Spatiotemporally dynamic electric fields for brain cancer treatment: an in vitro investigation

Objective. The treatment of glioblastoma (GBM) using low intensity electric fields (∼1 V cm−1) is being investigated using multiple implanted bioelectrodes, which was termed intratumoral modulation therapy (IMT). Previous IMT studies theoretically optimized treatment parameters to maximize coverage with rotating fields, which required experimental investigation. In this study, we employed computer simulations to generate spatiotemporally dynamic electric fields, designed and purpose-built an IMT device for in vitro experiments, and evaluated the human GBM cellular responses to these fields. Approach. After measuring the electrical conductivity of the in vitro culturing medium, we designed experiments to evaluate the efficacy of various spatiotemporally dynamic fields: (a) different rotating field magnitudes, (b) rotating versus non-rotating fields, (c) 200 kHz versus 10 kHz stimulation, and (d) constructive versus destructive interference. A custom printed circuit board (PCB) was fabricated to enable four-electrode IMT in a 24-well plate. Patient derived GBM cells were treated and analyzed for viability using bioluminescence imaging. Main results. The optimal PCB design had electrodes placed 6.3 mm from the center. Spatiotemporally dynamic IMT fields at magnitudes of 1, 1.5, and 2 V cm−1 reduced GBM cell viability to 58%, 37% and 2% of sham controls respectively. Rotating versus non-rotating, and 200 kHz versus 10 kHz fields showed no statistical difference. The rotating configuration yielded a significant reduction (p < 0.01) in cell viability (47 ± 4%) compared to the voltage matched (99 ± 2%) and power matched (66 ± 3%) destructive interference cases. Significance. We found the most important factors in GBM cell susceptibility to IMT are electric field strength and homogeneity. Spatiotemporally dynamic electric fields have been evaluated in this study, where improvements to electric field coverage with lower power consumption and minimal field cancellations has been demonstrated. The impact of this optimized paradigm on cell susceptibility justifies its future use in preclinical and clinical trial investigations.


Introduction
New treatments for glioblastoma (GBM) are imperative, as it remains the most common incurable primary brain cancer (Nam and de Groot 2017). The clinical treatment standard for GBM is currently surgical resection followed by concurrent chemotherapy (temozolomide) and radiotherapy (Nam and de Groot 2017), but survival outcomes remain poor. Advancements in the field of electrotherapy have given rise to the use of low Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. intensity, non-ablative electric fields to control the growth of brain tumors (Kirson et al 2007, Hottinger et al 2016, Swanson et al 2016, Xu et al 2016, Lok et al 2017, Di Sebastiano et al 2018, Deweyert et al 2019, Fabian et al 2019, Shah et al 2020. Our group has shown that the delivery of tumor suppressing electric fields using implantable bioelectrodes, termed intratumoral modulation therapy (IMT), is efficacious in preclinical investigations (Xu et al 2016, Di Sebastiano et al 2018, Deweyert et al 2019 using a single stimulating electrode. Electric fields of intermediate frequency (200 kHz) produced from low voltage (2 V) sources impede the growth of high grade gliomas, including GBM, while non-neoplastic neurons and brain tissue remains relatively unaffected (Di Sebastiano et al 2018, Deweyert et al 2019. We and others have demonstrated computer simulations to be useful tools to analyze and plan electric field distributions in realistic preclinical and clinical scenarios (Miranda et al 2014, Korshoej et al 2016, Wenger et al 2018, Iredale et al 2020, 2022. Electric field simulations of single electrode in vitro IMT models suggest that while the coverage is sufficient for preclinical models, improvements in the extent of such coverage would be required to advance to human scale tumors (Di Sebastiano et al 2018, Deweyert et al 2019, Iredale et al 2020, 2022. This has been suggested through the use of multiple electrodes programmed with different relative phase shifts of the input voltage waveforms, which has been shown to theoretically increase tumor coverage and homogeneity (Iredale et al 2020(Iredale et al , 2022. Previous IMT computer simulation, optimization and treatment planning studies (Iredale et al 2020(Iredale et al , 2022 have highlighted the theoretical benefit of using spatiotemporally dynamic (rotating) electric fields to increase electric field coverage over time. The optimization of relative phase shifts of input waveforms results in electric fields that rotate during the waveform period. These fields are scalable to cover human-size tumors, using low voltage waveforms (2-4 V) that produce sufficient field magnitude (∼1 V cm −1 ) to suppress human GBM cell viability (Hottinger et al 2016, Swanson et al 2016, Stupp et al 2017, Ballo et al 2019. We have shown that a previously established IMT optimization algorithm (Iredale et al 2020) and treatment planning system (Iredale et al 2022) are applicable to in vitro, in vivo, and human tumor scenarios with phase shift, voltage and electrode location optimization parameters. Rotating fields provide increased field coverage and homogeneity compared to non-rotating fields, partly explaining why rotating fields are more effective. In addition, the telophase dielectrophoresis mechanism of action suggests field direction could play a role, supported previously with analysis of cell survival versus division axis with parallel orientation showing a significant decrease in cell viability (Kirson et al 2004). In 2D, rotating electric fields would provide a full 360 degrees of field direction, impacting dividing cells equally, regardless of division axis. While rotating electric fields are theoretically beneficial, there has yet to be in vitro field measurements or investigation of the impacts on GBM cell survival. The validation of delivered electric field is imperative for accurate stimulation and requires measurement of the delivered voltage and programming adjustment for each experiment trial. In this study, the electrical conductivity of the in vitro media Dulbecco's Modified Eagle Medium (DMEM) was measured and employed in our computer simulations used to map the electric field. It was also used to determine the required voltage programming. An in vitro IMT device was designed, developed, and used to deliver rotating electric fields to patient derived GBM cells. The effects of spatiotemporally dynamic electric fields of different (a) magnitudes, (b) rotation, (c) frequency, and (d) interference were evaluated with experiments designed using supporting computer simulations. Improved field delivery validation and simulation based reprogramming methods established in this study provide a framework for future preclinical and clinical investigations. The cell response to various field patterns gives insight to the optimization goals implemented in the planning system in the future.

