Sequential data assimilation for mechanical systems with complex image data: application to tagged-MRI in cardiac mechanics

Alexandre Imperiale,Philippe Moireau,Dominique Chapelle

doi:10.1186/s40323-020-00179-w

Abstract

Tagged Magnetic Resonance images (tagged-MRI) are generally considered to be the gold standard of medical imaging in cardiology. By imaging spatially-modulated magnetizations of the deforming tissue, indeed, this modality enables an assessment of intra-myocardial deformations over the heart cycle. The objective of the present work is to incorporate the most valuable information contained in tagged-MRI in a data assimilation framework, in order to perform joint state-parameter estimation for a complete biomechanical model of the heart. This type of estimation is the second major step, after initial anatomical personalization, for obtaining a genuinely patient-specific model that integrates the individual characteristics of the patient, an essential prerequisite for benefitting from the model predictive capabilities. Here, we focus our attention on proposing adequate means of quantitatively comparing the cardiac model with various types of data that can be extracted from tagged-MRI after an initial image processing step, namely, 3D displacements fields, deforming tag planes or grids, or apparent 2D displacements. This quantitative comparison—called discrepancy measure—is then used to feed a sequential data assimilation procedure. In the state estimation stage of this procedure, we also propose a new algorithm based on the prediction–correction paradigm, which provides increased flexibility and effectiveness in the solution process. The complete estimation chain is eventually assessed with synthetic data, produced by running a realistic model simulation representing an infarcted heart characterized by increased stiffness and reduced contractility in a given region of the myocardium. From this simulation we extract the 3D displacements, tag planes and grids, and apparent 2D displacements, and we assess the estimation with each corresponding discrepancy measure. We demonstrate that—via regional estimation of the above parameters—the data assimilation procedure allows to quantitatively estimate the biophysical parameters with good accuracy, thus simultaneously providing the location of the infarct and characterizing its seriousness. This shows great potential for combining a biomechanical heart model with tagged-MRI in order to extract valuable new indices in clinical diagnosis.

Highlights

Cardiac biomechanical modeling has made tremendous progress over the past decades, and some accurate models are available to represent the complex deformations of the organ—among other quantities of interest—over full heartbeats, frequently based on multi-physics and multi-scale formulations, see e.g. [1,2] and references therein.As for all natural systems—as e.g. in geophysics—a great challenge consists in dealing with the many unknown or uncertain quantities—initial conditions, boundary conditions, and various physical parameters—that need to be prescribed for running model simulations [3]
Tagged-MRI represents the “gold standard” in cardiac imaging, and great benefits are expected from using the corresponding rich kinematical information for performing the joint state-parameter estimation of the system, and of various modeling parameters of high potential value in terms of clinical diagnosis assistance
In this data assimilation framework, a crucial ingredient lies in the adequate formulation of a discrepancy operator to compare the model and the data

Summary

Introduction

Cardiac biomechanical modeling has made tremendous progress over the past decades, and some accurate models are available to represent the complex deformations of the organ—among other quantities of interest—over full heartbeats, frequently based on multi-physics and multi-scale formulations, see e.g. [1,2] and references therein.As for all natural systems—as e.g. in geophysics—a great challenge consists in dealing with the many unknown or uncertain quantities—initial conditions, boundary conditions, and various physical parameters—that need to be prescribed for running model simulations [3]. Concerning the specific problem of estimation in cardiac biomechanical modeling, difficulties arise from both (1) the complexity of the models considered, and (2) the nature of the available measurements, often relying on medical imaging [5]. An effective estimation methodology has been proposed by [6] for this type of model, based on a so-called sequential approach— known as observer method. In this approach, the dynamical model is corrected at each time using the computed discrepancy between the current simulation and the actual measurements, see [7]. It was shown to be extendable to data consisting of segmented surfaces as obtained by processing various types of medical imaging dynamical sequences

Objectives

Results

Discussion

Conclusion