Toward an optimum prosthetic trileaflet aortic-valve design* D h a n j o o N. G h i s t a t Biomedical Engineering Division, Indian Institute of Technology, Madras-36, India Abstract--The paper presents an optimum leaflet valve design, for a given valve size, satisfying the design criteria of: (1) minima/stress concentration in the leaflets; (2) optimal Cusp shape to effect a smooth washout upon valve closure and to provide minima/meridiona/surface contact between leaflets, so as to minimise haemo/ysis and prevent adjacent leaflets from sticking to each other; (3) the pressure difference across the leaflet, at valve opening, not exceeding a limiting value (specified, in this paper to be I - 4 mm Hg) ; and (4) to guarantee an adequate working life (of, say, I - 2 • 105 hours). The valve leaflet is characterised as a shell surface with two principal radii of curvature R1, R2 and subtending angles 01, 02. These constitute the shape parameters of the valve design. The first two criteria, outlined above provide the following values of the shape parameters: 01 = 150 ~ 02 = 9 3 ~ R I = 0 . 8 9 R , R 2 = 0.87R. The advocated leaflet material is Avcothan-51, selected on the basis of its biological compatibility. For this material, whose static and fatigue properties are available, the leaflet thickness is determined (for given valve size) in order to satisfy the third and fourth criteria (listed in the above paragraph) ensuring a valve opening leaflet pressure differentia/of I - 4 mm Hg and a prescribed lifetime TI (of, say, 1-2 x 105 hours, the equivalent of 12-24 years).

there is no reliable prosthetic leaflet valve in wide clinical use. Hence it is relevant to design a prosthetic leaflet valve (such as that illustrated in Fig. 1) that fulfils the following requirements:

1. Introduction

Objective THE purpose of this paper is (a) to present the criteria for optimum prosthetic aortic valves (b) to formulate these criteria, in mechanics terms, for a prosthetic trileaflet aortic valve (c) to determine the valve shape parameters to satisfy the criteria (d) to evolve a synthesis procedure for determining an optimum set of design (valve cusp thickness and material) parameters of the leaflet valve for satisfying the design criteria and hence to afford guidelines for the design of a long-term durable prosthetic valve.

(a) The valve must be able to withstand cycles of loading and unloading for an acceptable life-

Background From accumulated clinical and experimental data with various prosthetic (ball-disc type) heart valves and the analytical studies (B~LLHOUSE and TALaOT, 1969), it is evident that the trileaflet central-flow device has a better mechanical efficiency, superior hydraulic characteristics and flow patterns that cause much less trauma (causing thrombus, artherosclerosis and haemolysis) compared with the occluding-type ball and disc valves. On the other hand, experience with leaflet valves, such as the Muller Valve (MULLER et aL, 1960), shows that fatigue fractures of the leaflets do occur. At present, "First received 6th June 1974 and in final form 24th July 1975 tMr. Ghista is currently with the Biomedical Research Division, NASA-Ames Research Center, Moffett Field, Calif. 94035, USA

122

leaflet

I cornmissurol post

rim velour strip

Fig. I A prosthetic trileafiet aortic valve

Medical and Biological Engineering

March 1976

span (about 3.75-7.5 • 108 cycles which corresponds to 12-24 years:~) without the fatigue failure stress being exceeded in the leaflet. (b) The pressure differential loading which causes the valve leaflet to open (by a buckling process) must be minimal (not greater than 1-4 mm Hg). (c) The shape of the valve cusp must be such that the stresses in the cusp membrane are minimal (which in turn promotes a longer lifespan). (d) The cusp shape must provide a smooth washout (Fig. 2). We further stipulate that the surface contact between coapting cusps must be minimal along the meridian of the cusp surface, so that red-blood-cell damage between the contacting surfaces is minimised; this would also prevent the cusps from sticking and offering a resistance to valve opening. At the same time, when the valve closes, the cusps must coapt along the free edges, and the lengths of the free edges must hence be greater than the valve diameter.

ourselves with the design of a typical cusp, which in turn is characterised by its shape and material property parameters. Valve geometry for design analysis

