Introduction to Modelling in Bioengineering
This chapter outlines the basic principles of computational modelling with particular application to physiology and medicine. An overview of the modelling process is provided, along with a description of basic model types, including linear versus non-line
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Introduction to Modelling in Bioengineering
1.1 Modelling and Simulation in Medicine and Biology In mathematics and engineering, modelling is defined as the formulation of a mathematical or computational representation of a physical system. Such representations (or models) are typically solved numerically using a computer: a process known as simulation. The terms mathematical modelling (i.e. representing a system with equations) and computational modelling (replicating a system on computer) are largely synonymous insofar that numerical computation is utilised in both. Modelling is central to science itself. Since the time of the ancient Greeks, mathematical principles have been regarded as integral to understanding the cosmos. Plato for instance, was said to have placed an inscription over the doors of his philosophical Academy: “let no one ignorant of geometry enter under my roof” [16].1 However the first great triumph of modelling occurred in the 17th century with the publication of Isaac Newton’s “Mathematical Principles of Natural Science” (otherwise known as the “Principia”), in which he expounded his laws of motion and the inverse-square law of gravity, accurately accounting for the complex motions of the planets with a simple and elegant mathematical description. Since then, modelling has continued to enjoy enormous success throughout the fields of physics and engineering. However the slowest areas of science to succumb to mathematical description have arguably been those of medicine and biology, owing largely to the overwhelming complexity and variation found in living systems. There are no analogous simple laws of biology as in physics which lend themselves to simple mathematical formulation. Despite the complexity inherent in biological systems, the last several decades have seen major advances in the application of mathematics to biology, physiology and medicine. Modelling is increasingly being utilised to study the integrative behaviour of complex biological systems [5, 13, 14, 17], also known as systems biology. Today, computational modelling is used extensively for biomedical research and medical device development in areas as diverse as biomechanics and orthopaedics, 1 mhde…j
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© Springer-Verlag Berlin Heidelberg 2017 S. Dokos, Modelling Organs, Tissues, Cells and Devices, Lecture Notes in Bioengineering, DOI 10.1007/978-3-642-54801-7_1
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1 Introduction to Modelling in Bioengineering
fluid dynamics, drug delivery, tissue ablation, neurostimulation and many others. Computer models are increasingly being utilised for virtual prototyping of medical devices and implants [19]. Standards for reporting medical simulations are under active development [6], as are standards for the representation and exchange of biological models [3, 12]. Major initiatives are underway for developing multiscale physiological models ranging from the molecular through to the whole-organ and organ systems scale [20]. Furthermore, patient-specific computer simulations are increasingly b
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