Mathematical models are often used to describe and, in some cases predict, excitable cellular behaviour that is based on observed experimental results. With the increase of computational power, it is now possible to solve such models in a relatively short time. This, along with an increasing knowledge of cellular and subcellular processes, has led to the development of a large number of complex cellular models, capable of describing a broad range of excitable cell behaviour. But the use of complex models can also lead to problems. Most models can accurately reproduce results associated with the data on which the models are based. However, results from complicated models, with large numbers of variables and parameters, are less reliable if the model is not placed under the same physiological conditions as defined by the model author. In order to test a model??s suitability and robustness over a range of physiological conditions, one needs to fit model parameters against experimental data observed under those conditions. By using the modelling standard and repository offered by CellML, model users can easily select and adapt a large number of models to set up their own applications to fit model parameters against user-supplied experimental data. However, currently there is a lack of software that can utilise CellML model for parameter fitting. In this thesis, a Java-based utility has been developed, capable of performing least square parameter optimisation for a wide range of CellML models. Using the developed software, a number of parameter fits and identifiability analyses were performed on a selected group of CellML models. It was found that most of the models were ill-formed, with larger numbers of parameters worsening model identifiability. In some cases, the usage of multiple datasets and different objective functions can improve model identifiability. Finally, the developed software was used to perform parameter optimisation against two sets of action potentials from a sinoatrial node experiment, in the absence and presence of E9031, a specific ion channel blocker.

Mathematical models are often used to describe and, in some cases predict, excitable cellular behaviour that is based on observed experimental results. With the increase of computational power, it is now possible to solve such models in a relatively short time. This, along with an increasing knowledge of cellular and subcellular processes, has led to the development of a large number of complex cellular models, capable of describing a broad range of excitable cell behaviour. But the use of complex models can also lead to problems. Most models can accurately reproduce results associated with the data on which the models are based. However, results from complicated models, with large numbers of variables and parameters, are less reliable if the model is not placed under the same physiological conditions as defined by the model author. In order to test a model??s suitability and robustness over a range of physiological conditions, one needs to fit model parameters against experimental data observed under those conditions. By using the modelling standard and repository offered by CellML, model users can easily select and adapt a large number of models to set up their own applications to fit model parameters against user-supplied experimental data. However, currently there is a lack of software that can utilise CellML model for parameter fitting. In this thesis, a Java-based utility has been developed, capable of performing least square parameter optimisation for a wide range of CellML models. Using the developed software, a number of parameter fits and identifiability analyses were performed on a selected group of CellML models. It was found that most of the models were ill-formed, with larger numbers of parameters worsening model identifiability. In some cases, the usage of multiple datasets and different objective functions can improve model identifiability. Finally, the developed software was used to perform parameter optimisation against two sets of action potentials from a sinoatrial node experiment, in the absence and presence of E9031, a specific ion channel blocker.

Simulating the human heart is a challenging problem, with simulations being very time consuming, to the extent that some can take days to compute even on high performance computing resources. There is considerable interest in computational optimisation techniques, with a view to making whole-heart simulations tractable. Reliability of heart model simulations is also of great concern, particularly considering clinical applications. Simulation software should be easily testable and maintainable, which is often not the case with extensively hand-optimised software. It is thus crucial to automate and verify any optimisations. CellML is an XML language designed for describing biological cell models from a mathematical modeller’s perspective, and is being developed at the University of Auckland. It gives us an abstract format for such models, and from a computer science perspective looks like a domain specific programming language. We are investigating the gains available from exploiting this viewpoint. We describe various static checks for CellML models, notably checking the dimensional consistency of mathematics, and investigate the possibilities of provably correct optimisations. In particular, we demonstrate that partial evaluation is a promising technique for this purpose, and that it combines well with a lookup table technique, commonly used in cardiac modelling, which we have automated. We have developed a formal operational semantics for CellML, which enables us to mathematically prove the partial evaluation of CellML correct, in that optimisation of models will not change the results of simulations. The use of lookup tables involves an approximation, thus introduces some error; we have analysed this using a posteriori techniques and shown how it may be managed. While the techniques could be applied more widely to biological models in general, this work focuses on cardiac models as an application area. We present experimental results demonstrating the effectiveness of our optimisations on a representative sample of cardiac cell models, in a variety of settings.