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 The commercial
software package ABAQUS (HKS Inc., Pawtucket, RI) was used to solve a
finite element (FE) model of the pusher plate, blood sac and pump case
(Figure 1 V1 design) most recently. The pusherplate
and pump case were treated as rigid and constructed with planar elements.
The blood sac was constructed of 8-noded continuum elements (Figure 1),
with 10 elements through the thickness of the sac. The sac was treated as
homogeneous, isotropic, and hyperelastic.
Material properties were derived from a uniaxial
tension test performed on a tensile testing machine at 100 mm/min (Instron Corp, Canton,
MA, Model
#4201). The simulation utilized a pump case without any taper, as previous
2D analysis confirmed that tapering the pump case dramatically increased
stresses in the blood sac (Haut
Donahue, T.L., Weiss, B., Rosenberg,
G., Jacobs, C.R., Finite Element Analysis of
Stresses Developed in Blood Sacs of a Pusherplate
Blood Pump. Computer Methods in
Biomechanics and Bioengineering, 6(1):
7-15, 2003).. A radius of
curvature of 3/16th of an inch (4.76 mm) was used for the blood sac and the
thickness of the sac was 0.015 inches (0.381 mm). The 3D FE model was run
in two steps, with contact between the pusher plate and blood sac being treated
as frictionless as was contact between the blood sac and pump case. During
the first non-linear quasi-static step, an internal pressure of 100 mm Hg
was applied evenly to the inside of the blood sac. Displacements and rotations
were constrained to zero for the pusher plate and the pump case during the
first step which pressurized the blood sac. While maintaining a constant
internal pressure of 100 mm Hg, the second step simulated the systolic
ejection phase during which the pusher plate was displaced to compress the
blood sac. Quasi-static analysis was used allowing for nonlinearities due
to contact and material deformation. The model currently runs on a Sun
Ultra 80 with 4 processors, and each simulation requires approximately 20
days of runtime due to the large number of elements in contact.
The greatest stresses and strain in the blood sac are at
0.256 inches (6.5 mm) of compression (or pusher plate displacement). The
stresses are continuous around the blood sac, and local increases that were
present in 70cc and V0 designs are not present near the location of the
ports. No significant differences in stresses or strains were noted for a
cross-section through the port (location A on
Figure 2) compared to a region away from the port (location B on Figure 2).
The addition of the ports, in the new location, to the blood sac does not
appear to alter the maximum stresses or strains in the bending region of
the sac. Thus moving the port out of the roll region reduces the stresses
in a previously high stressed   area.
We examined the
maximum principal stress and maximum principal strains throughout the
ejection stroke (Figure 3). Two major differences are noted between the earlier
axisymmetric (Haut Donahue, T.L., Weiss, B., Rosenberg, G., Jacobs, C.R., Finite Element Analysis of Stresses Developed in Blood
Sacs of a Pusherplate Blood Pump. Computer Methods in Biomechanics and
Bioengineering, 6(1): 7-15,
2003) and newest 3D model.
The first being the stress or strain value at the beginning of the ejection
stroke. The previous axisymmetric model predicted
strains of ~12% and stresses of ~70 psi (~460 kPa) to be present after the first step which applies
an internal pressure of 100 mm Hg (Figure 4). These values increased slightly
to a plateau of ~ 16% and ~94 psi (655 MPa). In the 3D model, which has a much more refined
mesh, strains of only 2.5%, and stresses of 19.2 psi(132
kPa) were noted at the beginning of the ejection
stroke. These values are much smaller than previously predicted with the axisymmetric model. However, both the axisymmetric and 3D models predict that over much of
the ejection stroke the strains are constant (Figure 4). The second difference
between the models is that the 3D model predicts a slight decrease in peak
principal stress and strain values immediately following the initiation of
pusher plate displacement. This was not seen in the axisymmetric
model (for the same pump case design and radius blood sac). While the axisymmetric model and the 3D model both use a hyperelastic formulation for the material property
definition of the blood sac, we recently collected more accurate data on
the material properties in the range of strains seen in the axisymmetric model (0-100%). Hence, the 3D model uses new
values were slightly stiffer than previously used and could account  for some difference in absolute
values of stress and strain.
Figure 4. A) Maximum
principal strain in the blood sac. B) Maximum principal stress in the
blood sac.
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This project is part of a larger effort by Pennsylvania State University-
Artificial Organs Group.
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