Monodomain Research Articles

Parallel Optimization of 3D Cardiac Electrophysiological Model Using GPU.

Large-scale 3D virtual heart model simulations are highly demanding in computational resources. This imposes a big challenge to the traditional computation resources based on CPU environment, which already cannot meet the requirement of the whole computation demands or are not easily available due to expensive costs. GPU as a parallel computing environment therefore provides an alternative to solve the large-scale computational problems of whole heart modeling. In this study, using a 3D sheep atrial model as a test bed, we developed a GPU-based simulation algorithm to simulate the conduction of electrical excitation waves in the 3D atria. In the GPU algorithm, a multicellular tissue model was split into two components: one is the single cell model (ordinary differential equation) and the other is the diffusion term of the monodomain model (partial differential equation). Such a decoupling enabled realization of the GPU parallel algorithm. Furthermore, several optimization strategies were proposed based on the features of the virtual heart model, which enabled a 200-fold speedup as compared to a CPU implementation. In conclusion, an optimized GPU algorithm has been developed that provides an economic and powerful platform for 3D whole heart simulations.

Crank–Nicolson ADI Galerkin finite element method for two-dimensional fractional FitzHugh–Nagumo monodomain model

In this paper, a two-dimensional fractional FitzHugh–Nagumo monodomain model (2D-FFHNMM) with zero Dirichlet boundary condition is considered. The model consists of a coupled two-dimensional space fractional nonlinear reaction–diffusion model (2D-SFNRDM) and an ordinary differential equation. The 2D-SFNRDM and ordinary differential equation are decoupled at each time step. A new Crank–Nicolson alternating direction implicit (ADI) Galerkin finite element method for the 2D-SFNRDM is developed. The stability and convergence of the numerical method are discussed. Finally, some numerical examples on 2D-SFNRDM and 2D-FFHNMM are given for verification of our theoretical analysis.

Patient-specific modeling of ventricular activation pattern using surface ECG-derived vectorcardiogram in bundle branch block

Patient-specific computational models have promise to improve cardiac disease diagnosis and therapy planning. Here a new method is described to simulate left-bundle branch block (LBBB) and RV-paced ventricular activation patterns in three dimensions from non-invasive, routine clinical measurements. Activation patterns were estimated in three patients using vectorcardiograms (VCG) derived from standard 12-lead electrocardiograms (ECG). Parameters of a monodomain model of biventricular electrophysiology were optimized to minimize differences between the measured and computed VCG. Electroanatomic maps of local activation times measured on the LV and RV endocardial surfaces of the same patients were used to validate the simulated activation patterns. For all patients, the optimal estimated model parameters predicted a time-averaged mean activation dipole orientation within 6.7 ± 0.6° of the derived VCG. The predicted local activation times agreed within 11.5 ± 0.8 ms of the measured electroanatomic maps, on the order of the measurement accuracy.

A semi-alternating direction method for a 2-D fractional FitzHugh–Nagumo monodomain model on an approximate irregular domain

A FitzHugh–Nagumo monodomain model has been used to describe the propagation of the electrical potential in heterogeneous cardiac tissue. In this paper, we consider a two-dimensional fractional FitzHugh–Nagumo monodomain model on an irregular domain. The model consists of a coupled Riesz space fractional nonlinear reaction–diffusion model and an ordinary differential equation, describing the ionic fluxes as a function of the membrane potential. Second, we use a decoupling technique and focus on solving the Riesz space fractional nonlinear reaction–diffusion model. A novel spatially second-order accurate semi-implicit alternating direction method (SIADM) for this model on an approximate irregular domain is proposed. Third, stability and convergence of the SIADM are proved. Finally, some numerical examples are given to support our theoretical analysis and these numerical techniques are employed to simulate a two-dimensional fractional FitzHugh–Nagumo model on both an approximate circular and an approximate irregular domain.

Optimal monodomain approximations of the bidomain equations used in cardiac electrophysiology

The bidomain model is the current most sophisticated model used in cardiac electrophysiology. The monodomain model is a simplification of the bidomain model that is less computationally intensive but only valid under equal conductivity ratio. We propose in this paper optimal monodomain approximations of the bidomain model. We first prove that the error between the bidomain and monodomain solutions is bounded by the error ‖B - A‖ between the bidomain and monodomain conductivity operators. Optimal monodomain approximations are defined by minimizing the distance ‖B - A‖, which reduces for solutions over all ℝdto minimize the Lpnorm of the difference between the operator symbols. Similarly, comparing the symbols pointwise amounts to compare the propagation of planar waves in the bidomain and monodomain models. We prove that any monodomain model properly propagates at least d planar waves in ℝd. We next consider and solve the optimal problem in the L∞and L2norms, the former providing minimal propagation error uniformly over all directions. The quality of these optimal monodomain approximations is compared among themselves and with other published approximations using two sets of test cases. The first one uses periodic boundary conditions to mimic propagation in ℝdwhile the second is based on a square domain with common Neumann boundary conditions. For the first test cases, we show that the error on the propagation speed is highly correlated with the error on the symbols. The second test cases show that domain boundaries control propagation directions, with only partial impact from the conductivity operator used.

