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

Abstract

SummaryA central problem in biomechanical studies of personalized human left ventricular modelling is estimating the material properties and biophysical parameters from in vivo clinical measurements in a timeframe that is suitable for use within a clinic. Understanding these properties can provide insight into heart function or dysfunction and help to inform personalized medicine. However, finding a solution to the differential equations which mathematically describe the kinematics and dynamics of the myocardium through numerical integration can be computationally expensive. To circumvent this issue, we use the concept of emulation to infer the myocardial properties of a healthy volunteer in a viable clinical timeframe by using in vivo magnetic resonance image data. Emulation methods avoid computationally expensive simulations from the left ventricular model by replacing the biomechanical model, which is defined in terms of explicit partial differential equations, with a surrogate model inferred from simulations generated before the arrival of a patient, vastly improving computational efficiency at the clinic. We compare and contrast two emulation strategies: emulation of the computational model outputs and emulation of the loss between the observed patient data and the computational model outputs. These strategies are tested with two interpolation methods, as well as two loss functions. The best combination of methods is found by comparing the accuracy of parameter inference on simulated data for each combination. This combination, using the output emulation method, with local Gaussian process interpolation and the Euclidean loss function, provides accurate parameter inference in both simulated and clinical data, with a reduction in the computational cost of about three orders of magnitude compared with numerical integration of the differential equations by using finite element discretization techniques.

Gaussian process emulation to accelerate parameter estimation in a mechanical model of the left ventricle: a critical step towards clinical end-user relevance

“…This method was found to be the best in the comprehensive comparison presented in Davies et al (2019) and represents a benchmark for the current study, along with the expensive optimization problem solved in Gao et al (2015).…”

“…We have extended an earlier study (Davies et al, 2019) and compared the paradigms of loss versus output emulation, as discussed in Section 4.1, using both separate univariate output GPs and multivariate output GPs, as discussed in Section 4.3. For the latter case, the method proposed in Conti and O'Hagan (2010) was used.…”

“…in the form of MRI scans, the resulting proxy objective function can be minimized at low computational costs, without the need for any further computationally expensive simulations from the original mathematical model. The present article follows up on a recent proofof-concept study that explored the application of univariate-output Gaussian processes (GPs) in the context of emulating left-ventricular cardiac dynamics (Davies et al, 2019). We extend this work with a more realistic emulator that allows for spatial correlations between strains at different positions in the LV wall, using multivariate output GPs, an extended comparative analysis with different emulations strategies, and a quantification of the efficiency versus accuracy trade-off in comparison with standard numerical procedures for the original mathematical model.…”

Comparative Evaluation of Different Emulators for Cardiac Mechanics

“…This work compares different methods, including Gaussian processes, neural networks and random forests, on the task of emulating the HO model which allows for a subject's specific LV geometry to be accounted for. This builds on earlier, proof of concept work [5,6], which demonstrated the effectiveness of emulation for a fixed LV geometry. Accounting for subject-specific variations in LV geometry is crucial for practical applications.…”

“…The first of these is a finite element reconstruction of the LV geometry, which 126-1 we denote H . Patient-specific reconstructions can be generated in real-time from MRI scans, the details of which have been previously reported [5]. Secondly, we must specify the material parameter vector…”