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Katayama et al

The sinus of Valsalva relieves abnormal stress on aortic valve leaflets
by facilitating smooth closure
Susumu Katayama, BE, Nobuyuki Umetani, BE, Seiryo Sugiura, MD, PhD, and Toshiaki Hisada, PhD

Objective: Recently, various modifications have been made to aortic root replacement procedures to include thepseudosinus in the synthetic graft, but its effect on valve function still remains to be elucidated. The purpose ofthis study was to compare the flow dynamics and its influence on the stress/strain in the valve leaflet in two typesof aortic root, either with or without the pseudosinus, with a simulation model.
Methods: The proximal portions of the ascending aorta and aortic valves were modeled with blood flowing inside. Blood flow and the motion of aortic valve leaflets were studied while applying a physiologic pressure waveform using fluid–structure interaction finite element analysis. Waveforms were varied to simulate the change in
cardiac contractility.
Results: In the aorta without the sinus, the time during which the valve was open was longer and the rapid valve
closing velocity was faster under all conditions studied. In the pseudosinus model, we could clearly observe vortex formation from the early phase of ejection, which seemed to facilitate the gradual but smooth closure of thevalve. Valve leaflets without the sinus were subject to greater stress and underwent bending deformation in thelongitudinal direction.
Conclusions: Sinuses of Valsalva facilitate the smooth closure of the aortic valve, thereby avoiding the building
up of abnormal stress in the leaflet. Such an effect may assure the durability of valve leaflets in aortic grafts witha pseudosinus.

Video clip is available online.

Supplemental material is available online.

ACD

Sinuses of Valsalva, with their characteristic morphologic
features, have attracted the interest of researchers, and earlier
modeling studies have suggested that the sinuses function
not only to prevent the contact of valve leaflet with the aortic
wall, but also to facilitate valve closure by the formation ofvortices inside them.1,2 The emergence of valve-sparing aortic root replacement procedures for the treatment of patientswith aortic root disease has provided us with the unique opportunity to test such hypotheses. Leyh and colleagues3
compared patients who had undergone tube replacement of
the aortic root (reimplantation [David I] procedure) and
From the Department of Human and Engineered Environmental Studies, Graduate
School of Frontier Sciences, The University of Tokyo, Kashiwa-shi, Chiba, Japan.
This study was supported by Core Research for Evolutional Science and Technology(CREST) program by Japan Science and Technology Agency (JST).
Received for publication Feb 25, 2008; revisions received April 22, 2008; accepted for
publication May 19, 2008.
Address for reprints: Seiryo Sugiura, MD, PhD, Department of Human and Engineered Environmental Studies, Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwa-no-ha, Kashiwa-shi, Chiba, Japan (E-mail: Sugiura@k.u-tokyo.ac.jp).
J Thorac Cardiovasc Surg 2008;136:1528-35
0022-5223/$34.00
Copyright Ó 2008 by The American Association for Thoracic Surgery
doi:10.1016/j.jtcvs.2008.05.054

1528

those who had undergone separate replacement of the sinuses of Valsalva (remodeling [Yacoub] procedure) to findthat the near-normal opening and closing characteristics ofvalves were achieved by the preservation of the shape andindependent mobility of the sinuses. On the other hand, deOliveira and associates,4 based on a decade of following
up surgically treated patients, reported a reduced risk of
postoperative aortic insufficiency in patients with reimplantation. They concluded that the implantation procedure secures the entire aortic valve inside the Dacron graft toprevent dilatation of the aortic root and concomitant regurgitation. However, they also recognized the elimination of sinuses as a shortcoming of their technique, and they, as wellas other surgeons, have modified their reimplantation techniques to create graft pseudosinuses.5-7
Although it is generally assumed that smooth opening andclosing relieved the abnormal stress and strain on leaflets,
neither clinical observations3,8-10 nor experimental studies
using a mock circulation11,12 could provide us with detailed
information on the stress and/or strain distribution in theleaflet to clarify this assumption. An alternative approachto overcome such technical difficulty and obtain stress andstrain distribution is a simulation study using finite element
analysis. Grande-Allen and associates13 created finite element models of the aortic root and valve with a cylindrical
graft, a tailored graft sutured just above the valve, and a pseudosinus graft, to find that the cylindrical graft created thegreatest stress. Beck, Thubrikar, and Robicsek14 also compared the finite element models of the tubular aortic root
and the root with sinuses under pressure to find that a stressconcentration along the leaflet attachment develops only in