Development of finite element models for studying the electrical excitation of myocardium

The propagation of the electrical excitation wave in the isotropic and anisotropic finite element models of the myocardium is studied. The geometrical image of the heart is constructed on the basis of magnetic resonance tomography (MRT) data by the region growing method. A filtering algorithm is proposed for elimination of excess details. The propagation of the myocardium excitation impulse is described in the framework of the monodomain model of conductivity. The Aliev–Panfilov and Beeler–Reuter equations are used to relate the transmembrane current to transmembrane potential. The model equations are solved by the splitting method. The influence of the degree of approximation on the performance of the finite element model is investigated. The interaction between the additional excitation source and the propagating excitation wave is considered. The proposed model allowed us to trace the propagation of the excitation impulse through the curvilinear isotropic media and in the 3D image of the heart obtained on the basis of MRT data.

Two-step genetic algorithm to solve the inverse problem in electrocardiography for cardiac sources

This study is concerned with the numerical analysis of the inverse problem in electrocardiography. We propose a new method (two-step algorithm) based on the application of genetic algorithm with the Tikhonov method to calculate the electrical sources on the heart. In the literature, the solution reconstructed by the classical Tikhonov method is based on the minimum energy norm using a closed geometry. This solution could be very different from the original source on the heart. Compared with the classical inverse problem method, the two-step algorithm improves the accuracy of the solution with respect to the original distribution. Finally, to validate our results, we create a distribution over the heart by using a model of electrical activity (Monodomain model), and then using our method, we make the reconstruction of the potential distribution.

Integrative Approaches in Computational Biomedical Imaging 2013

Increasingly wider availability of biomedical imaging modalities, such as X-ray computed tomography (CT), magnetic resonance imaging (MRI), ultrasonic imaging, positron emission tomography (PET), single-photon emission computed tomography (SPECT), and optical imaging, have led to significant progresses in both biomedical research and clinical practice. Advancements in imaging technology and image informatics have facilitated and enabled quantitative understanding of the biological structures, functional organisms, and pathological mechanisms. This special issue presents 14 latest research contributions in computational biomedical imaging. The focuses have been on the computational principles, strategies, methods, and algorithms that create, extract, and understand imaging data of biomedical significance. The first group of papers has showcased the development and applications of rigorous optimization techniques in biomedical imaging. The work based on dual unscented Kalman filtering provides a reliable and efficient platform to understand the BOLD signals from fMRI. In the other paper, the robust discrete particle swarm optimization algorithm is adopted to solve the branch-cut phase unwrapping problem of MRI data. Without the need for a regularization penalty term, a semigreed method for bioluminescence tomography reconstruction is fast and stable for small animal imaging. The second group of papers has addressed image segmentation and tissue characterization problems, ever popular among image analysis researchers. The work of L. Li et al. applies machine learning techniques to characterize lymph node metastasis in gastric cancer from gemstone spectral imaging with much improved outcomes, while G. V. Sanchez. Ferrero et al. make new advances in ultrasonic speckle characterization using generalized Gama distribution and generalized Gama mixture model. In recent years, physically meaningful modeling and simulation have become integral components for model-constrained imaging and model-based image understanding. Thus, the third group of papers has continued the stride in this direction. The propagation of myocardial electrical activation is simulated using a monodomain model, without the need of explicit mesh constraints. In similar spirit, one work performs forward modeling of 3D optical molecular imaging with simplified spherical harmonics approximation using extended finite element method. The final group of papers has highlighted some new imaging modalities and their potential use in clinical practice. The further development of ultrasound-based quantitative imaging of Young's modulus with high accuracy is presented in this issue. And the novel Diffusion Kurtosis Imaging shows that more detailed classification of brain tissues is clinical significance. We appreciate the many high quality submissions to this special issue from leading researchers in computational biomedical imaging. Because of space limitation, we can only accept a small number of most exciting works. We sincerely hope that the remaining interesting research outcomes will be soon published in other venues.

