A probabilistic reduced-order modeling framework for patient-specific cardio-mechanical analysis

TL;DR

A probabilistic reduced-order modeling (ROM) framework to dramatically reduce the computational effort of such models while providing a credibility interval is presented.

Abstract

Cardio-mechanical models can be used to support clinical decision-making. Unfortunately, the substantial computational effort involved in many cardiac models hinders their application in the clinic, despite the fact that they may provide valuable information. In this work, we present a probabilistic reduced-order modeling (ROM) framework to dramatically reduce the computational effort of such models while providing a credibility interval. In the online stage, a fast-to-evaluate generalized one-fiber model is considered. This generalized one-fiber model incorporates correction factors to emulate patient-specific attributes, such as local geometry variations. In the offline stage, Bayesian inference is used to calibrate these correction factors on training data generated using a full-order isogeometric cardiac model (FOM). A Gaussian process is used in the online stage to predict the correction factors for geometries that are not in the training data. The proposed framework is demonstrated using two examples. The first example considers idealized left-ventricle geometries, for which the behavior of the ROM framework can be studied in detail. In the second example, the ROM framework is applied to scan-based geometries, based on which the application of the ROM framework in the clinical setting is discussed. The results for the two examples convey that the ROM framework can provide accurate online predictions, provided that adequate FOM training data is available. The uncertainty bands provided by the ROM framework give insight into the trustworthiness of its results. Large uncertainty bands can be considered as an indicator for the further population of the training data set.

Figures (24)

• Figure 1: Schematic of the considered full-order cardiac model. Patient-specific input (circles) is mapped on patient-specific output (diamonds) by combining a NURBS-based fitting algorithm with an isogeometric cardiac solver.
• Figure 2: Schematic of the developed ROM framework. The framework considers the same input (circles) as the FOM (Figure \ref{['fig:HFmodel']}) on which it is based. Since the ROM framework incorporates the scan-fitting algorithm in the online stage, it generates the same spline anatomy output as the FOM (light blue filled diamond). In the online stage, it also generates hemodynamical and mechanical output in the same form as that of the FOM, albeit based on a simplified ROM (open diamonds). If required, these output quantities can also be evaluated using the FOM in a subsequent offline stage, after which they can be used as additional training data.
• Figure 3: (a) Schematic representation of the isogeometric cardiac model, illustrating the coupling between the 0D and 3D model components. (b) Typical isogeometric cardiac analysis result (see Ref. willems_echocardiogram-based_2024 for details), showing the displacement magnitude at end-systole relative to end-diastole.
• Figure 4: Comparison between the nonlinear rotational-symmetric (nonlinear rsym.) function proposed by Arts et al.arts_relation_1991, a linear Taylor series expansion of this function around $\eta=0.345$ (linear rsym.), and the linear empirical relation (linear cyl.) proposed by Arts et al.arts_epicardial_1982. (a) Fiber stress-pressure ratio for varying $V/V_{\mathrm{w}}$ values; (b) Fiber strain comparison for varying $V/V_{\mathrm{w}}$ values.
• Figure 5: Example illustrating sequential learning using a Gaussian process. (a) The initial fit between the GP prediction and only two observations or data points. (b) The fit after the addition of two data points. (c) The fit after adding more data points and maximizing the marginal likelihood.