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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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