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Katayama et al

Acquired Cardiovascular Disease

the tubular root. Although these studies gave strong support
to surgeons’ beliefs, the simulation was done only by applying pressure to the model, thus totally ignoring the influenceof the blood flow, which most of the surgeons and researchers are interested in. The capabilities of the fluid–
structure interaction finite element method for the analysisof the aortic valve were first shown by Nicosia and colleagues15 using a commercial software package; subsequently, de Hart and coworkers16 analyzed the normal
aortic root using the fictitious domain method. However,owing to the numerical instability of the method, an unphysiologically low Reynolds number flow was introduced.
We17 have developed a numerical approach for fluid–
structure interaction analysis based on the arbitrary Lagrangian–Eulerian (ALE) finite element method and applied it to
the multiphysics simulation of the heart.18-21 In this study,
we applied this method to the analysis of the dynamics of aortic valve opening and closure in two different models of theaortic root, with or without the sinuses of Valsalva. It will beclearly shown that the sinuses, by promoting vortex formation, facilitate the smooth closure of the aortic valve and circumvent the development of abnormal stress in the leaflets.
METHOD
Modeling the Aortic Root
We created the shapes of cylindrical graft and pseudosinus graft with thedimensions shown in Figure 1, A. Then, we modeled the blood domain bytetrahedral finite elements with four velocity nodes and four pressure nodes,
resulting in the total numbers of elements and the degree of freedom (DOF)of 4408 (24990 DOF) for the cylindrical model and 52620 (30658 DOF) forthe pseudosinus model. For the valve leaflets, we adopted discrete Kirchhoff
triangular shell elements with anisotropic material property originating fromthe fiber orientation15,22 (Figure 1, B). Furthermore, the edge of each leaflet
was made thicker according to the literature.23 For the material properties ofthe valve, see Table E1.

The Heart and the Systemic Circulation as Boundary
Conditions
To the distal end of the models, we connected the 3-element Windkessel
model of systemic circulation. Pumping function of the heart was simulated
by applying the physiologic pressure wave (minimum 75 mm Hg, maximum 120 mm Hg). To simulate cases in which contractility of the heart iseither depressed (heart failure) or augmented, we varied the peak pressure
to 90% (P90) or 110% (P110) of the control (P100) condition while keeping the pressure time products constant (Figure 1, C). This was intended because we usually observed a slowed time course of contraction when thecontractility was depressed.

Computation
We used a strongly coupled fluid–structure interaction finite element
analysis program, which we have developed17 and applied to various problems such as pulsation of the heart.18-21 In this program, the Navier–Stokes
equation is described in ALE coordinates, which artificially deform andmove according to the instantaneous deformation of the fluid–structure interface. Furthermore, the fluid meshes and structure meshes are generated tocoincide with each other on the interface at the beginning of the analysis.
Therefore, the geometric compatibility and balance of traction forces are automatically satisfied by merging both meshes on the interface. The disadvantage of the method is the distortion of ALE meshes. Because thefluid–structure interface moves largely in the case of a heart valve problem,
excessive ALE mesh distortion occurs, resulting in the degradation of element performance. To avoid such a problem, we applied an automaticmesh reconnecting algorithm, which our group has developed. All of the
program codes were written in the laboratory.

RESULTSThe flow dynamics and the motion of the valves in cylindrical and pseudosinus grafts can be seen in the online supplementary Movies E1 and E2. In the pseudosinus graft, we
can clearly observe the formation of vortices of counterclockwise rotation in the sinuses, which seems to facilitate
the closure by pushing the leaflets. In the cylindrical graft,the edges of the leaflets make contact with the wall when
they are fully open and the closure seemed to be retarded.
Peak velocity values were 0.95 m/s (P90), 1.04 m/s(P100), and 1.16 m/s (P110) and the corresponding Reynolds numbers were 2995, 3278, and 3657, respectively.
Motion of the Leaflets
To quantify the motion of the leaflets and compare thesimulation results with clinical observations, we traced theedge of the leaflet and plotted the distance from the axis of
the aorta as a function of time, as we do in M-mode echocardiography (Figure 2, A), and calculated the slow closing distance (SCD ¼ [D1D2]/D1) and closing time (Figure 2, B).
SCD values were greater for pseudosinus models (P) thanfor cylindrical models (C) under all of the conditions studied, but the difference was pronounced in response to low
ejecting pressure (P vs C [%]: 8.9 vs, 5.1 [P110], 7.7 vs
4.6 [P100], and 6.3 vs 0.6 [P90]) (Figure 3, A). On the contrary, although the differences were small, closing timetended to be longer with the cylindrical model (P vs C [s]:0.22 vs 0.24 [P110], 0.24 vs 0.25 [P100], and 0.26 vs 0.28
[P90]) (Figure 3, B). We also calculated the rapid valve closing velocity (RVCV) as the ratio between D2 and rapid closing time (RCT in Figure 2, B). RVCV was also faster forcylindrical models (P vs C [cm/s]: 50.6 vs 52.1 [P110],49.8 vs 58.5 [P100], and 30.8 vs 42.7 [P90]) (Figure 3, C).
These results can be taken to indicate that, in the presence