Methods
In vitro electrical conductivity measurement To ensure that the desired electric field is being delivered to the target, the reduction in voltage induced by the low impedance of the culturing medium must first be considered so that the input voltage can be adjusted to account for this loss. This voltage drop is measured in vitro to determine the electrical conductivity and ensure that the electric field simulations are accurate. The electric fields produced from IMT electrodes in vitro were simulated in COMSOL Multiphysics (v5.4) at 200 kHz, where experimental geometries were replicated to provide an accurate representation of the electric field distribution over time. We measured the conductivity of our culturing media in a 3.5 cm diameter in vitro dish with 2 ml of DMEM at 37°C (figure 1). A 0.25 mm diameter platinum wire electrode was placed 2.6 cm away from a grounded electrode.
We measured the impedance of the in vitro circuit by accounting for the internal resistance that is present in waveform generators. The relationship between the programmed input voltage V prog and the voltage delivered across the load V meas is dependent on the internal resistance of the waveform generator (50 Ω) and the impedance of the load Z The low load impedance would result in an appreciably lower measured voltage compared to the programmed voltage, requiring an adjustment to the input voltage to make up for this voltage drop. We determined the impedance of the system using the programmed voltage V prog and measurements of the delivered voltage V . meas A waveform generator (Highland Technology T340 four-channel compact function generator) programmed to a 2 V amplitude sine wave at 200 kHz frequency was applied to one electrode while the other was grounded. An oscilloscope (Siglent SDS1104X-E) was used to measure the voltage amplitude when the circuit is open (V prog ) and when the circuit is closed (V meas ) (figure 1(a)), with each measurement repeated three times. The medium's electrical properties were determined by comparing the measured system impedance in vitro to the simulated impedance values for a range of DMEM electrical conductivities (0.1-2 S m −1 ), and a range of permittivity constants (1-1000) computed in COMSOL.

