A computationally efficient physiologically comprehensive 3D–0D closed-loop model of the heart and circulation

Augustin, Christoph M.; Gsell, Matthias A. F.; Karabelas, Elias; Willemen, Erik; Prinzen, Frits W.; Lumens, Joost; Vigmond, Edward J.; Plank, Gernot

doi:10.1016/j.cma.2021.114092

Cited by 38 publications

(65 citation statements)

References 98 publications

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“…However, several studies [ 69 – 71 ] have shown that active stresses in the cross-fibre direction can be as large as 40% of those in fibre directions due to a dispersion of cardiomyocytes in tissue. This was already considered in Finsberg et al [ 25 ] and recently in a mechanistically more accurate mechanical framework in Augustin et al [ 11 ] and we see no obstacle in using other active mechanical models for the presented approach. Fifth, the representation of cellular EP and the [ Ca 2+ ] i evolution was simplified.…”

Section: Discussionsupporting

confidence: 52%

“…Substantial differences were only found for end-diastolic volumes; this was to be expected because the 3D model of human LV EM does not account for the atrial kick. This limitation could be addressed by coupling the 3D model of human LV or biventricular (biV) EM to a closed-loop lumped 0D model, see, e.g., [ 11 , 12 ], which represents the function of the remaining chambers and the circulation. However, this would require estimation of additional parameters of the closed-loop model which is beyond the scope of this work.…”

Section: Discussionmentioning

confidence: 99%

“…This choice of time step size is motivated by previous works using the same meshes [ 18 ]. To increase stability we considered Rayleigh damping of the generalised- α scheme used for the time integration of Equation (2) , see [ 11 ]. Additionally, we made use of an approach developed by Regazzoni and Quarteroni [ 46 ] to stabilise velocity-dependent active stress models of cardiac mechanics.…”

Section: Methodsmentioning

confidence: 99%

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An Integrated Workflow for Building Digital Twins of Cardiac Electromechanics—A Multi-Fidelity Approach for Personalising Active Mechanics

et al. 2022

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Personalised computer models of cardiac function, referred to as cardiac digital twins, are envisioned to play an important role in clinical precision therapies of cardiovascular diseases. A major obstacle hampering clinical translation involves the significant computational costs involved in the personalisation of biophysically detailed mechanistic models that require the identification of high-dimensional parameter vectors. An important aspect to identify in electromechanics (EM) models are active mechanics parameters that govern cardiac contraction and relaxation. In this study, we present a novel, fully automated, and efficient approach for personalising biophysically detailed active mechanics models using a two-step multi-fidelity solution. In the first step, active mechanical behaviour in a given 3D EM model is represented by a purely phenomenological, low-fidelity model, which is personalised at the organ scale by calibration to clinical cavity pressure data. Then, in the second step, median traces of nodal cellular active stress, intracellular calcium concentration, and fibre stretch are generated and utilised to personalise the desired high-fidelity model at the cellular scale using a 0D model of cardiac EM. Our novel approach was tested on a cohort of seven human left ventricular (LV) EM models, created from patients treated for aortic coarctation (CoA). Goodness of fit, computational cost, and robustness of the algorithm against uncertainty in the clinical data and variations of initial guesses were evaluated. We demonstrate that our multi-fidelity approach facilitates the personalisation of a biophysically detailed active stress model within only a few (2 to 4) expensive 3D organ-scale simulations—a computational effort compatible with clinical model applications.

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Section: Discussionsupporting

confidence: 52%

Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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An Integrated Workflow for Building Digital Twins of Cardiac Electromechanics—A Multi-Fidelity Approach for Personalising Active Mechanics

et al. 2022

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“…An abstract way to model the influence of the circulatory system is to use a 3D-0D coupled approach ( 23 , 36 – 38 ). To adequately define the interface between the circulatory system pressures and the fluid simulation boundary pressures, we introduced the prolonged trunks in the left heart to model the pulmonary veins and the aorta.…”

Section: Discussionmentioning

confidence: 99%

Sequential Coupling Shows Minor Effects of Fluid Dynamics on Myocardial Deformation in a Realistic Whole-Heart Model

Brenneisen

Daub

Gerach

et al. 2021

Front. Cardiovasc. Med.

