Mechanics of the Mitral Valve Michael S. Sacks Strut ... · Muralidhar Padala WallaceH.CoulterDepartmentofBiomedical Engineering, GeorgiaInstituteofTechnologyandEmory University,

1

cvcdanLc

N

mp

J

Downloa

Muralidhar PadalaWallace H. Coulter Department of Biomedical

Engineering,Georgia Institute of Technology and Emory

University,315 Ferst Drive,

Atlanta, GA 30332-0535e-mail: [email protected]

Michael S. SacksDepartment of Bioengineering,

University of Pittsburgh,Pittsburgh, PA 15219;

McGowan Institute for Regenerative Medicine,University of Pittsburgh,

Pittsburgh, PA 15219e-mail: [email protected]

Shasan W. Lioue-mail: [email protected]

Kartik Balachandrane-mail: [email protected]

Wallace H. Coulter Department of BiomedicalEngineering,

Georgia Institute of Technology and EmoryUniversity,

315 Ferst Drive,Atlanta, GA 30332-0535

Zhaoming HeDepartment of Mechanical Engineering,

Texas Tech University,P.O. Box 41021,

Lubbock, TX 79409-1021e-mail: [email protected]

Ajit P. YoganathanWallace H. Coulter Department of Biomedical

Engineering,Georgia Institute of Technology and Emory

University,315 Ferst Drive,

Atlanta, GA 30332-0535e-mail: [email protected]

Mechanics of the Mitral ValveStrut Chordae Insertion RegionInterest in developing durable mitral valve repair methods is growing, underscoring theneed to better understand the native mitral valve mechanics. In this study, the authorsinvestigate the dynamic deformation of the mitral valve strut chordae-to-anterior leaflettransition zone using a novel stretch mapping method and report the complex mechanicsof this region for the first time. Eight structurally normal porcine mitral valves werestudied in a pulsatile left heart simulator under physiological hemodynamic conditions�120 mm peak transvalvular pressure, 5 l/min cardiac output at 70 bpm. The chordalinsertion region was marked with a structured array of 31 miniature markers, and theirmotions throughout the cardiac cycle were tracked using two high speed cameras. 3Dmarker coordinates were calculated using direct linear transformation, and a secondorder continuous surface was fit to the marker cloud at each time frame. Average arealstretch, principal stretch magnitudes and directions, and stretch rates were computed,and temporal changes in each parameter were mapped over the insertion region. Stretchdistribution was heterogeneous over the entire strut chordae insertion region, with thehighest magnitudes along the edges of the chordal insertion region and the least alongthe axis of the strut chordae. At early systole, radial stretch was predominant, but by midsystole, significant stretch was observed in both radial and circumferential directions.The compressive stretches measured during systole indicate a strong coupling betweenthe two principal directions, explaining the small magnitude of the systolic areal stretch.This study for the first time provides the dynamic kinematics of the strut chordae insertionregion in the functioning mitral valve. A heterogeneous stretch pattern was measured,with the mechanics of this region governed by the complex underlying collagen architec-ture. The insertion region seemed to be under stretch during both systole and diastole,indicating a transfer of forces from the leaflets to the chordae and vice versa throughoutthe cardiac cycle, and demonstrating its role in optimal valve function.�DOI: 10.1115/1.4001682�

Keywords: mitral valve, anterior leaflet, chordae tendineae, dynamic strainmeasurement, collagen fiber orientation

IntroductionThe mitral valve �MV� is the left atrioventricular valve that

ontrols blood flow between the left atrium �LA� and the leftentricle �LV�. It has a parachute like structure whose opening andlosing dynamics are governed by the transvalvular pressure gra-ient and a complex force balance between the annulus, leaflets,nd chordae tendineae, as shown in Fig. 1�a�. During diastole, aegative transvalvular pressure gradient between the LA and theV opens the valve, allowing diastolic LV filling. Systolic myo-ardial contraction increases LV pressure, providing the momen-

Contributed by the Bioengineering Division of ASME for publication in the JOUR-

AL OF BIOMECHANICAL ENGINEERING. Manuscript received September 3, 2009; finalanuscript received April 14, 2010; accepted manuscript posted April 28, 2010;

ublished online June 15, 2010. Assoc. Editor Rudolph Gleason.

ournal of Biomechanical Engineering Copyright © 20

ded 11 Aug 2010 to 140.254.87.101. Redistribution subject to ASM

tum for the valve leaflets to move toward the mitral annular planeuntil the leaflets coapt/overlap. As the leaflets move basally, thefinite length and elasticity of the chordae tendineae restricts theleaflets from prolapsing into the LA. Thus, proper leaflet closureand coaptation geometry are determined largely by the balance ofcoaptation forces due to transvalvular pressure gradient andchordal tethering forces �1,2�.

