Papers by Pongui Ngoma Diogene Vianney
Functional Imaging and Modelling of the Heart, 2017
We developed numerical methods to optimally adjust the parameters in cardiac electrophysiology mo... more We developed numerical methods to optimally adjust the parameters in cardiac electrophysiology models, using optimal control and non-differentiable optimization methods. We define three optimal control problems to capture the main features of the cardiac action potential (AP). The first two control problems adjust parameters in single-cell models to recover the duration of the various phases of the AP or the trans-membrane potential at a given cell recorded over time. A third control problem is defined to adjust the conductance in the monodomain model to recover the conduction speed of an AP wave. The methodology is used to adjust parameters in the monodomain model with Mitchell-Schaeffer ion kinetics to recover the phase durations and conduction velocity in three cardiac tissues. Error on the phase durations lies within 1–3%, except for the depolarization time. The Aliev-Panfilov and Mitchell-Schaeffer model are adjusted to experimental recording of the trans-membrane potential obtained through optical fluorescence imaging. The Mitchell-Schaeffer model achieves a better fit to the data.
International Journal of Numerical Methods and Applications, 2017
Nonlinear Analysis and Differential Equations, 2017
We consider the effect of numerical integration in finite element methods for nonlinear parabolic... more We consider the effect of numerical integration in finite element methods for nonlinear parabolic system describing a two component model for the single-phase, miscible displacement of one compressible fluid by another in a porous medium. We give some sufficient conditions on the quadrature scheme to ensure that the order of convergence is unaltered in the presence of numerical integration. Optimal order L 2-error estimates and almost optimal L ∞-error estimates are derived when the imposed external flows are smoothly distributed.
International Journal of Applied Mathematical Research, 2017
We consider the effect of numerical integration in finite element procedures applied to a nonlin... more We consider the effect of numerical integration in finite element procedures applied to a nonlinear system of two coupled partial differential equations describing the miscible displacement of one incompressible fluid by another in a porous meduim. We consider the use of the numerical quadrature scheme for approximating the pressure and velocity by a mixed method using Raviart - Thomas space of index and the concentration by a standard Galerkin method. We also give some sufficient conditions on the quadrature scheme to ensure that the order of convergence is unaltered in the presence of numerical integration. Optimal order estimates are derived when the imposed external flows are smoothly distributed.
Applied Mathematics-A Journal of Chinese Universities, 2001
Applied Mathematical Sciences, 2015
Ionic models are used to describe the evolution of the electrical potential across the cardiac ce... more Ionic models are used to describe the evolution of the electrical potential across the cardiac cell membranes. The Mitchell-Schaeffer model is a simple two variables nonlinear ionic model with a limited set of parameters. This model can still capture the main features of the cardiac action potential, namely the action potential duration (APD), the conduction velocity (CV), depolarisation time (DT), recovery time (RT), etc. In this paper we have developed an optimization method to recover the specific characteristics ADP, DT and RT by identifying the values that the four parameters τ = [τ in , τ out , τ open , τ close , σ] of the Mitchell-Schaeffer must take. By using the fonction ode in Scilab, Mitchell-Schaeffer model solutions have been oabtained numerically.
Parameter Identification for a non -differentiable ionic model used in cardiac electrophysiology,... more Parameter Identification for a non -differentiable ionic model used in cardiac electrophysiology, Applied Mathematical Sciences., 9(150)(2015) 7483-7507. Pongui Ngoma D. V, Yves Bourgault and Hilaire Nkounkou, Numerical methods for parameter identification of cardiac electrophysiology models, Mathematical Biosciences and Engineering., Accepted in press. Nguimbi G., Pongui Ngoma D.V. and Likibi Pellat R., The effect of numerical integration in mixed finite element approximation in the simulation of miscible displacement, Int.J.of Appl. Math. Res., 6(2)(2017)44-48. Nguimbi G., Pongui Ngoma D.V. and Likibi Pellat R., The effect of numerical integration in Galerkin methods for compressible miscible displacement in porous media, Nonlin. Anal.and Diff. Equ., 5(1)(2017)17-34. Nguimbi G., Pongui Ngoma D.V. and Likibi Pellat R., The effect of numerical integration in finite element methods for general nonlinear hyperbolic equations, Nonlin. Anal.and Diff. Equ., 5(1)(2017)1-15. Nguimbi G., Pongui Ngoma D.V. and Likibi Pellat R., The effect of numerical integration in mixed methods for compressible miscible displacement when molecular dispersion included, Int.
Ionic models are used to describe the evolution of the electrical potential across the cardiac ce... more Ionic models are used to describe the evolution of the electrical potential across the cardiac cell membranes. The Mitchell-Schaeffer model is a simple two variables nonlinear ionic model with a limited set of parameters. This model can still capture the main features of the cardiac action potential, namely the action potential duration (APD), the conduction velocity (CV), depolarisation time (DT), recovery time (RT), etc. In this paper we have developed an optimization method to recover the specific characteristics ADP, DT and RT by identifying the values that the four parameters τ = [τ in , τ out , τ open , τ close , σ] of the Mitchell-Schaeffer must take. By using the fonction ode in Scilab, Mitchell-Schaeffer model solutions have been oabtained numerically.
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Papers by Pongui Ngoma Diogene Vianney