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Abbreviations and Acronyms
ALE ¼ arbitrary Lagrangian–EulerianC¼ cylindrical graft
DOF ¼ degree of freedomP¼ pseudosinus graft
P90¼ peak pressure of 90%
P100 ¼ control peak pressure
P110 ¼ peak pressure of 110%
RVCV ¼ rapid valve closing velocity
SCD ¼ slow closing distanceAcquired Cardiovascular Disease

Katayama et al

24

60
24
12

5

A

B
R2
R1

C

150

P110

ACD

Pressure [mmHg]

P100

C

P90
120

90

60
0.0

0.1

0.2

0.3

Time [sec]FIGURE 1. Configurations of the model. A, Cylindrical (left) and pseudosinus (right) aortic roots with details of their dimensions. B, Valvular leaflet
and fiber orientation (right). C, Simulated aortic pressure was applied to the proximal end of the model aortic root. To the distal end, a 3-element Windkessel
model was connected. R1, Characteristic impedance (100 dynes $ s $ cm5); R2, peripheral resistance (1600 dynes $ s $ cm5); C, capacitance (2.1 3 103 L/
mm Hg).

of pseudosinuses, the valvular leaflets initiate their motion
from the earlier phase of ejection and gradually returnto their closing positions. On the other hand, with thecylindrical model, valves are wide open until the late phase1530

of ejection, during which the flow direction is reversed
to increase the regurgitant fraction (P vs C [%]: 0.7 vs
4.4 [P110], 1.6 vs 4.2 [P100], and 0.4 vs 5.4 [P90])(Figure 3, D).

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Katayama et al

Acquired Cardiovascular Diseaseett]). Interestingly, the bending strains in the fiber direction
did not differ appreciably between the two models. Comparison of peak stress (s) values followed similar pattern tothe strain values (C vs P [kPa]: 15.9 vs 8.6 [membranesjj],
9.8 vs 5.6 [membranestt], 48.0 vs 48.1 [bendingsjj], 20.3
vs 14.8 [bendingstt], 45.3 vs 41.8 [totalsjj], 20.8 vs 15.7
[totalstt]) (Figure 4, B).

0.3
Pseudosinus
Cylindrical

0.2

0.1

A

0.0
0.0

0.1

0.3

0.2

Time [sec]

D1
D2

RCT

B

Closing time

FIGURE 2. Motion of the leaflet. A, The distance from the axis of the aorta
is shown as a function of time. Solid line, Pseudosinus model; dotted line,
cylindrical model. B, Schematic diagram showing the indices characterizing
the motion of leaflet. D1, Maximum distance; D2, distance immediately
before the rapid closing. RCT, Rapid closing time.

Strains and Stresses in the Leaflets
We also compared the strains and stresses in the leaflets
between the two models. Taking into consideration the anisotropic material property reflecting the fiber orientationand the complex deformation each leaflet undergoes during
the ejection, we calculated the peak stretch (membrane),bending, and total strains (e) parallel (jj) and perpendicular(tt) to the fiber orientation. As shown in Figure 4, A, the leaflets in the cylindrical model experience greater peak strains,
especially in the direction perpendicular to the fiber orientation (C vs P: 0.022 vs 0.012 [membraneejj], 0.042 vs 0.024[membraneett], 0.069 vs 0.069 [bendingejj], 0.087 vs 0.064[bendingett], 0.065 vs 0.060 [totalejj], 0.089 vs 0.068 [total-

