1.
BIWWC~J
Fhnted m
Vol. :I.
OO?l-9.90 118S.UlO + .@I
No.
Pnpmon
circa,hum
t’rnr pk
A MECHANICAL ANALYSIS OF THE CLOSED HANCOCK
HEART VALVE PROSTHESIS
E. P. M. ROLISEA~. A. A. VAN STEENHOVENand J. D. JANSSEN
Department
of Mechanical
Engineering.
Eindhovcn
University
of Technology,
The Netherlands
H. A. HUYSMANS
Department
of Thorax
Surgery, University
of Leiden. The Netherlands
Abstract-In
order IO obtain mechanical specifications for the design of an artificial leaflet valve prosthesis. a
geometrically non-linear numerical model is developed of a closed Hancock leaflet valve prosthesis. In this
model. the tibre reinforcement of the leaflet and the viscoelastic properties of frame and leaflets are
incorporated. The calculations are primarily restricted to I,‘6 part of the valve and a time varying pressure
load is applied. The calculations are verified experimentally by measuring the commissure displacements and
leaflet centre displacement of a Hancock valve. The numerically obtained commissure displacements are
found to be linearly dependent on the pressure load, and the slope of the curves is hardly dependent on
loading type and loading velocity. Experimentally a difference is found between the three commissure
displacements. which is also predicted numerically using a simplified asymmetric total valve model. Besides.
experimentally a clear dependency ofcommissure displacements on frame size is found. For the leaflet centre
displacement. a qualitative agreement exists between numerical prediction and experimental result, although
the numerical predicted values are systematically higher. The numerically obtained stress distributions
revealed that the maximum von Mises intensity in the membranes occurs in the vicinity of the commissure in
the free leaflet area (0.2 N mm- ‘). Wrinkling of the membranes may occur in the coaptation area near the
leaflet suspension. The maximum fibre stress is found near the aortic ring in the libres which form the
boundaries of the coaptation area (0.64 N mm _z).These locations seem to correlate with some common
regions of tissue valve failure.
INTRODUCTION
In order to develop a numerical model for an arbitrary
leaflet valve prosthesis, a Hancock valve is analysed
and tested.The valve is essentiallyasymmetrical due to
the asymmetrical geometry of the porcine aortic valve
(Sauren. 198 I). Before mounting the aortic valve in the
frame, the entire valve is treated with glutaraldehyde
under a hydrostatic pressure of about 13 kPa (Broom
and Thomson, 1979). After the treatment, the leaflets
and a small part of the surrounding sinus and left
ventricle tissue are cut out from the total valve. This
piece of tissue. shown schematically in Fig. la, is then
mounted in the frame (see Fig. lb) using Dacron cloth.
After mounting, this cloth covers the frame. the sewing
ring. the hard metal ring and a small part of the sinus
and left ventricle tissue.
Earlier attempts to make a mechanical model of a
leaflet valve have been undertaken by Ghista and Reul
( 1977) who used relatively simple linear expressionsfor
the calculation of the membrane stressesin an isotropic model without fibre reinforcement and without
flexible leaflet suspension. Christie and Medland
( 1982) performed a non-linear finite element analysis
of bioprosthetic heart valves with fibre reinforcements.
In their model. purely elastic material behaviour was
assumed and the leaflet suspension was a rigid one.
Hamid et al. (1985)evaluated numerically the influence
Recrired 21 Xfurch
1986: in rerisedjorm
30 Seprembcr 1987.
545
ofstent flexibility on the magnitude and distribution of
stresseson the closed leaflets of a Hancock valve. Nonlinearities due to geometry and material properties,
and pressure dependent boundary conditions were
included in their model, but the influence of both the
anisotropy due to the fibre reinforcement of the leaflet
and the visco-elastic properties of frame and leaflet
were not taken into account. Experimental analysesof
the mechanical behaviour of a closed leaflet valve
prosthesis were also performed. For example,
Thomson and Barralt-Boyes (1977) measured optically the radial commissure displacements of two
Hancock valves in a mock circulation device.
Thubrikar cr ul. (1982) determined stresses in the
leaflets of a porcine bioprosthesis in the closed and
opened position, by putting radiopaque markers on
the valves and analysing their displacements under
X-ray control.
In the present study a mechanical model of a closed
leaflet valve prosthesis is aimed at. which incorporates
a geometrically non-linear relationship between deformations and displacements. explicit modelling of
the fibre reinforcement of the leafletsand the viscoelastic material properties of frame and leaflets. For the
sake of reduction of calculation time, the numerical
model has been primarily restricted to l/6 part of the
valve. hence assuming 120” symmetry. As the Hancock
valve is essentially asymmetric, a simplified (linear,
purely elastic) asymmetric valve model is also used to
analyse the relation between numerical model and
experiment. The numerical results will be verified by
E. P. M. ROUSSEAUet PI.
546
Fig. 1. (a) The frame of the Hancock Icatlet valve prosthesis. (b) A schematic outline of thecrownlikc piece of
tissue cut from a trcatcd porcine aortic valve, which is mounted in the frame.
measuring
the radial
commissure
frame
displacements)
vertical displacement
top displacements
and
(i.e.
by measuring
the
of the valve centre for several
sizes of valve prosthesis. In case of the Hancock
valve
the viscoelastic properties of the frame will appear to
be such that they probably
distribution
hardly
affect the stress
within theclosed leaflets. However, for the
design study of a new valve prosthesis a mechanical
model of a leaflet valve needs to be available in which
the viscoelastic properties of the frame can be changed
Fig. 2. Definition of the geometry parameters AJA,. H, and
such that they may influence the stress situation in the
9,.
closed valve during diastole. To verify such a mechanical model in case of the Hancock
experiments
loading
rampwise
are performed
mainly
in
rate; a slow rate for the frame denoted
by
loading
which
valve. various
differ
(i) leaflet surface A,/A,,
3) (Ai) and the total projected
A, =
loading.
