A Simulation-Based Method to Study the LQT1 Syndrome Remotely Using the EMI Model

Domínguez, Sebastián; Reimer, Joyce; Green, Kevin R.; Zolfaghari, Reza; Spiteri, Raymond J.

doi:10.1007/978-3-030-14647-4_12

Cited by 5 publications

(8 citation statements)

References 34 publications

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“…Following a similar approach to that in [5,4], to construct the linear system for the EMI model, where A = A EMI , q = y EMI , and f = y, we employ a mixed RT0-P0-P1c scheme to find approximations to the ion current in Ω, the intracellular and extracellular potentials u (k) i…”

Section: Spatial Discretization: Finite Element Methodsmentioning

confidence: 99%

“…Ongoing developments in high-performance computing make it feasible to perform meaningful simulations at such a level of detail. Due to the relative newness of the EMI model, however, there are only a handful of studies that explore its capabilities [5,4,6,7,8,9,10,11], and only one of these studies examines it in relation to the bidomain model [11]. In the present study, we compare the bidomain model to the EMI model in the context of unipolar stimulation of refractory cardiac tissue, an application relevant to the design of pacemakers and defibrillators.…”

Section: Introductionmentioning

confidence: 99%

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Physiological accuracy in simulating refractory cardiac tissue: the volume-averaged bidomain model vs. the cell-based EMI model

Reimer

Domínguez-Rivera

Sundnes

et al. 2023

Preprint

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The refractory period of cardiac tissue can be quantitatively described using strength-interval (SI) curves. The information captured in SI curves is pertinent to the design of anti-arrhythmic devices including pacemakers and implantable cardioverter defibrillators. As computational cardiac modelling becomes more prevalent, it is feasible to consider the generation of computationally derived SI curves as a supplement or precursor to curves that are experimentally derived. It is beneficial, therefore, to examine the profiles of the SI curves produced by different cardiac tissue models to determine whether some models capture the refractory period more accurately than others. In this study, we compare the unipolar SI curves of two tissue models: the current state-of-the-art bidomain model and the recently developed extracellular-membrane-intracellular (EMI) model. The EMI model's resolution of individual cell structure makes it a more detailed model than the bidomain model, which forgoes the structure of individual cardiac cells in favour of treating them homogeneously as a continuum. We find that the resulting SI curves elucidate differences between the models, including that the behaviour of the EMI model is noticeably closer to the refractory behaviour of experimental data compared to that of the bidomain model. These results hold implications for future computational pacemaker simulations and shed light on the predicted refractory properties of cardiac tissue from each model.

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Section: Spatial Discretization: Finite Element Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Physiological accuracy in simulating refractory cardiac tissue: the volume-averaged bidomain model vs. the cell-based EMI model

Reimer

Domínguez-Rivera

Sundnes

et al. 2023

Preprint

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“…The scaling factor for the Na + channel diffusion, d Na þ is kept constant when the channel cluster size is increased. In our simulations, we consider Na + channel clusters consisting of 4,36,196 or 900 Na + channels (see Fig 2).…”

Section: The Poisson-nernst-planck (Pnp) Equationsmentioning

confidence: 99%

“…This limits the modeling capabilities of these models. At the level of individual cardiomyocytes (� μm), cell-based (EMI) models representing both the extracellular (E) space, the cell membrane (M) and the intracellular (I) space can be applied; see, e.g., [2][3][4][5]. The EMI models increase the modeling capabilities, allowing parameters to vary between and within individual cardiomyocytes, at the cost of significantly increased computing efforts needed to solve the equations; see, e.g., [6].…”

Section: Introductionmentioning

confidence: 99%

Nano-scale solution of the Poisson-Nernst-Planck (PNP) equations in a fraction of two neighboring cells reveals the magnitude of intercellular electrochemical waves

et al. 2023

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The basic building blocks of the electrophysiology of cardiomyocytes are ion channels integrated in the cell membranes. Close to the ion channels there are very strong electrical and chemical gradients. However, these gradients extend for only a few nano-meters and are therefore commonly ignored in mathematical models. The full complexity of the dynamics is modelled by the Poisson-Nernst-Planck (PNP) equations but these equations must be solved using temporal and spatial scales of nano-seconds and nano-meters. Here we report solutions of the PNP equations in a fraction of two abuttal cells separated by a tiny extracellular space. We show that when only the potassium channels of the two cells are open, a stationary solution is reached with the well-known Debye layer close to the membranes. When the sodium channels of one of the cells are opened, a very strong and brief electrochemical wave emanates from the channels. If the extracellular space is sufficiently small and the number of sodium channels is sufficiently high, the wave extends all the way over to the neighboring cell and may therefore explain cardiac conduction even at very low levels of gap junctional coupling.

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“…To study at the microscopic level the relationship between tissue morphology and the propagation of the depolarization wave, and to investigate the role of the distributions of the extracellular space around cells on the conduction velocity, Stinstra et al [43][44][45] introduced a 3D model of cardiac tissue. Spiteri et al [12] used the cell-based model to simulate the effects of a cardiac condition called long QT syndrome (LQTS). They compared simulations from data from healthy cells, cells that exhibit the syndrome, and cells that have been treated with a drug to restore healthy heart function.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of finite element methods for the cardiac extracellular-membrane-intracellular model: Steklov–Poincaré operator and spatial error estimates

Fokoué,

Bourgault

2023

ESAIM: M2AN

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The extracellular-membrane-intracellular (EMI) model consists in a set of Poisson equations in two adjacent domains, coupled on interfaces with nonlinear transmission conditions involving a system of ODEs. The unusual coupling of PDEs and ODEs on the boundary makes the EMI models challenging to solve numerically. In this paper, we reformulate the problem on the interface using a Steklov–Poincaré operator. We then discretize the model in space using a finite element method (FEM). We prove the existence of a semi-discrete solution using a reformulation as an ODE system on the interface. We derive stability and error estimates for the FEM. Finally, we propose a manufactured solution and use it to perform numerical tests. The order of convergence of the numerical method agrees with what is expected on the basis of the theoretical analysis of the convergence.

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A Simulation-Based Method to Study the LQT1 Syndrome Remotely Using the EMI Model

Cited by 5 publications

References 34 publications

Physiological accuracy in simulating refractory cardiac tissue: the volume-averaged bidomain model vs. the cell-based EMI model

Physiological accuracy in simulating refractory cardiac tissue: the volume-averaged bidomain model vs. the cell-based EMI model

Nano-scale solution of the Poisson-Nernst-Planck (PNP) equations in a fraction of two neighboring cells reveals the magnitude of intercellular electrochemical waves

Numerical analysis of finite element methods for the cardiac extracellular-membrane-intracellular model: Steklov–Poincaré operator and spatial error estimates

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