Simulations of Aortic Root
Compared with studies using mock circulation,1,11,12 simulation studies using the finite element method have advantages in that (1) the shape and the material properties of themodel and experimental conditions can be altered and controlled over a wide range, (2) detailed data on the distributionof flow velocity and pressure are available, and (3) stress/
strain distribution in the aortic wall and/or valvular leaflet
can be calculated. In particular, stress data are important
but hard to obtain in clinical settings.
However, so far, we can find only a few simulation studies
in which fluid–structure interactions were analyzed, probably owing to the computational difficulties.15,16,24 Amongthese studies, Nicosia and colleagues15 constructed an anatomically accurate 3-dimensional finite element model inwhich both the aortic root and valves were represented by
Hughes–Liu shell elements. They analyzed the blood flow
and the motion of the valve leaflet during ejection by using
LS-Dyna—an explicit finite element commercial code.
Their pioneering work showed the potential capabilities ofthe fluid–structure finite element analysis for heart valve
problems. However, some unphysiologic conditions, suchas the 98.5% reduction in the bending stiffness of the valve
leaflets, were introduced to reproduce their pliability, which
in turn enforced the scaling down of the magnitude of thepeak diastolic pressure to avoid valve element distortion. After Nicosia and colleagues,15 de Hart and associates,16 using
the fictitious-domain method, successfully showed that vortex formation in the sinuses of Valsalva is essential for thesmooth operation of the aortic valve. In contrast to the present study, however, their computation was carried out withan unphysiologically low Reynolds number (900) owing
to the numerical instabilities inherent in the algorithm.
Furthermore, a comparison of two clinically relevant
models, namely, cylindrical and pseudosinus, based on
fluid–structure interaction analysis, has been made for the

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DISCUSSION
In this study, we applied the fluid–structure interaction finite element method to analyze the flow dynamics in the aortic root and the motion of the aortic valve. Comparison of twomodels with or without the sinuses of Valsalva clearly demonstrated their functional role in achieving the smooth closure of
the valves. These results also have relevance to aortic root surgery, modifications to the procedures for which have been
proposed to improve the prognoses of patients.

Acquired Cardiovascular Disease

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0.30

10

0.25

Closing time [sec]SCD [%]

8

6

4

2

0

A

P90

P100

P110

B

0.10

0.00
P90

P100

P110

P90

P100

P110

6

5

Regurgitant fraction [%]50

RVCV [cm/sec]

0.15

0.05

60

40

30

20

4

3

2

1

10

C

0.20

0
P90

P100

P110

CylindricalD

0

Pseudosinus

FIGURE 3. Comparison of valve functions. A, Slow closing distance (SCD). B, Closing time. C, Rapid valve closing velocity (RVCV). D, Regurgitant
fraction. White bar, Cylindrical model; black bar, pseudosinus model.

ACD

first time. Although we can find the finite element analysis
studies comparing the principal tensile stress of leaflets
between the cylindrical graft and pseudosinus graft,13,14
in those study, the calculation was carried out for only thediastolic period by applying the pressure, thus completely
ignoring the influence of blood flow.
Comparison With Experimental and Clinical Studies
Using the time-resolved 3-dimensional magnetic resonance velocity mapping, Markl and associates10 comparedvortex formation among patients who had undergone cylindrical graft (David I procedure) and those who had undergone neosinus graft (David V and David V-Smod [Stanfordmodification]), with normal volunteers as controls. Even
though vorticity was increased in patients who underwent
the David V procedure, because the difference did not reachstatistical significance, they concluded that, although vortex
formation was enhanced by the David V procedure, normal
vorticity was preserved even without the sinus creation in1532

the graft. Direct comparison with the current simulation results is difficult, because in this study a rigid tube with perfect cylindrical form was used, but a small degree of vortex
formation was also identified in our simulation (Movie E2).
In a study comparing the motion of the leaflets between
the patients who had undergone tube graft and those who
had undergone remodeling (Yacoub) procedure, Leyh andcoworkers3 reported that, in patients who had undergone remodeling, SCD was greater but closing time was shorter,
consistent with the present results. A similar tendency wasreported for the comparison between patients with a tube
graft and those with a newly developed graft with a pseudosinus.8 However, the RVCV differed between the two studies. Leyh and coworkers3 found that the RVCV was slower
for tube grafts, but De Paulis and associates8 reported results
to the contrary.
In vitro studies may help to resolve this discrepancy. Friesand coworkers11 placed a porcine aortic root operated on witheither the David (cylinder) or Yacoub (remodeling) procedure

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Acquired Cardiovascular Disease

BendingMembrane

Total

0.10

Strain [-]

0.08
0.06
0.04
0.02

A

0.00

400
350

Stress [kPa]

