405. Epub 2009/11/17. [PubMed: 19915178]

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FIGURE 1.(a) Representative generated pressure and flow patterns recorded from flow loop, with thevertical lines indicating the image acquisition time points for both native and BHV valvestates, showing excellent reproducibility. (b) Overhead image of the valve within the Pyrexconduit shown the boroscope imaging tubes and index matching fluid.

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FIGURE 2.(a) Representative image pairs showing the overall laser dot densities showing the largenumber of data points defining the leaflet surface and (b) resulting 3D reconstruction. Notethe subtle surface features apparent in the reconstructed surface. Also shown is the locationof the free edge and large dots indicating the location of the commissures.

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FIGURE 3.Representative BHV reconstructions at end diastole (red) and end systole (green) states inboth the (a) transverse and (b) axial views. In (c) is an end diastolic image from twosuccessive simulated cardiac cycles with the first surface in blue and the second cycle ingrey showing excellent reproducibility. As in Fig. 2, the location of the free edge isidentified along with large dots indicating the location of the commissures. Also shown isthe location of focal high curvature region (arrow) in (b).

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FIGURE 4.Sequence of shaded surface renderings of native and BHV leaflets from the same valvegoing through a complete opening-open-closing cycle. View is axial, looking into the flow.In addition to the observed persistent bend occurring in the BHV leaflet (arrow), the veryrapid “snap-like” closing within 10 ms can be seen highlighted in time intervals between630 and 640 ms.

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FIGURE 5.Cross sectional views of the free edge of a typical valve when opening, with the numbersindicating the frame time in ms. The native valve’s free edge section shows a relatively earlyopening and smoothly progresses to fully open state at 360 ms. Majority of the bendingoccurs to the left and right, where the middle stays flat. The BHV leaflet however staysclose longer and opens faster. Arrow points to a focal high curvature region that occurredonly in the BHV leaflet. Majority of the bending occurs to the left and right, where themiddle stays flat. The BHV leaflet however stays closed longer and opens faster. Arrowpoints to high bending that occurred only in the BHV valves.

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FIGURE 6.Plot of native and BHV leaflet surface showing the minor principal curvature bII (in mm−1)over a complete simulated cardiac cycle. Note for native leaflet, the location of highcurvature shifts during cycle, where as the BHV leaflet remains the same. Region of highcurvature in the BHV leaflet (arrow) occupied approximately 10% of the total leafletsurface.

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FIGURE 7.Major and minor curvature histograms for all valves averaged at key time points over thesimulated cardiac cycle. In general, the BHV valve demonstrated larger regions of highercurvatures, as evidenced by shift in histogram toward larger curvature magnitudes for bothprincipal curvatures.

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FIGURE 8.Quantified collagen fiber disruption in porcine BHVs either (a) subjected to in vitro AWT28

or (b) explanted from patients after several years of in vivo function for non valve relatedproblems.27 Here, regions of structural damage to the collagen fiber network are indicated asblack or hatched areas (arrows).These damaged regions were detected by the presence ofsubstantial skew, as shown in (c, d). Here, extracted collagen fiber distributions fromstructurally intact and damage regions show distinct increases in the skew, due to shearingof the fibers shown schematically in (d).17 The spatial locations of persistent bending in thetreated leaflets compared untreated were located in similar regions of the leaflet (e, f). Anarrow also shows regions of high curvature experienced by the leaflet.

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Sugimoto and Sacks

TAB

LE 1

Imag

e ac

quis

ition

tim

e sc

hem

a

Fra

me

Tim

e (m

s)P

hase

Fra

me

Tim

e (m

s)P

hase

Fra

me

Tim

e (m

s)P

hase

10

Clo

sed

935

0O

pen

1762

0C

losi

ng

220

0C

lose

d10

360

Ope

n18

630

Clo

sing

325

0C

lose

d11

400

Ope

n19

640

Clo

sing

430

0O

peni

ng12

450

Ope

n20

650

Clo

sing

531

0O

peni

ng13

500

Ope

n21

660

Clo

sed

632

0O

peni

ng14

550

Ope

n22

700

Clo

sed

733

0O

peni

ng15

600

Ope

n23

750

Clo

sed

834

0O

peni

ng16

610

Clo

sing

2480

0C

lose

d


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Sugimoto and Sacks

TAB

LE 2

Key

dim

ensi

onal

cha

nges

fro

m th

e fu

lly c

lose

d to

ful

ly o

pene

d po

sitio

ns f

or th

e fi

ve v

alve

s st

udie

d.

