Chapter 7
Remodeling
In Chap. 1, remodeling is defined as a change in material properties. Such changes
are generally caused by alterations of internal structure. A classic example is
remodeling of cancellous bone (also called trabecular or spongy bone). During
the 1860s, observations on the structure of cancellous bone in the femur led to
what became known as Wolff’s law of trabecular architecture (Koch 1917; Cowin
2001). This “law” posits that bone trabeculae align with principal directions of
stress and remodel to maintain this correlation when loading conditions change.
The basic idea stems from images showing that the trabeculae, like principal
directions, appear to intersect at approximately right angles (Fig. 7.1). Although
theoretical considerations have since shown that this hypothesis is based on flawed
assumptions, it may hold in some average sense (Cowin 2001). Moreover, the
writings of Wolff and others led Roux (1885) to propose the concept of functional
adaptation, which is commonly accepted and still guides much of the ongoing
research in tissue growth and remodeling.
Like growth, remodeling is an integral part of development, as well as functional
adaptation in response to disease, injury, and altered mechanical loads. During heart
development, for example, peak blood pressure and wall stress increase by two
orders of magnitude, but strains at the outer surface (epicardium) change relatively
little (Fann et al. 1991; Taber et al. 1994). These findings indicate that the elastic
modulus of the myocardium increases by two orders of magnitude, consistent
with experimental measurements (Humphrey 2002; Zamir and Taber 2004). The
increased stiffness is caused by maturing cardiomyocytes (heart muscle cells) as
they become filled with highly organized sarcomeres, as well as the addition of
collagen to the extracellular matrix.
At the tissue level, remodeling can be simulated by letting the material constants
evolve with time, as in time-varying elasticity theory (see Sect. 5.4.2). They also
could depend on stress, e.g., see Eq. (6.115). During the last two decades, however,
most theories for remodeling account for the microstructural changes that underlie
© Springer Nature Switzerland AG 2020
L. A. Taber, Continuum Modeling in Mechanobiology,
https://doi.org/10.1007/978-3-030-43209-6_7
341
Remodeling
In Chap. 1, remodeling is defined as a change in material properties. Such changes
are generally caused by alterations of internal structure. A classic example is
remodeling of cancellous bone (also called trabecular or spongy bone). During
the 1860s, observations on the structure of cancellous bone in the femur led to
what became known as Wolff’s law of trabecular architecture (Koch 1917; Cowin
2001). This “law” posits that bone trabeculae align with principal directions of
stress and remodel to maintain this correlation when loading conditions change.
The basic idea stems from images showing that the trabeculae, like principal
directions, appear to intersect at approximately right angles (Fig. 7.1). Although
theoretical considerations have since shown that this hypothesis is based on flawed
assumptions, it may hold in some average sense (Cowin 2001). Moreover, the
writings of Wolff and others led Roux (1885) to propose the concept of functional
adaptation, which is commonly accepted and still guides much of the ongoing
research in tissue growth and remodeling.
Like growth, remodeling is an integral part of development, as well as functional
adaptation in response to disease, injury, and altered mechanical loads. During heart
development, for example, peak blood pressure and wall stress increase by two
orders of magnitude, but strains at the outer surface (epicardium) change relatively
little (Fann et al. 1991; Taber et al. 1994). These findings indicate that the elastic
modulus of the myocardium increases by two orders of magnitude, consistent
with experimental measurements (Humphrey 2002; Zamir and Taber 2004). The
increased stiffness is caused by maturing cardiomyocytes (heart muscle cells) as
they become filled with highly organized sarcomeres, as well as the addition of
collagen to the extracellular matrix.
At the tissue level, remodeling can be simulated by letting the material constants
evolve with time, as in time-varying elasticity theory (see Sect. 5.4.2). They also
could depend on stress, e.g., see Eq. (6.115). During the last two decades, however,
most theories for remodeling account for the microstructural changes that underlie
© Springer Nature Switzerland AG 2020
L. A. Taber, Continuum Modeling in Mechanobiology,
https://doi.org/10.1007/978-3-030-43209-6_7
341