Gaussian Process Regressions for Inverse Problems and Parameter Searches in Models of Ventricular Mechanics

Abstract

Patient specific models of ventricular mechanics require the optimization of their many parameters under the uncertainties associated with imaging of cardiac function. We present a strategy to reduce the complexity of parametric searches for 3-D FE models of left ventricular contraction. The study employs automatic image segmentation and analysis of an image database to gain geometric features for several classes of patients. Statistical distributions of geometric parameters are then used to design parametric studies investigating the effects of: (1) passive material properties during ventricular filling, and (2) infarct geometry on ventricular contraction in patients after a heart attack. Gaussian Process regression is used in both cases to build statistical models trained on the results of biophysical FEM simulations. The first statistical model estimates unloaded configurations based on either the intraventricular pressure or the end-diastolic fiber strain. The technique provides an alternative to the standard fixed-point iteration algorithm, which is more computationally expensive when used to unload more than 10 ventricles. The second statistical model captures the effects of varying infarct geometries on cardiac output. For training, we designed high resolution models of non-transmural infarcts including refinements of the border zone around the lesion. This study is a first effort in developing a platform combining HPC models and machine learning to investigate cardiac function in heart failure patients with the goal of assisting clinical diagnostics.

Fast Parameter Inference in a Biomechanical Model of the Left Ventricle by Using Statistical Emulation

“…A potential approach to overcome this problem is emulation (e.g. Kennedy and O'Hagan (2001), Conti et al (2009) and Conti and O'Hagan (2010)), which has recently been explored in the closely related contexts of cardiovascular fluid dynamics (Melis et al, 2017), the pulmonary circulatory system (Noè et al, 2017) and ventricular mechanics (Achille et al, 2018).…”

Model order reduction for left ventricular mechanics via congruency training

“…While the FE formulation could be in principle applied to arbitrarily complex geometric domains such as detailed multi-chamber models, this study targeted only the behavior of left ventricles (LVs). Specifically, we employed a parameter axisymmetric representation of ventricular anatomy that was recently employed to automatically process the Sunnybrook Cardiac MRI database [27, 32]. Figure 2 shows axial and longitudinal cross-section profiles of the two LV geometries that were selected as representative of the normal (N) and heart failure (HF) subject groups included in the database.…”

“…Figure 2 shows axial and longitudinal cross-section profiles of the two LV geometries that were selected as representative of the normal (N) and heart failure (HF) subject groups included in the database. To at least partially correct for the fact that all imaged ventricle configurations are subjected to non-negligible loads (e.g., due to intraventricular pressure and external boundary conditions), we first “unloaded” the geometries reconstructed from MRI using Gaussian Process regression under the assumption of a 10% mid-wall end-diastolic strain for the N geometry and a 15% mid-wall strain for the HF one (see leftmost and central columns for cross-section profiles at end-diastole and after unloading, respectively) [27]. The 2 idealized anatomies were then discretized into 3-D meshes of 34 590 (N) and 49 121 (HF) linear tetrahedral elements (see righmost column).…”

“…For this reason, we built a Gaussian Process regression model mapping the geometric parameters of the left ventricle (i.e., { R b , L, Z, H , Ψ 0 , e }) to the 8 parameters of the LO module (i.e., { α, β, γ, a, b, c, µ 1 , µ 2 }). To train the regression model, we randomly sampled 150 virtual anatomies uniformly distributed over the range of geometric features observed for the patients included in the Sunnybrook Cardiac MRI datasets [27]. 3-D high-resolution simulations were run for all geometries and under all training conditions (see Table 2).…”

“…Alternative strategies have proposed training purely statistical models (e.g., Gaussian Process regressions [25]) on a relatively limited number of high-resolution runs (e.g., see [26, 27] for applications in diastolic filling). Once fitted to a sampled training set, statistical models can be used as efficient surrogates for the computationally expensive simulations.…”