The strut chordae are the two thickest chordae that insert intothe ventricular surface of the leaflets, midway between the annu-lus and the free edge, as shown in Fig. 1�b�. The strut chordaeplay an important role in the mitral valve leaflet kinematics andleft ventricular function �3,4�. During systolic valve closure, thestrut chordae maintain good anterior leaflet curvature, and duringdiastole restrict the anterior leaflet from obstructing the left ven-
tricular outflow tract. Also, the strut chordae are thought to main-
AUGUST 2010, Vol. 132 / 081004-110 by ASME

E license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

tpcclebtiicewwa

iWicsMmf

2

fTtsstfttnvrhdmcAbtm

ow

0

Downloa

ain annular-ventricular continuity, which, if disturbed, may im-air left ventricular function. These chordae have a thick,ylindrical collagenous core that extends from the base of thehord at the papillary muscle head to the insertion zone in theeaflet, where the cylindrical core fans out into a planar collag-nous leaflet structure. At the insertion zone, the collagen distri-ution is spatially heterogeneous, resulting in complex mechanicshat are not completely understood. Chen et al. �5� were the first tonvestigate the mechanics of the chordal insertion region underdealized biaxial loading conditions and proposed a three coeffi-ient phenomenological strain energy density function to fit thexperimental results. However, the strain energy density functionas derived based under equibiaxial loading conditions alone,hich likely does not represent the physiological deformations

nd multidimensional loading of the valve.The fact that these data do not exist encourages investigation

nto understanding the complex mechanics of this transition zone.e know this region to be structurally complex and functionally

mportant since it “spreads” the stresses of the uniaxially loadedhordae to the multiaxially loaded planar leaflet. Thus, in thistudy we sought to investigate the dynamic strain behavior of the

V anterior strut chordae insertion using native mitral valvearked with a dense, local marker array that would ensure a faith-

ul representation of the local deformation.

Methods

2.1 Valve Preparation. Fresh porcine hearts were obtainedrom the local abattoir and transported to the laboratory on ice.he LA was excised, providing an en face view of the MV, and

he valve size was measured using a standard annuloplasty ringizer �Edwards Lifesciences LLC, Irvine, CA�. Porcine valves ofize 28 were used in this study, as they best represent the size ofhe valves in humans. The valves were then carefully extractedrom the hearts with the annular and subvalvular components in-act, and stored in isotonic saline solution �0.9% vol/vol� for lesshan 24 h before being sewn onto ring made of Dacron® in theative �i.e., without chemical fixation� state. Upon suturing thealve onto a planar D-shaped annulus and sewing small plasticings on the PMs, the valve was mounted in the Georgia Tech lefteart simulator shown in Figs. 2�a�–2�c�. Thirty-one miniatureots ��300−500 � and intermarker distance of 2 mm� werearked on the anterior strut chordae insertion region using a bio-

ompatible dye �Shandon tissue dye, Thermo Inc., Milford, MA�.triangular pattern of markers were used, extending from the

ase of the anterior leaflet at the strut chordal insertion region tohe cylindrical region on the strut chordae shown in Fig. 3�a�. This

Fig. 1 „a… An intact mitral valve in a sectioned heart showinantero-lateral papillary muscle „ALPM…, and postero-medial pannular and subvalvular components with the red arrows sh

arker arrangement allowed for surface strain measurement over

81004-2 / Vol. 132, AUGUST 2010


the entire chordal insertion region and helped in delineating theheterogeneity in the surface strains from the chord to the leaflet.

2.2 Hemodynamic Testing. The MV was mounted into thein vitro left heart simulator and tested at a heart rate of 70 bpm,cardiac output �CO� of 5.0 liters per minute, a peak transvalvularpressure gradient of 120 mm Hg, and a systolic duration of 290ms. CO was measured with an electromagnetic flow probe �FM501D, Carolina Medical Electronics, Inc., King, NC�. LV pressureand transmitral pressure �LV pressure−LA pressure� were mea-sured with a differential pressure transducer �DP9-40, ValidyneEngineering Corp., Northridge, CA�, and both were recorded us-ing an online data acquisition system �DAQCard-1200, NationalInstruments Corp., Austin, TX�.

