Tumor-treating fields dosimetry in glioblastoma: Insights into treatment planning, optimization, and dose-response relationships.

Tumor-treating fields (TTFields) are currently a Category 1A treatment recommendation by the US National Comprehensive Cancer Center for patients with newly diagnosed glioblastoma. Although the mechanism of action of TTFields has been partly elucidated, tangible and standardized metrics are lacking to assess antitumor dose and effects of the treatment. This paper outlines and evaluates the current standards and methodologies in the estimation of the TTFields distribution and dose measurement in the brain and highlights the most important principles governing TTFields dosimetry. The focus is on clinical utility to facilitate a practical understanding of these principles and how they can be used to guide treatment. The current evidence for a correlation between TTFields dose, tumor growth, and clinical outcome will be presented and discussed. Furthermore, we will provide perspectives and updated insights into the planning and optimization of TTFields therapy for glioblastoma by reviewing how the dose and thermal effects of TTFields are affected by factors such as tumor location and morphology, peritumoral edema, electrode array position, treatment duration (compliance), array "edge effect," electrical duty cycle, and skull-remodeling surgery. Finally, perspectives are provided on how to optimize the efficacy of future TTFields therapy.

How the Number and Distance of Electrodes Change the Induced Electric Field in the Cortex during Multichannel tDCS.

Multichannel transcranial direct current stimulation (tDCS) is a promising approach to target neuromodulation of neural networks by making use of variable number of electrodes and distances to facilitate/inhibit specific connectivity patterns. Optimization of the electric field (EF) spatial distribution through computational models can provide a more accurate definition of the stimulation settings that are more effective. In this study, we investigate the effect of increasing the number of cathodes around a central anode placed over the target. We demonstrate that anode-cathode distance has the largest influence in the EF and using more than 3 cathodes did not result in considerable changes in the EF magnitude and direction. This could be relevant for simultaneous tDCS-electroencephalography (EEG) applications, by saving electrode positions for EEG acquisition. Clinical Relevance- This study demonstrates that distance between electrodes is more relevant than electrode number in determining the electric field distribution, and that a highly-focused stimulation can be equally effective with fewer electrodes.

A comprehensive analysis of the impact of head model extent on electric field predictions in transcranial current stimulation.

Objective.MRI-based head models are used to predict the electric field (E-field) in the brain in transcranial current stimulation. The standard field of view of clinical MRI often only covers the head down to the skull base, which has usually lead to models truncated at the level of the nose. Although recent pipelines can artificially extend the head model to the neck, the need for implementing full head models preserving skull holes such as the foramen magnum remains controversial. The objective of this work is to analyse the impact of head model extent on E-field accuracy, with emphasis on specific electrode montages.Approach. A full head model containing an open foramen magnum and a cut head model with closed skull were compared in terms of predicted E-field. Several electrode montages, including fronto-occipital montages recently used in validation studies, were simulated. Local and global metrics were used to evaluate the error for both E-field magnitude and distribution, along with tangential and normal components over different cortical areas. The percentage of current flowing through the lower head was also computed.Results. Regarding E-field magnitude, small relative differences (RDs) below 7% were found in grey matter for classical montages. Although considerably higher RDs near 50% were found for fronto-occipital montages, absolute errors of 0.1 V m-1were only found in non-targeted regions such as the cerebellum. Differences in tangential and normal E-fields were similar and followed the same trend observed for E-field magnitude. Our results also showed a high correlation between the percentage of current shunted through the lower head and the absolute E-field differences.Significance. The influence of head model extent on E-field accuracy depends on electrode montage. Standard cut head models provide sufficiently accurate predictions for both E-field magnitude and distribution in targeted brain areas. However, fronto-occipital montages exhibited larger errors, which might be considered in further validation studies.

A Computational Analysis of the Electric Field Components in Transcranial Direct Current Stimulation.

