Lower Residual Limb for Prosthetic Socket Design - Computational Biomechanics of the Musculoskeletal System - page 154

provided a better understanding of the effects on stress distribution over the residual limb of socket
modifications (Zhang, 1995; Reynolds and Lord, 1992); material properties of the sockets (Quesada
and Skinner, 1991) and liners (Simpson, Fisher, and Wright, 2001); alignment (Reynolds and Lord,
1992; Sanders and Daly, 1993); residual limb geometry (Zhang, 1995) and mechanical properties
(Reynolds and Lord, 1992); and frictional properties at the interface (Zhang and Lord, 1995).
Simulation of the mechanical interaction between the limb and socket in FE modeling is chal-
lenging because of frictional and sliding actions at the interface. In addition, the residual limb is
donned into a socket with a different shape from the naked residual limb surface. In some models, it
was assumed that the residual limb and prosthetic socket were fully connected as one body assigned
different mechanical properties (Reynolds and Lord, 1992; Sanders and Daly, 1993; Steege, Schnur,
and Childress, 1987). This reduced the difficulties of modeling and computational time. However,
it did not take into account slippage at the interface and large in-plane stresses that might develop
on the surface of the limb. Another commonly adopted assumption is that the shape of the residual
limb and the rectified socket are the same (Reynolds and Lord, 1992; Quesada and Skinner, 1991;
Steege, Schnur, and Childress, 1987; Zachariah and Sanders, 2000). Under this assumption, modifi-
cations to the socket shape aiming to redistribute the load to load-tolerant regions cannot be imple-
mented in the FE model. The stresses imposed on the residual limb after donning into the rectified
socket, defined as pre-stresses in this chapter, were ignored under the above assumption.
Different methods have been used to account for friction/slip. Zhang et al. (1995) added interface
elements between the socket and the limb and allowed sliding between the two bodies if the calcu-
lated shear stresses exceeded the frictional limit. However, if using interface elements the model
must enforce point-to-point physical connections between the limb surface and the inner surface
of the socket. An automated contact method was used by Zachariah and Sanders (2000). In this
method, the residual limb and prosthetic socket were modeled as two deformable bodies. The FE
software package simulated contact between the two bodies by automatically detecting any overlap-
ping of interface nodes and imposing a nonpenetration condition constraint to the overlapped nodes.
However, Zachariah and Sanders (2000) did not calculate pre-stresses produced by donning the
residual limb into the shape-rectified socket.
In some models, simulation of donning the residual limb into a rectified socket has been imple-
mented by applying radial displacements to the nodes of the unrectified socket to deform it into the
rectified socket shape (Zhang et al., 1995; Silver-Thorn and Childress, 1997). This method requires
a significantly longer modeling time because all the nodes at the areas that require shape modifica-
tions have to be identified and changes of coordinates imposed. It is also difficult to implement this
with automeshing techniques in model development.
This chapter illustrates a technique that simulates the contact at the limb-socket interface, con-
sidering both the friction/slip and pre-stress conditions by using an automated contact method.
Neither point-to-point connections to simulate the friction/slip condition nor radial nodal displace-
ments to simulate pre-stress were required.
13.2 model develoPment
The model, also described in Lee et al. (2004), was based on the geometry of the residual limb of a
55-year-old, right-sided trans-tibial amputee. He was 158 cm tall and 80 kg in mass, with a residual
limb length of 14.7 cm measured from the mid-patellar tendon to the distal end of the residual limb.
13.2.1 G eometrieS
The geometries of the residual limb surface and the internal bones were obtained by taking mag-
netic resonance imaging (MRI) scans of the residual limb in supine lying and knee extended posi-
tions, with axial cross-sectional images taken at 6-mm intervals. To reduce the distortion of the
soft tissues at the posterior regions during the scanning procedure, the subject wore an unrectified