Biomedical Engineering Reference
In-Depth Information
4.6
Models of Tissue Differentiation. Application to Bone Fracture Healing
Mechanistic models aim to understand how the mechanical signals are transferred
to tissues, how cells sense these signals, and how they are translated into the cascade
of biochemical reactions that stimulate cell expression and cell differentiation
[43, 78].
Pauwels [79] probably formulated the first mechanistic tissue differentiation
theory. This theory regarded the strain and stress invariants as the mechanical
stimuli that guided the differentiation process. Deviatoric strain was assumed the
stimulus for the formation of collagen fibers, and octahedral strain for the formation
of cartilage. Pauwels formulated a set of differentiation rules, which are summarized
in Figure 4.5(a), which allowed prediction of the appearance of different tissues in
the fracture site. This theory was based on the clinical observation and experience.
Later, Perren and Cordey [80, 81], on the basis of their clinical studies, proposed
the interfragmentary movement as the stimulus that guided differentiation in the
fracture site. The interfragmentary strain (IS) was defined as the ratio between
the relative displacement of the fracture fragments and the gap size. A tissue
that ruptures at a certain strain level cannot be formed in a region experiencing
strains greater than this (Figure 4.5b). This theory only considers longitudinal or
axial strains. Contributions of the other strains, which could also be important, are
neglected.
Carter
et al
. [47, 82, 83] proposed a differentiation theory, based on the ideas of
Pauwels, aimed at analyzing how mechanical history affects tissue differentiation.
The main hypothesis is that growth, maintenance, and remodeling of the tissue are
achieved by the transfer of mechanical energy to the energy needed for chemical
reactions. They considered that tissue differentiation was dependent on the stress
level, and mainly on the invariants of the stress tensor (octahedral and deviatoric
components). The studies of Carter
et al
. [84] were the first to use finite element
models to explore the relationship between local stress/strain distribution and
differentiated tissue types, and thus the first to quantify the level of mechanical
stimulus. This theory has been used to study fracture healing [84, 85] and distraction
osteogenesis [86].
Claes
et al
. [35, 87, 88] in a multidisciplinary work proposed a new tissue
differentiation theory. They simulated the fracture callus in a finite element model,
at different stages of bone healing. They established as differentiation hypothesis
that the hydrostatic pressure and the principal strains determine the differentiation
pathway. These works were based not only on the FEA but also on data from
animal experiments and cell cultures. This theory has been used to study fracture
healing at fixed times [89] and, also combined with fuzzy logic rules, to predict the
evolution of tissues in the fracture callus [90, 91].
Prendergast
et al
. [92, 93] also formulated a model of tissue differentiation.
They developed a biphasic poroelastic finite element model of tissues and the
validation was based on experiments at a loaded implant interface. They proposed
two biophysical stimuli to control differentiation: solid shear deviatoric strain and