The valve shape may be defined by means of (a) mathematical equations of spheroid, paraboloid of revolution and elliptical paraboloid shell surfaces fitted to leaflet surface geometry obtained by pressurising silicone-rubber moulds of freshly excised human aortic valves, as performed by GOULD et al. (1972); such a representation affords the freedom to choose two shape-characterising design parameters; (b) a shell characterised by two equivalent principal radii of curvature R~, R2 and two subtending angles 01, 02 (in the ranges 150 ~ < 01 < 180 ~ 75~ 02 < 270~ as verified by CHON6 et al. (1971), based on careful measurements of the geometries of excised human aortic valve leaflets; this representation, schematically illustrated in Fig. 3, provides a choice of four shape parameters. F o r the stress-design criterion, then, it is convenient to express the (maximal) stresses in terms of the pressure loading (on the shell surface), the shape parameters St and the size R by means of an explicit relation of type a = a(P, R, S,)

well rounded base a l l o w s good washout

a n a r r o w base is conducive t o clot formation

a

b

Fig, 2 Schematics of a a smooth washoutpromoting cusp shape b a poor design not permitting scouring action;' and sharp corners may lead to flow separation and resulting clot formation

.

.

.

.

.

.

.

(l)

.

which enables us to readily assess the influence of variation of St on the stress (a) level. The Chong model (1971) enables such a convenient explicit representation, as opposed to the finite-element analysis models of GOULD et al. (1972) and of HAMID and GmSTA (1974). Hence the Chong model will be employed here to characterise and optimise the leaflet shell geometry. 01

These criteria must now be formulated mathematically in terms of the valve size (to cater to various subjects) and the defined design parameters characterising the valve (shape) geometry and its material properties. These design parameters are determined to satisfy all the criteria. The mathematical analyses, concerning the formulation of the design criteria and the synthesis procedure to determine the optimum values of the design parameters, are presented in the following sections.

G

2 Design analysis In designing the prosthetic trileaflet aortic valve of a given diameter (2R), we need only concern ~By setting such stringent requirements, we are making allowance for a deterioretion of the cusp material in vivo and a consequential reduction of the lifespan

Medical and Biological Engineering

M a r c h 1976

15 Fig. 3 Chong model of valve leaflet shell geometry (showing relationships between geometrical parameters and valve-ring radius R) 123

The maximal stress concentrations* (i.e. ~r/P) furnished by the Gould and H a m i d - G h i s t a models are of the order of 14--20 (for spherical and ellipticalparaboloid geometries) whereas for the Chong m o d e l i t is 14 forOl = 1 5 0 ~ = 180 ~ R2 ---- 6-3mm and Rl = 7 ram. Thus, since the Chong model provides stress-concentration levels of the same order as furnished by the finite-element models (which account for the geometry more accurately), we can justifiably employ it as the valve model for our design analysis. The design analysis consists in formulating the design criteria in terms of the valve geometry (R1, R2, 01, 02) and material property parameters. The

express the radii of curvatures Rx, R2 in terms of the radius R of the aorta at the base of the valve. It can be observed from Fig. 3 that the dimension EG, which is the width of the valve leaflet, is expressed as EG = 2(O1 E) sin (01/2) = 2R1 sin (01/2)

(5)

At the same time, we can note that EG = 2(OE) sin 60 ~ = 2R sin 60 ~ = 1.73R

(6)

Since OE is equal to the radius R of the valve ring or radius of the aorta to which the valve ring is sutured, the radius R denotes the valve size. Hence eqns. 5 and 6 provide RI .

~/(3)R . . . 2 sin (01/2)

.

.

.

.

(7)

As regards R2, w e note that the maximum meridional length of the leaflet (the length of the meridian joining points A and B, in Fig. 3) equals the cusp length L, i.e. L = R2 0z

. . . . . . . . .

(8)

R2 = L/02

. . . . . . . . .

(9)

and

Fig. 4 Optimal leaflet shape showing undesirable and ideal leaflet geometries

design optimisation will then consist of a determination of the optimum values of the parameters so as to satisfy the design criteria.

L = 1.5R

Rz = 1.5R/02

0-1 =

1- -~ +

(10)

. . . . . . . .

(11)

and hence

The leaflets are loaded maximally during diastole, when they come together and seal the aorta opening. Based on the CHON~ et al. model (1971), the stresses in the leaflet membrane under the pressure loading are given by (Fig. 3)

(01/2) J

. . . . . . . . .

