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The formulation and validation of mathematical models of calcium metabolism

Dawes, M. W. (1989). The formulation and validation of mathematical models of calcium metabolism. (Unpublished Doctoral thesis, City, University of London)


This thesis presents an example of and argument for the use of mathematical models in the study of physiological systems, and specifically calcium metabolism. It is shown through the example of calcium, that the use of isomorphic models incorporating in it processes soundly based upon the underlying physiology can produce useful insight concerning the structure and control mechanisms of metabolic systems. Further even though these models can be theoretically and practically unidentifiable, a high degree of empirical validity can be observed. Models such as these are fundamental to the continued development of understanding and the basis for directed physiological experimentation.

This thesis begins with a survey of the physiology of calcium metabolism, and a critical classification of existing models related to calcium. The distinction between curve fitted tracer models and those based in some way upon the underlying physiology is highlighted. The first model produced was an attempt to incorporate unit processes into a tracer model. This approach was shown to be unsatisfactory, as the uncertain identity of the model compartments hindered meaningful development.

A second model was produced from scratch according to the methodology, soundly based upon physiologically meaningful compartments, and control structures. This model was further refined using a form of structural sensitivity analysis, to reduce the complexity of the model whilst still retaining those elements needed to predict the short-term dynamics of calcium. Thus some of those elements originally included were shown to be superfluous.

This iterative approach to model development was further extended by considering extra situations, and specifically hypocalcaemic stimuli, to evolve a model, with better empirical behaviour. The validity of this model is then examined over a wide range of experimental situations, and shown to provide predictions that are consistent with available data. This validity is present despite the unidentifiability of the model, and provides useful insight into the physiological control of calcium. This approach should be valid for other physiological systems.

The feasibility of applying this approach to the long term behaviour of calcium is then investigated, leading to the production of a long term model firmly based upon unit processes at the level of the bone cells involved. This model is shown to be internally valid and is a suitable vehicle for investigation of the long term situation.

Publication Type: Thesis (Doctoral)
Subjects: Q Science > QA Mathematics
Q Science > QD Chemistry
Departments: School of Science & Technology > Mathematics
School of Science & Technology > School of Science & Technology Doctoral Theses
Doctoral Theses
Text - Accepted Version
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