Estimation of passive and active properties in the human heart using 3D tagged MRI

Advances in medical imaging and image processing are paving the way for personalised cardiac biomechanical modelling. Models provide the capacity to relate kinematics to dynamics and-through patient-specific modelling-derived material parameters to underlying cardiac muscle pathologies. However, for clinical utility to be achieved, model-based analyses mandate robust model selection and parameterisation. In this paper, we introduce a patient-specific biomechanical model for the left ventricle aiming to balance model fidelity with parameter identifiability. Using non-invasive data and common clinical surrogates, we illustrate unique identifiability of passive and active parameters over the full cardiac cycle. Identifiability and accuracy of the estimates in the presence of controlled noise are verified with a number of in silico datasets. Unique parametrisation is then obtained for three datasets acquired in vivo. The model predictions show good agreement with the data extracted from the images providing a pipeline for personalised biomechanical analysis.</p

Efficient numerical methods for the solution of coupled multiphysics problems

Multiphysics systems with interface coupling are used to model a variety of physical phenomena, such as arterial blood flow, air flow around aeroplane wings, or interactions between surface and ground water flows. Numerical methods enable the practical application of these models through computer simulations. Specifically a high level of detail and accuracy is achieved in finite element methods by discretisations which use extremely large numbers of degrees of freedom, rendering the solution process challenging from the computational perspective. In this thesis we address this challenge by developing a twofold strategy for improving the efficiency of standard finite element coupled solvers. First, we propose to solve a monolithic coupled problem using block-preconditioned GMRES with a new Schur complement approximation. This results in a modular and robust method which significantly reduces the computational cost of solving the system. In particular, numerical tests show mesh-independent convergence of the solver for all the considered problems, suggesting that the method is well-suited to solving large-scale coupled systems. Second, we derive an adjoint-based formula for goal-oriented a posteriori error estimation, which leads to a time-space mesh refinement strategy. The strategy produces a mesh tailored to a given problem and quantity of interest. The monolithic formulation of the coupled problem allows us to obtain expressions for the error in the Lagrange multiplier, which often represents a physically relevant quantity, such as the normal stress on the interface between the problem components. This adaptive refinement technique provides an effective tool for controlling the error in the quantity of interest and/or the size of the discrete system, which may be limited by the available computational resources. The solver and the mesh refinement strategy are both successfully employed to solve a coupled Stokes-Darcy-Stokes problem modelling flow through a cartridge filter.</p

Efficient numerical methods for the solution of coupled multiphysics problems

Multiphysics systems with interface coupling are used to model a variety of physical phenomena, such as arterial blood flow, air flow around aeroplane wings, or interactions between surface and ground water flows. Numerical methods enable the practical application of these models through computer simulations. Specifically a high level of detail and accuracy is achieved in finite element methods by discretisations which use extremely large numbers of degrees of freedom, rendering the solution process challenging from the computational perspective. In this thesis we address this challenge by developing a twofold strategy for improving the efficiency of standard finite element coupled solvers. First, we propose to solve a monolithic coupled problem using block-preconditioned GMRES with a new Schur complement approximation. This results in a modular and robust method which significantly reduces the computational cost of solving the system. In particular, numerical tests show mesh-independent convergence of the solver for all the considered problems, suggesting that the method is well-suited to solving large-scale coupled systems. Second, we derive an adjoint-based formula for goal-oriented a posteriori error estimation, which leads to a time-space mesh refinement strategy. The strategy produces a mesh tailored to a given problem and quantity of interest. The monolithic formulation of the coupled problem allows us to obtain expressions for the error in the Lagrange multiplier, which often represents a physically relevant quantity, such as the normal stress on the interface between the problem components. This adaptive refinement technique provides an effective tool for controlling the error in the quantity of interest and/or the size of the discrete system, which may be limited by the available computational resources. The solver and the mesh refinement strategy are both successfully employed to solve a coupled Stokes-Darcy-Stokes problem modelling flow through a cartridge filter.This thesis is not currently available in OR

ADJOINT-BASED A POSTERIORI ERROR ESTIMATION FOR COUPLED TIME-DEPENDENT SYSTEMS ∗

Abstract. We consider time-dependent parabolic problems coupled across a common interface which we formulate using a Lagrange multiplier construction and solve by applying a monolithic solution technique. We derive an adjoint-based a posteriori error representation for a quantity of interest given by a linear functional of the solution. We establish the accuracy of our error representation formula through numerical experimentation and investigate the effect of error in the adjoint solution. Crucially, the error representation affords a distinction between temporal and spatial errors and can be used as a basis for a blockwise time-space refinement strategy. Numerical tests illustrate the efficacy of the refinement strategy by capturing the distinctive behavior of a localized traveling wave solution. The saddle point systems considered here are equivalent to those arising in the mortar finite element technique for parabolic problems

Studying Dynamic Myofiber Aggregate Reorientation in Dilated Cardiomyopathy Using in Vivo Magnetic Resonance Diffusion Tensor Imaging