2.3 Image Acquisition. Two high speed cameras �A504K,Basler Inc., Germany� of 1280�1024 pixel resolution wereplaced at approximately 30 deg from each other at the back of thetransparent left ventricle, focused on the chordae insertion region.The motion of the strut chordae insertion region during the entirecardiac cycle was recorded as a series of TIFF® images at a speedof 250 frames per second using an image grabber �EPIX CL3SD,Buffalo Grove, IL�. The two cameras and hemodynamic data ac-quisition were triggered simultaneously to synchronize the imageswith the transvalvular pressure. The valves were tested under nor-mal PM positions, which were defined as perpendicular to theannulus plane with minimal tension in the chordae tendineae.

2.4 Surface Strain Calculations. The strain measurementmethods are similar to those reported previously to measure leafletstrains by our laboratory �6–8�. Briefly, custom MATLAB

® softwarewas used to digitize the markers and obtain the �x ,y� pixel coor-dinates of each marker in the acquired images. Direct linear trans-formation was used to reconstruct the array of 3D spatial coordi-nates, using a calibration cube of known dimensions. To computethe strain field, a custom MATHCAD program was used �PTC,Needham, MA� to transform the 3D coordinates into an in-planecoordinate system �u-v-n� based on a tangent plane. The u-v co-ordinates were then projected onto the deformed surface, and thus,formed a convective coordinate system that deforms with the sur-face. The origin of the u-v-n system was located at the center ofthe marker array, with corresponding unit vectors, eu, ev, and en.In this study, eu was defined parallel to markers 1 and 7, en, whichis the surface normal, was computed using en=euXem4−m31, whereem4−m31 is the unit vector parallel to markers 4 and 31, and ev

n u

he mitral annular plane, anterior leaflet, chordae tendineae,illary muscle „PMPM…; „b… an excised mitral valve with intacting the strut chordae insertion regions

g tap

=e Xe . Each marker x-y-z coordinate triplet for each frame was

Transactions of the ASME


sc

ligceeficc

J

Downloa

ubsequently translated and rotated into the reference frame u-v-noordinate system.

To compute for the strain field within the insertion region de-imited by the markers, we used a finite element-based surfacenterpolation. The position of any marker in the reference state isiven by R0�u ,v�=ueu+vev+nen, where n represents the normalomponent. To fit the marker array, a C2 cubic hermite shapelement was used for each displacement component. The refer-nce surface fit gave the initial shape of the insertion region de-ned by the 31 marker array. The metric tensor in the referenceonfiguration g0 was computed from R0 using the formulae dis-ussed in a previous paper �7,9�. To determine the strains for each

Fig. 2 „a… Schematic of the Georgia Techsutured onto a silicone annulus with twmuscles, ready for mounting into the simsimulator

Fig. 3 „a… Photograph of the mitral valve wmarked using tissue dye; „b… schematic ofthat were used for data processing. The lef
leaflet while the right ridge is closer to the co
ournal of Biomechanical Engineering


frame f and component i= �1,3�, the displacements for eachmarker di

f were first computed as the difference between the ref-erence and deformed spatial marker positions. Thus, the positionvector for frame f of any point on the deformed surface is givenby Rf�u ,v�=d1

f eu+d2f ev+d3

f en+R0�u ,v�, where dif�u ,v� is the fit-

ted displacement field for the axial component i in the currentframe f . From Rf, the components of the metric tensor gf in thedeformed configuration were computed, and the resulting Almansi�i.e., Eulerian� finite strain tensor for each frame was determinedusing e=0.5�gf −g0�. The principal values of e were expressed asprincipal stretches �1 and �2, with a corresponding principal angle

t heart simulator; „b… a native mitral valvelastic rings attached onto the papillary

tor; and „c… functional mitral valve in the

the anterior strut chordal insertion regionsubzones in the chordal insertion regionge is closer to the A2 cusp of the anterior

lefo pula

iththet rid

mmissures.

AUGUST 2010, Vol. 132 / 081004-3


�ruwa

Hwpl

scaeorvsnd

3

Psiae

icr

0

Downloa

p referred to the u-axis of the reference state. The areal stretch,epresenting the total change in the leaflet area, was computedsing �=�1��2. The corresponding stretch rates for each frameere computed using a three-point numerical derivate algorithm

nd expressed as percent per second.

