On the possibility for computing the transmembrane potential in the heart with a one shot method: An inverse problem

Nielsen, Bjørn Fredrik; Cai, Xing; Lysaker, Marius

doi:10.1016/j.mbs.2007.06.003

Cited by 30 publications

(41 citation statements)

References 32 publications

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“…Suppose the discrete Poisson equation (11) has a size of m and v has a size of n, deriving the lead-field matrix requires one to solve a m by m linear system for n times. For a bidomain model in three dimension, m and n can easily reach hundreds of thousands.…”

Section: Solve the Inverse Problemmentioning

confidence: 99%

“…It still remains an open problem to accurately calculate the transmembrane potentials at an arbitrary time instance, because this inverse problem is severely ill-posed and the solution is not unique. Methods for localizing myocardial ischemia have been proposed such as the model-based optimization [10] or the level set method [11], but these methods avoid direct calculation of TMPs by parameterizing the location and shape of ischemic regions. Another study [12] localized myocardial ischemia by calculating the integral of TMPs during the ST-segment and reported very optimistic recoveries, as the integration supposedly reduced the effect of measurement noise.…”

Section: Introductionmentioning

confidence: 99%

“…We formulated the inverse problem as a minimization problem constrained by some partial differential equations (PDE) that models the forward problem. The framework of constrained minimization was introduced to the inverse TMP problem by Nielson et al [11], and we generalized it and included more constraints. This approach differs from the traditional approach of forming a lead-field matrix and "inverting" it by direct Tikhonov regularization, and has two advantages: 1) less computational cost, and 2) it allows a flexible setting of the discretization resolution for the TMPs and other state variables.…”

Section: Introductionmentioning

confidence: 99%

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Identifying myocardial ischemia by inversely computing transmembrane potentials from body-surface potential maps

Kirby

MacLeod

et al. 2011

2011 8th International Symposium on Noninvasive Functional Source Imaging of the Brain and Heart and the 2011 8th International

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We attempted to solve the inverse electrocardiographic problem of computing the transmembrane potentials (TMPs) throughout the myocardium from a body-surface potential map, and then used the recovered potentials to estimate the size and location of myocardial ischemia. We modeled the bioelectric process by combining a static bidomain heart model with a torso conduction model. Although the task of computing myocardial TMPs at an arbitrary time instance is still an open problem, we showed that it is possible to obtain TMPs with moderate accuracy during the ST segment by assuming all cardiac cells are at the plateau phase. Moreover, the inverse solutions yielded a good estimate of ischemic regions, which is of more clinical interest than merely reporting the voltage values. We formulated the inverse problem as a minimization problem constrained by a partial differential equation that models the forward problem. This framework greatly reduces the computational costs compared with the traditional approach of building the lead-field matrix. It also enables one to flexibly set different discretization resolutions for the source variables and other state variables, a desirable feature for solving ill-posed inverse problems. We conducted finite element simulations of a phantom experiment over a 2D torso model with synthetic ischemic data. Preliminary results indicated that our approach is feasible and suitably accurate for the common case of transmural myocardial ischemia.

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Section: Solve the Inverse Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Identifying myocardial ischemia by inversely computing transmembrane potentials from body-surface potential maps

Kirby

MacLeod

et al. 2011

2011 8th International Symposium on Noninvasive Functional Source Imaging of the Brain and Heart and the 2011 8th International

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“…Generally, approaches to solving this inverse ECG problem can be relied on potential-based model, including epicardial, endocardial, or transmembrane potentials, which is used to evaluate the potential values on the cardiac surface [3] at certain time instants. Moreover, the cardiac electrophysiological information is closely associated with the transmembrane potentials (TMPs) of the myocardial cells.…”

Section: Introductionmentioning

confidence: 99%

Study on Parameter Optimization for Support Vector Regression in Solving the Inverse ECG Problem

Jiang

Jiang²,

Zhu³

et al. 2013

Computational and Mathematical Methods in Medicine

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The typical inverse ECG problem is to noninvasively reconstruct the transmembrane potentials (TMPs) from body surface potentials (BSPs). In the study, the inverse ECG problem can be treated as a regression problem with multi-inputs (body surface potentials) and multi-outputs (transmembrane potentials), which can be solved by the support vector regression (SVR) method. In order to obtain an effective SVR model with optimal regression accuracy and generalization performance, the hyperparameters of SVR must be set carefully. Three different optimization methods, that is, genetic algorithm (GA), differential evolution (DE) algorithm, and particle swarm optimization (PSO), are proposed to determine optimal hyperparameters of the SVR model. In this paper, we attempt to investigate which one is the most effective way in reconstructing the cardiac TMPs from BSPs, and a full comparison of their performances is also provided. The experimental results show that these three optimization methods are well performed in finding the proper parameters of SVR and can yield good generalization performance in solving the inverse ECG problem. Moreover, compared with DE and GA, PSO algorithm is more efficient in parameters optimization and performs better in solving the inverse ECG problem, leading to a more accurate reconstruction of the TMPs.

