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Metamodelling of dynamic models of the heart

Final Report Summary - METAMODELLING (Metamodelling of dynamic models of the heart)

In this project we have explored the potential of multivariate metamodelling techniques for assisting in the development of models of cardiac physiology. Both cell-level models and whole-organ models have been used as test cases. A new methodological framework for combined model parameter fitting and analysis of model mechanisms has been developed and a user-friendly software for this will be made available. The methodology combines metamodel-based (regression-based) sensitivity analysis, analysis of parameter identifiability from measured data, parameter fitting and identification of redundant model components for model reduction.

The developed methodology has been tested on two cell-level models of cardiac contraction, with the purpose of re-fitting the model parameters to data for mouse, rat and human at 37 °C, to analyse the identifiability of the parameters from sets of measured data and estimate the uncertainty in the obtained parameter estimates. Reduced model versions were also found that replicate the measured data with sufficient accuracy. The parameter estimates found for mouse, rat and human were compared using Principal Component Analysis, and maps of the parameter spaces of the two contraction models have been presented, that show distinct regions corresponding to mouse, rat and human data, respectively. Two papers have been submitted based on these results. In the first paper, the methodology is presented and illustrated through a re-fitting of model parameters using a combination of measured and synthetic data for mouse. The second paper presents an application of the methodology for re-fitting model parameters using rat and human data, along with an analysis of inter-species differences in cardiac contraction based on a comparison of the parameter estimates obtained for mouse, rat and human.

In addition to the above mentioned applications of the methodology, the parameter fitting pipeline and sensitivity analysis methodology was also applied in the development of patient-specific models of whole-heart physiology by re-fitting model parameters to measured data for 4 patients. These results are still unpublished, but the work on this will continue after the present project ends. The developed metamodels linking the input parameters to the model outputs for these large, computationally demanding models will be used for reducing computational costs of running these models.

A review on use of Partial Least Squares Regression in multivariate metamodelling and analysis of the behaviour of complex dynamic models has also been submitted in this project.

The final results of this project are
1) Metamodels of whole-organ spatiotemporal models of cardiac physiology that can be used both for reduction of computational demand through acting as substitutes for the differential equation based models, for sensitivity analysis, parameter fitting and model comparison.
2) Methodology and software for sensitivity analysis and parameter estimation that are useful for model construction and validation, especially with the aim to reduce model complexity through identification of redundant model components.
3) Methodology for systematic exploration of the parameter spaces of models and comparison of model alternatives facilitating more efficient model parameterisation and reduction of models to the minimal complexity replicating measured data.
4) Species-specific parameter values for models of cardiac physiology.

The methodology produced in this project will be made available to computational modellers and will be applicable to all areas of science utilising dynamic mathematical modelling. Within cardiac physiology, utilisation of the produced methodology will facilitate more efficient parameterisation of e.g. patient-specific, species-specific or temperature-specific models, facilitating clinical use of models. More effective and extensive use of models in the clinics implies a large socio-economic impact since it facilitates the development of new intervention strategies as well as patient-specific treatments.