Multifidelity-CMA: a multifidelity approach for efficient personalisation of 3D cardiac electromechanical models

Efficient approximation of cardiac mechanics through reduced-order modeling with deep learning-based operator approximation

Reducing the computational time required by high-fidelity, full-order models (FOMs) for the solution of problems in cardiac mechanics is crucial to allow the translation of patient-specific simulations into clinical practice. Indeed, while FOMs, such as those based on the finite element method, provide valuable information on the cardiac mechanical function, accurate numerical results can be obtained at the price of very fine spatio-temporal discretizations. As a matter of fact, simulating even just a few heartbeats can require up to hours of wall time on high-performance computing architectures. In addition, cardiac models usually depend on a set of input parameters that are calibrated in order to explore multiple virtual scenarios. To compute reliable solutions at a greatly reduced computational cost, we rely on a reduced basis method empowered with a new deep learning-based operator approximation, which we refer to as Deep-HyROMnet technique. Our strategy combines a projection-based POD-Galerkin method with deep neural networks for the approximation of (reduced) nonlinear operators, overcoming the typical computational bottleneck associated with standard hyper-reduction techniques employed in reduced-order models (ROMs) for nonlinear parametrized systems. This method can provide extremely accurate approximations to parametrized cardiac mechanics problems, such as in the case of the complete cardiac cycle in a patient-specific left ventricle geometry. In this respect, a 3D model for tissue mechanics is coupled with a 0D model for external blood circulation; active force generation is provided through an adjustable parameter-dependent surrogate model as input to the tissue 3D model. The proposed strategy is shown to outperform classical projection-based ROMs, in terms of orders of magnitude of computational speed-up, and to return accurate pressure-volume loops in both physiological and pathological cases. Finally, an application to a forward uncertainty quantification analysis, unaffordable if relying on a FOM, is considered, involving output quantities of interest such as, for example, the ejection fraction or the maximal rate of change in pressure in the left ventricle.

Characterizing interactions between cardiac shape and deformation by non-linear manifold learning

In clinical routine, high-dimensional descriptors of the cardiac function such as shape and deformation are reduced to scalars (e.g. volumes or ejection fraction), which limit the characterization of complex diseases. Besides, these descriptors undergo interactions depending on disease, which may bias their computational analysis. In this paper, we aim at characterizing such interactions by unsupervised manifold learning. We propose to use a sparsified version of Multiple Manifold Learning to align the latent spaces encoding each descriptor and weighting the strength of the alignment depending on each pair of samples. While this framework was up to now only applied to link different datasets from the same manifold, we demonstrate its relevance to characterize the interactions between different but partially related descriptors of the cardiac function (shape and deformation). We benchmark our approach against linear and non-linear embedding strategies, among which the fusion of manifolds by Multiple Kernel Learning, the independent embedding of each descriptor by Diffusion Maps, and a strict alignment based on pairwise correspondences. We first evaluated the methods on a synthetic dataset from a 0D cardiac model where the interactions between descriptors are fully controlled. Then, we transfered them to a population of right ventricular meshes from 310 subjects (100 healthy and 210 patients with right ventricular disease) obtained from 3D echocardiography, where the link between shape and deformation is key for disease understanding. Our experiments underline the relevance of jointly considering shape and deformation descriptors, and that manifold alignment is preferable over fusion for our application. They also confirm at a finer scale the characteristic traits of the right ventricular diseases in our population.

Applications of artificial intelligence in cardiovascular imaging

Research into artificial intelligence (AI) has made tremendous progress over the past decade. In particular, the AI-powered analysis of images and signals has reached human-level performance in many applications owing to the efficiency of modern machine learning methods, in particular deep learning using convolutional neural networks. Research into the application of AI to medical imaging is now very active, especially in the field of cardiovascular imaging because of the challenges associated with acquiring and analysing images of this dynamic organ. In this Review, we discuss the clinical questions in cardiovascular imaging that AI can be used to address and the principal methodological AI approaches that have been developed to solve the related image analysis problems. Some approaches are purely data-driven and rely mainly on statistical associations, whereas others integrate anatomical and physiological information through additional statistical, geometric and biophysical models of the human heart. In a structured manner, we provide representative examples of each of these approaches, with particular attention to the underlying computational imaging challenges. Finally, we discuss the remaining limitations of AI approaches in cardiovascular imaging (such as generalizability and explainability) and how they can be overcome.

Using parametric model order reduction for inverse analysis of large nonlinear cardiac simulations

Predictive high-fidelity finite element simulations of human cardiac mechanics commonly require a large number of structural degrees of freedom. Additionally, these models are often coupled with lumped-parameter models of hemodynamics. High computational demands, however, slow down model calibration and therefore limit the use of cardiac simulations in clinical practice. As cardiac models rely on several patient-specific parameters, just one solution corresponding to one specific parameter set does not at all meet clinical demands. Moreover, while solving the nonlinear problem, 90% of the computation time is spent solving linear systems of equations. We propose to reduce the structural dimension of a monolithically coupled structure-Windkessel system by projection onto a lower-dimensional subspace. We obtain a good approximation of the displacement field as well as of key scalar cardiac outputs even with very few reduced degrees of freedom, while achieving considerable speedups. For subspace generation, we use proper orthogonal decomposition of displacement snapshots. Following a brief comparison of subspace interpolation methods, we demonstrate how projection-based model order reduction can be easily integrated into a gradient-based optimization. We demonstrate the performance of our method in a real-world multivariate inverse analysis scenario. Using the presented projection-based model order reduction approach can significantly speed up model personalization and could be used for many-query tasks in a clinical setting.

Population-based priors in cardiac model personalisation for consistent parameter estimation in heterogeneous databases

Personalised cardiac models are a virtual representation of the patient heart, with parameter values for which the simulation fits the available clinical measurements. Models usually have a large number of parameters while the available data for a given patient are typically limited to a small set of measurements; thus, the parameters cannot be estimated uniquely. This is a practical obstacle for clinical applications, where accurate parameter values can be important. Here, we explore an original approach based on an algorithm called Iteratively Updated Priors (IUP), in which we perform successive personalisations of a full database through maximum a posteriori (MAP) estimation, where the prior probability at an iteration is set from the distribution of personalised parameters in the database at the previous iteration. At the convergence of the algorithm, estimated parameters of the population lie on a linear subspace of reduced (and possibly sufficient) dimension in which for each case of the database, there is a (possibly unique) parameter value for which the simulation fits the measurements. We first show how this property can help the modeller select a relevant parameter subspace for personalisation. In addition, since the resulting priors in this subspace represent the population statistics in this subspace, they can be used to perform consistent parameter estimation for cases where measurements are possibly different or missing in the database, which we illustrate with the personalisation of a heterogeneous database of 811 cases.