Automatic Model Calibration with MCMC: Applications to a Lumped Parameter Cardiovascular System Model

Abstract: Computational physiological models continue to increase in complexity without the foresight or system identification expertise needed to calibrate them to available clinical data. Complex models require the calibration of many parameters. However, available clinical data is often insufficient for the unique identification of the whole parameter set. Therefore, to calibrate a patient-specific model it is beneficial to determine the specific predictions that the model will make and then verify that the uncertainty of these predictions with respect to the uncertain parameters is acceptable. We have developed a pipeline that reduces the set of fitting parameters to make them structurally identifiable, then uses MCMC to determine the confidence interval of a task-specific prediction, thus verifying practical identifiability. This approach is demonstrated on a lumped parameter model of the cardiovascular system fit to brachial artery cuff pressure, echocardiogram volume measurements from patients presenting for routine cardiac catheterisation examination, and synthetic cerebral blood flow data that approximates what will be obtained from future 4D-flow MRI data. This method successfully reduces the parameter set of a cardiovascular system model from 12 parameters to 6 structurally identifiable parameters. Subsequently the MCMC approach gave a confidence interval on cerebral pressure prediction in the middle cerebral artery that was within the user defined acceptable bounds. Thus, the method achieved a task-specific practically identifiable model calibration. The proposed pipeline determines a structurally identifiable parameter set, then runs an MCMC analysis to verify acceptable prediction uncertainty. The method is able to calibrate the model to clinical data to provide a task-specific personalised representation that can be used for prediction of unobserved variables. The approach allows straightforward automation for general models and arbitrary datasets, enabling automated fitting of purpose-specific parameters to clinical data with minimal user input.