Electrode construct design optimization
In vitro experiments to validate simulated electric field began with the choice of well size and the design of a custom four electrode IMT electrode construct. The electrode geometry containing four, 0.45 mm diameter platinum-iridium wire electrodes was created in COMSOL, along with 1 ml of DMEM with electrical conductivity determined from the in vitro measurement, and a dielectric constant of 80 (Arnold andFuhr 1994, Chen et al 2009). In COMSOL, electrical insulation was applied on all outer boundaries and stimulating voltage controlled sinusoidal waveform terminal boundaries on the wire electrode surfaces were applied with experiment and electrode specific voltage amplitude A, phase shift , f and frequency f . A tetrahedral mesh was created for the geometry for computing the electric field. Electrode separation and programming (voltage and phase shift) was determined using the custom IMT optimization algorithm (Iredale et al 2020(Iredale et al , 2022 to cover the central 6 mm diameter with a homogeneous 1 V cm −1 time averaged electric field. The electrode separations were then used to produce the electrode construct in a 24-well plate, a well sizing that most closely represents the maximum coverable tumor diameter of 2.1 cm using four electrodes at 2 V found previously (Iredale et al 2020).

Experiment design optimization
The in vitro experiments were designed using electric field simulations. The IMT optimization algorithm (Iredale et al 2020(Iredale et al , 2022 was utilized to optimize electrode voltage and phase shift programming with respect to electric field target coverage and homogeneity, and to compare different field amplitudes and programming scenarios. The voltage drop was considered in all cases, where the simulated impedance and desired voltage was used in equation (1) to determine the programmed input voltage necessary to produce the desired electric field.
The first experiment (a) investigated the electric field dose-response curve of rotating fields at 200 kHz. All models used the fixed phase shift configuration (0, π/2, π, and 3π/2 radians) previously found optimal (Iredale et al 2020), with delivered voltage amplitudes selected for 1 V cm −1 , 1.5 V cm −1 and 2 V cm −1 dish coverage. Cell survival results S were then fitted to an adapted linear quadratic (LQ) model S A e 1 1, where E is the electric field intensity, and fit parameters of A, a and . b The next set of experiments compared (b) rotating versus non-rotating fields at 1 V cm −1 , (c) 200 kHz versus 10 kHz rotating fields at 1 V cm −1 , and (d) constructive versus destructive interference. The rotating experimental arms used the phase shifted configuration (0, π/2, π and 3π/2 radians) (Iredale et al 2020), with voltage amplitudes selected to cover the dish with a field of 1 V cm −1 at either 200 kHz (ideal frequency for GBM (Rominiyi et al 2021)) or 10 kHz (maximum available frequency for existing implantable stimulation devices (Megía García et al 2020)). The non-rotating arm contained a pair of ground and a pair of in phase stimulating electrodes with voltage selected to deliver 1 V cm −1 at 200 kHz, where the pattern of adjacent ground and stimulating electrodes was previously found to produce constructive interference when no phase shifting was used (Iredale et al 2020). A final configuration investigated the importance of field optimization and homogeneity, by using a destructive interference configuration (producing a field of 0 V cm −1 at the center of the region of interest) with alternating ground and stimulating electrodes at (i) the same input voltage and (ii) the same total system power as the rotating constructive interference scenario.
In vitro IMT model GBM cells employed in this study were derived from patient tumors (Xu et al 2016, Di Sebastiano et al 2018, and had been transfected with the firefly luciferase gene to enable bioluminescence imaging (BLI) for cell viability evaluation. Two cell lines (labelled GBM23 and GBM25) were used in this study. Cells were cultured in DMEM with 10% fetal bovine serum at 37°C, 5% CO 2 , passaged at 80% confluence by splitting 1:2 using 0.25% trypsin with 0.91 mM ethylenediaminetetraacetic acid (EDTA). Culture media was changed twice weekly. GBM cells (3 × 10 4 ) were plated with 1 ml of DMEM in four wells of a 24-well plate and fitted with the custom-designed four electrode IMT delivery device. The stimulation was delivered using a four-channel waveform generator (Highland Technology T340) and a four-channel oscilloscope (Siglent SDS1104X-E) was used to validate the voltages and phase shifts delivered by each electrode. Experimental wells received continuous three-day stimulation (72 h) with experiment specific voltage and phase shift IMT waveforms applied to each electrode. Sham wells contained the electrode hardware but received no stimulation.
Cell viability was analyzed after the treatment period using BLI where 8 μl of 150 μg ml −1 D-luciferin (PerkinElmer) was added to the culture media, the emission intensity captured (IVIS Lumina XRMS, PerkinElmer) and the mean photon flux measured (Living Image, Xenogen). Measurement data are presented as mean ± standard deviation. Biological data sets were analyzed in MATLAB (v2022a) for normality (Öner and Deveci Kocakoç 2017), and compared using a 2-sample, 2-tailed t test, with results presented as mean ± standard error and significance assumed at p < 0.05.

