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.
Highlights
It is widely recognized that, when integrated with in vivo data from cardiac magnetic resonance imaging (MRI), computational modelling of cardiac biomechanics can provide unique insights into cardiac function in both healthy and diseased states (Wang et al, 2015; Chabiniok et al, 2016; Gao, Aderhold, Mangion, Luo, Husmeier and Berry, 2017)
We have introduced two emulation frameworks which can be used to infer the parameters of the left ventricular (LV) biomechanical model; see Sections 3.3.1 and 3.3.2
We have applied these methods with two loss functions, the Mahalanobis loss function and the Euclidean loss function, and two interpolation methods, low rank Gaussian processes (GPs) and local GPs; see Sections 3.4.1 and 3.4.2
Summary
It is widely recognized that, when integrated with in vivo data from cardiac magnetic resonance imaging (MRI), computational modelling of cardiac biomechanics can provide unique insights into cardiac function in both healthy and diseased states (Wang et al, 2015; Chabiniok et al, 2016; Gao, Aderhold, Mangion, Luo, Husmeier and Berry, 2017). Recent mathematical studies have demonstrated that passive myocardial stiffness is much higher in diastolic heart failure patients compared with healthy subjects (Xi et al, 2014). The biophysical parameters defining the myocardial properties (as described by the HO law) can be inferred in an approximate maximum likelihood sense by using an iterative optimization procedure, as discussed in Gao et al (2015). In the context of mathematical physiology, this procedure is referred to as solving the inverse problem
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