The Modelling of Biological Growth:
a Pattern Theoretic Approach
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This book accomplishes two major tasks. First, we present the first of its kind, genetically-based mathematical model for biological growth called the Growth as Random Iterated Diffeomorphisms ("GRID"). We unravel its potential for analysis and prediction of growth patterns at microscopic (cellular) and macroscopic (multicellular) levels. Through stochastic formalization of the GRID model we show that the growth of biological shape is a "digital" stochastic process at the microscopic level (on the fine time scale) and an "analog" deterministic process at the macroscopic level (on the coarse ti...
This book accomplishes two major tasks. First, we present the first of its kind, genetically-based mathematical model for biological growth called the Growth as Random Iterated Diffeomorphisms ("GRID"). We unravel its potential for analysis and prediction of growth patterns at microscopic (cellular) and macroscopic (multicellular) levels. Through stochastic formalization of the GRID model we show that the growth of biological shape is a "digital" stochastic process at the microscopic level (on the fine time scale) and an "analog" deterministic process at the macroscopic level (on the coarse time scale). Second, we develop a systematic GRID-based approach for image analysis of growth into an algorithmic tool that will carry out an automatic estimation of the growth characteristics of the organism directly from image data. We follow maximum a posteriori (MAP) estimation methodology and construct a biologically meaningful cost function that measures not only the mismatch in images of initial and grown organisms but also cell activities driving observed shape changes. We apply the inference algorithm for characterization of larval growth of the Drosophila wing disc.
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