Results
In vitro electrical conductivity measurement Measurement of the delivered voltage in vitro resulted in a mean (± standard deviation) difference V V prog meas of 0.14 ± 0.01 V, with voltage ratio V V prog meas / of 1.08 ± 0.01, corresponding to an impedance of 625 ± 34 Ω. In this model, for the range of frequencies 10-200 kHz, the impact of permittivity variations are negligible and the impedance and resistance are equivalent (Z R » ), since the inverse resistance (0.0088 S) term dominates the capacitance (4.2416 × 10 -12 F) term fC 2p (5 × 10 −6 F s −1 ) in the parallel RC impedance formula. With the electrical conductivity s inversely proportional to resistance, and in our case, the impedance Z, conductivity can be expressed as CZ .
1 s = -The proportionality constant C is geometry dependent and was computed in COMSOL as 933.7 m −1 for this specific geometrical configuration (two electrodes placed 2.6 cm apart in a 3.5 cm diameter in vitro dish with 2 ml DMEM at 37°C). Using this relation and the measured impedance of 625 ± 34 Ω, the conductivity of DMEM is determined to be 1.5 ± 0.1 S m −1 , which was then used in future in vitro simulations.

Electrode construct design optimization
The optimal electrode configuration was four equally spaced electrodes, each placed 6.3 mm from the center of a 1.56 cm diameter well (24-well plate). This configuration covers the well with a homogeneous 1 V cm −1 electric field when electrodes are programmed to deliver 1.06 V sine waves with equally spaced phase shifts (0, π/2, π and 3π/2 radians). The 24-well plate provides a balance between human scale and reasonably delivered voltages (1-4 V). A custom electrode construct using this geometrical configuration was manufactured on a printed circuit board (PCB) with the capability to stimulate three dishes simultaneously with one sham dish ( figure 2).

Experiment design optimization
The optimal stimulation for the 200 kHz (and 10 kHz) rotating 1 V cm −1 average electric field in experiment (a) and (c) (figure 3) is to apply equally spaced phase shifts (0, π/2, π and 3π/2 radians) to each electrode with 1.06 V amplitude sinusoidal waveforms. The impedance for this model was computed in COMSOL to be 113 Ω, with a current amplitude of 9.41 mA, and an average power of 4.99 mW per electrode, for a total of 20.0 mW for this configuration. An explanation of impedance and current calculations are included in the supplementary materials. Field magnitudes of 1.5 and 2 V cm −1 for this rotating field required programmed voltage increases to 1.59 and 2.12 V respectively (with an accompanying increase in current and power). The non-rotating electric field in experiment (b) (figure 3) contains two consecutive stimulating electrodes with 0 phase shift, and two consecutive ground electrodes, and a voltage of 2.3 V applied to the two stimulating electrodes, resulting in 1 V cm −1 field coverage. The simulated impedance was calculated to be 225 Ω, with a current amplitude of 10.2 mA and average power of 11.7 mW per active electrode, for a total power dissipation of 23.5 mW for this configuration.
For the final experiment (d), alternating ground and 1.06 V stimulating electrodes (same voltage as rotating scenario) produced a field of 0 V cm −1 in the center of the dish (figure 3). This configuration resulted in an impedance of 171 Ω, current of 6.19 mA, and average power of 3.28 mW per electrode (6.56 mW total). The resulting electric field had an average 0.6 V cm −1 magnitude over the whole well, with the central 3 mm radius being covered with only 0.2 V cm −1 . Adjusting the voltage in this configuration to 1.86 V resulted in a total system power of 20.0 mW, the same as the rotating scenario, and an average electric field of 1 V cm −1 to the whole dish and 0.4 V cm −1 to the central 3 mm.
The programmed voltage required to deliver the correct voltage to the electrodes (compensating for the load impedance-induced voltage drop) was validated at the time of each experiment by measuring the delivered voltage with a four-channel oscilloscope, with results summarized in the supplementary materials (figure S1).

