Keywords

1 Introduction

1.1 Tumor Treating Fields (TTFields)

Tumor Treating Fields (TTFields) is an anti-mitotic cancer treatment technique used for solid tumors. It consists in applying an electric field (EF) with a frequency between 100 and 500 kHz in two perpendicular directions alternately to affect the mitosis of tumoral cells [1]. TTFields are FDA-approved for the treatment of recurrent glioblastoma (GBM) since 2011, of newly diagnosed GBM cases since 2014, and of malignant pleural mesothelioma since 2019, after the promising results from the EF-11 [2], EF-14 [3] and STELLAR [4] clinical trials, respectively. The mechanisms by which TTFields act are not completely understood, but in-vitro studies showed that these EFs can slow down the rate at which tumoral cells divide or even completely arrest cell proliferation for EF intensities at the tumor of at least 1 V/cm [1, 5].

In patients, TTFields are applied using a specific device named Optune (Novocure, Haifa, Israel) which consists in an electric field generator connected to four arrays with 9 transducers each. These arrays work in pairs to induce an EF in the tumor in two perpendicular directions alternately. The rationale behind the application of the fields in more than one direction is based on the results of the in-vitro study by Kirson et al. [5] that showed an increase of 20% in the number of tumoral cells arrested during mitosis when two directions were used alternately compared to a single direction.

Post-hoc analyses of clinical trials data showed that the time that a patient is on active treatment, i.e., the treatment compliance, significantly affects the expected overall survival (OS) [6]. Patients with recurrent GBM tumors that participated in the EF-11 trial and whose daily compliance was at least 18 hours had an OS of 7.7 months, whereas those who were under treatment less than these 18 daily hours had an OS of 4.5 months. More recently, Ballo et al. [7] used data from newly diagnosed GBM patients who took part on the EF-14 clinical trial to find a relation between TTFields dose and treatment outcome. The results showed that the OS survival is significantly different in patients whose average electric field in the tumor was at least 1.06 V/cm (24.3 months vs. 21.6 months), thus corroborating what was seen in in-vitro studies [1]. In the same study, the authors suggested a new metric, the power density (PD), that could be used to evaluate treatment efficacy instead of the electric field. By defining the dose in the tumor in the terms of PD, TTFields planning will be more like other cancer treatment techniques planning, such as radiotherapy, as this metric quantifies the energy that is deposited in tissues. The same study showed that the threshold that best divides patients into the two groups with the most significant difference in terms of OS is 1.15 mW/cm3.

1.2 Optimization of the Array Placement: The NovoTAL System

To optimize the PD in both directions, the array layouts are strategically placed on the scalp in regions that maximize the dose delivered to the tumor. The NovoTAL system (Novocure, Haifa, Israel) is an FDA-approved tool used to help certified physicians find the best array layouts for each patient. The importance of personalized array layouts is clearly shown in the literature by different authors. The study by Wenger et al. [8] was the first work to quantify the importance of creating personalized treatment maps for each patient based on tumor location. In general, the average field intensity in the tumor increased between 32 and 45% when array positioning was adjusted to the tumor location. Smaller improvements were seen in the work by Korshoej et al. [9], in which adapted layouts led to an enhancement of the average field strength in the tumor between 9% and 23%.

In the NovoTAL system personalized head models are created and several array layouts are tested to find the one that yields the best option for each patient. One of the approaches that is most commonly considered comprehends an extensive search in which a finite number of layouts, available in the NovoTAL database, are tested and the one that induces the highest EF in the tumor is chosen. After the best layout is known small adjustments can be made to optimize the induced electric field. A detailed description of how this software works can be found in [10].

1.3 Heat Transfer During Treatment

In the studies mentioned above, the choice of which layout to use was based solely on the electric field delivered to the tumor. However, there are other factors that can affect the current that is injected in each array pair during the therapy and consequently the predicted treatment efficacy. As TTFields are applied for long periods of time, the temperature of the head increases inevitably because of the Joule effect. To avoid any thermal harm to tissues, the Optune device monitors the temperature of the scalp and keeps it around 39.5 °C by controlling the amount of current that is injected into each array pair. As the EF produced at the tumor by a given pair of arrays is proportional to the injected current, a decrease in the injected current implies a reduction in the EF at the tumor.