Eqns. 9 and 10 yield

Stresses in valve leaflet in terms o f valve cusp's shape and size parameters

tr2 = ~PRI ( 1 - [ 1 - k ( l - c o s 0 2 ) ] sin (01/2)/

Now, from anatomical data, it is observed that, on average, the cusp length is one and a half times the aortic radius at the valve base; i.e.

(3)

sin ( 0 1 / 2 ) k = R2/RI = ~ / ( 3 ) - 02 Now, substitution of eqns. 7 and 11 in eqns. 3 and 4 yields 0- 2

~-~ - 8 9

--

~(3)PR [1 - F{1 - k ( 1 - cos 02)}] 4h sin (01/2)

(12)

~/(3) PR [ 1 F 0-1 - 2hsin (01/2) [ 1 - ~-~ + -~sin (01/2)1

(4) 03)

where k = R2/R1.

where

Now we invoke anatomical considerations to *Ratio of the maximum stress to the app/ied pressureloading

124

k = ~/(3) sin (01/2), 02

F - sin (01/2) (01/2)

Medical and Biological Engineering

March 1976

symmetry axis. Of course, along the rim there must be complete contact between leaflets, so that each leaflet is supported by the adjacent leaflets against diastolic pressure by coaptation. The undesirable surface contour from the point of facilitating smooth washout is also shown in Fig. 4. Hence, for a well designed leaflet, not only must the symmetry line be tangent to the leaflet surface (meridional) curve of radius R2 at A (Fig. 5), but also the meridian curve centre 02 must lie on the normal to the symmetry axis, as shown in Fig. 5. This geometrical constraint in turn puts a constraint requirement on 02, which is now derived. With reference to Fig. 5, we have

Criteria o f optimal leaflet shell's meridional shape

Fig. 4 delineates the leaflet geometry in the meridional plane passing through the line of symmetry (AB of Fig. 3) of the leaflet. In order that the leaflet shape provides a smooth washout-facilitating surface contour, the valve cusp must be tangent to the symmetry axis of the aorta at its rim A. Further, the contact along the meridian must be minimal, in order to minimise blood trauma; so, we might as well specify that only the rim of the cusp must be in contact with the neighbouring leaflet and hence with the

BO = R = B C sin (6+~) = B C sin ( n - 0 2 )

(14)

A C = B C = R2 tan (02/2) . . . . .

(15)

Combining eqns. 14 and 15, we have R = R2 tan (02/2) sin ( n - 0 2 ) . . . .

(16)

On combining eqns. 16 and 11, we get tan (02/2) sin 02 _ sin2(02/2)

02

~

2

3

(17)

The above relationship yields the values 0 2 = 9 8 ~,170 ~ Fig. 5 Relationships between geometrical parameters of optimal cusp

0'016

0

IL

0'014

4

8

IJ

~

.

. . . . . . .

(18)

which are the values for the optimal cusp shape.

T x 1 0 -5, h

12

16

I

1

20

~ X limiting opening pressure criterion curves, for \ ~ / 133.375 N/m2 (1ram Hg), ~ ~ . 266.755 N/m2 (2mm Hg), k ~ ~ ' ~ /400.125 N/m2(3mm Hg), and ~/~533"125 N/m2 (4rnm Hg) opening pressures urob, ty criterion curves, for

0.012 ~. ~.

t-

~.

0"010

~.

~. ~

~

~

120mm Hg, .lOOmm Hg, and 80mm .g mean / ~pressure /

~

~

~

~

0'008

0,006 0 O,...,.......--.--O

0,004

0

I

I

5

10 E x 10-6 N/m 2

I

15

20

Fig. 6 Curves, representing (a) the criterion (eqn. 30) of valve opening pressure difference of I--4 mm Hg plotted on the h/R against E design parameter space, (b) the longevity criterion (eqn. 35) plotted on the h/R against T design co-ordinate space (for ~L=lSOO.2mm Hg, C= 12,383.5mm Hg, b=0.037) Medical

