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6 Growth
cell migration) or water (swelling). Tissues can lose volume (negative growth or
atrophy) by cells dying or becoming smaller, as well as by matrix degradation or
de-swelling.
The specific growth mechanism depends on the type of tissue, as well as its age.
The liver, for example, grows by hyperplasia, whereas muscles grow mainly by
hypertrophy. Muscle cells grow longer by adding sarcomeres in series or thicker
by adding sarcomeres in parallel. Interestingly, the heart grows primarily, but not
exclusively, by hyperplasia before birth and hypertrophy after birth (Burton and
Goss 1972; Grossman 1980).
How growth affects mechanics depends on scale. At the front of a crawling
cell, for instance, polymerizing actin filaments grow longer and push the cell
membrane outward, compressing the actin while causing local tangential tension
in the membrane. At the microscale, therefore, parts of the cell are in tension while
other parts are in compression. If the cell is surrounded by other cells, the outwardprotruding membrane pushes against neighboring cells, which push back with equal
force. At the tissue scale, therefore, the cell is in a net state of compression in the
direction of actin polymerization.
At the tissue level, all growth mechanisms produce similar effects. For example,
tissue-level stresses are the same whether growth occurs by cellular hyperplasia or
hypertrophy. Distinguishing between different processes typically requires experiments, such as measuring changes in proliferation rate and cell size. With this
information, multiscale modeling can be used to study microscale mechanics. One
way to construct a model linking the cell and tissue scales is to develop a cell-level
model and use an averaging procedure to create a finite element for a tissue-level
model. Currently, considerable effort is being devoted to developing numerical
methods for bridging multiple spatial scales, from the molecular to subcellular to
cell to tissue to organ levels. In this book, we generally consider only one spatial
scale at a time.
In most cases, we assume that growth occurs without a change in mechanical
properties. When a cell divides, this assumption implies that the daughter cells
eventually acquire the same stiffness as the parent cell. Although some types
of growth are associated with a change in stiffness, we treat such changes as
remodeling, rather than part of the growth process itself. Growth, remodeling, and
morphogenesis sometimes occur simultaneously and can affect each other.
For instance, as discussed above, the mature heart grows by hypertrophy,
but hypertrophy can be either “good” or “bad.” The hearts of athletes undergo
the good kind of hypertrophy, called physiologic hypertrophy. In this case, the
heart grows larger, while material properties remain essentially unchanged, and
function is enhanced. In contrast, hypertrophy in response to high blood pressure
(hypertension) is accompanied by increased collagen content, or fibrosis, which
stiffens the tissue and negatively affects function. This abnormal growth is termed
pathologic hypertrophy.
6 Growth
cell migration) or water (swelling). Tissues can lose volume (negative growth or
atrophy) by cells dying or becoming smaller, as well as by matrix degradation or
de-swelling.
The specific growth mechanism depends on the type of tissue, as well as its age.
The liver, for example, grows by hyperplasia, whereas muscles grow mainly by
hypertrophy. Muscle cells grow longer by adding sarcomeres in series or thicker
by adding sarcomeres in parallel. Interestingly, the heart grows primarily, but not
exclusively, by hyperplasia before birth and hypertrophy after birth (Burton and
Goss 1972; Grossman 1980).
How growth affects mechanics depends on scale. At the front of a crawling
cell, for instance, polymerizing actin filaments grow longer and push the cell
membrane outward, compressing the actin while causing local tangential tension
in the membrane. At the microscale, therefore, parts of the cell are in tension while
other parts are in compression. If the cell is surrounded by other cells, the outwardprotruding membrane pushes against neighboring cells, which push back with equal
force. At the tissue scale, therefore, the cell is in a net state of compression in the
direction of actin polymerization.
At the tissue level, all growth mechanisms produce similar effects. For example,
tissue-level stresses are the same whether growth occurs by cellular hyperplasia or
hypertrophy. Distinguishing between different processes typically requires experiments, such as measuring changes in proliferation rate and cell size. With this
information, multiscale modeling can be used to study microscale mechanics. One
way to construct a model linking the cell and tissue scales is to develop a cell-level
model and use an averaging procedure to create a finite element for a tissue-level
model. Currently, considerable effort is being devoted to developing numerical
methods for bridging multiple spatial scales, from the molecular to subcellular to
cell to tissue to organ levels. In this book, we generally consider only one spatial
scale at a time.
In most cases, we assume that growth occurs without a change in mechanical
properties. When a cell divides, this assumption implies that the daughter cells
eventually acquire the same stiffness as the parent cell. Although some types
of growth are associated with a change in stiffness, we treat such changes as
remodeling, rather than part of the growth process itself. Growth, remodeling, and
morphogenesis sometimes occur simultaneously and can affect each other.
For instance, as discussed above, the mature heart grows by hypertrophy,
but hypertrophy can be either “good” or “bad.” The hearts of athletes undergo
the good kind of hypertrophy, called physiologic hypertrophy. In this case, the
heart grows larger, while material properties remain essentially unchanged, and
function is enhanced. In contrast, hypertrophy in response to high blood pressure
(hypertension) is accompanied by increased collagen content, or fibrosis, which
stiffens the tissue and negatively affects function. This abnormal growth is termed
pathologic hypertrophy.