Biomedical Engineering Reference
In-Depth Information
The smallest functional unit of a skeletal muscle is the motor unit (MU), which
contains all muscle fibers within a muscle that are innervated by the same α -
motoneuron. Therefore, to be able to model the physiological recruitment of MUs
in a muscle, it is necessary to enhance the geometrical TA model with functional
information of the MU distribution. As the fibers within one MU are distributed
throughout the muscle, a muscle fiber assignment algorithm based on physiological
properties has been developed by Röhrle et al. ( 2012 ). The key characteristics of the
functional grouping include an exponential distribution of muscle fibers per MU,
meaning that, in accordance with the work of Enoka and Fuglevand ( 2001 ), there
exist many small MUs composed of slow-twitch muscle fibers with slow fatiguing
properties and a few large MUs composed of fast-twitch fibers with fast fatiguing
properties. The distribution of single MUs can be obtained experimentally. The ex-
periments, however, are limited to determine the distribution of one/a few MUs per
muscle. A thorough description is not available (cf., Monti et al., 2001 ). Hence, as-
signing the muscle fibers to MUs has been done based on published information on
MU centers and MU territories. The reader is referred to Röhrle et al. ( 2012 )for
more details about the algorithm to assign muscle fibers to MUs.
The functional aspects of the skeletal muscle model can be described by three
(sub-)models, which are coupled with each other. Firstly, the neuro-physiological
model describes motor unit recruitment and rate coding. Secondly, the electrophys-
iological model of a single muscle fiber describes the major biochemical processes
within a half-sarcomere, and, thirdly, the continuum-mechanical model links the
neuro-physiological and electrophysiological model to muscle force generation. An
overview on the key characteristics of each component and how the different com-
ponents are linked to each other can be found in Fig. 8.1 .
As depicted in Fig. 8.1 , the skeletal muscle model is driven by the MU-
recruitment model. As currently implemented, the recruitment model determines
the times when single MUs fire, i.e. determining the efferent input. The MU recruit-
ment model is currently only unidirectionally coupled to the electrophysiological
and mechanical model. While providing the signals to recruit single fibers of a MU,
it does not incorporate any feedback from the Golgi-tendon organ, muscle spindles,
or other receptors, i.e. afferent input. Therefore, the link between the mechanical
model and the motor recruitment model has been only indicated in Fig. 8.1 by a
dashed arrow. This, however, is work in progress.
8.4 The Multiscale Constitutive Equation
As described above, the electrophysiological behavior on the cellular level is
coupled to the continuum-mechanical model. Within this context, the coupling
is achieved through a multiscale constitutive equation. As already indicated in
Sect. 8.2 , the 'macroscopic' α in Eq. ( 8.1 ) is replaced by an expression contain-
ing cellular parameters, specifically, the parameters A 1 and A 2 , which describe the
concentration of myosin heads in the attached pre- and post-powerstroke states. In
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