Realistic electric field (E-field) models of the brain have cast doubt on classical targeting approaches used in transcranial direct current stimulation (tDCS). In apparent contradiction with physiological results, modeling studies predict similar or even higher E-field values in regions between the electrodes distant to the presumed targeted areas. As an explanation, not only the magnitude, but the direction of the E-field over specific cortical structures, have been shown to be determinant for the stimulation outcome. This work examines the magnitude and distribution of tangential and normal E-field components over different cortical areas in a representative brain atlas for various electrode montages commonly used in clinical applications. We have confirmed a general trend in the distribution of tangential and normal E-fields on gyri and sulci areas, respectively, partially independent of electrode configuration. The differences found between the various montages are also discussed.

A Review on Tumor-Treating Fields (TTFields): Clinical Implications Inferred From Computational Modeling.

Tumor-treating fields (TTFields) are a cancer treatment modality that uses alternating electric fields of intermediate frequency (∼100-500 kHz) and low intensity (1-3 V/cm) to disrupt cell division. TTFields are delivered by transducer arrays placed on the skin close to the tumor and act regionally and noninvasively to inhibit tumor growth. TTFields therapy is U.S. Food and Drug Administration approved for the treatment of glioblastoma multiforme, the most common and aggressive primary human brain cancer. Clinical trials testing the safety and efficacy of TTFields for other solid tumor types are underway. The objective of this paper is to review computational approaches used to characterize TTFields. The review covers studies of the macroscopic spatial distribution of TTFields generated in the human head, and of the microscopic field distribution in tumor cells. In addition, preclinical and clinical findings related to TTFields and principles of its operation are summarized. Particular emphasis is put on outlining the potential clinical value inferred from computational modeling.

Neuromodulation of lower limb motor responses with transcutaneous lumbar spinal cord direct current stimulation.

OBJECTIVE: Trans-spinal direct current stimulation (tsDCS) is a promising technique to modulate spinal circuits. Combining clinical with modelling studies can improve effectiveness of tsDCS protocols. The aim of this study is to measure the effects of lumbar tsDCS on motor spinal responses and observe if these are consistent with the electric field (E-field) predicted from a computational model. METHODS: The exploratory study design was double-blind crossover and randomized. tsDCS was delivered for 15 min (anodal, cathodal, sham) at L2 vertebra level (2.5 mA, 90 C/cm2) in 14 healthy subjects. F-wave, H-reflex, cortical silent period, motor evoked potential and sympathetic skin response were analyzed. Statistical methods were applied with Bonferroni correction for multiple comparisons, a p < 0.05 was set as significant. A human volume conductor model was obtained from available databases. E-field distributions in the spinal grey matter (GM) and white matter (WM) were calculated. RESULTS: No tsDCS effects were observed. E-field magnitude predicted in the lumbosacral spinal GM and WM was <0.15 V/m, insufficient to ensure neuromodulation, which is consistent with the absence of effects. CONCLUSION: The tsDCS protocol applied did not change motor response to delivered stimulus, thus we observed no effect on motor spinal circuits. SIGNIFICANCE: Future tsDCS protocols should be supported by computational models.

Transcutaneous spinal direct current stimulation of the lumbar and sacral spinal cord: a modelling study.

OBJECTIVE: Our aim was to perform a computational study of the electric field (E-field) generated by transcutaneous spinal direct current stimulation (tsDCS) applied over the thoracic, lumbar and sacral spinal cord, in order to assess possible neuromodulatory effects on spinal cord circuitry related with lower limb functions. APPROACH: A realistic volume conductor model of the human body consisting of 14 tissues was obtained from available databases. Rubber pad electrodes with a metallic connector and a conductive gel layer were modelled. The finite element (FE) method was used to calculate the E-field when a current of 2.5 mA was passed between two electrodes. The main characteristics of the E-field distributions in the spinal grey matter (spinal-GM) and spinal white matter (spinal-WM) were compared for seven montages, with the anode placed either over T10, T8 or L2 spinous processes (s.p.), and the cathode placed over right deltoid (rD), umbilicus (U) and right iliac crest (rIC) areas or T8 s.p. Anisotropic conductivity of spinal-WM and of a group of dorsal muscles near the vertebral column was considered. MAIN RESULTS: The average E-field magnitude was predicted to be above 0.15 V m-1 in spinal cord regions located between the electrodes. L2-T8 and T8-rIC montages resulted in the highest E-field magnitudes in lumbar and sacral spinal segments (>0.30 V m-1). E-field longitudinal component is 3 to 6 times higher than the ventral-dorsal and right-left components in both the spinal-GM and WM. Anatomical features such as CSF narrowing due to vertebrae bony edges or disks intrusions in the spinal canal correlate with local maxima positions. SIGNIFICANCE: Computational modelling studies can provide detailed information regarding the electric field in the spinal cord during tsDCS. They are important to guide the design of clinical tsDCS protocols that optimize stimulation of application-specific spinal targets.