(ii) commissure
MATERIALS
Geometry
and material
A&D %lETtlODS
geometrical
data
of the
19-21 and 23 mm valves are given in Table la and
supplied by Hancock Inc. The symbols in this table are
defined in Fig. la. The asymmetric geometry of the
Hi
(i = 1. 2, 3) which
is
Table I. (a) Geometrical data for the different frame sizes. All
measures arc in mm. For definition of the symbols see Fig. la
Framesize
(mm)
porcine aortic valve mounted in the Hancock valve is
sufficiently described by the next three parameters (see
Fig. 2):
height
1 A;.
i-1
the valve base.
properties
The
leaflet surface:
defined as the distance between commissure point i and
The frame construction consists of three similar
parts with unequal cross-sectional angles (120” - 135”
- 105”) (see Fig. lb).
of the
3
and a faster one for the leaflets
denoted by physiological
being the quotient
projected leaflet area belonging to frame top i (i = I, 2,
23
h,
h,
I...,
r*,
WI
w.?
14.6
16.0
6.1
6.7
9.4
10.4
8.3
9.3
I.3
1.4
2.0
2.2
17.2
7.1
Il.4
10.3
I.5
2.4
I
I.1
I.1
1.1
541
A mahanical analysis of heart valve prosthesis
Table 1. (b) The geometry of the Hancock valve as characterized by the leaflet surface areas A,/A,, the
commissurc heights Hi and the angks 0, (see Fig. 2). The SD. of each parameter amounts to 0.05.0.1 mm
and I’ respectively. For the 23-l mm valvealsothe I coordinatesof the points A. 8. C. D and E asusedin
thenumerical model are given (seeFig. 4~). For A. 8, D and E these z-coordinates are taken to heequalfor
the three valveparts (SD. are 0.2 mm)
Frametop
I
Valve
19
21
23-l
23-2
0.37
0.35
0.29
0.37
23-l
l-2-3
0.5
l-2-3
7.0
At/A, I 2
0.32
0.37
0.32
0.32
I
10.6
Hi (mm)
1
2
12.9
3
I
2
3
I
0.31
0.28
0.39
0.31
8.8
9.6
12.1
12.2
6.8
9.0
14.3
10.9
9.1
It.9
14.5
12.0
50
64
50
41
3
13.1
(iii) angle Cpi(i = I, 2.3) made by the upper boundary of the coaptation area i. and the ‘horizontal axis’.
The values of A,/A, (i = 1. 2. 3) were determined
from photographs of the bottom of the valve. The
commissure height Hi and the angle 4, were measured
using a moving crosstable (Carl Zeiss) having an
absolute measurement accuracy of 0.001 mm in each
point. The measurement data for the four valves
considered are listed in Table I b. Besides, for the
numerical modelling (see Fig. 4) another geometrical
characterization is given by the coordinates of the
points A. B, C, D and E. Here, the surface BCDE
representsthe coaptation area and ABE represents the
free leaflet area. BC. CD, DE and AE are straight lines.
The z coordinates of the points A. B, C. D and E were
measured in the same way as H, and 4, were measured.
For one 23 mm valve these data are also given in
Table lb. The thickness of the leaflet in all cases is
about 0.4 mm (Rousseau er al., 1981). Finally, leaflets
of the Hancock prosthesisarc reinforced with collagen
bundles. A typical fibre pattern is illustrated in Fig. 4b.
The properties of the frame material (polypropene)
were obtained in two parts. The Young’s modulus of
the polypropene was determined by DSM (1977) and
was found to be 1582 N mm-* at a temperature of
23°C. The Poisson ratio was found to have a constant
value of v = 0.4. Besides,some relaxation experiments
were performed on polypropene test specimens
(60 mm long. 3 mm wide. 0.5 mm thick) which wcrc
clamped in a Zwick 1434 testing equipment. The test
specimenswere strained in a steplikc way within 0.5 s
and from the stress relaxation the viscous properties
were determined in the way as outlined below.
The viscoeiasticmaterial properties of the Hancock
leaflet tissue were determined using the experimental
procedure developed by Sauren et 111.(1983). The
experiments were performed on strips of about 3 mm
wide which were cut in the circumferential direction
from the leaflets. This direction globally corresponds
l-2-3
‘a.5
75
61
48
58
60
68
45
44
l-2-3
4.6
to that of the collagen network. The experiment,
extensively described by Rousseau et al. (1983). involved straining of the specimen with a constant
elongation rate, followed by maintaining the specimen
length at a predetermined level. Two parameters were
defined in order to quantify theelastic behaviour of the
tissue: E, being the slope of the stress-strain curve for
the unloaded situation and E,, being the slope of the
curve for the situation corresponding with a pressure
load of I3 kPa.
The viscoelastic behaviour of frame and leaflet was
characterized by the reduced relaxation function G(f).
used by Fung (1972). This function is defined as
G(r) =
F(r)
F(r = 0')
where F(r) is the measured force responseat time r to a
stepchangc in the length at timer = 0. Fung (1972) has
proposed to describe the material behaviour using a
so-called continuous relaxation spectrum between two
boundaries 0, and 0,. However, for the polypropene
this does not give an appropriate description of the
material behaviour. An extra parameter (5,) has to be
added to the reduced relaxation function G(r) so that
the continuous spectrum given by Fung (1972) get a
better fit. This gives
I +s,
G(r) =
* 0,
e-“‘dr
J u,
+ K
uJ1
- e-“‘dr
s 0, r
1 + S”(0, -O,)+Kln(O,/U,)
’
(21
In this equation. So, K. 0, and 0, are the viscoelastic
parameters which have to be determined. For the soft
tissues (leaflets and libres) 5, equals zero. K is the
parameter which has the greatest influence on the total
amount of relaxation after a large time interval. The
time constant 0, has an influence on the slope of the
relaxation function just after the beginning of relaxation and the time constant tIZ is a measure for the time
E. P. M. Rousseauet nf.
s48
which is naxssary to reach the maximum relaxation.
Further physical interpretation of the parameters K.
S,,. 8, and 8, should be handled carefully (Lauren and
Rousseau. 1983). The reduced relaxation function G(r)
has to be determined from the load response of the
specimen to a step change in the length of the
specimen. As it is physically impossible to realize a true
step change, a finite time interval rr of about 0.1 s for
the leaflet material and of about 0.5 s for the polypropene was considered.
