Biomedical Engineering Reference
In-Depth Information
8.1 Introduction
Dynamic human motion is achieved via the controlled activation of skeletal mus-
cles. Activation of skeletal muscles is consciously initiated through neural impulses
originating by the central nervous system causing skeletal muscles to shorten and/or
to produce force in a controlled fashion. The muscle forces exerted through the
contraction subsequently move the joints to accomplish predetermined tasks. These
tasks are quite often required to take place against the action of external forces.
The outcome of this entire process largely depends on the force-generation proper-
ties of the muscles, the anatomical and physiological features of the skeletal system
and the underlying neuronal control system. To obtain a better understanding of the
principles leading to dynamic motion, mathematical models play a crucial role.
In general, modeling the dynamics of the musculoskeletal system can be cate-
gorized into two methodologies: (i) inverse dynamics and (ii) forward dynamics.
In inverse dynamics, the body motion and external forces are provided to compute
joint forces and moments that produce the observed motion. Information about the
level of activation of the involved muscles is typically not included in simulations
appealing to inverse dynamics. Hence, the motion-based nature of such simulations
provides limited information on the muscles' (material) behavior (actively contract-
ing skeletal muscles are stiffer than non-activated ones). Without the knowledge of
muscle activity many predictions concerning the mechanical behavior of the muscu-
loskeletal system cannot be investigated. In forward dynamics, skeletal muscles are
selectively activated and the resultant movement is computed. The activation pattern
to achieve a specific target is either guided by a control algorithm, e.g., the
λ
-model
(equilibrium point hypothesis) by Feldman (
1974
), or determined by an optimiza-
tion procedure (e.g., Anderson and Pandy,
2001
; Pandy,
2001
; Erdemir et al.,
2007
).
The cost function of the optimization needs to be specified to obtain meaningful so-
lutions with respect to specific goals, e.g., energy minimization during walking or
joint stability through co-contraction. The choice of the cost function can be quite
subjective to the researcher's preference.
The parameters within the cost function depend on the modeling parameters of
the musculoskeletal system, in particular the modeling parameters of the muscular
actuators. In state-of-the-art mechanical skeletal muscle models, the anatomical and
physiological complexity of the muscle is reduced to a few physiological parame-
ters such as the point of origin, the direction of force, the average muscle length and
the physiological cross-sectional area (PCSA). The point of origin, the direction of
force, and the muscle insertion define the line of action (maybe redirected through
via points) of such simplified skeletal muscle models. Hence, such models are often
referred to as one-dimensional (1D) skeletal muscle models. The line of action and
cross-sectional areas are typically obtained by means of magnetic resonance imag-
ing (MRI) or examining cadavers. The magnitude of the exerted muscle forces is
either linearly related to the PCSA (Barbenel,
1974
) or obtained by 3-element Hill-
type models (Zajac,
1989
; Anderson and Pandy,
2001
). The Hill-type models are by
far the most commonly used skeletal muscle models for analyzing movement.
More recently, 3D continuum-mechanical models have been introduced to over-
come the crude simplifications of 1D lumped-parameter models. The advantage