300
250
200
150
100
50

B

0

Cylindrical

Pseudosinus

in a mock circulation and recorded the motion of the valve.
The difference in SCD was similar to the clinical observation
mentioned above, as well as the present results, but they foundthat the differences in RVCV were dependent on cardiac output and that the RVCV was greater for the David procedure
only at low cardiac output, similar to the present result (Figure 3, C). These contradictory results may have arisen because the patients in the study by Leyh and colleagues3 hadrelatively high cardiac function (ejection fraction > 60%)
compared with patients in other studies (about 50%).
As we mentioned earlier, the stresses and/or strains in theleaflet during ejection are hard to measure, but there has beena study in which strains were compared among the various
surgical procedures.12 From the images of porcine aorticroots operated on differently and placed in the mock circulation, the authors of this study calculated the cusp-bending deformation index in mid-systole as the fold depth normalized
to the size of the leaflet. Although the index of strain used inthis study was just an estimate, their results demonstrated
a greater strain associated with the reimplantation procedure(tube graft), compatible with our simulation result.
Implications
Although the creation of sinuses in remodeling procedures introduces the smooth closure of the aortic valve,3a long-term follow-up study demonstrated a better prognosis
for patients undergoing the reimplantation (David I) procedure in terms of freedom from aortic regurgitation,4 mainly
because of the more reliable annular stabilization with thistechnique. However, the importance of the sinuses of Valsalva is widely recognized by cardiac surgeons, and various
modifications to the reimplantation procedure have been
proposed to achieve both annular stability and the creationof sinuses.6-8,25,26 Although these techniques are expected
to enhance the long-term durability of the leaflet, greater
knowledge of the functional anatomy of the aortic root is required to achieve optimal results.27 The current simulation
would serve as a useful tool for designing tailor-made aortic
grafts and, in fact, has provided us with new insight into themechanics of the aortic valve leaflet during ejection.
Shown in Figure 5, A, are the stress distributions in theleaflets during the late phase of ejection for pseudosinus (upper panel) and cylindrical (lower panel) grafts (Movie E3).
It can clearly be seen that the leaflet in the cylindrical graft isbent in its middle portion by being pushed by the retrograde
flow from both sides (Movie E4). On the other hand, theleaflet in the pseudosinus graft has already returned halfway
to the closed position, as evidenced by the large SCD, andaccommodates the retrograde flow only on one side to avoid
the abnormal bending stresses perpendicular to the fiber

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FIGURE 4. Strain and stress in the leaflet. A, Strain (e). B, Stress (s). Values for membrane (tensile), bending, and total are shown in parallel (jj) and perpendicular (tt) to the fiber direction. White bar, Cylindrical model; black bar, pseudosinus model.

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FIGURE 5. Stress in the leaflet and deformation. A, Close-up views of the leaflet in the late phase of ejection for pseudosinus (upper panel) and cylindrical(lower panel) models. Stress values shown in color coding indicate the higher stress in the cylindrical model. B, Schematic diagrams showing the direction ofstress and induced deformation of the leaflets for pseudosinus (upper panel) and cylindrical (lower panel) models. Movies corresponding to this figure areavailable online.

orientation (Figure 5, B). So far, the stresses in the leaflet
have been discussed mainly during diastole when leaflets
are in the closed position, but the current simulation study
demonstrated another important time point when abnormal
stresses could build up, as well as the importance of fluid–
structure interaction in consideration of designing the aortic
root grafts.
Limitation of the StudyIn this simulation, only the short segment of ascending
aorta was modeled as a rigid tube. Furthermore, appliedpressure and systemic circulation approximated by the
3-element Windkessel model are simplifications of the
1534

real situation. These points should be improved to achieve
more realistic and useful simulations. Use of clinicalimaging data should also be considered. We are now
working to model the entire thoracic aorta with realistic
properties based on patients’ computed tomographic data.
CONCLUSION
Sinuses of Valsalva facilitate the smooth closure of theaortic valve, thereby avoiding the building up of abnormal
stress in the leaflet. With further improvement in modeling,
the fluid–structure interaction analysis of aortic root dynamics can be a powerful tool for the optimum design of aortic
root surgery.