From the response of the leaflet material, first the
stress-strain curve was determined and the parameters
E. and E,, were obtained. Next, the parameters K. 0,
and 8, were determined by fitting the measured
relaxation curve on relation (2) using the least squares
method. The viscoelastic material properties of the
polypropene were determined in the same way. All
measured material properties are given in the last
column of Table 2. For further detailed information
we refer to Rousseauet al. (1983) and Rousseau (1985).
From the relaxation experiments a clear difference is
observed between the viscoelastic material behaviour
of the polypropene and the glutaraldehyde treated
tissue.This is elucidated by the frequency dependency
of the loss modulus. This parameter, which describes
the amount of energy dissipation and hence correlates
with the amount of hysteresis,can be calculated from
the continuous relaxation spectra (Rousseau, 198s).
Figure 3 shows the loss modulus versus frequency for
both materials. From this figure it isconcluded that the
loss modulus of polypropene has a maximum at
/z IO-’ Hz (periodic time T 2 IO’ s). On the contrary the maximum of the loss modulus of the leaflet
has a maximum at about /z 1 Hz (periodic time
T z I s). This means that the viscoelastic phenomena
of the frame are just notable in case of a very low
loading rate and those of the leaflets at a much higher
one. More specifically, the results indicate that the
viscous properties of the valve leaflet are quite well
notable during a cardiac cycle (f 4 1 Hz). while the
influence of the viscous properties of the frame may
then be neglected.
77te numerical
model
The mechanical behaviour of the closed Hancock
valve has been examined using a non-linear finite
element package (MARC, 1983). First, l/6 part of the
valve has been analysed, hence assuming 120” symmetry. In the geometry of the l/6 part of the valve,
which is shown in Fig. 4. the surface BCDE represents
the coaptation area and ABE representsthe free leaflet
area. The geometric data as obtained from Table 1
were averaged over the three valve parts. These
averaged values are given in Fig. 4a. The free leaflet
surface ABE is further described by straight lines
between AB and BE. For AB the intersection of a
sphere. with its central point in the y-: plane, and the
cylinder surrounding the frame. was taken. As outlined
earlier the leaflets of the Hancock valve are reinforced
with collagen bundles. Fig. 4b shows how this fibre
reinforcement was modelled in the numerical model.
Finally. a constant leaflet thickness amounting to
0.4 mm was assumed, the fibre diameter was 0.4 mm.
the diameter of the aortic ring amounted to 0.8 mm
and the sinus wall tissue was assumed to have a
thickness of 1.6 mm.
The frame was modelled with cylindrical beam
elements, having the material properties of polypropene as described before. The leaflet tissue was
modelled with membranes (Young’s modulus = E,)
and truss elements (Young’s modulus = Et ,). Besides,
the leaflet is assumed to be incompressible. For
numerical reasons the value of the Poisson’s ratio was
chosen to be 0.49. Finally, the time-dependent material
behaviour of membranes and fibres (= truss elements)
was taken equal. To incorporate the viscoelastic material properties of leaflet and frame the continuous
relaxation spectrum has been transformed into a
generalized Maxwell model with n branches (2n + I
parameters) as required for the input deck of the
polypropene
\
lo.5
frequency
(a)
(Hz)
10’
10’
frequency
(Hz)
16
(bl
Fig. 3. The loss modulus of the polypropene (a) and of the glutaraldehyde-treated
tissue (b). The
modulusis given as a dimensionless quantity: the values ate divided by the maximum value.
loss
Linear elastic
Linear elastic
Diameter
= 0.4 mm
Diameter
= 0.8 mm
Diameter
= 0.4 mm
Leaflet
suspension
Free leaflet
area
Coaptation
area
Fibre
reinforccmcnl
Aortic ring
Dacron
Membrane
Membrane
Membrane
Truss
Truss
Truss
27-46
47-73
74-125
126132
133-136
r>0,
I S-26
u, < T
0
S(t) =
0
K/r
r<0,
r>0,
0, < c < @I
(-)
v =0.4 (-)
E = 1000 (Nmm-*)
0, = 0.0019 (s)
0, = 23.0 (s)
E = 23.0 (N mm-‘)
v=O.5(-)
E = loo0 (Nmm-‘)
v=O.S(-)
K =0.05
K =o.os (-)
0, = 0.0019 (s)
u2 = 23.0 (s)
E = I.8 (Nmm“)
v=O.49(-)
Viscoelastic
v = 0.4 ( - )
E = 1582 (Nmm-‘)
Thickness
= 0.4 mm
u,
Linear elastic
<
Thickness
= l.6mm
r<e,
so+ K/r
E = 5.0 (Nmm-‘)
v=O.49(-)
S(r) =
0.926 IO-’ (s-l)
O.IOSI (-)
3.4 (S)
63270 (s)
So =
K=
8, =
61 =
Viscoelastic with a
continuous relaxation
spectrum S(r):
Diameter
l-l.5 mm
Polypropcnc
frame
Material parameters
Material description
Geometry
Modelled valve
part
Cylindrical
beam
Element
‘)‘pc
l-14
Element
number
Table 2. Description of the elements, geometric and material properties
E. P. M. ROUSSEAUet al.
(a)
(b)
B
(cl
Fig. 4. (a) The basic geometry of the total valve. BCDE = coaptation area; ABE = free leaflet area; ABC
= aortic ring. Some z coordinates are given for the 23 mm valve. (b) Geometry of the fibre-reinforcements.
(c)The total mesh of the leaflet valve prosthesis.
MARC
program
formation
package (MARC,
1983). This trans-
and the resulting material
given elsewhere (Rousseau,
parameters
are
with regard to the surrounding
tissues
had to be made. The sinus wall tissue was assumed to
be purely elastic and modelled with membranes.
Young’s modulus
of this tissue was estimated
some tensile experiments
analogously
of
fibres,
the
The
Young’s
modulus
Nmm-‘(Roffer
ranges
al., 1971).For
the Young’s modulus of the Dacron used in the valve
prosthesis the arbitrary
chosen, and
elements.
the
value of 1000 N mm-*
Dacron
was
modelled
by
was
truss
from
The l/6 part of the valve was modelled with 75 nodes
to those de-
and 136 elements; the mesh is shown in Fig. 4c. The
scribed for the leaflet tissue, its value being about
5 N mm-‘.
form
between4OOOand7500
1985).