Recent computational studies [11,12,13] modelled how TTFields were applied considering these thermal restrictions, quantified the temperature increases in tissues and predicted what physiological changes could occur when TTFields were applied. These works showed that heating was very localised, and it occurred mainly underneath the regions where the transducers were placed. The scalp was the tissue that heated up the most and the brain the one whose temperature varied the least. In each tissue, the temperature increased the most at the surface and quickly decreased with depth [13].

1.4 Aim of the Work

Given that the scalp’s temperature limits the dose that is administrated to the tumor, and consequently the predicted treatment effectiveness, in this work we investigated the impact of including this parameter on the choice of the best layout for TTFields treatment.

2 Methods

2.1 The Simplified Head Model (SHM)

As a first step we used a simplified head model (SHM) to investigate the impact that the temperature might have in the metric used to choose the best layout. This model is composed by several spheroid shells each one representing a different tissue of interest (scalp, skull, CSF, brain and ventricles) as shown in Fig. 1. The dimensions assigned to each shell were based on the typical dimensions of the head of patients that participated in the EF-14 clinical trial. A spherical lesion with a radius of 7.1 mm was also added to the model to mimic a GBM tumor.

Fig. 1
A drawing of the Simplified Head Model which looks like a circle. Diametres of several tissues have been described in the circle among them Scalp is the largest with 75 and 100 millimetres.

Axial cut through the center of the model (plane z = 0). Each tissue was represented as a spheroid shell with the values of the main semi-axes, a and b, shown in the table on the right, in mm. The scalp is represented in orange, the skull in blue, CSF, which also fills the ventricles, in yellow and the brain in green. A spherical lesion, with the center at (34,18,0) mm and diameter of 15.2 mm, in brown, was also added to the model to mimic a GBM tumor

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To maximize the number of layouts that could be tested we created several models with transducer arrays placed in different regions of the scalp. All models were created using the Materialise 3-matic software. One important consideration to bear in mind when placing the arrays is that the 2 pairs should induce EFs with directions as close as possible to being perpendicular to increase the number of affected tumoral cells [1]. One pair, hereinafter referred to as pair 0, was placed as depicted in the top row of Fig. 2, in red. The array vector (AV), which was defined as the line that connects the two central transducers of each pair, passed through the center of the tumor. The direction of the array vector is 0° when it points along the y-axis and 90° when it points along the x-axis. The perpendicular pair, pair 90, in blue in the center of the top row of Fig. 2, was rotated about the z-axis and its array vector also passed through the center of the tumor. In this work, we also considered the combinations between pair 0 and the pairs that were rotated by 75° and 105°, pair 75 and 105, respectively, as it might not always be possible to ensure a complete perpendicularity between pairs in a real-case scenario. In total, we build seven different models in which the pairs were separated by 90° ± 15° (Fig. 2). In all pairs the array vector passed through the center of the virtual lesion.

Fig. 2
A photo depicts seven spheroid model designs among them two of the layout has the highest number of Red pairs which is 165 and one of them has the highest number of Blue pairs which is 75.

Top view of the seven spheroid models used. For each pair there is a maximum of three possible complimentary pairs that can be used. For pair 0 these three pairs were rotated by 75° (upper row, left), 90° (upper row, middle) and 105° (upper row, right). For all layouts, the array vector of each pair passed through the center of the tumor, which is represented in black. The pair with the longest array vector is colored in red, whereas the pair with the shortest array vector is colored in light blue. The position of the tumor was the same for all layouts

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The arrays are a 3×3 matrix of transducers separated by 44 mm in one direction and by 22 mm in the other, thus representing the Optune system. The radius of each transducer is 10 mm, and its thickness is 1 mm. Between each transducer and the scalp, a layer of gel with a radius of 10.3 mm and variable thickness was added to optimize the current flow into the head.

