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What does modeling involve? Why should we care about modeling? Do I have to be a math whiz to succeed? How can this book help me to get started in modeling (in case I do care)? These are some of the questions we try to answer in this introductory chapter. This chapter is critical and should not be skipped.
What is modeling?
By modeling, we mean developing a replica on a computer of a physical process that interests us so that we can manipulate the process on the computer. In contrast with a computer-aided design (CAD) model which deals mostly with geometric or solid modeling, shading, etc., we must include the detailed physics of the system in order to evaluate its performance. In short, such a model involves simplifying the geometry and physics of a real situation and solving the simplified equations that describe the physics, using a software that is primarily an equation solver.
You have modeled before. As a child, you learned that the area of a trapezoid is the height multiplied by the average of the two bases. If we program this on a calculator, so that we only have to input the height and the two bases and the calculator spits out the area, we have a model for area calculation.
Simulation is an important component of the engineering design process in many sectors. The integration of simulation into undergraduate engineering education in an appropriate manner, so that it enhances the fundamentals, and also provides students with a cutting-edge tool, has been in the forefront of education thinking, as evidenced by the interest in a recent workshop at Cornell University (ISTEC, 2008), and in a report by the National Science Foundation (NSF, 2006). The tremendous growth in biomedical engineering over the last 10–15 years has encouraged increased quantitative treatment of biomedical product, process and equipment design, and design of treatment procedures. Such quantitative treatment has made simulation into a useful tool in biomedical applications as well. The synergy between increased use of simulation and the availability of improved interfaces has brought down the barriers to the use of simulation, from only specialized modelers, to just about anyone who has the necessary prerequisite of the physical process (engineering science content such as heat transfer or mass transfer). The increased need in industry and research, and the lower barrier to modeling can be integrated further by having all the essential information under one umbrella – which is the goal for this book. This introductory book walks a person without any prior knowledge in modeling through all of the necessary steps thus helping them to join the modeling community, and thereby enabling a productivity tool for design and research.
This book presents a full spectrum of views on current approaches to modeling cell mechanics. The authors come from the biophysics, bioengineering and physical chemistry communities and each joins the discussion with a unique perspective on biological systems. Consequently, the approaches range from finite element methods commonly used in continuum mechanics to models of the cytoskeleton as a cross-linked polymer network to models of glassy materials and gels. Studies reflect both the static, instantaneous nature of the structure, as well as its dynamic nature due to polymerization and the full array of biological processes. While it is unlikely that a single unifying approach will evolve from this diversity, it is the hope that a better appreciation of the various perspectives will lead to a highly coordinated approach to exploring the essential problems and better discussions among investigators with differing views.