Optimizing Electric-Field Delivery for tDCS: Virtual Humans Help to Design Efficient, Noninvasive Brain and Spinal Cord Electrical Stimulation.

Noninvasive electrical stimulation of the central nervous system is attracting increasing interest from the clinical and academic communities as well as from high-tech companies. This interest was sparked by two landmark studies conducted in 2000 and 2001 at the University of G?ttingen, Germany. Michael Nitsche and Walter Paulus showed that by passing a weak, almost imperceptible electric current between two electrodes on the scalp, they could alter the way the human brain responds to stimuli and that the effect persisted for some time after the current was stopped. These findings opened the prospect of therapeutic applications of transcranial direct-current stimulation (tDCS).

The Frequency-Dependent Neuronal Length Constant in Transcranial Magnetic Stimulation.

BACKGROUND: The behavior of the dendritic or axonal membrane voltage due to transcranial magnetic stimulation (TMS) is often modeled with the one-dimensional cable equation. For the cable equation, a length constant λ0 is defined; λ0 describes the axial decay of the membrane voltage in the case of constant applied electric field. In TMS, however, the induced electric field waveform is typically a segment of a sinusoidal wave, with characteristic frequencies of the order of several kHz. OBJECTIVE: To show that the high frequency content of the stimulation pulse causes deviations in the spatial profile of the membrane voltage as compared to the steady state. METHODS: We derive the cable equation in complex form utilizing the complex frequency-dependent representation of the membrane conductivity. In addition, we define an effective length constant λeff, which governs the spatial decay of the membrane voltage. We model the behavior of a dendrite in an applied electric field oscillating at 3.9 kHz with the complex cable equation and by solving the traditional cable equation numerically. RESULTS: The effective length constant decreases as a function of frequency. For a model dendrite or axon, for which λ0 = 1.5 mm, the effective length constant at 3.9 kHz is decreased by a factor 10 to 0.13 mm. CONCLUSION: The frequency dependency of the neuronal length constant has to be taken into account when predicting the spatial behavior of the membrane voltage as a response to TMS.

Opportunities for Guided Multichannel Non-invasive Transcranial Current Stimulation in Poststroke Rehabilitation.

Stroke is a leading cause of serious long-term disability worldwide. Functional outcome depends on stroke location, severity, and early intervention. Conventional rehabilitation strategies have limited effectiveness, and new treatments still fail to keep pace, in part due to a lack of understanding of the different stages in brain recovery and the vast heterogeneity in the poststroke population. Innovative methodologies for restorative neurorehabilitation are required to reduce long-term disability and socioeconomic burden. Neuroplasticity is involved in poststroke functional disturbances and also during rehabilitation. Tackling poststroke neuroplasticity by non-invasive brain stimulation is regarded as promising, but efficacy might be limited because of rather uniform application across patients despite individual heterogeneity of lesions, symptoms, and other factors. Transcranial direct current stimulation (tDCS) induces and modulates neuroplasticity, and has been shown to be able to improve motor and cognitive functions. tDCS is suited to improve poststroke rehabilitation outcomes, but effect sizes are often moderate and suffer from variability. Indeed, the location, extent, and pattern of functional network connectivity disruption should be considered when determining the optimal location sites for tDCS therapies. Here, we present potential opportunities for neuroimaging-guided tDCS-based rehabilitation strategies after stroke that could be personalized. We introduce innovative multimodal intervention protocols based on multichannel tDCS montages, neuroimaging methods, and real-time closed-loop systems to guide therapy. This might help to overcome current treatment limitations in poststroke rehabilitation and increase our general understanding of adaptive neuroplasticity leading to neural reorganization after stroke.

Improving Tumor Treating Fields Treatment Efficacy in Patients With Glioblastoma Using Personalized Array Layouts.