2.2 The Realistic Head Model (RHM)

After the simulations with the simplified head model were completed, we used a realistic head model (RHM) to verify if the conclusions drawn hold for more complex geometries. The RHM was the same one used in previous studies on heat transfer during TTFields [11,12,13], This model was built based on the Colin27 template, and it was segmented into scalp, skull, CSF, grey matter (GM) and white matter (WM). Similar to what was done with the SHM, a spherical virtual lesion was added to mimic a GBM tumor. The latter consisted in a necrotic core, with a diameter of 14 mm, surrounded by an active tumor shell, with a diameter of 20 mm. A description of the complete framework followed to build this model can be found in [14, 15]. The arrays were then placed on the scalp using Materialise 3-matic, in positions defined by the NovoTAL system. The final head model is shown in Fig. 3.

Fig. 3
An image of two head models in which the anterior part is paired with the posterior part and the left side is paired with the right part. One model is front facing and one back.

Realistic head model used with the arrays placed in the regions suggested by the NovoTAL system. The anterior array (in blue) is paired with the posterior one (in green) and the left array (in red) is paired with the right one (in yellow). A: Anterior; P: Posterior; L: Left and R: Right

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2.3 Equations and Physical Properties

As previously noted, current is injected alternately in two directions. Thus, to model TTFields, it is necessary to calculate the electric field distribution twice. At the frequency at which TTFields work for GBM treatment, 200 kHz, it is possible to use the electroquasistatic approximation of Maxwell’s equation. In this case, the calculation of the electric potential is simplified, and Laplace’s equation can be used:

$$ \nabla \left[\left(\sigma +j{\epsilon}_a2\pi f\right)\nabla \phi \right]=0 $$
(1)

where σ is the electric conductivity (S/m), j the imaginary constant, ϵa the absolute permittivity (F/m), f the frequency (Hz) and ϕ the electrostatic scalar potential (V).

As Optune controls the potential difference between the two arrays of the same pair, we imposed a Dirichlet boundary condition (V =  ± V0) at the outer surfaces of the transducers of the same array. At the remaining outer boundaries of the model, we assumed a null value for the normal component of the current density, whereas at the internal boundaries we considered continuity of the latter quantity. The electric field distribution was obtained for the two array pairs in each layout.

After solving the electric studies, we used Pennes’ equation to solve for the temperature distribution:

$$ \rho c\frac{\partial T}{\partial t}=\nabla \cdotp \left(k\nabla T\right)+\omega {\rho}_b{c}_b\left({T}_b-T\right)+{Q}_{met}+\sigma {\left|\left|E\right|\right|}^2 $$
(2)

where ρ is the density (kg/m3), c the specific heat at constant pressure (J/(kg oC)), T the temperature (°C), t the time (s), k the thermal conductivity (W/(m oC)), ω the blood perfusion (1/s), Qmet the metabolic rate (W/m3), assumed to be constant in the simulations, and E the electric field vector (V/m). The last term on the right-hand side represents the contribution of the EFs in increasing the temperature. Its values were taken alternately from each array pair. The subscript b stands for blood and Tb was 36.7 °C in all studies.

At the outer boundaries, we accounted for energy exchanges with the environment, at 24 °C, through convection and radiation, whereas at the internal boundaries we assumed that heat conduction occurred between adjacent tissues and materials.

The values assigned to each physical property were based on the literature. The electric parameters were retrieved from Ballo et al. [7] and the thermal parameters were the same as the standard values reported in Gentilal and Miranda [12].

All simulations were performed in COMSOL Multiphysics v5.2a.

