Biomedical Engineering Reference
In-Depth Information
One-dimensional representation of muscles is sufficient in many applications, but
many cases also require three-dimensional modeling. Three-dimensional modeling
of muscle not only allows studying more complex structures but also leads to more
realistic simulations. Three-dimensional muscle simulations can be obtained by us-
ing
finite element methods
(FEM) by subdividing muscles (and other anatomical
entities) into small elements and applying continuum mechanics (see Sect.
6.2.1
).
As one of the earliest work, Chen and Zeltzer [
19
] modeled individual muscles as
coarse linear elastic finite elements and used a Hill's type model to approximate
the constitutive behavior. Active muscle forces were approximated as parametric
functions and embedded into selected edges between vertices of a FEM-based solid.
Blemker and Delp [
20
] developed and evaluated a new formulation for creating
three-dimensional finite element models that represent complex muscle geometry
and the variation in moment arms of fibers within a muscle. This 3D muscle model
has the advantage to represent complex muscle path motion but it is computationally
expensive and impractical to use in real-time applications. At the same time, Teran et
al. [
21
] used a finite volume method (FVM) with quasi-incompressible, transversely
isotropic, hyper-elastic constitutive model to simulate soft tissue contraction and
deformation. B-spline solids were used to model fiber directions, and the muscle
activation levels were derived from key-frame animations. They claimed that FVM
inherently requires less computation and memory usage in comparison with FEM.
Later, Lee et al. [
22
] introduced one of the most detailed biomechanical model of the
human upper body composed of a dynamic articulated skeleton, Hill's type muscle
actuators including the force-velocity relation, and realistic finite element simulation
of soft tissues and skin deformation. They used inverse dynamic with target poses
and co-activation as input to compute muscle activation. The activation is then used
to simulate skeleton dynamics and soft tissue deformation. The skin and underlying
soft tissues were also simulated using FEM.
By using these detailed three-dimensional representations, accuratemusculoskele-
tal simulation is achievable. In addition to be more accurate in comparison to one-
dimensional representations, three-dimensional representations lead tomore realistic
visualization which is usually one goal in computer animation. But the computa-
tion cost and time consuming procedures of these methods make them impractical
in many real world applications. Moreover, making three-dimensional representa-
tions of anatomical entities require generic or subject-specific data, as discussed in
Sect.
6.2.3
.
6.2.2.3 The Connective Tissue and Skin
The human skin has experimentally been approximated as a layered, nonlinear, thin,
elastic and incompressible material. In computer animation and graphics, many mod-
els of physical skin have been proposed, notably for anatomy-based character rigging,
and especially for body parts where skin deformation is clearly visible. It is some-
times important that a model can exhibit dynamics effects (e.g. jigging and bulging)
and not only pure kinematics effects from geometric rigging techniques, as it thus