PURPOSE: To investigate tumors of different size, shape, and location and the effect of varying transducer layouts on Tumor Treating Fields (TTFields) distribution in an anisotropic model. METHODS AND MATERIALS: A realistic human head model was generated from MR images of 1 healthy subject. Four different virtual tumors were placed at separate locations. The transducer arrays were modeled to mimic the TTFields-delivering commercial device. For each tumor location, varying array layouts were tested. The finite element method was used to calculate the electric field distribution, taking into account tissue heterogeneity and anisotropy. RESULTS: In all tumors, the average electric field induced by either of the 2 perpendicular array layouts exceeded the 1-V/cm therapeutic threshold value for TTFields effectiveness. Field strength within a tumor did not correlate with its size and shape but was higher in more superficial tumors. Additionally, it always increased when the array was adapted to the tumor's location. Compared with a default layout, the largest increase in field strength was 184%, and the highest average field strength induced in a tumor was 2.21 V/cm. CONCLUSIONS: These results suggest that adapting array layouts to specific tumor locations can significantly increase field strength within the tumor. Our findings support the idea of personalized treatment planning to increase TTFields efficacy for patients with GBM.

The effect of inter-electrode distance on the electric field distribution during transcutaneous lumbar spinal cord direct current stimulation.

Previous studies have indicated potential neuromodulation of the spinal circuitry by transcutaneous spinal direct current stimulation (tsDCS), such as changes in motor unit recruitment, shortening of the peripheral silent period and interference with supraspinal input to lower motor neurons. All of these effects were dependent on the polarity of the electrodes. The present study investigates how the distance between the electrodes during tsDCS influences the electric field's (E-field) spatial distribution in the lumbar and sacral spinal cord (SC). The electrodes were placed longitudinally along the SC, with the target electrode over the lumbar spine, and the return electrode above the former, considering four different distances (4, 8, 12 and 16 cm from the target). A fifth configuration was also tested with the return electrode over the right deltoid muscle. Peak values of the E-field's magnitude are found in the lumbo-sacral region of the SC for all tested configurations. Increasing the distance between the electrodes results in a wider spread of the E-field magnitude distribution along the SC, with larger maximum peak values and a smoother variation. The fifth configuration does not present the highest maximum values when compared to the other configurations. The results indicate that the choice of the return electrode position relative to the target can influence the distribution and the range of values of the E-field magnitude in the SC. Possible clinical significance of the observed effects will be discussed.

Evaluation of the electric field in the brain during transcranial direct current stimulation: A sensitivity analysis.

The use of computational modeling studies accounts currently for the best approach to predict the electric field (E-field) distribution in transcranial direct current stimulation. As with any model, the values attributed to the physical properties, namely the electrical conductivity of the tissues, affect the predicted E-field distribution. A wide range of values for the conductivity of most tissues is reported in the literature. In this work, we used the finite element method to compute the E-field induced in a realistic human head model for two electrode montages targeting the left dorso-lateral prefrontal cortex (DLPFC). A systematic analysis of the effect of different isotropic conductivity profiles on the E-field distribution was performed for the standard bipolar 7×5 cm2 electrodes configuration and also for an optimized multielectrode montage. Average values of the E-field's magnitude, normal and tangential components were calculated in the target region in the left DLPFC. Results show that the field decreases with increasing scalp, cerebrospinal fluid (CSF) and grey matter (GM) conductivities, while the opposite is observed for the skull and white matter conductivities. The tissues whose conductivity most affects the E-field in the cortex are the scalp and the CSF, followed by the GM and the skull. Uncertainties in the conductivity of individual tissues may affect electric field values by up to about 80%.

Effects of prefrontal anodal transcranial direct current stimulation on working-memory and reaction time.