2.4 Conditions of the Simulations and Metrics Used

As described in the work by Chaudry et al. [16], during treatment planning with NovoTAL the electric field in the tumor is predicted by injecting 900 mA of current (amplitude) into each array pair independently. Additionally, in the work by Ballo et al. [7], the local minimum power density (LMiPD) is defined as the lowest of the two power densities induced in each voxel in the tumor. Thus, we combined these two approaches and, when only the electric field was considered as a metric to evaluate the effectiveness of a layout, we injected 900 mA into each array pair, and we calculated the LMiPD in the tumor. As noted by Wenger et al. [10], it is desirable to use MR images with a resolution of at least 1 mm × 1 mm × 1 mm for TTFields planning. Thus, the values of the power density in the tumor were exported from COMSOL considering a regular grid spaced by 1 mm in every direction. After the minimum power density was obtained for each voxel, we calculated the average LMiPD in the tumor for each layout. Each electric study took around 4 minutes using the SHM and 30 minutes using the RHM in a workstation with dual core Intel Core i9-10900X X-series processors clocked at 3.7 GHz and with 64 GB of RAM.

When the temperature was also accounted for during treatment planning a different approach had to be followed as the amount of current that could be injected into each array pair depended on the temperature of the scalp. We used a method previously reported [13] in which we started by injecting 400 mA amplitude of current into each pair alternately with a switching time of one second. We then predicted the maximum temperature that the scalp would reach underneath each array pair in regions where the thermistors are typically placed, and we iteratively fine-tuned the injected current to induce the desired maximum temperature underneath both pairs.

Predicting the temporal evolution of the temperature distribution required a time-dependent study, with the electric field in Eq. (2) switching between that produced by each of the two array pairs every second. Only the first 5 minutes of treatment were simulated due to the time taken by these simulations. In order to estimate the steady state temperature, we fitted the following general equation to the variation of the highest temperature in the scalp:

$$ T={C}_1\left(1-\exp \left(-t/{C}_2\right)\right)+{C}_3 $$
(3)

where C1 (°C) represents the maximum contribution that the EF has in increasing the temperature of the scalp, C2 (s) is a time constant related to how quick the heat is transferred and C3 (°C) represents the initial temperature of the scalp.

The maximum temperature, Tmax, can then be predicted by taking the limit as t tends to infinity:

$$ {T}^{\textrm{max}}\equiv \lim \left(t\to \infty \right)T={C}_1+{C}_3 $$
(4)

All data curve fitting were performed using Matlab’s 2020 curve fitting toolbox (cftool).

In the case of the RHM the desired temperature limit was the optimal working point for the Optune device, 39.5 °C. For the SHM, we had to slightly increase this threshold, to 40.5 °C, as the minimum current that is typically injected in patients, 400 mA, already induced a temperature higher than 39.5 °C. The time-dependent studies took around 10 hours for the SHM and 34 hours using the RHM in the workstation aforementioned.

3 Results and Discussion

3.1 Simplified Head Model

3.1.1 LMiPD Values When Only the Electric Field Is Considered

The values of the LMiPD when 900 mA (amplitude) were injected into each pair using the simplified head model are presented in Table 1.

Table 1 LMiPD values in the tumor when 900 mA (amplitude) were injected into each pair. Each layout is named after the two pairs which compose it, where the first pair is the one with the longest array vector and consequently the highest resistance
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The values of the LMiPD were very similar for all layouts (range: 6.30–6.88 mW/cm3). The worst layout for this tumor position, layout 165/75, induced a LMiPD that was only 8% lower than the one induced by the best layout, layout 15/105. These values were mainly limited by the lower EF induced by the pair with the longest array vector. In general, a longer array vector corresponds to a more resistive current path. However, resistance values also did not change considerably across layouts: 90–93 Ω for the pair with the highest AV and 77–82 Ω for the complimentary pair. Under these conditions, the parameter that defined which was the best layout is the distance between the tumor and each array (Fig. 2). In layout 15/105 the tumor is very close to two arrays of different pairs thereby increasing the induced PD in both directions. The distance between the tumor and the closest array of pair 15 is 55 mm, a value only slightly higher when compared to the distance to the closest array of pair 105, 48 mm. On the other hand, in layout 165/75, the distance between the tumor and the closest array of pair 75 is only 36 mm, but this value increases to 78 mm when the distance to the closest array of pair 165 is considered. Thus, the LMiPD in the tumor will be higher for layout 15/105 compared to layout 165/75 for the same injected current.