Low-temperature elastic anomalies in CaTiO3: dynamical characterization

Pulse–echo ultrasonic measurements of elastic coefficients of CaTiO3 show anomalous behavior around 200 K, with a notable rise in the attenuation coefficient. Molecular dynamics simulation is used to simulate the elastic response of a mono-domain (MDm) and a poly-domain (PDm) configuration of CaTiO3 using the Vashishta–Raman interatomic potential. The PDm is obtained by cooling the melt from 3600 to 300 K at a rate of 0.5 K ps−1, so that it recrystallizes to the PDm orthorhombic configuration. The elastic behavior is simulated in the temperature range from 300 to 20 K. In the MDm, it is observed that the bulk modulus varies linearly with temperature, while in the PDm an anomalous hardening is seen around 210 K. The bulk modulus of the PDm fluctuates strongly and is lower than that of the MDm. Neither the pair correlation function nor the Ti–Ti–O bonding angle indicate a true structural phase transition in this range of temperatures. Given the absence of any apparent change in the structure, a possible explanation for this phenomenon is the emergence of a certain class of dynamical instability associated with domain wall motion. Curiously, the pressure fluctuations in both the MDm and PDm configurations follow a power law distribution f ∼ P−α, with the exponent independent of applied strain and temperature. Time series for pressure are used to analyze the dynamics by time-delay reconstruction techniques. The calculus of embedding and correlation dimension indicates that in the polycrystalline configuration, low-dimension dynamics (<26) appears, which tend to disappear at higher temperatures.

Photoalignment in Rheology of Liquid Crystals

The application of photoalignment technique for rheological study of liquid crystals is considered. Such technique can be used for the initial preparation and rotation of mono domain samples of liquid crystals. It provides new possibilities in measurements of anisotropic viscosities of liquid crystals. Three shear and the rotational viscosities of nematic liquid crystals can be determined at additional usage of the electric field.

The Effects of Control Domain Size on Optimal Control Problem of Monodomain Model

this paper, we study the effects of the size of the control domain on the optimal control problem of monodomain model. The optimal control problem of monodomain model is a nonlinear optimization problem that is constrained by the monodomain model that represents the electrical behavior of the cardiac tissue. Two test cases with different sizes of control domain are considered, namely Test Case 1 and Test Case 2. Numerical results show that the excitation wavefront is successfully dampened out by the optimal applied current in both test cases. However, Test Case 2 (with smaller size of the control domain) requires more iteration as well as longer time to dampen the excitation wavefront. Our numerical results also indicate that higher current is required in the dampening process when the size of the control domain changed to a smaller one. Keywordsfinite element method, Monodomain model, Optimal control, Cardiac electrophysiology

P‐90: Surface Pinning Effect on Blue‐Phase Liquid Crystal

AbstractThis paper reports surface treatment effect on liquid crystalline blue phase morphology and electro‐optical performances at various temperatures. We have succeeded to achieve homogeneous monodomain blue phase morphology by surface treatment. Operating voltage and hysteresis of the proposed device is greatly reduced compared to the non surface treated cell, owing to dramatic increase in Kerr constant. Uniform mono domain morphology has better electric field withstand capability so that its original texture restored after electric field addressing.

Magnetic bit stability: Competition between domain-wall and monodomain switching

We numerically study the thermal stability properties of computer memory storage realized by a magnetic ellipse. In the case of practical magnetic random-access memory devices, the bit can form a spin texture during switching events. To study the energy barrier for thermally induced switching, we develop a variational procedure to force the bit to traverse a smooth path through configuration space between the points of stability. We identify textured configurations realizing domain-wall propagation, which may have an energy barrier less than that of the corresponding monodomain model. We contrast the emergence of such micromagnetic effects in thermal versus field-induced switching.

Numerical Solution for PDE-Constrained Optimization Problem in Cardiac Electrophysiology

paper, we present the numerical solution for the PDE- constrained optimization problem arises in cardiac electrophysiology. The monodomain model, which is a well- established model for simulating electrical behavior of the cardiac tissue, appears as the constraint in our problem. Our objective is to search for the optimal applied current, which is able to dampen out the excitation wavefront of the transmembrane potential during defibrillation process. The modified Dai-Yuan nonlinear conjugate gradient method is employed for computing the optimal applied current, and our numerical results show that the excitation wavefront is successfully dampened out by the optimal applied current.

Efficient simulation of cardiac electrical propagation using high order finite elements

We present an application of high order hierarchical finite elements for the efficient approximation of solutions to the cardiac monodomain problem. We detail the hurdles which must be overcome in order to achieve theoretically-optimal errors in the approximations generated, including the choice of method for approximating the solution to the cardiac cell model component. We place our work on a solid theoretical foundation and show that it can greatly improve the accuracy in the approximation which can be achieved in a given amount of processor time. Our results demonstrate superior accuracy over linear finite elements at a cheaper computational cost and thus indicate the potential indispensability of our approach for large-scale cardiac simulation.