Transcranial direct current stimulation (tDCS) has proven to be a useful tool in the scientific research community, particularly for clinical investigation purposes. Neuroimaging studies indicate that there is a connection between the prefrontal cortex (PFC) and working memory (WM), as well as between the primary motor cortex and reaction time (RT). Thus, our goal was to evaluate the effect of anodal stimulation of the PFC, with respect to WM and RT. We tested 20 healthy subjects randomized into two groups - half received active stimulation and the other half sham stimulation. Participants underwent two stimulation sessions of 10 minutes each, separated by a 10-minute interval for rest. The task was performed during the stimulation periods, and consisted in the display of a list of words for the subject to read and memorize. Afterwards, a new list was shown and the subject was asked to to press a key when a repeated word appeared. A current of 1 mA was delivered via a foc.us gamer headset. After both stimulations, the participants answered an Adverse Effects Questionnaire. Statistical tests were performed to compare the accuracy, error rate, and reaction time values for active vs. sham and first vs. second stimulations. The results obtained led us to infer that there were no significant improvements in the performance of the active group in comparison with the sham group, in terms of WM and overall RT values. However, RT data analysis indicated that active simulation subjects showed significantly lower values when compared to the sham group, only for the first stimulation period. Due to emerging technological advances, the videogame industry has started to invest in the commercialization of products that promise to enhance neural functions and, thus, improve gamers' performance. The results obtained provide evidence of the importance of testing such commercial devices. The scientific community should have an active role in the validation of these claims.

Investigating an alternative ring design of transducer arrays for tumor treating fields (TTFields).

Tumor treating fields (TTFields) is a therapy that inhibits cell proliferation and has been approved by the U.S Food and Drug Administration (FDA) for the treatment of Glioblastoma Multiforme. This anti-mitotic technique works non-invasively and regionally, and is associated with less toxicity and a better quality of life. Currently a device called Optune™ is clinically used which works with two perpendicular and alternating array pairs each consisting of 3×3 transducers. The aim of this study is to investigate a theoretical alternative array design which consists of two rings of 16 transducers and thus permits various field directions. A realistic human head model with isotropic tissues was used to simulate the electric field distribution induced by the two types of array layouts. One virtual tumour was modelled as a sphere in the white matter close to one lateral ventricle. Four alternative ring design directions were evaluated by activating arrays of 2×2 transducers on opposite sides of the head. The same amount of current was passed through active transducer arrays of the Optune system and the ring design. The electric field distribution in the brain differs for the various array configurations, with higher fields between activated transducer pairs and lower values in distant areas. Nonetheless, the average electric field strength values in the tumour are comparable for the various configurations. Values between 1.00 and 1.91 V/cm were recorded, which are above the threshold for effective treatment. Increasing the amount of field directions could possibly also increase treatment efficacy, because TTFields' effect on cancer cells is highest when the randomly distributed cell division axis is aligned with the field. The results further predict that slightly changing transducer positions only has a minor effect on the electric field. Thus patients might have some freedom to adjust array positions without major concern for treatment efficacy.

Simplified realistic human head model for simulating Tumor Treating Fields (TTFields).

Tumor Treating Fields (TTFields) are alternating electric fields in the intermediate frequency range (100-300 kHz) of low-intensity (1-3 V/cm). TTFields are an anti-mitotic treatment against solid tumors, which are approved for Glioblastoma Multiforme (GBM) patients. These electric fields are induced non-invasively by transducer arrays placed directly on the patient's scalp. Cell culture experiments showed that treatment efficacy is dependent on the induced field intensity. In clinical practice, a software called NovoTalTM uses head measurements to estimate the optimal array placement to maximize the electric field delivery to the tumor. Computational studies predict an increase in the tumor's electric field strength when adapting transducer arrays to its location. Ideally, a personalized head model could be created for each patient, to calculate the electric field distribution for the specific situation. Thus, the optimal transducer layout could be inferred from field calculation rather than distance measurements. Nonetheless, creating realistic head models of patients is time-consuming and often needs user interaction, because automated image segmentation is prone to failure. This study presents a first approach to creating simplified head models consisting of convex hulls of the tissue layers. The model is able to account for anisotropic conductivity in the cortical tissues by using a tensor representation estimated from Diffusion Tensor Imaging. The induced electric field distribution is compared in the simplified and realistic head models. The average field intensities in the brain and tumor are generally slightly higher in the realistic head model, with a maximal ratio of 114% for a simplified model with reasonable layer thicknesses. Thus, the present pipeline is a fast and efficient means towards personalized head models with less complexity involved in characterizing tissue interfaces, while enabling accurate predictions of electric field distribution.