c

and Biological

Engineering

March

1976

125

Criteria o f minimal stress in the leaflet In order that the stress levels of a~ and 0"2 are minimal we need to determine the optimal values of 0~ and 02 that minimise 0"x and or2, as given by eqns. 12 and 13. On substituting the values obtained for 02 in eqns. 12 and 13, we would want to determine the associated optimum values of 0~ that minimise the stress level in the valve leaflet. We would hence naturally want to determine the values of the set at which 0"a equals 0"2. However, in the anatomical range of 150~ < 0~ < 180~ and 75~ < 02 < 270 ~ we cannot have 0"~ = 0"2 for 02 = 98~ or 170~ Hence we do the next best thing and determine the value of 01, corresponding to 02 = 98~ and 170~ that yields the minimum value of the greater of the two stresses aa and 0-2.* In the range of 150~ < 0~ < 180~ we obtain the optimal values of 0~ and 02 equal to 0i = 150~

02 = 98~

.

. . . .

0-2 = 0.485 -PR h-

R2 = 1.5R/02 = 0.87R

. . . . .

R~ = 3R/2 sin (0~/2) = 0.89R

....

(23)

which, on substitution of (Fig. 6)

BA = 2R2 sin (02/2)

. . . . . .

(24)

and for R2 and 02 from eqns. 21 and 19 becomes ,~2__~

1.73(1 _ v2)~/2 ( h )

. . . . .

(25)

R being the aortic radius at the base of the valve. The critical buckling pressure Pb is expressed in terms of a unified critical pressure parameter Be, given by

(BAy( 1 - v 2)

Bc,=--E-\2h]

(20/ (21)

. . . . .

(26)

which, following substitution for BA, from eqn. 24, yields

(22)

Thus all the shape parameters of the valve leaflet have been determined. What remains to be determined, to effect the optimal valve design, are the valve leaflet thickness h and the leaflet material parameters. Having selected the material on the basis of its blood compatibility, the leaflet thickness will be determined by a synthesis procedure to satisfy two further criteria, i.e. the valve has a specified fatigue life of T hours and that the valve opens readily (by the leaflets buckling) under an acceptable pressure difference (of, say, 1-4 mm Hg).

Criteria for least resistance to opening A healthy natural valve opens when the pressure difference across the cusp is of the order of 1--4 mm Hg or less. The valve opening is initiated by a buckling phenomenon and the buckling wave travels up along the valve-leaflet meridian; this mechanism of valve opening has been observed in a pulse duplicator. To ensure proper and instantaneous opening of the valve as soon as the ventricular pressure exceeds the aortic pressure, the buckling pressure (namely the critical value of the pressure "By accepting a value of ~2 that does not precise/y4ulfil the condition given by eqn. 17, we can have o l = ~ r 2 for 02 = 88"58 ~ and 01 = 169 .63~ This minimum stress level geometry is being employed by H. Reul (of the Helmholtz Institute, Aachen) to fabricate the optimum Avcothorne-51 leaflet valve--based on a collaborative effort between the author and Dr. Reul

126

).2 = (BA___)~{12(1 - v2)}'i2 4hR2 . . . . .

(19)

On substituting the optimum values of 0~ and 02 from eqn. 19 in the stress expressions (eqns. 12 and 13) and in the (anatomically based) parametrical relations (eqns. 7 and 11), we obtain 0-1 = 0.399 -~-_ ;

differential across the cusp) pb must be of the order of 1 ~ m m Hg. Based on the analogy with buckling of clamped spherical domes of radius R2, the critical buckling pressure p~ can be taken to be dependent on a unified geometrical parameter ).2 given by (FLUGGE, 1962)

Bcr = 0 . 2 ( 1 - v 2 ) - ~-

. . . .

(27)

The critical pressure pb is then obtained from the following relationship [adopted from the spherical shell buckling relationship (FLUGGE, 1962)] between Be, and 22: Bcr = 1.3~. = 0.057), 4

,

2.08 < 2 < 3]

,

3< 2 < 5

= 4.1522-83.73,

/

(28)

5 < 2 < 10

To obtain the explicit relation between Pb, R, h, E and v, we substitute expressions for Be, and ).2 from eqns. 27 and 25 into eqn. 28. However, let us first examine the range of 2 for a prosthetic (or even a natural) aortic valve. The range of h can be 0.2 mm to 0.4 mm (it is about 0.4ram for a natural valve); the range of R can be from 7 to 12 ram. The (R/h) ratio hence varies from 18 to 60. The value of v can vary from almost 0 (for silk fabrics) to 0.5 (for silicone rubber). Hence it can be seen from eqn. 28 that the pertinent range of ). is such that the last relationship of eqn. 28 is aptly applicable, yielding the following expression for p~ (by combining eqns. 25, 27 and 28).