2.5 Collagen Orientation in the Chordal Insertion Region.igh spatial resolution small angle light scattering �SALS� scansere taken from the insertion region �7� to gain insight into thelanar fibrous structure of the insertion region using the estab-ished methods �10�.

2.6 Statistical Methods. For each valve, the leaflet strain,train rate, and principal vectors were calculated over 1 completeardiac cycle. Since data acquisition was triggered identically forll the valves, the temporal strain data were averaged over theight valves. At each time point the mean �1 standard deviationf the calculated strain, strain rate, and peak strain magnitudes iseported. The principal vectors were also averaged over the eightalves and normalized. Comparison of strain magnitudes betweenubregions was performed using paired t-test, as the data wasormally distributed. Groups were determined to be statisticallyifferent if p�0.05.

Results

3.1 Reference Surface Fitting and Marker Arraylacement. The finite element surface fitting technique fit thepatial positions of the 31 marker array very well, with R2

0.98 and a mean error of �0.07 mm. Along the edges of thensertion zone shown in Fig. 3�b�, the changes in surface curvaturere significant, as shown in Fig. 4�a�, though the calculated localrror of the fitted surface at this region is as low as 20%.

3.2 Strain Field Results. The stretch field over the chordalnsertion region is heterogeneous with higher stretch magnitudesoncentrated at the edges of the insertion region than the central

Fig. 4 „a… Deformation of the 3D mesh during differenplane motion of the nodes near the edges of the choentire marked region of the anterior strut chordae insewere used for the three dimensional surface fitting ution. The X-axis represents the circumferential directradial direction and also the axis of the strut chordaeinterest. The region to the left of the center line is closon the right is closer to the commissural sections.

egion. Figure 4�b� shows the local areal stretch magnitude

81004-4 / Vol. 132, AUGUST 2010


mapped over the region delimited by the markers, and the hetero-geneity of the stretch magnitude is clearly evident. Figure 5 showsthe temporal changes in the areal stretch at the edges of the inser-tion region. During diastole, areal stretch is small and homog-enous throughout the insertion region; however, with systolic pro-gression, the stretch is heterogeneous with higher magnitudes atthe edges and lower magnitudes at the center. Peak areal stretch isconsistently higher at the markers on the left and right edges ofthe insertion zone than the central line. For example, markers 1, 4,and 7 shown in Fig. 3�b� lie on the same horizontal line but are atthe left edge, center, and right edge, respectively. The peak arealstretch magnitude is different at each of these markers, i.e.,1.89�0.73 at marker 1, 1.22�0.33 at marker 4�p=0.044 com-pared with marker 1�, and 1.60�0.42 at marker 7 �p=0.05 com-pared with marker 4�. However, there is no significant differencebetween the measured stretch at markers 1 and 7 �p=0.354�.Overall, the temporal changes in the areal stretch pattern are dif-ferent between the three regions—the left edge �markers 1, 15,and 25� has a gradual increase in stretch until it reaches a peak,after which it gradually restores back to the reference state, thecentral region �markers 4, 17, 26, and 31� has minimal stretchthroughout the cardiac cycle, whereas the right edge �markers 7,19, and 27� has a rapid increase in stretch, followed by unloadingwithin a very short period, as shown in Fig. 6.

3.3 Major and Minor Principal Stretches. Figure 7�a�shows a typical mapping of the major principal stretch magnitudesand vectors, and Fig. 7�b� shows the minor principal stretch on theentire region of the strut chordae insertion during systolic valveclosure. Similar to trends in the areal stretch, major principalstretch magnitude is significantly higher along the edges of theinsertion region than the center. Regional stretch in the radialdirection is significantly higher in the subregions along the leftchordal edge and the right basal edge compared with rest of theinsertion region. The direction of the major principal stretch is

hases of the cardiac cycle, demonstrating the out-of-al insertion region; „b… areal stretch mapping on the

n region. The red dots represent the 31 markers thatg triangular finite elements and for stretch computa-

along the anterior leaflet, the Y-axis represents thend the Z-axis represents the normal to the region ofto the A2 cusp of the anterior leaflet, while the region

t prdrtio

sinion, a

est

predominantly in the radial direction throughout systole, with the



vpMbctcfttobmot

trtfirts�llrast

sl

J

Downloa

ectors pointing toward the annulus. Small changes in the princi-al vector, indicating that cross-fiber shear stretch is quite small.inor principal stretch magnitude is significantly higher on the

asal edges of the insertion zone than the center or toward thehord, with the minor principal stretch vector predominantly inhe circumferential direction. Figure 8 shows the temporalhanges in the major principal stretch at selected markers on dif-erent subregions of the chordal insertion zone, and Fig. 9 showshe changes in the minor principal stretch at the same locations. Inhe major principal direction, the maximum stretch is at marker 31n the strut chord, followed by the right edge and the smallesteing along the left edge of the chordal insertion zone. In theinor principal direction, the maximum stretch is at the left edge

f the chordal insertion zone, followed by the right edge and thenhe central axis.