Solving Optimal Control Problem of Monodomain Model Using Hybrid Conjugate Gradient Methods

We present the numerical solutions for the PDE‐constrained optimization problem arising in cardiac electrophysiology, that is, the optimal control problem of monodomain model. The optimal control problem of monodomain model is a nonlinear optimization problem that is constrained by the monodomain model. The monodomain model consists of a parabolic partial differential equation coupled to a system of nonlinear ordinary differential equations, which has been widely used for simulating cardiac electrical activity. Our control objective is to dampen the excitation wavefront using optimal applied extracellular current. Two hybrid conjugate gradient methods are employed for computing the optimal applied extracellular current, namely, the Hestenes‐Stiefel‐Dai‐Yuan (HS‐DY) method and the Liu‐Storey‐Conjugate‐Descent (LS‐CD) method. Our experiment results show that the excitation wavefronts are successfully dampened out when these methods are used. Our experiment results also show that the hybrid conjugate gradient methods are superior to the classical conjugate gradient methods when Armijo line search is used.

A Meshfree Method for Simulating Myocardial Electrical Activity

An element-free Galerkin method (EFGM) is proposed to simulate the propagation of myocardial electrical activation without explicit mesh constraints using a monodomain model. In our framework the geometry of myocardium is first defined by a meshfree particle representation that is, a sufficient number of sample nodes without explicit connectivities are placed in and inside the surface of myocardium. Fiber orientations and other material properties of myocardium are then attached to sample nodes according to their geometrical locations, and over the meshfree particle representation spatial variation of these properties is approximated using the shape function of EFGM. After the monodomain equations are converted to their Galerkin weak form and solved using EFGM, the propagation of myocardial activation can be simulated over the meshfree particle representation. The derivation of this solution technique is presented along a series of numerical experiments and a solution of monodomain model using a FitzHugh-Nagumo (FHN) membrane model in a canine ventricular model and a human-heart model which is constructed from digitized virtual Chinese dataset.

The Effects of Control Domain Position on Optimal Control of Cardiac Arrhythmia

We study the effects of control domain position on optimal control problem of cardiac arrhythmia. The well‐established mathematical model, namely, the monodomain model, is used to represent the electrical behavior of the cardiac tissue. Two test cases are considered in this paper: the control domain for Test Case 1 is close to the excitation domain, while the control domain for Test Case 2 is a little bit far away from the excitation domain. The modified Dai‐Yuan nonlinear conjugate gradient method is employed for computing the optimal applied extracellular current. Our experiment results show that the excitation wavefronts are successfully dampened out for both test cases. Also, experiment results show that the position of the control domain for Test Case 1 is preferable than that of Test Case 2 during the defibrillation process.

Modified Fletcher-Reeves and Dai-Yuan Conjugate Gradient Methods for Solving Optimal Control Problem of Monodomain Model

In this paper, we present the numerical solution for the optimal control problem of monodomain modelwith Rogers-modified FitzHugh-Nagumo ion kinetic. The monodomain model, which is a well-known mathematical model for simulation of cardiac electrical activity, appears as the constraint in our problem. Our control objective is to dampen the excitation wavefront of the transmembrane potential in the observation domain using optimal applied current. Various conjugate gradient methods have been applied by researchers for solving this type of optimal control problem. For the present paper, we adopt the modified Fletcher-Reeves method and modified Dai-Yuan methodfor computing the optimal applied current. Numerical results show that the excitation wavefront is successfully dampened out by the optimal applied current when the modified Fletcher-Reeves method is used. However, this is not the case when the modified Dai-Yuan method is employed. Numerical results indicate that the modified Dai-Yuan method failed to converge to the optimal solution when the Armijo line search is used.

A Study of Mechanical Optimization Strategy for Cardiac Resynchronization Therapy Based on an Electromechanical Model

An optimal electrode position and interventricular (VV) delay in cardiac resynchronization therapy (CRT) improves its success. However, the precise quantification of cardiac dyssynchrony and magnitude of resynchronization achieved by biventricular (BiV) pacing therapy with mechanical optimization strategies based on computational models remain scant. The maximum circumferential uniformity ratio estimate (CURE) was used here as mechanical optimization index, which was automatically computed for 6 different electrode positions based on a three-dimensional electromechanical canine model of heart failure (HF) caused by complete left bundle branch block (CLBBB). VV delay timing was adjusted accordingly. The heart excitation propagation was simulated with a monodomain model. The quantification of mechanical intra- and interventricular asynchrony was then investigated with eight-node isoparametric element method. The results showed that (i) the optimal pacing location from maximal CURE of 0.8516 was found at the left ventricle (LV) lateral wall near the equator site with a VV delay of 60 ms, in accordance with current clinical studies, (ii) compared with electrical optimization strategy of E RMS, the LV synchronous contraction and the hemodynamics improved more with mechanical optimization strategy. Therefore, measures of mechanical dyssynchrony improve the sensitivity and specificity of predicting responders more. The model was subject to validation in future clinical studies.