To model the complete valve prosthesis also some
assumptions
of about 30 N mm- ’ (Gilding et (II.. 1984); when it is in
the
Not much was known about the material
used elements are described in Table 2. The MARC
package
allows
for coupling
of elements
with
properties of the aortic ring. Sauren er al. (1983) stated
unequal number of degrees of freedom (DOF)
that the aortic ring is much stitTer than the other valve
nodal
parts. Therefore,
relevance is that DOF’s
we modelled the aortic ring by truss
points.
A
necessary condition
for
with corresponding
an
in the
physical
numbers
elements, having a Young’s modulus of IO00 N mmm2.
do have the same meaning. Because for the membrane
For Dacron somedataare
elements as well as for the beam and truss elements
known. When the Dacron is
in the form of patch material, it has a Young’s modulus
DOF
I. 2 and 3 denote the displacements with respect
A me&at&al analysis of heart valveprosthesis
to the global coordinate-system, the displacement
compatibility in the nodal points is guaranteed. Extra
DOFs belonging to beam elements and denoting
rotations cause incompatibility of the displacements
between the nodal points. thus violating in a mild
manner the physical connection of frame and leaflet
suspension.The element-incompatibility artifact is not
encountered between the truss and membrane elements as they have equal nodal degrees of freedom.
During calculation the valve was loaded incrementally with a time varying uniform pressure load over
the free leaflet area. The model did not account for the
transition of material points from the free leaflet area
to the coaptation area. Hence, the valve model was
fixed rigidly at the base while symmetry conditions
were applied at the planes (b = 30” and 4 = 90” (see
Fig. 4a). This means that all points in the coaptation
area and in the leaflet centre were only able to move in
vertical direction. In order to give the membrane and
truss elements an initial stiffness. the model was first
prestrained by loading the initial mesh with a very
12-’
551
small pressure load This was done for the first
increments (Ape, Ape. lOApe and SOApe. Ap,
= 7.5 IO-* kPa for increment 0. 1. 2 and 3 respectively). From increment 4. the valve was loaded according to the following patterns
(i) A load increasing linearly with time until a pressure difference of 12 kPa was obtained. followed by
a decreasing load with the same velocity, until the
starting point was reached (Fig. Sa). The total loading
and unloading time was varied (0.02-3600 s). This
loading will be denoted by rampwise loading.
(ii) A physiological loading (Fig. Sb), which resembles the in uirro measured pressure difference
across the valve during a simulated cardiac cycle.
These load patterns were chosen to investigate the
influence of the different viscoelastic properties, especially the different relaxation times of frame and
leaflets. It has to be stressedthat inertial effectsare not
treated. both in the rampwise and physiologic cases.
For both loading cases the loading time could be
varied by adjusting the increment time.
fb)
t
bP
UCPJ)
‘)
1
O*
0
Fig. 5. Loading
patterns for the
numericalmodel.
(a) Rampwise
loading. (b) Physiological
loading.
552
E. P. M. Rousss~u cl al.
The following
stress quantities
by the von
were determined
in the leaflet. illustrated
(i) The stress distribution
Mises intensity
S for
the membranes,
defined as
S = J&j&,
(3)
where Sij are the components
of the deviatoric
stress
tensor.
(ii) The tensile stresses in the fibres.
(iii) The
minimum
principal
stress in the mem-
branes between the fibres. The membrane
the MARC
element of
program package has the same constitutive
behaviour for positive as for negative strain. When the
strain has a negative value, for example in the coaptation
area, actually
the membrane
will buckle. An
element which correctly accounted for the possibility
of wrinkling
minimum
was not available.
principal
desirable stress-situation
Furthermore,
When observing the
stresses, an indication
for experimental
lowing displacements
of an un-
is obtained.
verification
the fol-
in the valve were calculated
(iv) The radial corm&sure
displacement
as a func-
(v) The axial displacement
m
(01
tion of time and of pressure load.
of the valve centre both
as a function of time and of prcssurc load.
To analyse numerically
the inlluencc of the asym-
metry of the valve upon the displaccmcnts
centrc and commissurcs.
total
valve
a numerical
was designed
the
of leaflet
model of the
geometry
of
which
was described using the gcomctric parameters as surnmar&d
in Table
I. WC simplified
the total
model by assuming linear elastic material
of
the diffcrcnt
linear
valve
relationship
parts
between
and
by
strain
valve
bchaviour
assuming
a
and elongation;
this is acceptable because the aim of this analysis is to
find a correction
of the symmetric
parison, also the commissure
part of the symmetric
model. For com-
displacements
valve model
under the same assumptions.
of 1/6th
was calculated
The mesh of the total
model is given in Fig. 6. The valve was loaded with a
Fig. 6. The mrsh of the total rsymmclrical
model.
pressure load of I2 kPa across the free leaflet areas.
Next, the commissurc and leatlet centre displacements
of the asymmetrical and symmetrical
compared.
valve model were
To that end the initial slope of the curves
representing the commissure displacement
load as well as the leaflet ccntre
vs pressure
displacement
vs
pressure load were determined.
I). see Fig. 7. The pressure load was first increased up
to a level of 20 kPa immediately
to 1.4 kPa. To determine
velocity the valve was loaded within
within
Next,
Exprrimentol
For
model
loading
rerijicution
experimental
of
the entire
prosthesis (242 Aortic)
followed by a decrease
the influence of the loading
150 s as well as
1800 s with a constant velocity.
the valve was subjected
in a mock circulation
to a physiological
device developed
by
Leliveld (1974). This mock circulation device which has
verification
valve
of
the
prosthesis.
was mounted
numerical
a Hancock
in a rigid valve
housing such that the base of the valve was fixed. This
been described earlier by van Steenhoven er al. (1982)
mainly
consists of a left ventricle,
aorta
and load
impedance (see Fig. 8a). The left ventricle is simulated
by a moving piston system in which the movements of
was realized by fixing the valve using the sewing ring
the piston are controlled
and using a well fitting valve housing. First, the valve
the inflow side a sturdy silastic leaflet valve is mounted
was loaded in a rampwise
simulating
static pressure was applied
way. To that end a hydroto the closed valve pros-
pump
the mitral
is connected
by a regulated air pressure. At
valve. The inflow
to a reservoir
side of the
with
overflow,
thesis by means of a fluid column, the height of which
simulating
was controlled
constant supply pressure during the pump relaxation
using a gear-wheel
pump (Verder
I l4-
the left atrium.
