Biomedical Engineering Reference
In-Depth Information
rough overview of the cellular variables that control contraction in skin and nerve
wounds and are qualitatively consistent with the evidence presented in this chapter.
In a skin wound, the major parameters that determine the macroscopic contrac-
tile force,
F
c
, are considered to be the number of fibroblasts that have been differ-
entiated into contractile cells,
N
, the contractile force generated by an individual
cell,
f
i
, and the fraction of cells,
ϕ
, that are oriented along a major deformation axis
(Fig.
8.5
). Assuming for model simplicity that
F
c
is directly proportional to each of
these parameters, we have (Yannas 2005d):
F Nf
ϕ
=
(8.1)
c
i
Considering the lack of reliable data, especially with
N
and
ϕ
, that can be inserted
in Eq. 8.1, it is clear that this model simply serves the purpose of summarizing in a
compact form the critical cell-scale parameters that are expected to determine the
macroscopic contraction force.
In a transected peripheral nerve, the macroscopic contraction force appears to
be generated within assemblies (capsules) of contractile cells which surround the
healing stumps. Myofibroblasts organize themselves into a capsule that surrounds
each stump. The long axes of myofibroblasts inside the capsule show a circumfer-
ential orientation, indicative of the direction of force application around the healing
nerve stump (see Figs.
8.13
and
8.15
) (Soller et al. 2012). Each of the nerve stumps
behaves as a separate wound; it closes spontaneously (capping) by formation of
scar (Chamberlain et al. 2000a) and the final state is often referred to as a neuroma.
The “pressure cuff” theory proposes a mechanism to explain the spontaneous
healing behavior of nerve stumps in the presence of the contractile cell capsule
(Yannas 2001c). It states that compressive forces applied to a nerve stump by a thick
capsule of contractile cells compress the stump sufficiently to lead to a reduction in
cross section that corresponds to a small number of myelinated axons in the cross
section of the regenerated nerve. The long axes of myofibroblasts inside the capsule
show a circumferential orientation, indicative of the direction of force application
around the regenerating nerve (hoop stress). The pressure cuff mechanism appears
to explain a large number of data on the success or failure of implants of various
types that have been independently studied in efforts to induce peripheral nerve
regeneration (Yannas 2007).
Capsule thickness and the macroscopic contraction force that deform the nerve
cross section are related in a simple mathematical model. The deformation of the
nerve radius is described in terms of a linear elastic model where a capsule with
thickness,
δ
, is a sleeve of uniform thickness wrapped around a cylindrical regen-
erating nerve (undeformed radius
R
o
, Young's modulus
E
, Poisson's ratio
ν
) (Soller
et al. 2012). It is assumed that the capsule applies to the nerve stump a circumfer-
ential compressive stress,
σ
, directly proportional to the capsule thickness:
σ = k·δ
,
where
k
is a constant. With these assumptions, the model predicts a linear reduction
in the radius of nerve tissue from
R
o
to
R
with increasing capsule thickness,
δ
(Soller
et al. 2012):