Val

ve

Cha

nge

in c

omm

issu

rean

gle

untr

eate

d(°

)

Cha

nge

in c

omm

issu

rean

gle

trea

ted

(°)

Lea

flet

excu

rsio

nun

trea

ted

(mm

)

Lea

flet

excu

rsio

ntr

eate

d (m

m)

b cir

cun

trea

ted

clos

ed (

mm

−1)

b cir

cun

trea

ted

open

ed (

mm

−1)

Δb c

irc

untr

eate

d(m

m−1

)

b cir

ctr

eate

dcl

osed

(m

m−1

)

b cir

ctr

eate

dop

ened

(m

m−1

)

Δb c

irc

trea

ted

(mm

−1)

178

.579

.59.

3112

.41

0.11

2−

0.17

20.

284

0.19

0−

0.07

60.

266

271

.094

.010

.88

10.4

80.

200

−0.

083

0.28

30.

407

−0.

102

0.50

9

382

.568

.011

.48

6.93

0.25

9−

0.09

00.

349

0.27

2−

0.16

10.

433

491

.571

.010

.76

4.96

0.12

6−

0.21

90.

345

0.11

0−

0.13

50.

245

590

.069

.015

.81

11.6

40.

234

−0.

146

0.38

00.

173

−0.

117

0.29

0

Mea

n ±

SE

M82

.70

± 3

.78

76.4

0 ±

4.8

711

.65

± 1

.10

9.28

± 1

.43

0.18

6 ±

0.0

29−

0.14

2 ±

0.0

260.

328

± 0

.019

0.23

0 ±

0.0

51−

0.11

8 ±

0.0

140.

349

± 0

.052

Not

e th

at th

e co

mm

issu

re a

ngle

rep

rese

nts

the

chan

ge in

ang

le f

rom

ful

ly c

lose

d to

ful

ly o

pene

d, w

ith th

e m

ean

for

both

leaf

let s

ides

pre

sent

ed f

or e

ach

leaf

let.

Lea

flet

exc

ursi

on w

as e

stim

ated

as

the

dist

ance

the

poin

ts in

the

cent

ral b

elly

reg

ion

disp

lace

d. T

he c

ircu

mfe

rent

ial c

urva

ture

bci

rc r

epre

sent

s th

e ci

rcum

fere

ntia

l sec

tion

curv

atur

e at

the

mid

sec

tion

of th

e va

lve

(see

Eq.

(3)

). T

here

wer

e no

stat

istic

ally

sig

nifi

cant

dif

fere

nces

bet

wee

n th

e op

en a

nd c

lose

d st

ates

for

eac

h pa

ram

eter

usi

ng p

≤ 0

.05.


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Sugimoto and Sacks

TAB

LE 3

Maj

or (

b I)

and

min

or (

b II)

pri

ncip

al c

urva

ture

val

ues

(in

mm

−1 )

for

unt

reat

ed a

nd tr

eate

d le

afle

ts a

t key

tim

e po

ints

(n

= 5

).

Pre

-ope

nO

peni

ngF

ully

ope

nC

losi

ngC

lose

d

Unt

reat

ed

bI

M

ean

0.21

80.

154

0.16

80.

215

0.23

0

S

tand

ard

devi

atio

n0.

133

0.16

10.

171

0.18

80.

120

S

kew

0.88

70.

956

0.98

51.

144

1.07

9

M

ode

0.10

00.

000

0.00

00.

000

0.10

0

Tre

ated

bI

M

ean

0.22

70.

222

0.18

80.

227

0.24

0

S

tand

ard

devi

atio

n0.

115

0.16

10.

155

0.16

50.

122

S

kew

1.10

71.

382

1.21

11.

380

1.14

6

M

ode

0.10

00.

000

0.00

00.

000

0.10

0

Unt

reat

ed

bII

M

ean

−0.

072

−0.

125

−0.

120

−0.

114

−0.

042

S

tand

ard

devi

atio

n0.

140

0.12

00.

120

0.13

60.

129

S

kew

−0.

512

−0.

207

−0.

165

−0.

105

−0.

324

M

ode

0.00

0−

0.10

0−

0.10

0−

0.10

00.

000

Tre

ated

bII

M

ean

−0.

014

−0.

089

−0.

111

−0.

114

−0.

019

S

tand

ard

devi

atio

n0.

129

0.15

70.

181

0.17

60.

139

S

kew

−0.

107

0.07

2−

0.06

0−

0.07

8−

0.13

4

M

ode

0.00

0−

0.10

0−

0.10

0−

0.10

00.

000


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