Background The objective of this study is to assess the dynamic alterations of myocardial microstructure and strain between diastole and systole in patients with dilated cardiomyopathy relative to healthy controls using the magnetic resonance diffusion tensor imaging, myocardial tagging, and biomechanical modeling. Methods and Results Dual heart-phase diffusion tensor imaging was successfully performed in 9 patients and 9 controls. Tagging data were acquired for the diffusion tensor strain correction and cardiac motion analysis. Mean diffusivity, fractional anisotropy, and myocyte aggregate orientations were compared between both cohorts. Cardiac function was assessed by left ventricular ejection fraction, torsion, and strain. Computational modeling was used to study the impact of cardiac shape on fiber reorientation and how fiber orientations affect strain. In patients with dilated cardiomyopathy, a more longitudinal orientation of diastolic myofiber aggregates was measured compared with controls. Although a significant steepening of helix angles (HAs) during contraction was found in the controls, consistent change in HAs during contraction was absent in patients. Left ventricular ejection fraction, cardiac torsion, and strain were significantly lower in the patients compared with controls. Computational modeling revealed that the dilated heart results in reduced HA changes compared with a normal heart. Reduced torsion was found to be exacerbated by steeper HAs. Conclusions Diffusion tensor imaging revealed reduced reorientation of myofiber aggregates during cardiac contraction in patients with dilated cardiomyopathy relative to controls. Left ventricular remodeling seems to be an important factor in the changes to myocyte orientation. Steeper HAs are coupled with a worsening in strain and torsion. Overall, the findings provide new insights into the structural alterations in patients with dilated cardiomyopathy.ISSN:1941-9651ISSN:1942-008

Multiphysics and multiscale modelling, data–model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics

International audienceWith heart and cardiovascular diseases continually challenging healthcare systems worldwide, translating basic research on cardiac (patho)physiology into clinical care is essential. Exacerbating this already extensive challenge is the complexity of the heart, relying on its hierarchical structure and function to maintain cardiovascular flow. Computational modelling has been proposed and actively pursued as a tool for accelerating research and translation. Allowing exploration of the relationships between physics, multiscale mechanisms and function, computational modelling provides a platform for improving our understanding of the heart. Further integration of experimental and clinical data through data assimilation and parameter estimation techniques is bringing computational models closer to use in routine clinical practice. This article reviews developments in computational cardiac modelling and how their integration with medical imaging data is providing new pathways for translational cardiac modelling

Non-invasive Model-Based Assessment of Passive Left-Ventricular Myocardial Stiffness in Healthy Subjects and in Patients with Non-ischemic Dilated Cardiomyopathy

International audiencePatient-specific modelling has emerged as a tool for studying heart function, demonstrating the potential to provide non-invasive estimates of tissue passive stiffness. However, reliable use of model-derived stiffness requires sufficient model accuracy and unique estimation of model parameters. In this paper we present personalised models of cardiac mechanics, focusing on improving model accuracy, while ensuring unique parametrisation. The influence of principal model uncertainties on accuracy and parameter identifiability was systematically assessed in a group of patients with dilated cardiomyopathy (n 1⁄4 3) and healthy volunteers (n 1⁄4 5). For all cases, we examined three circumferentially symmetric fibre distributions and two epicardial boundary conditions. Our results demonstrated the ability of data-derived boundary conditions to improve model accuracy and highlighted the influence of the assumed fibre distribution on both model fidelity and stiffness estimates. The model personalisation pipeline—based strictly on non-invasive data—produced unique parameter estimates and satisfactory model errors for all cases, supporting the selected model assumptions. The thorough analysis performed enabled the comparison of passive parameters between volunteers and dilated cardiomyopathy patients, illustrating elevated stiffness in diseased hearts

Analysis of passive cardiac constitutive laws for parameter estimation using 3D tagged MRI

International audienceAn unresolved issue in patient-specific models of cardiac mechanics is the choice of an appropriate constitutive law, able to accurately capture the passive behavior of the myocardium, while still having uniquely identifiable parameters tunable from available clinical data. In this paper, we aim to facilitate this choice by examining the practical identifiability and model fidelity of constitutive laws often used in cardiac mechanics. Our analysis focuses on the use of novel 3D tagged MRI, providing detailed displacement information in three dimensions. The practical identifiability of each law is examined by generating synthetic 3D tags from in silico simulations, allowing mapping of the objective function landscape over parameter space and comparison of minimizing parameter values with original ground truth values. Model fidelity was tested by comparing these laws with the more complex transversely isotropic Guccione law, by characterizing their passive end-diastolic pressure–volume relation behavior, as well as by considering the in vivo case of a healthy volunteer. These results show that a reduced form of the Holzapfel–Ogden law provides the best balance between identifiability and model fidelity across the tests considered

Altered Aortic Hemodynamics and Relative Pressure in Patients with Dilated Cardiomyopathy

International audienceVentricular-vascular interaction is central in the adaptation to cardiovascular disease. However, cardiomyopathy patients are predominantly monitored using cardiac biomarkers. The aim of this study is therefore to explore aortic function in dilated cardiomyopathy (DCM). Fourteen idiopathic DCM patients and 16 controls underwent cardiac magnetic resonance imaging, with aortic relative pressure derived using physics-based image processing and a virtual cohort utilized to assess the impact of cardiovascular properties on aortic behaviour. Subjects with reduced left ventricular systolic function had significantly reduced aortic relative pressure, increased aortic stiffness, and significantly delayed time-to-pressure peak duration. From the virtual cohort, aortic stiffness and aortic volumetric size were identified as key determinants of aortic relative pressure. As such, this study shows how advanced flow imaging and aortic hemodynamic evaluation could provide novel insights into the manifestation of DCM, with signs of both altered aortic structure and function derived in DCM using our proposed imaging protocol