We have three speakers who will talk about their areas of research related to aspects of cardiovascular modelling. Details for each presentation are provided below:

Mihaela Paun
The importance of allowing for model mismatch in cardiovascular modelling

In this talk I will present a Bayesian approach to quantify the uncertainty of model parameters and haemodynamic predictions in a one-dimensional fluid-dynamics model of the pulmonary system by integrating mouse imaging data and haemodynamic data. The long-term aim is to devise a calibrated patient-specific model. I emphasize an often neglected, though important source of uncertainty: uncertainty in the mathematical model form, caused by the discrepancy between the model and the reality. I will demonstrate that minimising the mean squared error between the measured and the predicted data (the conventional method) in the presence of model mismatch leads to biased and overly confident parameter estimates and haemodynamic predictions. The proposed method in this study, based on Gaussian Processes, allows for model mismatch and corrects the bias, and is applicable to any cardiovascular model.

Alan Lazarus
Improving cardio-mechanic parameter estimation by including prior knowledge derived from ex-vivo data

Soft-tissue mechanical modelling in cardiac physiology is a topical research area, but a major challenge is to infer the biophysical parameters that determine the mechanical properties of the tissues and fibres non-invasively from cardiac magnetic resonance images. Knowledge of these parameters would be of significance to a clinical practitioner, providing information on disease prognosis as well as treatment planning. Of particular interest in that regard is to be able to learn these parameters efficiently and accurately, while also quantifying our uncertainty. Applying standard parameter estimation techniques relies on repeated evaluation of the mathematical model and the computational costs involved make these approaches ill-suited to the clinical setting. These computational complexities can be reduced by approximating the mathematical model with a statistical emulator, trained on a large batch of training simulations that are run in advance of the patient arriving in the clinic. These simulations are affected by the geometry of the left ventricle and this can change substantially between different patients. Problematically, the dimension required for accurate representation of the left ventricle geometry is too large to permit a dense enough coverage for accurate training of the emulator. This problem will be discussed in this talk, along with a solution that relies on a low dimensional representation of the left ventricle geometry.

Computational complexities aside, estimation of the constitutive parameters from strains extracted from in-vivo MRI scans can be challenging. The reason is that circumferential strains, which are relatively easy to extract from the CMR scans, are not sufficiently informative to uniquely estimate all parameters from the model. In this talk, I will show how cardio-mechanic parameter inference can be improved by incorporating prior knowledge from population-wide ex-vivo volume-pressure data. Our work is based on an empirical law known as the Klotz curve, which allows us to incorporate the behaviour of the tissue at higher pressure regions.

Agnieszka Borowska
Bayesian optimisation for improving accuracy and efficiency of cardio-mechanic parameter estimation

Parameter inference in cardio-mechanic models using clinical in vivo data is computationally challenging. The primary reason for this is that the equations underlying these models do not admit closed form solutions and hence need to be solved using computationally expensive numerical procedures. In consequence, computational run times associated with numerical optimisation or sampling are excessive for the uptake of these models in the clinical practice. I will discuss how the framework of Bayesian optimisation (BO) -- an efficient statistical technique of global optimisation -- can be employed to address this issue. BO seeks the optimum of an unknown black-box function by sequentially training a statistical surrogate-model and using it to select the next query point by leveraging the associated exploration-exploitation trade-off. I will then present how to guarantee that the estimates based on in vivo data are realistic also for high-pressures, unobservable in vivo, by including a penalty term based on a previously published empirical law developed using ex vivo data. Finally, I will demonstrate in two real-data case studies that the proposed BO procedure outperforms the state-of-the-art inference algorithm for cardio-mechanic parameter estimation in terms of both accuracy and efficiency.