Computational models of non-invasive brain and spinal cord stimulation.

Non-invasive brain and spinal cord stimulation techniques are increasingly used for diagnostic and therapeutic purposes. Knowledge of the spatial distribution of the induced electric field is necessary to interpret experimental results and to optimize field delivery. Since the induced electric field cannot be measured in vivo in humans, computational models play a fundamental role in determining the characteristics of the electric field. We produced computational models of the head and trunk to calculate the electric field induced in the brain and spinal cord by transcranial magnetic stimulation, transcranial direct current stimulation and transcutaneous spinal cord direct current stimulation. The field distribution is highly non-uniform and depends on the type of technique used, on the position of the stimulation sources, and on anatomy. In future these models may be improved by using more accurate and precise values for the physical parameters as they become available, by combining them with neuronal models to predict the outcome of stimulation, and by better segmentation and meshing techniques that make producing individual models practicable.

Influence of electrode configuration on the electric field distribution during transcutaneous spinal direct current stimulation of the cervical spine.

Transcutaneous spinal direct current stimulation (tsDCS) is a recent technique with promising neuromodulatory effects on spinal neuronal circuitry. The main objective of the present study was to perform a finite element analysis of the electric field distribution in tsDCS in the cervical spine region, with varying electrode configurations and geometry. A computational model of a human trunk was generated with nine tissue meshes. Three electrode configurations were tested: A) rectangular saline-soaked sponge target and return electrodes placed over C3 and T3 spinous processes, respectively; B1) circular saline-soaked sponge target and return electrodes placed over C7 spinous process and right deltoid muscle, respectively; B2) same configuration as B1, considering circular shaped electrodes with sponge and rubber layers and a small circular connector on the top surface. The electric field distribution for cervical tsDCS predicted higher magnitude in configurations B1 and B2, reaching a maximum of 0.71 V/m in the spinal white matter and 0.43 V/m in the spinal grey matter, with values above 0.15 V/m in the region of the spinal circuits related with upper limb innervation. In configuration A, the values were found to be <; 0.15 V/m through the entire spinal cord. Electric fields with magnitude above 0.15 V/m are thought to be effective in neuromodulation of the human cerebral cortex, so the configurations B1 and B2 could be an optimal choice for cervical tsDCS protocols. Computational studies using realistic models may be a powerful tool to predict physical effects of tsDCS on the cervical spinal cord and to optimize electrode placement focused on specific neurologic patient needs related with upper limb function.

Investigating the cortical regions involved in MEP modulation in tDCS.

Transcranial magnetic stimulation (TMS) is used in several studies to evaluate cortical excitability changes induced by transcranial direct current stimulation (tDCS) of the primary motor cortex. Interpretation of these results, however, is hindered by the very different spatial distribution of the electric field (E-field) induced by the two techniques and by the different target neurons that they might act upon. In this study we used the finite element method to calculate the E-field distribution induced by TMS and tDCS in a realistically shaped model of a human head. A model of a commercially available figure-8 coil was placed over a position above the identified hand knob (HK) region. We also modeled two configurations of bipolar tDCS montages with one of the electrodes placed over the HK and a return electrode over the contralateral orbital region. The electrodes over the HK were either rectangular in shape, with an area of 35 cm(2) or cylindrical with an area of π cm(2) (1 cm radius). To compare the E-field distribution in TMS and the two tDCS models, average values of the E-field's magnitude as well as the polar and azimuthal angle were investigated in the HK region and premotor areas. The results show that both techniques induce fields with different magnitudes and directions in the HK: the field in tDCS is predominantly perpendicular to the cortical surface, contrary to what happens in TMS where the field is mostly parallel to it. In the premotor areas, the magnitude of the E-field induced in TMS was well below the accepted threshold for MEP generation, 100 V/m. In tDCS, the magnitude of the field in these areas was comparable to that induced at the HK with a significant component perpendicular to the cortical surface. These results indicate that tDCS and TMS target preferentially different neuronal structures at the HK. Besides, they show that premotor areas may play a role in the tDCS-induced after effects on motor cortex excitability.

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

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.