3.4 Stretch Rates. Stretch rates in the two principal direc-ions are used to assess the regional variations in strains. Table 1eports the stretch rate at three markers on the left edge, three onhe central axis, three on the right edge of the insertion zone, andnally one marker on the strut chord. In the major principal di-ection, the stretch rates on the left edge are significantly higherhan the right edge and the central axis, where the stretch rate ismallest. Maximum stretch rates are recorded on the strut chordaemarker 31� that corroborated with previous findings from ouraboratory �11�. In the minor principal direction, there are fewocalized regions of high stretch rate compared with the rest of theegion of interest. These hot spots are mainly at the regions thatre close to the A2 cusp that has the largest basal motion duringystolic coaptation �markers 1 and 15�, and in the region close tohe leaflet commissure �markers 7 and 19�.

3.5 Ultrastructural Examination. SALS results demon-trated a complex transition from the highly aligned chordae to the

Fig. 5 The averaged areal stretch plotted at subregions in thigher along the edge than compared with the centerline, whand diminished basally along the center line.

eaflet main body �as shown in Fig. 10�. In particular, we observed



a drop in alignment �orientation index values changed from 25deg to 45 deg within a few mm, see inset�. We also noted sub-stantial arching in the vicinity of the insertions.

4 DiscussionData from this study shows a heterogeneous stretch mapping

over the insertion region with higher stretching of the tissue alongthe edges of the insertion zone than the center, as systole pro-gressed. To clearly elucidate the mechanics of the insertion zone,both the temporal changes and spatial heterogeneity at each timepoint are presented in Figs. 7–9. As the cardiac cycle progressedfrom diastole to peak systole, there was a gradual increase in thestretch across the region, with the highest stretch at the left andright edges of the insertion region, and the lowest stretch at thebasal end of the chordal insertion into the leaflet, as shown in Fig.7. The results show that the areal stretch rapidly increases at theapical segments �below the horizontal line connecting markers15–19� and along the insertion zone edges, while minimal stretchwas recorded at the central region around markers 4, 10, 11, and12 during early systole. As systole progressed, this pattern ofstretch remained consistent, but with increasingly higher stretchmagnitudes at the edges of the insertion zone and a smaller regionat the center that remains undeformed. Examining the mesh de-formation shown in Fig. 4�a� during systole, it seems that thetissue along the axis of the strut chordae remains undeformed, butthe two edges of the insertion zone on either sides of this axisundergo significant out of plane deformation. In such a case, if theinsertion zone had a uniformly distributed collagen matrix, onewould expect that the maximum deformation would be at the cen-tral axis, as it acts like a fulcrum to the two bending edges. How-ever, the experimental results show the contrary, with the maxi-mum stretch along the edges and very little stretching at the

chordal insertion region. The peak stretch was significantlythe stretch magnitude was small at the strut chordal region

heere

central axis. This not-so-obvious stretch pattern, the authors be-

AUGUST 2010, Vol. 132 / 081004-5


lwbtafispcfmitta

eirltttmmvwr

0

Downloa

ieve, is due to the microstructural arrangement of collagen fibers,herein the collagen core from the strut chord splits into twoundles that run along the leaflet boundaries, while the collagen inhe interior/central part of the zone may be more circumferentiallyligned, as shown in Fig. 10. However, the composition of thesebers along the insertion zone edges was not investigated in thistudy; thus, the effect of microstructure on the observed stretchattern is purely speculative. The observed areal stretch patternorrelated very well with the facts known about the physiologicalunction of the mitral valve, wherein the A2 and A1/A3 cuspsove more basally to obtain good valve closure than the region of

nsertion of the strut chord. This basal cusp motion stretches theissue increasingly at either edge of the chordal insertion zonehan the central region, which is more or less a part of the leafletlready.