This reservoir provides a
A
mechanicalanalysisof heart valveprosthesis
Fig. 7. Schematic outline of the rampwise loading system. p
= pump: p.c. = pump control; vh - valve housing; v = valve;
Ap = recording of the pressure load.
553
phase. Between the ventricle and aorta different valve
prosthesescan be mounted within a persper housing.
A bottle compliance is connected at the beginning of
the latex tube, to compensate for the rigidity of the
valve house and the flow meter. However, due to the
large valve housing necessaryfor these measurements,
high pressure peaks just after valve closure are inevitable. The load impedance at the end of the aorta is
designed as indicated by Westerhof et al. (1971). It
consists of two fluid resistances.coupled by a bottle
compliance. The fluid resistancesare composed of a
large number of parallel capillaries with an internal
diameter of 0.6 mm. The values of the components of
the load impedance are chosen in accordance with
Westerhof’s data for men. The fluid used is a
physiological saline solution.
Pressuresat the left ventricular (P,,) and aortic sides
(Pa,) of the valve were measured in both types of
loading with Statham P23dB pressure transducers
(IOU Hz, - 3dB). The pressuredilTerenceacrossthe valve
(AP) was obtained by subtracting the two pressures
electronically (Tektronix AM 502). In the mock circulation system the aortic flow was also measured at the
outflow of the valve housing by an extracorporeal
Fig. 8. (a) Schematic drawing of the mock circulation system. sc = servo control; s = supply: alv = artificial
left ventricle: vh I valve housing: a = aorta: Ii = load impedance: p = pump: Ap, q = recordings of pressure
dilTerence and flow. (b) Measurement
of the commissure displacements by using six electrical coils.
(c) Measurement of the displacemcnr of the leaflet cenlre by using an Alvar ultrasonic measuring device. The
double channel probe is positioned so that only the axial velocity is measured.
E. P. hi. Roussmu et al.
554
electromagnetic flow probe (Transflow 601, 100 Hz,
- 3 dB). The commissure displacement for each frame
top was measured using an inductive measuring device
(100 Hz) as developed by Arts and Reneman (1980)
and modified by van Renterghem( 1983). It essentially
consistsof two small electrical coils (Fig. 8b). One coil
was sutured at the commissure whereas the other coil
was glued to the nearest opposite wall of the valve
housing. The time varying current (100 kHz) through
the coil on the valve housing induced a voltage in the
coil on the commissure. From the induced voltage. the
distance between the two coils was derived
Ar=(r-rO)=rO{exp(Y/C’)-I}
(4)
with r0 = distance between the two coils in unloaded
condition (mm): r = actual distance between the two
coils (mm); Y = the induced voltage (V); C = a constant factor with a value of 2.05 (I/Y).
Finally, the leaflet centre displacement was
measured cinematographically in the rampwise loading situation and assessedby integrating the leaflet
centre velocity in the physiological loading case. In the
caseof the rampwise loading, use was made of a video
camera and recorder which registered the vertical
movement of the leaflet centre. In the case of the
physiological loading use was made of an adjusted
ultrasonic Doppler device (Alvar. 50 Hz. - 3 de). The
position of the probe was such that only the axial
component of the leaflet velocity was measured in the
plane of the pipe (see Fig. 8~). Using the range gate the
measuring volume (x 0.8 mm’) was focussed upon
the underside of the coaptation area in unloaded
situation. Care was taken that the measuring volume
was in the leaflet during the whole period that the valve
was closed. As no reflecting particles were added to the
fluid only the leaflet velocity was measured.
The analogue signals (pressures,pressuredifference,
flow, frame top displacement, leaflet centre velocity
and a triggering signal) were recorded on magnetic
tape using an instrumentation recorder (HP 3968A).
The signals of pressuredifference, frame top displacement, aortic flow and leaflet centre velocity were
digitized with a sampling frequency of 500 Hz. Before
digitizing, the signals passed through a low pass filter
(Krohn-hite 3750; 100 Hz, - 3dB) to prevent aliasing.
The digital data were then fed into a Prime (750)
minicomputer. The digitized signals were all averaged
over ten periodiccycles. Next, the velocity of the leaflet
centre was integrated numerically from the moment of
valve closure and shifted over about 8 ms to compensate for the electronical delay in the velocity meter
system. Finally, the commissure displacement and
leaflet centre displacement were determined as a
function of the pressure dilTerenceacross the valve.
REsULl?s
The commissure
displacements
For the case of rampwise loading, the predicted
commissure displacement of the valve model is given as
a function of pressure load in Fig. 9a. For the case of
physiological loading the displacementsare given both
as a function of time and of pressure load in Fig. 9b.
Comparing these figures. it is observed that the
commissure displacement as a function of pressure
load is nearly linear. The slope is equal to 0.0233 and
0.0225 mm kPa - ’ respectively. So, for the range of
load velocities studied here. with the numerial model
no viscoelastic phenomena were found for the commissure displacement as expected from the viscous
properties of the frame. However, when the load
velocity decreases,the amount of hysteresisincreases
(see the table in Fig. 9a).
A characteristic experimental result for a rampwise
loading pattern (loading and unloading time is about
3600s) is shown in Fig. IOa. Here, the measured
relation between commissure displacement and pressure load is given. From this a remarkable amount of
hysteresisis noticed. The amount of hysteresis,averaged over the three frame tops, is 13 ‘;/ and 25 I’/;,
respectively for a high loading velocity (rise time is
about 150s) and a low loading velocity (rise time is
about 1800s). which is considerably higher than
numerically predicted (9.5 and 1I.2 %. respectively).
