Uncertainty Quantification in Left Ventricular Cardiac Mechanics Models During Passive Filling Phase

Abstract

Cardiovascular disease remains the leading cause of death globally. To aid in guiding patient therapy, predicting prognosis, and improving diagnosis related to cardiovascular diseases, patient-specific computational models of the heart have been developed. Personalisation of these models requires the estimation of input parameters, such as the mechanical properties of the myocardium, from clinical measurements. These mechanical properties, such as the stiffness of the heart wall could be used as biomarkers, for example, for early detection of heart failure where the structure of the myocardium changes and thereby its mechanical properties change. Detecting these changes before irreversible damage would provide a novel avenue for diagnosing, treating, and monitoring disease. Robust estimation of the constitutive parameters that describe the mechanical behaviour of the tissues is difficult and confounded by the inherent uncertainties associated with real-world clinical measurements. This motivates the need for quantifying the effect of uncertainty in clinical data on the constitutive parameter estimates. Bayesian statistical methods and parameter estimation methods, specifically Bayesian hierarchical modelling (BHM) and Approximate Bayesian Computation (ABC), have been used in other scientific fields to perform uncertainty quantification (UQ), but these have not yet been widely applied in cardiac mechanics. This thesis presents the use of Bayesian statistical methods to investigate how uncertainties in clinical measurements affect the estimation of constitutive parameters of the left ventricle (LV) during the passive filling phase of the cardiac cycle. Two approaches were developed and implemented to perform parameter estimation and UQ. One used a BHM framework along with a statistical surrogate model of cardiac mechanics, while the other used a simulation-based approach and full FEM cardiac mechanics, specifically using ABC. The two approaches were applied to a cardiac mechanics model to quantify uncertainty in myocardial constitutive parameter estimates due to i) noise in the displacement of the left ventricular wall (observed data); and ii) heartbeat-to-heartbeat variability in LV measurements from catheters that were applied as boundary conditions in the cardiac mechanics model. In particular, the practical identifiability of c1 (intrinsic myocardial stiffness) and c2 (non-linearity in the direction of the myocardial fibres) of the Guccione constitutive relation, which describes the passive response of the myocardium, were investigated. Numerical experiments were performed to compare and contrast constitutive parameter estimates from the two methods against a ground truth. Both Bayesian statistical methods were found to be useful and effective in performing parameter estimation and UQ to account for multiple sources of error, especially when prior knowledge from a specific patient was included in the analysis (e.g. the shape of their LV). The results show that noise in the observed data and the beat-to-beat pressure variability contribute to the reduction in the precision of estimates of the constitutive parameters. Overall, this work can help further eliminate the barriers to the clinical translation of cardiac mechanics models for providing mechanical biomarkers for early diagnosis of diseases, such as heart failure