viii
Preface
molecules. In all these cases, continuum models can be a valuable tool for
understanding the behavior at one spatial scale without the additional complexity
of simulating events at smaller scales.
This book focuses almost exclusively on mechanics. The effects of biochemistry
and molecular signaling, which play major roles in regulating mechanobiological
processes, are generally not considered. Ultimately, realistic models should integrate
the effects of mechanics, cell signaling, and genetics across multiple scales. Combining continuum models at the cell, tissue, and organ levels with more mechanistic
models based on biophysical principles at subcellular levels could help bridge these
scales.
This book is written in the form of a textbook. The book includes numerous
examples, with additional problems provided at the end of each chapter. The book is
based on the one-semester graduate course Mechanics of Growth and Development,
which has been offered at Washington University since 1998. Students taking this
course typically have included first-year graduate students and a few seniors. Most
have been students in biomedical engineering. The only prerequisite is a course on
mechanics of materials.
Ideally, the material in this book would be divided into two semesters. The first
semester could focus on the fundamentals of continuum mechanics and nonlinear
elasticity (Chaps. 2 and 3) with applications to the biomechanics of soft tissues
(Chap. 4). With the addition of some material on viscoelasticity, bone, and other
selected topics, this course could serve as a stand-alone upper-level course on
biomechanics. The second semester would then be a course on mechanobiology,
including the mechanics of contraction, growth, remodeling, and morphogenesis
(Chaps. 5–8).
The latest version of my one-semester course began with a brief introduction
to cell and developmental biology (Chap. 1), followed by four weeks of nonlinear
elasticity (Sects. 3.1, 3.3, 3.4, 3.5.2, 3.6, 3.7, and 4.1–4.5). With this background,
I covered contraction (1 week), growth (2 weeks), remodeling (2 weeks), and
morphogenesis (4 weeks) (Chaps. 5–8). The amount of time spent on each of these
topics can be adjusted, depending on the interests of the instructor. Spending a full
month on morphogenesis is my own personal bias.
Throughout this book, I try to emphasize the importance of integrating theory
with experiments. In addition, many of the examples were chosen to help build
qualitative intuition. In my opinion, because of the intrinsic variability in biological
systems, a qualitative understanding of fundamental behavior is at least as important
as quantitative accuracy. The end-of-chapter problems, many of which require
numerical computation, force students to dig into analytical details that may
otherwise be glossed over.
I owe my deepest gratitude to my Ph.D. adviser, Professor Charles Steele
of Stanford University, who taught me the art of mathematical modeling in
biomechanics. His influence on my work continues to the present day. I am also
indebted to my former graduate students and post-docs, who did most of the heavy
lifting, especially regarding finite-element modeling and experimentation. Many of
the models presented for morphogenesis, as well as those for vascular growth and
Preface
molecules. In all these cases, continuum models can be a valuable tool for
understanding the behavior at one spatial scale without the additional complexity
of simulating events at smaller scales.
This book focuses almost exclusively on mechanics. The effects of biochemistry
and molecular signaling, which play major roles in regulating mechanobiological
processes, are generally not considered. Ultimately, realistic models should integrate
the effects of mechanics, cell signaling, and genetics across multiple scales. Combining continuum models at the cell, tissue, and organ levels with more mechanistic
models based on biophysical principles at subcellular levels could help bridge these
scales.
This book is written in the form of a textbook. The book includes numerous
examples, with additional problems provided at the end of each chapter. The book is
based on the one-semester graduate course Mechanics of Growth and Development,
which has been offered at Washington University since 1998. Students taking this
course typically have included first-year graduate students and a few seniors. Most
have been students in biomedical engineering. The only prerequisite is a course on
mechanics of materials.
Ideally, the material in this book would be divided into two semesters. The first
semester could focus on the fundamentals of continuum mechanics and nonlinear
elasticity (Chaps. 2 and 3) with applications to the biomechanics of soft tissues
(Chap. 4). With the addition of some material on viscoelasticity, bone, and other
selected topics, this course could serve as a stand-alone upper-level course on
biomechanics. The second semester would then be a course on mechanobiology,
including the mechanics of contraction, growth, remodeling, and morphogenesis
(Chaps. 5–8).
The latest version of my one-semester course began with a brief introduction
to cell and developmental biology (Chap. 1), followed by four weeks of nonlinear
elasticity (Sects. 3.1, 3.3, 3.4, 3.5.2, 3.6, 3.7, and 4.1–4.5). With this background,
I covered contraction (1 week), growth (2 weeks), remodeling (2 weeks), and
morphogenesis (4 weeks) (Chaps. 5–8). The amount of time spent on each of these
topics can be adjusted, depending on the interests of the instructor. Spending a full
month on morphogenesis is my own personal bias.
Throughout this book, I try to emphasize the importance of integrating theory
with experiments. In addition, many of the examples were chosen to help build
qualitative intuition. In my opinion, because of the intrinsic variability in biological
systems, a qualitative understanding of fundamental behavior is at least as important
as quantitative accuracy. The end-of-chapter problems, many of which require
numerical computation, force students to dig into analytical details that may
otherwise be glossed over.
I owe my deepest gratitude to my Ph.D. adviser, Professor Charles Steele
of Stanford University, who taught me the art of mathematical modeling in
biomechanics. His influence on my work continues to the present day. I am also
indebted to my former graduate students and post-docs, who did most of the heavy
lifting, especially regarding finite-element modeling and experimentation. Many of
the models presented for morphogenesis, as well as those for vascular growth and