A characteristic result of the experimentally dctermined commissure displacement during a
physiological lodding pattern is given in Fig. lob. It
shows:
the pressuredilrerence. averaged over ten cycles,as a
function of time during one cycle
the displacements for the three commissures, also
averaged over ten cycles, as a function of time.
Next, from the signal two parts were analysed
separately: the first part (fast fluctuations just after
valve closure; time z 0.2-0.4 s) and the second part
(valve behaviour during the remaining part of diastole;
time z 0.4-0.9 s). For the second part, the relation
between commissure displacement and pressure difference is also given in Fig. lob. From this figure, it is
observed that during a cardiac cycle the relation
between commissure displacement and pressureload is
nearly linear for the secondpart of the loading cycle, its
slope is denoted by CJ. For the first part also a nearly
linear relationship was found, its slope is denoted by
C,. For both parts, the slope was determined by a
linear regression analysis, the results of which are
shown in Table 3a; they do not differ significantly.
From the experiments it is furthermore concluded that
there is a considerable dimerence between the three
commissures and that no hysteresiscan be observed.
Table 3b summarizes the values for the slope of the
displacement-pressure curves during the second part
of the loading cycle (C,) for all valves measured. It is
seenthat the asymmetry of the frame top displacement
is present in all valves.For smaller valves,the slope CZ
decreases. Finally,
the mean slope of the
displacement-pressure curve of the 23-l mm valve
under rampwise loading conditions, denoted by C is
also inserted in Table 3a. They are slightly higher than
A mshanical analysis of heart valve prosthesis
(a)
pressure
load &Pa)
Fig. 9. (a) Numerical results corresponding to a rampwisc loading pattrrn: Ii) pressure load as a function of
time; (ii) commissurc displacement as a function of pressure load. (T = 3600s). (b) Numerical resuhs
corresponding to a physiological loading pattern: (i) physiologicalloading pattern; (ii) ealculaledcommissurc displacement as a function of time; (iii) commissurc displacement-pressure load relation.
those determined under a physiological loading
pattern.
To compare the experimental and numerical results
in more detail, the asymmetrical numerical model is
used. This model prediction is also inserted in
Table 3a. From this it is concluded that the asymmetrical commissure displacements are in good agreement with the experimental results for frame tops 1
and 2 while for frame top 3 an underestimation of its
displacement is found. There is also a fair agreement
between the slope obtained for the symmetrical linear
model and the averaged slope of the asymmetrical
linear model. Also the slope of the three experimental
commissure displacement-pressure load curves of one
valve were averaged. The values of the slope measured
with the mock-circulation system have an average
value of0.0227 (2 0.0040) mm kPa_‘. When comparing this value with the slope found numerically with
the symmetrical non-linear model (0.0225 mm kPa- ‘),
the conclusion is justified that the agreement between
theory and experiment is fair.
7he leaflet cenlre displacement
For the case of rampwise loading the predicted and
measured displacement of the leaflet centre (23-l mm
valve) are given as a function of the pressure load in
& P. M. ROUSSEAUet al.
556
0
prcsrurr
load
IkPc,)
(b)
top 3
iop 2
IOP 1
R
Fig. IO. (a) A characteristic result of the rampwisc experiment. (top 3. 23-l mm valve. rise time: 1800 s). A
mean slope 7 is defined in the pressure-displacement
relation. (b) Experimental results of the measurements
in the mock circulation system: (i) the pressure dinircnce across the valve. averaged over ten cycles; (ii) the
three commissure displacements. averaged over ten cycles: (iii) commissurc-displacement
pressure-load
relation of the quasi-static part of the load cycle.
10
A mechanical analysisof heart valveprosthesis
Table 3. (a) Values for the slope of the relation between commissure displacement
and pressure load, determined with the mock circulation system (C,, Cz) and with
the rampwise loading set-up (0. compared with the values found with the
asymmetrical numerical model and the symmetrical model (linear and non-linear).
The standard deviations are given between parentheses
Frame top number
C values in (mm kPa- ‘)
23-l mm valve
Symmetrical model
non-linear
Symmetrical model
linear
Asymmetrical model
linear
1
2
3
O.Ol40
(0.0005)
o.oi31
(0.0005)
0.0148
(0.0010)
0.0200
(0.0098)
0.0205
(0.0006)
0.023 I
(0.0030)
0.0310
(0.00l4)
0.0304
(0.0010)
0.0372
(0.0035)
0.0225
0.0183
0.0133
0.0208
0.0192
Table 3. (b) The pressure-commissurcdisplacement slopes for the second part of
the loading cycle for all measured valves. The S.D. are given between parentheses
CZ
(mm kPa- ‘)
valve
23-l
23-2
21
I9
I
0.0131
(0.0005)
0.0224
(0.000s)
0.0058
(0.0003)
0.0062
(0.0002)
Fig. 11. In Fig. 12 the numerical predicted leaflet centre
is given as a function of time and of
pressure load for the physiological case (for the
23-2 mm valve). From these figures it is observed that
the relation between the axial displacement of the
leaflet centre and the pressure load is non-linear, and
shows a small amount of hysteresis.
In Fig. 13 a characteristic experimental result is
given of the centre displacement during a simulated
cardiac cycle. In this figure the pressureload acrossthe
valve. the velocity of the leaflet centre and the integrated velocity signal arc shown as function of time
during the fast fluctuations in the cardiac cycle. In
Table 4 the values of pressure and displacement after
the fast fluctuations for the two measured valves are
summarized together with the numerical predictions.
From this table it can be seen that the numerical
predictions are constantly higher than the measured
Frame top number
2
0.0205
3
0.0304
(0.00l0)
0.0164
(0.00l0)
0.0047
(0.0003)
0.0043
(0.0002)
(O.ooo6)
0.0107
(O.OaO3)
0.0062
(0.0002)
0.0012
(O.OGul)
15
displacement
leaflet displacements.
%
E
i;
E’u
2%
$Q
16
0
pressure
looa
(wal
15
Fig. I I. Lcaflctccntre displacement for the 23-l mm valve in
the rampwise loading experiment. The solid line represents
the numerical prediction. The measured displacements are
indicated as dots.