pb

( l - i ) ',2

R

B_--~,~) \ ~ ]

Medical and Biological Engineering

(29) March 1976

Since Ph (the pressure at which the valve must open) must be --.~l-4mmHg, we have the following mathematical relation for the valve-opening criterion (where E is expressed in N/m 2)

ph

(1 - v2)1/2

Pm being the expected value of the pressure for a given subject. The lifetime T, obtained from eqn. 32 (corresponding to an expected stress Cryfor an expected mean pressure P,~), must be greater than the prescribed lifetime T~, yielding the relationship C1/b

(I - v~)

T-

60H ( t r : - (TL)lib

~> T~ . . . . .

(34)

133-375-533.5 N/m 2 For v = 0.496 (for Avcothane-51 polymer), we have the relationship

On substituting the expression for a : from eqn. 33 in the above equation, we obtain the following relationship representing the criterion for a guarantee of a lifetime TL: Cllb

60fl [0.485(P,~/(h/R)}- ~LI 1/b ~< 133-375-533-5N/m:

The above relationships (eqn. 30) are plotted on the h/R against E co-ordinate space in Fig. 6. F o r the satisfaction of the criterion, h/R must be less than the value provided by the pertinent curve. Durability: j~tigue resistance In general, for a material, the number of cycles N required for material failure to occur (with a certain probability of failure) at the applied stress (a:) can be expressed as (PRINGLE et al., 1968): . . . . . . .

3 Optimal-design-synthesis procedure We will now demonstrate the synthesis procedure for determining the design parameters of the valve (leaflet) so as to satisfy the design criteria (represented by eqns. 30 and 35), for the following data. Properties o f leaflet material A blood-compatible block polymer Avcothane-51 was selected for the valve material. This material has been employed by H. Reul (of Helmholtz-Institut fur Biomedizinische Technik an der R W T H Aachen, Germany), as a leaflet material; based on our collaborative research programme, the design concepts, of an optimum valve that are presented here, are being incorporated to develop an optimum leaflet valve. For the fatigue data of this material, the values of the fatigue properties (eqn. 31) are aL = 2.4 X l0 s N / m z (or 1800.2 mm Hg) ] /

C

(a) C and b are (experimentally obtained) material properties and

Medical and Biological Engineering

J

Physiological data H = 80 beats/min, R = 12ram

Pm = 100mmHg,

(32)

wherein n = number of cycles per hour, H is the average (expected) heart rate in beats per minute, and the working stress tr:, to equal the maximum stress in the yah,e, is given from eqn. 20 by . . . . . . .

(36)

This material, whose Poisson's ratio is 0.496, displays a quasilinear stress-strain characteristic, for strains less than 10%; in this range, its average Young's modulus is 107N/m a (or 10.197x102 kg/mZ).

(b) aL is the fatigue limit of the material. The lifetime (T hours) of the valve can now be expressed as

~R a: = 0 . 4 8 5 ~

16.51 x 105 N/m z (or 12,383.5mm Hg)}

b = 0.0337

(31)

wherein

cllb C11b T - n(cr:_trL)ll b - 60H(tr:_trL)I/~ .

(35)

(30)

Let us check the validity and applicability of this relationship by applying it to the natural valve for which h = 0.4ram, v = 0.5, R = 10ram and E = 49, 057-98, l l 4 N / m 2 (5-10kg/m:), since at the instant of opening of the valve the leaflets are stressed minimally and hence their stiffness corresponds to the pretransition stage (YAMADA, 1973). With the above data, po = 60-120 N / m 2 or 0.450.9 mm Hg, respectively, which is the right order of magnitude.

a : - - a L := CN -b

/> 7",

(33)

Specified lifetime T = 1-2x 105h Pressure difference required F o r the material data (given by eqn. 36), the valvedurability criterion, represented by eqn. 35, is plotted as a set of design parameter curves, in Fig. 6, on the h/R against T co-ordinate space; of the set

