PDE constrained optimization of electrical defibrillation in a 3D ventricular slice geometry

Chamakuri, Nagaiah; Kunisch, Karl; Plank, Gernot

doi:10.1002/cnm.2742

Cited by 6 publications

(15 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[15][16][17] Recently, patient-specific heart meshes and monodomain forward models have been studied with manual selection of optimal parameters. 40 In addition, adjoint-based PDE-constrained optimization for the monodomain/bidomain models is developing, 20,21,23 but the number of large scale (3D) studies is still very limited with the notable exception. 24 In this study, we have only considered optimization with respect to synthetically generated data as a step toward optimization using clinical measurements.…”

Section: Discussionmentioning

confidence: 99%

Inverse estimation of cardiac activation times via gradient‐based optimization

Kallhovd

Maleckar

Rognes

2017

Numer Methods Biomed Eng

View full text Add to dashboard Cite

Computational modeling may provide a quantitative framework for integrating multiscale data to gain insight into mechanisms of heart disease, identify and test pharmacological and electrical therapy and interventions, and support clinical decisions. Patient-specific computational cardiac models can help guide such procedures, and cardiac inverse modeling is a promising alternative to adequately personalize these models. Indeed, full cardiac inverse modeling is currently becoming computationally feasible; however, fundamental work to assess the feasibility of emerging techniques is still needed. In this study, we use a partial differential equation-constrained optimal control approach to numerically investigate the identifiability of an initial activation sequence from synthetic (partial) observations of the extracellular potential using the bidomain approximation and 2D representations of cardiac tissue. Our results demonstrate that activation times and duration of several stimuli can be recovered even with high levels of noise, that it is sufficient to sample the observations at the electrocardiogram-relevant sampling frequency of 1 kHz, and that spatial resolutions that are coarser than the standard in electrophysiological simulations can be used. The optimization of activation times is still effective when synthetic data are generated with a different cell membrane kinetics model than optimized for. The findings thus indicate that the presented approach has potential for finding activation sequences from clinical data modalities, as an extension to existing cardiac imaging approaches.

show abstract

Section: Discussionmentioning

confidence: 99%

Inverse estimation of cardiac activation times via gradient‐based optimization

Kallhovd

Maleckar

Rognes

2017

Numer Methods Biomed Eng

View full text Add to dashboard Cite

show abstract

“…For the spatial discretization of partial differential equations in the primal and dual equations, we employed the piecewise bilinear finite element method. The higher order Rosenbrock time stepping methods are used for the temporal discretization, specifically we used the ROWDA [16] method which has 3 internal stages to solve the algebraic system at each time step, see for more details in [13,Section 4]. Here we briefly mention the algorithmic procedure to solve the primal equations, for the complete implementation details we request the readers to refer [13].…”

Section: Numerical Approachmentioning

confidence: 99%

“…Set final termination time T = 4 msec. 2: Project the transmembrane solution from the tissue domain (u on Ω H ) to the integrated domain Ω by using inter-processor communication in parallel environment, as explained in [13]. Here zero entries are padded in the global solution vector which corresponds to the nodal points at the bath domain.…”

Section: Numerical Approachmentioning

confidence: 99%

“…To solve the complete optimality system we used the Newton-CG optimization, see for complete details in [13]. The line search algorithm based on an Armijo type condition.…”

Section: Numerical Approachmentioning

confidence: 99%

“…In cardiac electrophysiology, an optimal control problem constrained by the 2D tridomain equations has been investigated and the well-posedness of solution for this model and the related control problem has been proved in [1]. PDE constrained optimization techniques have been applied, for the first time, to the monodomain and bidomain model to predict optimized shock waveforms in 2D [11,12] and more recently for the optimal control of bidomain-bath model using Mitchell-Shaeffer model in 3D geoemtries [13,10]. The present work, devoted to the rigorous study of mathematical analysis of such complex bidomain-bath model equations and numerical realization combined with Fitz-Hugh Nagumo ionic model in realistic 3D geometries.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A 3D boundary optimal control for the bidomain-bath system modeling the thoracic shock therapy for cardiac defibrillation

Bendahmane

Chamakuri

Comte

et al. 2016

Journal of Mathematical Analysis and Applications

Self Cite

View full text Add to dashboard Cite

International audienceThis work is dedicated to study the cardiac defibrillation problem by using an optimal thoracic electroshock treatment. The problem is formulated as an optimal control problem in a 3D domain surrounded by the bath and including the heart. The control corresponds to the thoracic electroshock and the model describing the electrical activity in the heart is the bidomain model. The bidomain model is coupled with the quasi-static Maxwell's equation to consider the effect of an external bathing medium. The existence and uniqueness of a weak solution for the direct problem is assessed as well as the existence of a weak solution for the adjoint problem. The numerical discretization is realized using a finite element method for the spatial discretization and linearly implicit Runge-Kutta methods for the temporal discretization of the partial differential equations. The numerical results are demonstrated for the termination of re-entry waves

show abstract

Optimal Control for a Class of Infinite Dimensional Systems Involving an ‐term in the Cost Functional

2017

Self Cite

View full text Add to dashboard Cite

problem. MSC (2010) 49K20, 49K15, 49K21, 93C30, 90C46An optimal control problem with a time-parameter is considered. The functional to be optimized includes the maximum over time-horizon reached by a function of the state variable, and so an L ∞ -term. In addition to the classical control function, the time at which this maximum is reached is considered as a free parameter. The problem couples the behavior of the state and the control, with this time-parameter. A change of variable is introduced to derive first and second-order optimality conditions. This allows the implementation of a Newton method. Numerical simulations are developed, for selected ordinary differential equations and a partial differential equation, which illustrate the influence of the additional parameter and the original motivation.Notation. When there is no ambiguity, the time variable is sometimes omitted, or written only once (e. g. H (y, u, p) H (y(s), u(s), p(s)). First and second-order partial derivatives are denoted with the use of indexes. The first and second-order derivatives with respect to all variables (except the adjoint state p and the Lagrange multiplier λ, for the Hamiltonian and the Lagrangians) are denoted by D and D 2 , respectively. The partial derivative of a function ϕ with respect to a variable y in a direction z is denoted as ϕ y (y).z. When a function h is left-and right-continuous at a given time t, the left-and right-limits are denoted by h(t − ) and h(t + ), respectively, and the jump is denoted by [h] t .

show abstract

PDE constrained optimization of electrical defibrillation in a 3D ventricular slice geometry

Cited by 6 publications

References 37 publications

Inverse estimation of cardiac activation times via gradient‐based optimization

Inverse estimation of cardiac activation times via gradient‐based optimization

A 3D boundary optimal control for the bidomain-bath system modeling the thoracic shock therapy for cardiac defibrillation

Optimal Control for a Class of Infinite Dimensional Systems Involving an ‐term in the Cost Functional

Contact Info

Product

Resources

About