The major and minor principal stretch maps also provide inter-sting insights into the transition of forces and resulting mechan-cs during valve closure. During diastole, the chordal insertionegion seems to be in equilibrium between the tension from theeaflet and the chordae, which is evident from the radial orienta-ion of the major principal vectors in Fig. 7. At the beginning ofhe valve closure, the insertion zone was only radially stretched ashe anterior leaflet moved toward the annulus even if there is not

uch loading on the leaflet. As the anterior leaflet continued toove basally to coapt with the posterior leaflet with increasing

entricular pressure, increased magnitudes of principal stretchere measured. At the end of the valve closure, chordae insertion

Fig. 6 Temporal changes in the areal stretch at different pgeneity in the surface strains

egion reached equilibrium between the in-plane tension on the

81004-6 / Vol. 132, AUGUST 2010


leaflet and the axial load on the chordae. Though regionally thesetransitional stretch patterns are sensible, they are highly dependenton the leaflet coaptation as a boundary force condition. Theseresults show a strong coupling between the major and minor prin-cipal directions, and the complex biomechanics of the chordalinsertion zone.

The results from this study extend the mechanical measure-ments reported by Chen et al. performed under idealized equibi-axial loading conditions on porcine anterior mitral leaflets. Thenovelty of the current study the mechanical behavior of thechordal insertion region is quantified under physiological loadingconditions. Though the geometric and loading conditions are dif-ferent in the two studies, the results can be compared to under-stand the overall trend in the mechanics. Along the radial direc-tion, Chen et al. reported a maximum stretch of 35% closer to theleaflet and 20% closer to the strut chord and along the circumfer-ential direction, and a maximum stretch of 10% closer to theleaflet and �17% closer to the strut chord. In this study, themarker array �except for marker 31� represents the same region ofinterest as considered by Chen et al., and thus, qualitative com-parison between the results is justified. Figure 8 clearly shows thatthe average maximum stretch in the radial direction is �40% nearthe leaflet and �30% near the strut chord, thus agreeing withprevious results. Figure 9 shows that the average maximumstretch in the circumferential direction is �45% near the leafletand �20% near the strut chord. The higher leaflet deformation in

ts in the chordal insertion zone, demonstrating the hetero-
oin
the circumferential direction in this study than the biaxial data



J

Downloa

Fig. 7 „Top gallery… The series of images demonstrate the changes in the major principal stretch magnitudeand direction during systole; „bottom gallery… changes in the minor principal magnitude and direction during
systolic loading of the valve
Fig. 8 Temporal changes in the major principal stretch at different points in the chordal insertion zone, demonstrating the
heterogeneity in the surface strains
ournal of Biomechanical Engineering AUGUST 2010, Vol. 132 / 081004-7

ded 11 Aug 2010 to 140.254.87.101. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

cbdtadrte

Ta

LMMM

CMMM

RMMM

SM

0

Downloa

ould be attributed to the difference in the loading conditionsetween the two cases. It is worth noting that the static biaxialata do not capture the heterogeneity in the stretch pattern nor theemporal changes in the stretch, thus limiting the extent to which

quantitative comparison can be performed. This study providesetailed insights into the mechanics of the strut chordae insertionegion, which are not only interesting from a scientific perspec-ive, but may also have several clinical applications. To date sev-ral studies on the biomechanical of the mitral valve structure

Fig. 9 Temporal changes in the minor principal stretch at dheterogeneity in the surface strains

able 1 Peak major and minor principal stretch magnitudesnd stretch rates at markers 1, 4, 7, 15, 17, 19, 25, 26, 27, and 31

Max majorprincipalstretch

Max majorprincipal

stretch rate�%/s�

Max majorprincipalstretch

Max majorprincipal

stretch rate�%/s�

eft edgearker 1 1.19�0.13 207�80 1.81�0.74 719�448arker 15 1.24�0.27 197�112 1.17�0.23 170�138arker 25 1.38�0.24 197�98 1.08�0.11 64�60

enter linearker 4 1.10�0.09 45.6�44.4 1.19�0.24 98.7�144arker 17 1.09�0.09 39.4�25 1.10�0.14 103�119arker 26 1.09�0.10 64.3�28.5 1.05�0.06 53.2�18.8

ight edgearker 7 1.58�0.89 492�558 1.62�0.45 286�111arker 19 1.53�0.78 581�507 1.18�0.18 121�84arker 27 1.21�0.31 169.3�162 1.06�0.06 73�59.2