March 1976

17.7

of curves, we are interested in the curve for which P,, = 100 Hg. We note from Fig. 6 that for E = ]0 7 N / m 2, the criterion for the valve to open at a pressure of 1-4 mm Hg yields 0.00675 < h/R < 0.0t 1 On the other hand, the lifespan of 1-2 x l0 s h (equivalent to 12-24 years) dictates, from the durability curve (for P,, = 100 mm Hg), that 0.0056 < h/R < 0.0057 Of course, h/R greater than 0.0057 yields a longer lifetime and is, therefore, certainly acceptable. For practical considerations (in being able to produce a small material thickness), we select 0.00675 < h/R < 0.011

. . . . .

(37)

which also satisfies the specified lifetime requirements by a large safety margin. Then for R = 12 ram, we have

Of course, for R = 12 mm, the values of the valvecusp-shape parameters are obtained from eqns. 18, 21 and 22 as

R1--10.7ram,

R2 = 10.55 mm Thus, with the help of eqns. 21, 22 and 37, the design parameters of a series of optimum valves of different sizes can be determined. 5 Conclusion

An optimum leaflet valve design for a given valve size is presented to satisfy the design criteria of (a) minimal stress concentrations in the leaflets; (b) optimal cusp shape to effect a smooth washout upon valve closure and to provide a minimal meridional surface contact between the leaflets, so as to minimise haemolysis and leaflet sticking; (c) the pressure difference across the leaflet, at valve opening, to be 1-4 mm Hg;

128

0t -- 150~

02 = 9 8 ~,

R1 =0-89R,

R2 = 0 . 8 7 R

The leaflet material, Avcothane-51, is selected on the basis of its biological compatibility; its static and fatigue properties are available. The design-synthesis procedure is applied to select the leaflet thickness, for a given valve size, so as to satisfy the third and fourth criteria, ensuring a valve opening leaflet pressure difference of 1 - 4 m m H g and a more than adequate lifetime; the range of values of the leaflet thickness (in terms of the valve size R) is given by eqn. 37.

Acknowledgment--This investigation was carried out during the tenure by the author of a Homi Bhabha Memorial Fellowship. The author thanks H. Reul for valuable discussions. References

BELLHOUSE,B. J. and TALBOT, L. (1969) The fluid

0.08 m m < h < 0.132mm

Ot = 150~, 0 2 = 9 8 ~

(d) to guarantee a lifetime of T = (1-2 x 105 h). The first two criteria provide the values of the shape parameters (Fig. 3):

mechanics of the aortic valve. J. Fluid Mech. 35, 721. CHONG, P. K., HWANG, N, H. C. and. WILTING, D, S. (t971) Stress analysis of normal human aortic valve leaflets. Proceedings of 24th Annual Conference on Engineering in Medicine & Biology. FLUGGE, W. (1962) Handbook of engineering mechanics. McGraw-Hill. GOULD, R. L., CATALOGLU,A., DHATT, G., CHATTOPADHYAY,A. and CLARK, R. P. (1972) Stress analysis of the human aortic valve. National Symposium on Computerised Structural Analysis and Design, George Washington University, USA. HAMID, M. S. and GHISTA,O. N. (1974) Finite element analysis of human cardiac structures in PULMANO,V. A. and KABILA, A. P. (eds.) Finite element method~ in engineering. Clarendon Press, Oxford. MULLER, W. H., WARREN, W. D., DAMMANN, J. F., BECKWITH, J. and WOOD, J. E. (1960) Surgical relief of aortic insufficiency by direct operation on the aortic valve. Circ. 21, 587. PRINGLE,D. A. and HARKER,R. J. (1968) Environmental fatigue testing of moulded plastics for prosthetic heart valves. SESA Fall Meeting, San Francisco, Calif. YAMADA, n . (1973) Strength of biological materials. Williams & Wilkins, Baltimore.