E. P. M. ROWXAU et al.
558
time
(5)
(b)
-r
0
I
pressure
load
10
(kPa)
Fig. 12. Numerical prediction of the leaflet centrc displacement during the fast fluctuations just after valve
closure for the 23-2 mm valve. (a) Pressure load and leaflet centre displacement as a function of time.
(b) Displacement
7%~ stress distriburion
within rhe IeuJfers
vs pressure load.
expect to encounter
maximal element-incompatibility
artifact.
A contour
plot of the von Mises intensity
in the
In
Fig.
14b
a contour
plot
of
the
minimum
membranes of the valve loaded with IZ kPa is given in
principal stress is shown for the same loading situation
Fig. 14a. From this figure it is seen that the von Mises
as the one in Fig. 14a. From this figure it is observed
intensity has a maximum
in the vicinity of point Band
amounts to about 0.20 N mm-‘.
interpreted
cautiously
This result has to be
as precisely
here one would
that at IZ kPa the minimum
coaptation
is mainly
found in the
area in the vicinity of the leaflet suspension
(region between B and C).
A mechanical analysis of heart valve prosthesis
Table
559
4. Eapcrimcntal
and numerical
results of
the leaflet centrc displacement. The SD. are given
between parentheses
Experimental
AP
Au
Numerical
Au
Valve
(kPal
(mm)
(mm)
23-l
232
8.0
5.5
4.0
0.55
0.55
0.35
(0.05)
1.10
0.85
0.70
(0.0
(-)
terial parameters some of these parameters were varied
between
shows
some
marizes
minimum
Fig.
13. A characteristic experimental result of the leaflet
centrc displacement.
for
leaflet
intensity
principal
maximum
centre
Table 5
and
sum-
commissure
the
von
I in the membrane,
displacement,
the
stress in point 2 (see Fig. 4c) and
the tensile stress in fibre 5 (see Fig. 15). From this table
it can be observed that the commissure
and increasing
displacement
with decreasing frame stiffness
s(C) and r(B).
while
the other
par-
this ligure it is seen that the
ameters have only a slight influence. The leaflet centre
value of stress is found in fibres 5 and 8 and
displacement is sensitive for almost all parameters. The
given in Fig. IS. From
amounts
values.
analysed
the calculated
for point
increases remarkably
The fibre stresses at a pressure load of I2 kPa are
boundary
situations
the results
displacement,
Mises
arbitrary
the different
to about 0.64 N mm-’
in the vicinity of the
aortic ring. The hbre stress is nearly constant over the
free leaflet area (minimum
while in the coaptation
0.3. maximum 0.5 N mm - *)
arca the stress varies from 0.64
von Mises intensity
in point
the tibre and membranes
membranes
are stiffer,
geometry parameters.
I increases only when
are very thin or when the
but
is independent
Furthcrmorc,
of
the
the fibre stress in
to 0.0 N mm - ‘.
tibre 5 is dependent on (r,, rl,. E, and z(C). Finally, the
M&l
sensitive to the geometry
minimum
To
smsificity
get some
numerical
insight
into
the sensitivity
results on the different
geometry
of the
and ma-
only for
principal
stress in point
2 is not
and material
very
paramctcrs;
the case cl, = 0.2 mm is a large negalive value
found.
cl
•J
-002--006
(b)
>-002
Fig. 14. (a) Contour plot of the von Mists intensity in the membranes for a pressure load of I2 kPa.
(b) Contour plot of the minimum principal stress in the membranes for the same load value of I2 kPa.
E. P. M. ROUSSEAUef al.
ledrlel
anchorage
poS~llon
I”
Ieallet
1*a11et
centrc
Fig. IS. Tensile stress in the fibres.
Table 5. Model sensitivhia. cd = commissure displacement (mm); Icd = leaflet centre displacement (mm); vM = von Mises intensity in point I (N mm-‘k fs = fibre stressin fibre 5 (N mm-‘):
mps = negative
valuesof minimum principle
stress in point 2 (N mm _ ‘). (The diflerenl positions
in the leaflet are illustrated in Fig. 4e and the fibrc in Fig. IS)
Adjusted
situation
Boundary
values
cd
led
vM
fs
mps
0.21
I.36
0.278
0.47
0.110
0.39
0.1s
0.06
1.48
1.27
I.16
0.287
0.276
0.272
0.4x
0.47
0.45
0.110
0.110
0.106
0.1 mm
0.7 mm
0.24
0.28
I.85
1.07
0.307
0.253
0.56
0.37
0.093
0.114
0.2 mm
0.7 mm
0.30
0.27
1.61
I.16
0.502
0.195
0.76
0.33
0.173
0.078
I.15 Nmm-*
3.5 NmmSz
0.30
0.21
1.54
I.11
0.292
0.353
0.67
0.31
0.095
0.143
9.2 mm
14.5 mm
0.16
0.38
1.67
I.17
0.318
0.285
0.60
0.40
0.105
0.111
5.0 mm
1.9 mm
0.27
0.26
1.33
1.39
0.276
0.282
0.46
0.48
0.115
0.107
5.8 mm
8.2 mm
0.22
0.32
1.49
I.25
0.277
0.246
0.46
0.52
0.116
0.098
6.0 mm
3.1 mm
0.29
0.24
1.48
1.24
0.260
0.237
0.40
0.55
0.113
0.108
E rrame= 1582 N mm-*
d, = d, = 0.4 mm
E, - I.8 Nmm-*
zc= 12.1 mm
so = 6.5 mm
za = 7.0 mm
eE = 4.6 mm
E,=?XONmm-’
Rasic
model
1000 Nmm-*
3600
Nmm“
IO0000 Nmm-’
DISCUSSIOS
experiments.
pendent
The
commissure
displacements
of the valve are
on
The slope of the curves is hardly
loading
type
and
loading
de-
velocity
(Table 3). From the experiments a difference is found
found to be linearly dependent on the pressure load,
between the three commissure displacements. which is
both from
predicted
the numerical
predictions
and from
the
numerically
using a simplified
asymmetric
A mc&anical analysis of heart vdve prosthesis
total valve model. The agreement was fair for two
frame tops. The observed discrepancy between the
numerical prediction and the experimentally determined displacement of the third commissure is partly a
consequence of the underestimation due to the linear
theory, while also a change in the position of point B
during valve loading may contribute to this (seeTables
3 and 5). Furthermore, the experimentally determined
commissure displacements show a clear dependency
on valve size which is attributed to the smaller leaflet
surface areas and lower commissure heights of the
smaller valves. The commissure displacements were
also measured for Hancock valves by Thomson and
Barratt-Boyes (1977) whose resultscorrelate quite well
with our data. They found linear relationships between
commissure displacement and pressure load, and they
observed a remarkable difference between the displacements of the three frame tops of one valve
(displacements ranged between 0.00 and 0.29 mm for
the pressure load of 16 kPa). The value of the commissure displacement, calculated by Hamid et al.
