Practical identifiability and uncertainty quantification of a pulsatile cardiovascular model

Abstract

Mathematical models are essential tools to study how the cardiovascular system maintains homeostasis. The utility of such models is limited by the accuracy of their predictions, which can be determined by uncertainty quantification (UQ). A challenge associated with the use of UQ is that many published methods assume that the underlying model is identifiable (e.g. that a one-to-one mapping exists from the parameter space to the model output). In this study we present a novel workflow to calibrate a lumped-parameter model to left ventricular pressure and volume time series data. Key steps include using (1) literature and available data to determine nominal parameter values; (2) sensitivity analysis and subset selection to determine a set of identifiable parameters; (3) optimization to find a point estimate for identifiable parameters; and (4) frequentist and Bayesian UQ calculations to assess the predictive capability of the model. Our results show that it is possible to determine 5 identifiable model parameters that can be estimated to our experimental data from three rats, and that computed UQ intervals capture the measurement and model error.

Cardiovascular dynamics during head-up tilt assessed via pulsatile and non-pulsatile models

“…Two approaches were used: a local approach analyzing the model in a small neighborhood around known parameter values and a global approach examining the model behavior over the entire parameter space. More detailed discussion of this type of approach can be found in our resent study [15]. The analysis was done using both for the surrogate model output defined in (29) and for actual model output defined in (30).…”

Uncertainty quantification of simulated biomechanical stimuli in coronary artery bypass grafts

“…Recent studies have begun to examine the effects of uncertainty in cardiovascular simulation outputs [12]. These include studies of the impact of random field wall thickness on wall stress in abdominal aortic aneurysms [13], stochastic collocation to investigate uncertanties in a one-dimensional human arterial network [14], shape optimization of idealized bypass grafts under uncertainty [15], uncertainties in wall model parameters for one-dimensional approximations of blood flow [16], variability in coronary fractional flow reserve under uncertainty in geometry and boundary conditions [17], uncertainty in the context of virtual palliation surgery for single ventricle congenital heart disease [18], and others [19,20,21].…”

Cardiovascular models for personalised medicine: Where now and where next?

“…This was presaged by the observation by Irene Vignon-Clemental, at the International Conference on CFD in Medicine and Biology in Albufeira in 2015 that . Marquis et al [36] have published a rigorous examination of the personalisation process as applied to a pulsatile cardiovascular model. Whether personalised 0D models are used independently or as part of multi-scale models, it is often the case, especially in a routine clinical pathway, that physiological measurements that might support a model personalisation process are sparse (e.g.…”