Solving the ECG forward problem by means of a meshless finite element method

Computing volume potentials for noninvasive imaging of cardiac excitation

BACKGROUND

In noninvasive imaging of cardiac excitation, the use of body surface potentials (BSP) rather than body volume potentials (BVP) has been favored due to enhanced computational efficiency and reduced modeling effort. Nowadays, increased computational power and the availability of open source software enable the calculation of BVP for clinical purposes. In order to illustrate the possible advantages of this approach, the explanatory power of BVP is investigated using a rectangular tank filled with an electrolytic conductor and a patient specific three dimensional model.

METHODS

MRI images of the tank and of a patient were obtained in three orthogonal directions using a turbo spin echo MRI sequence. MRI images were segmented in three dimensional using custom written software. Gmsh software was used for mesh generation. BVP were computed using a transfer matrix and FEniCS software.

RESULTS

The solution for 240,000 nodes, corresponding to a resolution of 5 mm throughout the thorax volume, was computed in 3 minutes. The tank experiment revealed that an increased electrode surface renders the position of the 4 V equipotential plane insensitive to mesh cell size and reduces simulated deviations. In the patient-specific model, the impact of assigning a different conductivity to lung tissue on the distribution of volume potentials could be visualized.

CONCLUSION

Generation of high quality volume meshes and computation of BVP with a resolution of 5 mm is feasible using generally available software and hardware. Estimation of BVP may lead to an improved understanding of the genesis of BSP and sources of local inaccuracies.

Data-driven estimation of cardiac electrical diffusivity from 12-lead ECG signals

Diagnosis and treatment of dilated cardiomyopathy (DCM) is challenging due to a large variety of causes and disease stages. Computational models of cardiac electrophysiology (EP) can be used to improve the assessment and prognosis of DCM, plan therapies and predict their outcome, but require personalization. In this work, we present a data-driven approach to estimate the electrical diffusivity parameter of an EP model from standard 12-lead electrocardiograms (ECG). An efficient forward model based on a mono-domain, phenomenological Lattice-Boltzmann model of cardiac EP, and a boundary element-based mapping of potentials to the body surface is employed. The electrical diffusivity of myocardium, left ventricle and right ventricle endocardium is then estimated using polynomial regression which takes as input the QRS duration and electrical axis. After validating the forward model, we computed 9500 EP simulations on 19 different DCM patients in just under three seconds each to learn the regression model. Using this database, we quantify the intrinsic uncertainty of electrical diffusion for given ECG features and show in a leave-one-patient-out cross-validation that the regression method is able to predict myocardium diffusion within the uncertainty range. Finally, our approach is tested on the 19 cases using their clinical ECG. 84% of them could be personalized using our method, yielding mean prediction errors of 18.7ms for the QRS duration and 6.5° for the electrical axis, both values being within clinical acceptability. By providing an estimate of diffusion parameters from readily available clinical data, our data-driven approach could therefore constitute a first calibration step toward a more complete personalization of cardiac EP.

Computed basis functions for finite element analysis based on tomographic data

In bioelectromagnetics, the structures in which the electromagnetic field is to be computed are sometimes defined by a fine grid of voxels (3-D cells) whose tissue types are obtained by tomography. A novel finite element method is proposed for such cases. A simple, regular mesh of cube elements is constructed, each containing the same, integer number of voxels. There may be several different tissues present within an element, but this is accommodated by computing element basis functions that approximately respect the interface conditions between different tissues. Results are presented for a test model of 128 (3) voxels, consisting of nested dielectric cubes, driven by specified charges. The electrostatic potential computed with the new method agrees well with that of a conventional finite element code: the rms difference along the sample line is 1.5% of the highest voltage. Results are also presented for the potential due to a current dipole placed in a brain model of 181 × 217 × 181 voxels, derived from MRI data. The new method gives potentials that are different to those obtained by treating each voxel as an element by 1% of the peak voltage, yet the global finite element matrix has a dimension which is more than 50 times smaller.