trut Chordarker 31 1.72�1.00 739�784 1.05�0.08 61�62.1

81004-8 / Vol. 132, AUGUST 2010


have been reported �12–14�, but there is little understanding of thebiomechanical events that develop the complex mitral valve struc-ture from the endocardial cushions. It is speculated that the cush-ion tissue under increasing stretch from the papillary musclesseparating from the myocardium clearly delineates the leafletstructure and the chordal structure. Though this hypothesis is yetto be verified, this study provides insights into the mechanics ofthe complex transition zone, where the planar collagenous leafletmorphs into a cylindrical collagenous structure. In the future, thisknowledge could help researchers investigate the logical sequenceof events that govern the formation of the different components ofthe mitral valve structure. From a clinical perspective, knowledgeof the strut chordal insertion region may aid better surgical deci-sion making in using techniques such as chordal cutting, wherethe strut chordae on the anterior leaflet are severed. Such proce-dures could potentially alter the local and global valve mechanics,and may have detrimental effects on the durability of the valverepairs. Even though diffusion of basic mechanics knowledge intoclinical practice takes significant thrust and time, basic mechanicsstudies as this one may eventually aid in improved repair design�e.g., neochordae design�, clinical decision making, and design ofoptimal heart valve implants.

4.1 Limitations. Although this study elucidates the complexbiomechanics of the chordal insertion region, it has some inherentlimitations. In this study we used porcine mitral valves, whichmay, to some extent, differ in their structure, function, and micro-structure from those in humans. However, in a previous study, wehave shown the structural similarity between porcine and humanvalves, and thus, expect the differences to be within reasonablelimits. In addition, the ventricular model used in this study doesnot represent the physiological contractile muscle model in hu-mans, and thus, may have not completely simulated the loadingconditions in the actual human heart. A static planar annulus was

rent points in the chordal insertion zone demonstrating the
iffe
used in this study, which does not represent the physiologic saddle



slscttwfifmgb

5

A

a

J

Downloa

haped, dynamic mitral annulus. The authors acknowledge thisimitation and are developing a new annular model to mimic thephincteric motion and three-dimensionality of the annulus. Theomplex collagen fiber distribution and orientation entails inves-igation of the microstructure of the insertion region which ishree-dimensional. Finally, we assumed the reference image fromhich the anterior leaflet starts to move to annulus was a strain-

ree state during valve closure. It is possible that the chordaensertion region may bear some prestretch due to the fluid dragorces on the chordae, even before systolic valve closure. Thisay cause a small error in the stretch measurements. However,

iven the high reproducibility of the measurements, the authorselieve that this is a reasonable approach.

ConclusionsFrom the present study, we can draw the following conclusions:

�1� Heterogeneous stretches over the chordae insertion regionoccur in the strut chordae insertion region. The largestretches occurred in both sides across the ridge of the strutchordae in the basal area of strut chordae insertion region.The stretches on the two sides across chordae center lineare not significantly different.

�2� The strut chordae insertion area stretched in the radial di-rection at the beginning of valve closure and then stretchedin the circumferential direction. The minor principalstretches were compressive, while the major principalstretches are tensile at the end of valve closing, which sug-gests the strongly coupled stretches in two principal direc-tions and explains small areal stretches in the valve closingand opening.

�3� The stretches were nearly symmetrical with respect to thechordae center line during the mitral valve closing andopening. The stretches demonstrate a transition from theradial direction in the chordae to the circumferential direc-tion in the leaflet side.

�4� There is some radial stretch in the strut chordae insertionregion even when the valve is fully open, which restrictsthe anterior move further into the left ventricle outflowtract.

cknowledgmentThis work is supported by the NIH �Grant No. HL52009�. The

Fig. 10 „a… Image of an ovine MVAL fixed at 5 mm Hg showimaps of the collagen fiber orientation. Inset-high resolutionthe angular distribution of collagen fibers, defined by a nor−OI… /90‡�100%. The blue scale represents least oriented fibof fibers with the NOI.

uthors acknowledge Mr. Vikesh Thourani for the help with the



data analysis, and the members of the Cardiovascular Fluid Me-chanics Laboratory at Georgia Tech and Cardiovascular Biome-chanics Laboratory at the University of Pittsburgh.

References�1� Nielsen, S. L., Hansen, S. B., Nielsen, K. O., Nygaard, H., Paulsen, P. K., and

Hasenkam, J. M., 2005, “Imbalanced Chordal Force Distribution Causes AcuteIschemic Mitral Regurgitation: Mechanistic Insights From Chordae TendineaeForce Measurements in Pigs,” J. Thorac. Cardiovasc. Surg., 129�3�, pp. 525–531.

