MagnetoHemoDynamics in the aorta and electrocardiograms

Abstract

This paper addresses a complex multi-physical phenomenon involving cardiac electrophysiology and hemodynamics. The purpose is to model and simulate a phenomenon that has been observed in magnetic resonance imaging machines: in the presence of a strong magnetic field, the T-wave of the electrocardiogram (ECG) gets bigger, which may perturb ECG-gated imaging. This is due to a magnetohydrodynamic (MHD) effect occurring in the aorta. We reproduce this experimental observation through computer simulations on a realistic anatomy, and with a three-compartment model: inductionless MHD equations in the aorta, bi-domain equations in the heart and electrical diffusion in the rest of the body. These compartments are strongly coupled and solved using finite elements. Several benchmark tests are proposed to assess the numerical solutions and the validity of some modeling assumptions. Then, ECGs are simulated for a wide range of magnetic field intensities (from 0 to 20 T).

Comparison of three artificial models of the magnetohydrodynamic effect on the electrocardiogram

“…However other contributions should be considered for complete simulation of the MHD phenomenon. Even if the linear relation between the extracted MHD and the INRIA’s model is slighthly better than between the extracted MHD and the proposed model , it has been shown that the proposed method reflects more adequately the reality that the simplified equation proposed by Martin et al (2012). Applying SVD to the extracted MHD clearly shows that this effect is more complex than a simple eigenvector as suggested by Martin et al (2012).…”

“…Even if the linear relation between the extracted MHD and the INRIA’s model is slighthly better than between the extracted MHD and the proposed model , it has been shown that the proposed method reflects more adequately the reality that the simplified equation proposed by Martin et al (2012). Applying SVD to the extracted MHD clearly shows that this effect is more complex than a simple eigenvector as suggested by Martin et al (2012). This property is important when assessing the quality of a denoising technique for ECG acquired during MRI, since the reduced complexity of the model on INRIA’s model can bias the denoising results when applying dimensionality reduction techniques such as SVD or Independent Component Analysis.…”

“…Abi Abdallah (2007) has shown that such simplification yields a good approximation of the MHD contribution, but with a slight underestimation of its true value. Recently, modelling of the MHD effect has been recomputed by using realistic geometrical models and numerical methods the MHD model can be assumed (to a first approximation) to be linearly mixed with the myocardial electropential sources (Martin et al 2012, 2011). …”

“…Lastly, Martin et al (2012) developed a simulation based on finite element techniques, addressing the blood flow, the heart activity and the diffusion through the torso in a coupled fashion. In this last simulation, the authors concluded that the ECG acquired inside the MR bore can be approximated by the superposition of the ECG without magnetic field and of the MHD signal, which is proportional to the magnetic field B and to the flux q in cm 3 s −1 as follows;…”

Numerical simulation of electrocardiograms for full cardiac cycles in healthy and pathological conditions

“…The simulation of 12-lead ECG based on partial differential equations (PDE) -as opposed to cellular automata [64] -appeared during the last decade [5,41,50,51,60]. More recently, a focus on the T-wave was proposed [29,34].…”