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References

14. Beck A, Thubrikar MJ, Robicsek F. Stress analysis of the aortic valve with andwithout the sinuses of valsalva. J Heart Valve Dis. 2001;10:1-11.
15. Nicosia MA, Cochran RP, Einstein DR, Rutland CJ, Kunzelman KS. A coupled
fluid–structure finite element model of the aortic valve root. J Heart Valve Dis.
2003;12:781-9.
16. De Hart J, Peters GW, Schreurs PJ, Baaijens FP. A three-dimensional computational analysis of fluid–structure interaction in the aortic valve. J Biomech.
2003;36:103-12.
17. Zhang Q, Hisada T. Analysis of fluid–structure interaction problems with structural buckling and large domain changes by ALE finite element method. Comput
Methods Appl Mech Engrg. 2001;190:6341-57.
18. Watanabe H, Hisada T, Sugiura S, Okada J, Fukunari H. Computer simulation ofblood flow, left ventricular wall motion and their interrelationship by fluid–structure interaction finite element method. JSME Internatl J C. 2002;45:1003-12.
19. Watanabe H, Sugiura S, Hisada T. Finite element analysis on the relationship between left ventricular pump function and fiber structure within the wall. JSME Internatl J C. 2003;46:1330-9.
20. Watanabe H, Sugano T, Sugiura S, Hisada T. Finite element analysis of ventricular wall motion and intra-ventricular blood flow in heart with myocardial infarction. JSME Internatl J C. 2004;47:1019-26.
21. Watanabe H, Sugiura S, Hisada T. Multi-physics simulation of left ventricular filling dynamics using fluid–structure interaction finite element method. Biophys J.
2004;87:2074-85.
22. Swanson WM, Clark RE. Dimensions and geometric relationship of the humanaortic valve as a function of pressure. Circ Res. 1974;35:871-82.
23. Sahasakul Y, Edwards WD, Naessens JM, Tajik AJ. Age-related changes in aortic
and mitral valve thickness: implications for two-dimensional echocardiography
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24. Peskin CS, McQueen DM. A three-dimensional computational model for bloodflow in the heart: I. Immersed elastic fibers in a viscous incompressible fluid. J
Comp Phsyiol. 1989;81:372-405.
25. Cochran RP, Kunzelman KS, Eddy AC, Hofer BO, Verrier ED. Modified conduit
preparation creates a pseudosinus in an aortic valve–sparing procedure for aneurysm of the ascending aorta. J Thorac Cardiovasc Surg. 1995;109:1049-58.
26. David TE. Aoritc valve sparing operations. Ann Thorac Surg. 2002;73:1029-30.
27. David TE. Commentary. J Thorac Cardiovasc Surg. 2000;119:762-3.

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1. van Steenhoven AA, van Dongen MEH. Model studies of the closing behavior of
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New York: Springer-Verlag; 1997. p. 42-9.
3. Leyh RG, Schimidke C, Sievers H-H, Yacoub MH. Opening and closing characteristics of the aortic valve after different types of valve-preserving surgery. Circulation. 1999;100:2153-60.
4. de Oliveira NC, David TE, Ivanov J, Armstrong S, Eriksson MJ, Rakowski H,
et al. Results of surgery for aortic root aneurysm in patients with Marfan syndrome. J Thorac Cardiovasc Surg. 2003;125:789-96.
5. David TE, Armstrong S, Ivanov J, Feindel CM, Omran A, Webb G. Results ofaortic valve–sparing operations. J Thorac Cardiovasc Surg. 2001;122:39-46.
6. Demers P, Miller DC. Simple modification of ‘‘T. David-V’’ valve-sparing aortic
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7. Takamoto S, Nawata K, Morota T. A simple modification of ’David-V’ aortic root
reimplantation. Eur J Cardiothorac Surg. 2006;30:560-2.
8. De Paulis R, De Matteis GM, Nardi P, Scaffe R, Buratta MM, Chiariello L. Opening and closing characteristics of the aortic valve after valve-sparing procedureusing a new aortic root conduit. Ann Thorac Surg. 2001;72:487-94.
9. De Paulis R, De Matteis GM, Nardi P, Raffaele S, Bassano C, Chiariello L. Analysis of valve motion after reimplantation type of valve-sparing procedure (DavidI) with a new aortic root conduit. Ann Thorac Surg. 2002;74:53-7.
10. Markl M, Draney MT, Miller DC, Levin JM, Williamson EE, Pelc NJ, et al. TImeresolving three-dimensional magnetic resonance velocity mapping of aortic flowin healthy volunteers and patients after valve-sparing aortic root replacement.
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Cardiovasc Surg. 2000;119:753-63.

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TABLE E1. Material property of the valve
Elastic modulus in the fiber direction (EL)Elastic modulus perpendicular to the fiber
direction (ET)Poisson’s ratio (nLT)
Shear modulus (GLT)

700 kPa
233 kPa
0.45
80 kPaACD
1535.e1 The Journal of Thoracic and Cardiovascular Surgery c December 2008