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Background: The human heart is a masterpiece of the highest complexity coordinating multi-physics aspects on a multi-scale range. Thus, modeling the cardiac function in silico to reproduce physiological characteristics and diseases remains challenging. Especially the complex simulation of the blood's hemodynamics and its interaction with the myocardial tissue requires a high accuracy of the underlying computational models and solvers. These demanding aspects make whole-heart fully-coupled simulations computationally highly expensive and call for simpler but still accurate models. While the mechanical deformation during the heart cycle drives the blood flow, less is known about the feedback of the blood flow onto the myocardial tissue.Methods and Results: To solve the fluid-structure interaction problem, we suggest a cycle-to-cycle coupling of the structural deformation and the fluid dynamics. In a first step, the displacement of the endocardial wall in the mechanical simulation serves as a unidirectional boundary condition for the fluid simulation. After a complete heart cycle of fluid simulation, a spatially resolved pressure factor (PF) is extracted and returned to the next iteration of the solid mechanical simulation, closing the loop of the iterative coupling procedure. All simulations were performed on an individualized whole heart geometry. The effect of the sequential coupling was assessed by global measures such as the change in deformation and—as an example of diagnostically relevant information—the particle residence time. The mechanical displacement was up to 2 mm after the first iteration. In the second iteration, the deviation was in the sub-millimeter range, implying that already one iteration of the proposed cycle-to-cycle coupling is sufficient to converge to a coupled limit cycle.Conclusion: Cycle-to-cycle coupling between cardiac mechanics and fluid dynamics can be a promising approach to account for fluid-structure interaction with low computational effort. In an individualized healthy whole-heart model, one iteration sufficed to obtain converged and physiologically plausible results.

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“…Following the approach for 3D-0D coupling proposed in Augustin et al [30] and inspired by Gurev et al [31], Kerckhoffs et al [14], the coupling condition between an EM model of the heart cavities and a reduced-order circulatory model imposes that the volume change in each cavity (left ventricle LV, right ventricle RV, left atrium LA and right atrium RA) is balanced with the volume change in the attached circulatory system. For the sake of generality, we cast in what follows the general framework to couple a four-chamber heart model with a closed-loop circulatory system.…”

Section: D-1d Couplingmentioning

confidence: 99%

A coupling strategy for a 3D-1D model of the cardiovascular system to study the effects of pulse wave propagation on cardiac function

Caforio¹,

Augustin²,

Alastruey³

et al. 2021

Preprint

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The impact of increased stiffness and pulsatile load on the circulation and their influence on heart performance have been documented not only for cardiovascular events but also for ventricular dysfunctions. For this reason, computer models of cardiac electromechanics (EM) have to integrate effects of the circulatory system on heart function to be relevant for clinical applications. Currently it is not feasible to consider three-dimensional (3D) models of the entire circulation. Instead, simplified representations of the circulation are used, ensuring a satisfactory trade-off between accuracy and computational cost. In this work, we propose a novel and stable strategy to couple a 3D EM model of the heart to a one-dimensional (1D) model of blood flow in the arterial system. A personalised coupled 3D-1D model of LV and arterial system is built and used in a numerical benchmark to demonstrate robustness and accuracy of our scheme over a range of time steps. Validation of the coupled model is performed by investigating the coupled system's physiological response to variations in the arterial system affecting pulse wave propagation, comprising aortic stiffening, aortic stenosis or bifurcations causing wave reflections. Our results show that the coupled 3D-1D model is robust, stable and correctly replicates known physiology.

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A computationally efficient physiologically comprehensive 3D–0D closed-loop model of the heart and circulation

Cited by 38 publications

References 98 publications

An Integrated Workflow for Building Digital Twins of Cardiac Electromechanics—A Multi-Fidelity Approach for Personalising Active Mechanics

An Integrated Workflow for Building Digital Twins of Cardiac Electromechanics—A Multi-Fidelity Approach for Personalising Active Mechanics

Sequential Coupling Shows Minor Effects of Fluid Dynamics on Myocardial Deformation in a Realistic Whole-Heart Model

A coupling strategy for a 3D-1D model of the cardiovascular system to study the effects of pulse wave propagation on cardiac function

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