(1985)
assuming
isotropic
leaflet
properties
(0.125 mm-O.275 mm at a pressure load of 16 kPa.
depending on frame stillness). is considerable lower
than the numerical and experimental data we found.
This may indicate that the incorporation of the fibre
rcinforcemcnt of the leaflet in a numerical model of a
leaflet valve prosthesis is essential.
For the lea&t centre displacement a qualitative
agreement between numerical prediction and experimcntal result is found. However. the numerical prediction is systematically higher than experimentally
found. This discrepancy is certainly related to the fact
that the leaflet centre displacement is dependent on
nearly all geometrical and material parameters of the
valve as observed in the model sensitivity analysis. The
most uncertainly defined parameters of those summarized in Table 5 are flbre and membranes thicknesses.The experimental results indicate that they are
probably underestimated in the numerical model.
Resides,deviations between the material properties of
the tissue strips analysed and the present valve may be
present. Improving the numerical model may be
possible by introducing inhomogeneous fibre and
leaflet thickness, while also the boundary condition at
the coaptation area may be improved. As shown by
Hamid er al. (1985) the coaptation area increasesas the
leaget deforms due to an increasing pressure load.
However, this would result in an increasingcomplexity
of the model, whereas the uncertainties with regard to
the material properties still may lead to substantial
deviations.
From Fig. 14 it is observed that the maximum von
Mises intensity in the membranes is found in the
vicinity of point B and amounts to about
0.20 N mm-*. Negative values for the minimum principal stressare especially found in the coaptation area
near the leaflet suspension.This indicates that there the
membranes may wrinkle. which is an undesirable
situation. The tensile fibre stress has a maximum in
5661
fibres 5 and 8 in the vicinity of the aortic ring and
amounts to 0.64 N mm-‘. Christie and Medland
(1982) calculated the stressesin a leaflet which is firmly
attached to a rigid frame and found a maximum
principal stressof 0.2 N mm - ’ in the leaflet centre (at a
pressure load of 16 kPa). Thubrikar er al. (1982)
calculated stressesin the leaflet in circumferential and
radial directions as membrane stressesin a cylinder.
The radius of the leaflet was measured from a silicone
mold of the valve prepared at the diastolic pressure
gradient. They found a maximum stressin the leaflets
of 0.33 N mm- * in circumferential direction at a
pressure level of 13.3 kPa (100 mm Hg). Hamid et al.
(1985) calculated the stresses in a non-linear finite
element model of a valve with flexible stent. under the
assumption of isotropic properties of the leaflet tissue.
They also found the greatest stressin the vicinity of the
leaflet attachment to the frame (0. I5 N mm-’ in a
leaflet of 0.6 mm thick at a pressure load of 13.3 kPa).
The observed differences with our data are certainly
partly caused by differences between the underlying
assumptions for the models.
Finally, the question may be raised whether there is
any correlation between the calculated stress distribution and common regions of failure in tissuevalves.
Generally speaking, although the experimental evaluations show great discrepancies, the failure phenomena of leaflet valve prosthesesbasically may be divided
into the following three types
(I) tears and perforations in the central portions of
the leaflets (Carpentier er al., 1974; Brown et al., 1978;
Haworth et al.. 1978; Clark and Swanson, 1979:
Ishihara et al., 1982);
(2) tears in the leaflets in the vicinity of the commissures (McIntosh et al., 1975; Stinson er al., 1977;
Housman ef al.. 1978; Haworth et al.. 1978; Clark and
Swanson, 1979; Davies, 1980; lshihara er al., 1982);
(3) calcification in central leaflet regions and at the
base along leaflet attachment (Carpentier et ul.. 1974;
McIntosh et al.. 1975; Browner ul.. 1978; Davies. 1980:
Bodnar and Ross, 1982: lshihara er cl., 1982;Thubrikar
et al., 1983).
It is plausible that the tears and perforations in
the central portions of the leaflets and near the
commissures are related to the high tensile stresses
found in the membranes. The fact that tears may grow
perpendicular lo the free edge (Ishihara er al., 1982)
indicates that in the coaptation area close to the
commissure point, besides rupture of the membrane
parts, libre breakage may also occur due to the high
tensile stressesin fibre 8. Moreover, as a consequence
of the libre network, high negative values for the
minimum principal stressare found in the coaptation
area near the leaflet suspension.This indicates that the
membraneous parts between the fibres may wrinkle,
which is very unfavourable due to the accompanying
high bending strains. In summary, it is hypothesized
that leaflet rupture in a loaded closed valve prosthesis
may be caused by rupture of a membrane part between
flbres;fibre breakage and wrinkling of membrane parts
562
E. P. M.
ROUSSEAU
in thecoaptation area. The observedstressdistribution
is in agreement with this.
In conclusion it is stated that the numerical model as
described in this paper yields a reliable picture of the
mechanical behaviour of the Hancock bioprosthesis.
In a future study this model will be used for a
parameter variation study in order to formulate design
specitications for a new leaflet valve prosthesis.
,&know/edgements-We
wish to thank
Ir. W. A. M.
Brckelmansand Dr ir. A. A. H. J. Sauren for their advice. Ir. A.
A. M. Flaman for his numerical and experimental contributions and Mr J. W. G. Cauwenberg. Mr Th. J. A. G. van
Duppen and Mr L. H. G. Wouters
for their technical
assistance. We also thank Mrs E. J. Scheepens for her help in
preparing the manuscript. This investigation is supported by
the Netherlands Foundation for Technical Research (STW).
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