Assessing input parameter hyperspace and parameter identifiability in a cardiovascular system model via sensitivity analysis

We aim to clarify our understanding of the process of state-space model input parameter identification, known, within the clinical context, as model personalisation. To do so, we apply reference sensitivity and identifiability techniques to a lumped parameter, single ventricle representation of the systemic circulation, chosen in view of its relative simplicity and prior art. We attempt to quantify the reliability of input parameter identifiability through the lens of 4 clinically relevant measurements and the attendant difficulty in personalising the model. In turn, this that we extend existing methods which combine both parameter influence and orthogonality, to global sensitivities. By examining different parameter sensitivity evaluation methodologies, we investigate the stability of optimal parameter subsets which are commonly used to aid clinical investigations. In order to perform the personalisation process, one must understand the complexity of the high dimensional input parameter hyperspace associated with this class of model. By utilising Sobol indices, we propose a domain-agnostic and intuitive approach. This involves varying the bounds of the input parameter space relative to the model's base state. These investigations yield a pseudo-mapping of the input hyperspace, cementing our understanding of the role of identifiable input parameters in the state-space model. Our findings suggest a novel global methodology for input parameter identifiability and input hyperspace mapping, providing valuable insights into solving the personalisation process.