In vitro IMT model
Exposure of GBM23 cells to field magnitudes of 1 V cm −1 , 1.5 V cm −1 and 2 V cm −1 yielded field intensity dependent BLI peak signal, corresponding to mean cell viability fraction, of 0.58 ± 0.05 (n = 6), 0.37 ± 0.03 (n = 6), and 0.021 ± 0.006 (n = 6) relative to sham (figure 4). Cell survival results S were fit to a modified LQ model S A e 1 1, where E is the electric field intensity, with best fit parameters to be A= 25.1, a= 0.012 and b= 0.0038. This curve fit had an R-square value of 0.95.
Comparison between 200 kHz rotating and non-rotating fields at 1 V cm −1 , as well as 10 kHz rotating fields were analyzed for cell lines GBM23 and GBM25, where no statistical differences in cell viability were observed (figure 5). Rotating electric fields at 1 V cm −1 resulted in mean 0.53 ± 0.03 viability fraction (n = 12), nonrotating 1 V cm −1 fields resulted in 0.55 ± 0.06 viability (n = 12, p = 0.84), and 10 kHz rotating resulted in 0.49 ± 0.04 cell viability fraction (n = 12, p = 0.39). Applying a non-rotating electric field at the same voltage as the rotating case, but with destructive interference at 200 kHz to both cells lines resulted in a mean 0.99 ± 0.02 (n = 12) cell viability fraction relative to sham, statistically significant compared to the optimized rotating case with 0.53 ± 0.03 viability relative to sham (p < 0.001). Using the same power consumption as the rotating case,  the destructive interference model applied to GBM23 cells resulted in a mean 0.66 ± 0.03 viability relative to sham, statistically significant (n = 6, p < 0.01) when compared to the rotating case performed in parallel, with 0.47 ± 0.04 viability relative to sham ( figure 6).