�2� Nielsen, S. L., Nygaard, H., Fontaine, A. A., Hasenkam, J. M., He, S., Ander-sen, N. T., and Yoganathan, A. P., 1999, “Chordal Force Distribution Deter-mines Systolic Mitral Leaflet Configuration and Severity of Functional MitralRegurgitation,” J. Am. Coll. Cardiol., 33�3�, pp. 843–853.

�3� Espino, D. M., Shepherd, D. E., Hukins, D. W., and Buchan, K. G., 2005, “TheRole Of Chordae Tendineae in Mitral Valve Competence,” J. Heart Valve Dis.,14�5�, pp. 603–609.

�4� Jimenez, J. H., Soerensen, D. D., He, Z., He, S., and Yoganathan, A. P., 2003,“Effects of a Saddle Shaped Annulus on Mitral Valve Function and ChordalForce Distribution: An In Vitro Study,” Ann. Biomed. Eng., 31�10�, pp. 1171–1181.

�5� Chen, L., Yin, F. C., and May-Newman, K., 2004, “The Structure and Me-chanical Properties of the Mitral Valve Leaflet-Strut Chordae Transition Zone,”ASME J. Biomech. Eng., 126�2�, pp. 244–251.

�6� Sacks, M. S., Enomoto, Y., Graybill, J. R., Merryman, W. D., Zeeshan, A.,Yoganathan, A. P., Levy, R. J., Gorman, R. C., and Gorman, J. H., III, 2006,“In-Vivo Dynamic Deformation of the Mitral Valve Anterior Leaflet,” Ann.Thorac. Surg., 82�4�, pp. 1369–1377.

�7� Sacks, M. S., He, Z., Baijens, L., Wanant, S., Shah, P., Sugimoto, H., andYoganathan, A. P., 2002, “Surface Strains in the Anterior Leaflet of the Func-tioning Mitral Valve,” Ann. Biomed. Eng., 30�10�, pp. 1281–1290.

�8� He, Z., Ritchie, J., Grashow, J. S., Sacks, M. S., and Yoganathan, A. P., 2005,“In Vitro Dynamic Strain Behavior of the Mitral Valve Posterior Leaflet,”ASME J. Biomech. Eng., 127�3�, pp. 504–11.

�9� Smith, D. B., Sacks, M. S., Vorp, D. A., and Thornton, M., 2000, “SurfaceGeometric Analysis of Anatomic Structures Using Biquintic Finite ElementInterpolation,” Ann. Biomed. Eng., 28�6�, pp. 598–611.

�10� Sacks, M. S., Smith, D. B., and Hiester, E. D., 1997, “A Small Angle LightScattering Device for Planar Connective Tissue Microstructural Analysis,”Ann. Biomed. Eng., 25�4�, pp. 678–689.

�11� Ritchie, J., Jimenez, J., He, Z., Sacks, M. S., and Yoganathan, A. P., 2006,“The Material Properties of the Native Porcine Mitral Valve ChordaeTendineae: An In Vitro Investigation,” J. Biomech., 39�6�, pp. 1129–1135.

�12� Sacks, M. S., Merryman, W. D., and Schmidt, E. E., 2009, “On the Biome-chanics of Heart Valve Function,” J. Biomech., 42�12�, pp. 1804–1824.

�13� Sacks, M. S., and Yoganathan, A. P., 2007, “Heart Valve Function: A Biome-chanical Perspective,” Philos. Trans. R. Soc. London, Ser. B, 362�1484�, pp.1369–1392.

�14� Goetz, W. A., Lim, H.-S., Pekar, F., Saber, H. A., Weber, P. A., Lansac, E.,Birnbaum, D. E., and Duran, C. M. G., 2003, “Anterior Mitral Leaflet Mobility

the chordae; „b… corresponding SALS data showing detaileda of a chordal insertion region. The color legend representslized orientation index „NOI…, which is defined as NOI= †„90with the NOI, and the red scale represents good alignment

ngdatmaers

Is Limited by the Basal Stay Chords,” Circulation, 107, pp. 2969–2974.

AUGUST 2010, Vol. 132 / 081004-9


Documents

Mechanics of the Mitral Valve Michael S. Sacks Strut ... · Muralidhar Padala WallaceH.CoulterDepartmentofBiomedical Engineering, GeorgiaInstituteofTechnologyandEmory University,