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“…Este consiste en la caracterización de un modelo matemático de la actividad eléctrica celular cardiaca a partir de señales ECG [8][9][10][11][12][13]. En general el problema directo (la generación de señales ECG a partir de un modelo de actividad eléctrica celular cardiaca) se resuelve calculando una función de transferencia que relaciona los potenciales medidos a nivel de la superficie del cuerpo con las fuentes localizadas al interior del corazón [8,10].…”

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Modelo paramétrico de la actividad eléctrica celular cardiaca estimado a partir de registros electrocardiográficos estándares (Parametrical model of cardiac cell electrical activity estimated from standard electrocardiogram recordings)

Manríquez

Sérandour

2014

RIB

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Recibido 1 de febrero de 2013. Aprobado 10 de abril de 2013Parametrical model of cardiac cell electrical activity estimated from standard electrocardiogram recordings Resumen ─ El presente trabajo tiene como objetivo principal relacionar la actividad eléctrica cardiaca celular con la actividad eléctrica cardiaca medida en una sola derivación del electrocardiograma (ECG), mediante un modelo paramétrico de potencial de acción (PA) celular, lo cual se llevó a cabo relacionando dinámicas conocidas, matemáticamente modelables, que existen a nivel de una célula cardiaca, a dinámicas que pueden ser encontradas en un registro ECG estándar. La principal dinámica celular a relacionar con el ECG es la conocida como curva de restitución celular en tres dimensiones, la cual relaciona la duración del potencial de acción celular (APD) con el intervalo diastólico que lo precede y con el mismo APD pero del ciclo cardiaco precedente. Curvas de restitución similares se encontraron en señales ECG registradas durante el test isométrico handgrip, relacionando el intervalo QT con el intervalo TQ que lo precede y con el intervalo QT del ciclo cardiaco precedente. Siguiendo esta similitud, un modelo paramétrico de curva de restitución, extraído de un modelo de PA a tres corrientes iónicas, es ajustado a la curva de restitución del ECG con el fin de estimar los parámetros del modelo de PA. Este modelo es finalmente simulado estimulándolo con un tren de impulsos de frecuencia igual a la frecuencia cardiaca del sujeto experimentado. Los resultados muestran que la curva de restitución obtenida experimentalmente a partir del ECG es similar a la obtenida a partir de la simulación del modelo de PA. Más aún, el APD simulado del modelo sigue de forma satisfactoria la variación en el tiempo del intervalo QT del sujeto experimentado. Esto abre nuevas perspectivas en el análisis de la actividad celular a partir de registros ECG estándar.Palabras Clave ─ Modelado ECG, modelo de potencial de acción celular, intervalo QT, APD, curva de restitución. Abstract ─ The main purpose of this paper is to relate cellular cardiac electrical activity with the cardiac electrical activity measured in only one electrocardiogram (ECG) lead, through a cellular action potential (AP) parametrical model. This is performed by relating known dynamics, which can be mathematically modeled, existing at a cardiac cell level, to dynamics which can be obtained from a standard ECG recording. The main cellular dynamic used for relating with the ECG is the one known as three dimensional cellular restitution curve, which relates the action potential duration (APD) with its preceding diastolic interval and with the APD of the preceding cardiac cycle. Similar restitution curves were found in ECG signals recorded under the isometric handgrip test by relating the QT interval with its preceding TQ interval and with the QT interval of the preceding cardiac cycle. Following this similarity, a parametrical restitution curve, derived from a three ionic current cellular AP model was fitted to...

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On the possibility for computing the transmembrane potential in the heart with a one shot method: An inverse problem

Cited by 30 publications

References 32 publications

Identifying myocardial ischemia by inversely computing transmembrane potentials from body-surface potential maps

Identifying myocardial ischemia by inversely computing transmembrane potentials from body-surface potential maps

Study on Parameter Optimization for Support Vector Regression in Solving the Inverse ECG Problem

Modelo paramétrico de la actividad eléctrica celular cardiaca estimado a partir de registros electrocardiográficos estándares (Parametrical model of cardiac cell electrical activity estimated from standard electrocardiogram recordings)

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