Discussion
In this study, the theoretical improvement to target coverage and homogeneity from rotating electric fields generated by multiple electrodes was investigated in vitro for the first time. The impact of spatiotemporally dynamic electric fields on GBM cell viability was investigated by first validating that the desired electric field was delivered to preclinical models, by adjusting the programmed voltage to account for the voltage drop. The measured delivered voltage for a two-electrode in vitro scenario was used to determine the electrical conductivity of the in vitro media as 1.5 ± 0.1 S m −1 , using a geometrically accurate COMSOL simulation model. With the electrical conductivity known, COMSOL simulations can be used to determine the necessary applied voltage that is required to produce the desired electric field at the target. For preclinical experiments, the simulated voltage adjustment was also validated prior to stimulation by measuring the delivered voltage to the circuit. The electrical conductivity for DMEM computed in this study was compared to values presented in the literature. Due to the temperature sensitivity of electrical conductivity, only literature comparisons at 37°C were considered. Furthermore, below 10 MHz, electrolytic conductivity is considered frequency independent Computer simulations of the in vitro experimental model, used in conjunction with the IMT optimization algorithm to design a four-electrode IMT device provided a platform to demonstrate the impact of rotational fields. Electrodes placed 6.3 mm from the center of a 24-well plate most closely represented the largest spherical tumor volume coverable with four electrodes, previously found to be a 2.1 cm diameter tumor with electrodes places 7.5 mm from the center (Iredale et al 2020). For this geometry to produce optimal fields, each electrode must be separately programmable, a key feature of the IMT PCB and accompanying four-channel waveform generator. Expansion to the use of multiple electrodes in IMT has been theoretically supported (Iredale et al 2020(Iredale et al , 2022, with the impact on cell viability investigated for the first time in this work. The custom IMT in vitro delivery device and experiments were implemented on patient derived GBM cell lines and cell viability was observed with BLI. Rotating fields were effective at reducing cell viability in a field intensity dependent manner. Cell survival results S were fit to a modified LQ model with an R-square value of 0.95. This data fit suggests that, similar to radiotherapy, cells exposed to IMT fields have intrinsic linear and quadratic parameters, a and , b that influence cell survival (figure 4). With efficacy found to be dependent on not only field intensity, but field direction and exposure time (Korshoej et al 2019), it is important to consider such factors. Current external electric field devices provide only two field directions and have just begun to consider the impact of fractional anisotropy in the brain on the resulting intratumoral electric field. For in vitro studies such as the current investigation, fractional anisotropy is not present, but when expanding IMT to patient models, the fractional anisotropy should be considered for impacts on rotating fields applied with intratumoral electrodes. We did not find statistical difference in response between the spatiotemporal dynamic rotating electric field case versus the non-rotating case with both delivering the same field magnitude within the 3 mm radius in the center. However, the optimized rotating field had almost 20% lower power consumption (20.0 mW) compared to the non-rotating case (23.5 mW). We also noted that the non-rotating case exhibited field cancellations on the edges of the well, whose impact would be considerable for targets exceeding ∼3 mm radius. For the above reasons, spatiotemporally dynamic fields are preferred over their non-rotating counterparts. Interestingly, cell viability was not significantly different between 200 kHz and 10 kHz rotating fields, suggesting that previously thought inefficacious frequencies (Kirson et al 2004, 2007, Berkelmann et al 2019 could be effective with the rotating paradigm in certain cell lines. Furthermore, when we compared the two cell lines, the survival of GBM23 and GBM25 cells were not significantly different for the 200 kHz rotating scenario (58 ± 5% versus 48 ± 3%) (p = 0.13), the 10 kHz scenario (54 ± 7% versus 43 ± 5%) (p = 0.23), or the destructive interference voltage matched case (97 ± 4% versus 101 ± 3%) (p = 0.45) but were significantly different (69 ± 6% versus 40 ± 7%) for the non-rotating scenario (p = 0.01) (figure S2).
Through destructive interference, we created a central 'cold zone' of 0.2 V cm −1 in the central 3 mm radius of a well with average 0.6 V cm −1 field, by using the same stimulation voltages as the rotating electric field case, yielding 99 ± 2% viability experimentally. We then applied the same system power and whole well electric field (1 V cm −1 ) as the rotating case, with a central field of 0.4 V cm −1 , yielding 66 ± 3% cell viability experimentally, compared to 47 ± 4% for the rotating case. This suggests that even though we applied the same stimulation voltages, or the same system power, optimization of field homogeneity is critical for IMT field planning, and supports the methods previously established in IMT optimizations (Iredale et al 2020(Iredale et al , 2022. Evaluating the efficacy of spatiotemporally dynamic fields experimentally provides insight for future treatment planning optimization goals. Both field coverage and homogeneity will continue to be included as the objective goals with optimization parameters of phase shift, voltage, and electrode placement. Incorporation of Figure 6. Mean of the BLI peak signal normalized to sham ± standard error, proportional to the cell survival, for the cases of constructive interference 200 kHz rotating fields (0.47 ± 0.04, n = 6) and destructive interference power matched (0.66 ± 0.03, n = 6).
field rotation minimizes both field cold spots and power consumption. These qualities are impactful when translating IMT to the patient setting, where maximum coverage with minimal input current is vital to maximizing battery life of IMT implantable waveform generators. We can always do more: more replicates, more cell lines, and/or more comparisons, but we hope we have satisfactorily demonstrated how we designed and implemented a PCB that made performing in vitro experiments with multi-electrode stimulations consistent.

Conclusion
In this proof-of-concept study, the improved impact of electric field optimization was supported through in vitro GBM cell survival analysis. Electrical conductivity measurement of DMEM provided accurate optimizable computer simulations, used to determine required voltage, and calculate current and power. In vitro experiments designed and applied to patient derived GBM cells highlighted the considerations and effectiveness of using computerized optimization techniques to design subject-specific spatiotemporally dynamic IMT electric fields that minimize power delivered and cold spots within the treatment fields. With a patient-specific dose response of rotating electric fields established, future IMT studies can compare variation between patients, and determine the necessary inputs required for optimization techniques. The concept of spatiotemporally dynamic fields created through optimizing stimulation parameters can be utilized in future translational applications in rodents and patients, to further IMT development.