Medical and Biological Engineering

March 1976

Vers la conception optimale d'une valve aortique prosth6tique & trois feuilles Sommaire--L'article pr~sente uric conception optimale d'une valve ~. feuille pour valve de taillr donn~e et r6pondant aux crit~res de conception suivants: (1) concentration de contrainte minimum dans les feuilles; (2) forme optimum du sommet de faqon 5. produire l'6coulement total r6gulier &la fermeture de la valve et 5_ donner une surface de contact m6ridional minimum entre les feuilles afin de r6duire le plus possible l'h6molyse et le collement des feuilles adjacentes les unes aux autres; (3) diff6rence de pression ~. travers la feuille, & l'ouverture de la valve, ne d6passant pas une valeur limite (sp6cifi6e darts cet article comme 6tant de 1 ~. 4 mm de mercure); et (4) dur6e de fonctionnement suffisante garantie (soit 1 ~. 2 • 10 s heurs). La feuille de valve est caract6ris6e par une face ext6rieure ayant deux rayons d'arc principaux R~, R2 sous tendus par des angles 0~, 02. Ces donn6es constituent les param~tres de forme pour la construction de la valve. Les deux premiers crit~res d6crits ci-dessus donnent les valeurs suivantes aux param~tres de forme: 01 -- 150 ~ 02 = 98 ~ R1 = 0,89R, .R2 = 0,87R. Le mat6riau de fabrication de la feuille, Avcothane-S1, a 6t6 choisi pour sa compatibilit6 biologique. Pour ce mat6riau dont les propri6t6s statiques et de fatigue sont fournies, l'6paisseur de la feuille est d6termin6e (pour une valve de taille donn6e) de faqon ~. satisfaire les troisi~me et quartri~me crit~res (6num6r6s au paragraphe ci-dessus) c'est & dire d'assurer une diff6rence de pression de feuille d'ouverture de valve de 1 ~. 4 mm de mercure et une dur6e de fonctionnement TI prescrite (de par exemple 12 • 105 heures, soit l'6quivalent de 12/l 24 arts).

Zu einer optimalen prothetischen dreibliittrigen aortenkonstruktion Zusammenfassung--Diese Arbeit stcllt eine optimale bl~ttrige Klappenkonstruktion fiir eine gegebene Klappengr68e vor, die folgende Konstruktionskriterien erfi~llt: (1) minimale Beanspruchungskonzentration in den Bl~ttern; (2) optimale Zipfelform zur Erzielung einer reibungslosen Aussp/jlung bei Klappenverschlul3 und eines minimalen meridionalen Fl~chenkontakts zwischen den Bl~ttern, um die H~imolyse auf ein Mindestmal3 zu beschr~inken und nebeneinanderliegende Bl~.tter davor zu sch/jtzen, dab sie aneinanderkleben; (3) Gew~ihrleistung, dab der Druckunterschied i~ber das Blatt an der Klappen6ffnung einen bestimmten Grenzwert nicht /jbersteigt (in dieser Arbeit mit 1-4 mm Hg festgelegt); und (4) Gew~ihrleistung einer angemessenen Betriebslebensdauer (z.B. 1-2 • 105 Stunden). Das Klappenblatt wird als Schalenfl~che mit zwei Haupt-Rundungsradien R1, R2 und zwei gegen/jberliegenden Winkeln 0~, 02 dargestellt. Dies sind die Formparameter der Klappenkonstruktion. Die ersten beiden Kriterien, die vorstehend umrissen werden, ergeben folgende Werte fiir die Formparameter: 01 = 150 ~ 02 = 98 ~ R~ = 0,89R, R2 = 0,87R. Das Material des BlaRes, Avcothane, wurde aufgrund seiner biologischen Vertr~glichkeit gew~ihlt. Fiir diesen Stoff, dessen statische und Erm/jdungseigenschaften bekannt sind, wird die St~rke des Blattes bestimmt (f/Jr eine bestimmte Klappengr/3Be), um das dritte und vierte Kriterium zu erf/Jllen (die im vorstehenden Absatz aufgeftihrt wurden). Dies gew~,hrleistet einea Blattdruckunterschied beim Offnen der Klappe von 1-4 mm Hg und eine vorgeschriebene Betriebslebensdauer 7'1 (z.B. 12x 10 s Stunden, was 12-24 Jahren entspricht).

Medical and Biological Engineering

March 1976

129

Toward an optimum prosthetic trileaflet aortic-valve design.

Toward an optimum prosthetic trileaflet aortic-valve design* D h a n j o o N. G h i s t a t Biomedical Engineering Division, Indian Institute of Techn...
576KB Sizes 0 Downloads 0 Views