The electric field distribution in the brain during TTFields therapy and its dependence on tissue dielectric properties and anatomy: a computational study

Abstract

Tumor treating fields (TTFields) are a non-invasive, anti-mitotic and approved treatment for recurrent glioblastoma multiforme (GBM) patients. In vitro studies have shown that inhibition of cell division in glioma is achieved when the applied alternating electric field has a frequency in the range of 200 kHz and an amplitude of 1-3 V cm(-1). Our aim is to calculate the electric field distribution in the brain during TTFields therapy and to investigate the dependence of these predictions on the heterogeneous, anisotropic dielectric properties used in the computational model. A realistic head model was developed by segmenting MR images and by incorporating anisotropic conductivity values for the brain tissues. The finite element method (FEM) was used to solve for the electric potential within a volume mesh that consisted of the head tissues, a virtual lesion with an active tumour shell surrounding a necrotic core, and the transducer arrays. The induced electric field distribution is highly non-uniform. Average field strength values are slightly higher in the tumour when incorporating anisotropy, by about 10% or less. A sensitivity analysis with respect to the conductivity and permittivity of head tissues shows a variation in field strength of less than 42% in brain parenchyma and in the tumour, for values within the ranges reported in the literature. Comparing results to a previously developed head model suggests significant inter-subject variability. This modelling study predicts that during treatment with TTFields the electric field in the tumour exceeds 1 V cm(-1), independent of modelling assumptions. In the future, computational models may be useful to optimize delivery of TTFields.

Figures

Figure 1

Realistic human head model of s2. The tumour position is illustrated for two different views. At the right, the meshes representing the scalp and selected transducers, the WM, and the GM with the cerebellum are shown.

Figure 2

An axial slice above the tumour is shown in the anatomic image on the top left. The corresponding isotropic conductivity map is plotted below, in arbitrary colours - isotropic conductivity values are presented in table 1. For the anisotropic brain tissues, the dM tensor components are shown in the middle and vN in the right columns, respectively. Top panels illustrate the xx-component of the tensor, the bottom panels the yy-component of the tensor. The colour scale applies to GM and WM only. All conductivity values are given in S/m.

Figure 3

Electric field strength (V/cm) distribution in s2. Axial (top row), sagittal (middle row) and coronal (bottom row) slices through the spherical tumour for the LR (left panel) and AP (right panel) stimulations. Isotropic results are plotted on the left and corresponding anisotropic results for vN and dM are illustrated in the middle and right columns respectively. The colour range is the same for all figures and varies between 0 (dark blue) and 4 (dark red) V/cm.

Figure 4

ATV1 in the tumour shell (left) and brain parenchyma (right) as a function of scalp conductivity. Results are presented for LR (blue) and AP (green) setups for both anisotropic models, vN (solid) and dM (dotted).

Figure 5

Average electric field strength for varying conductivities of all tissues, obtained with the dM method. The x-axis corresponds to the scaled conductivity values, from Table 1. The results for the tumour shell are presented in the left column, the ones for the brain tissue in the right column. Results for LR and AP configurations are shown in the top and bottom rows, respectively.

Figure 6

The electric field (V/cm) with a fixed colour scale on axial slices through the tumour in s1 and s2 for LR (left) and AP array (right) configurations as indicated by active red arrays. Average electric field strengths (V/cm) in the brain, the shell and the core are presented for each panel.