Based only on the LMiPD values, the layout that would be chosen for this model is layout 15/105.

3.1.2 LMiPD Values When the Temperature Is Accounted for

To investigate how the temperature impacts treatment planning we started by injecting 400 mA into each array pair alternately with a switching time of 1 second and, at the end of the simulation, we predicted the maximum temperature that the scalp would reach underneath both pairs. We then iteratively fine-tuned the injected current to induce the highest average current, considering both pairs, that would lead to a maximum of 40.5 °C in the scalp.

Taking layout 0/75 as an example, Fig. 4 shows the maximum temperature variation of the scalp for different sets of injected currents.

Fig. 4
Two line graphs depict the maximum temperature in 0 and 75 pairs for three different ampere current flows, all the currents are in the same line in the 0 degree pair graph.

Scalp’s maximum temperature variation underneath pair 0 (left) and pair 75 (right) for different values of injected current. Each line corresponds to a different set of values denoted by X/Y mA, where X is the current injected in pair 0 and Y the current injected in pair 75. Current was injected alternately into each pair with a switching time of 1 second. Changing how much current was injected in pair 75 also changed the temperature of the scalp underneath pair 0

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The maximum temperature in the scalp for each set of injected currents was predicted using Eq. (4) and it is presented in Table 2. The minimum adjusted-R2 (A-R22) obtained during the curve fitting process was 0.9995.

Table 2 Maximum temperature predicted in the scalp underneath each pair of arrays when different sets of current were injected in each pair alternately with a switching time of 1 second
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An increase of 200 mA of current in pair 75, from 400 mA to 600 mA, led to a temperature increase of 2.8 °C in the scalp underneath this pair and of 0.4 °C underneath pair 0 as the two pairs were placed very close to each other. A more detailed description of the impact of the distance between array pairs is provided in the next subsection.

The same rationale was followed for the remaining 6 layouts. The LMiPD was then quantified for the current values that led to 40.5 °C in the scalp (Table 3). The lowest A-R2 was 0.9994.

Table 3 LMiPD values in the tumor for each layout when current was injected into each array pair alternately with a switching time of 1 second. In every case, the amount of current injected was iteratively refined to induce a maximum temperature of 40.5 °C in the scalp underneath each pair
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Accounting for the temperature led to a variation of 31% in the LMiPD values (range: 1.31–1.71 mW/cm3), a value higher than the 8% reported when only the electric field was used as a metric to predict treatment effectiveness. In general, the current injected into the most resistive pair did not vary by more than 25 mA (range: 400–425 mA), whereas the current injected into the complimentary pair varied between 575 and 625 mA.

Based on Table 3, the best treatment option is layout 30/135. When only the electric field was used as a criterion to choose layouts (Table 1), this layout would be the second choice, after layout 15/105. On the other hand, layout 15/105 would now be the third choice if information regarding scalp’s temperature was included during treatment planning.

3.1.3 Comparison Between LMiPD and T + LMiPD

Figure 5 depicts the variation in the ranking of the layouts based on the values of the LMiPD when the temperature is not accounted for during treatment planning (LMiPD) vs. when it is (T + LMiPD).

Fig. 5
A variation ranking table of two criteria electric fields in tumour and electric field plus temperature information where seven layouts are shown and the ranks are ranged from 1 to 7.

Variation in the ranking of the layouts based on two different criteria: only the electric field in the tumor (LMiPD) or the electric field in the tumor plus information regarding the temperature of the scalp (T + LMiPD). Each line represents a different layout

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Based on these data, it is noteworthy that layouts 0/75, 0/90 and 15/105 dropped in rank when information regarding scalp temperature was included in treatment planning. By definition, the LMiPD is limited by the pair that induces the lowest power density in the tumor. As less current is injected into the most resistive pair in these three layouts compared to the other four (first pair, Table 3), the LMiPD will be reduced. As it can be seen in Fig. 2, some pairs in these three layouts are close to each other and thus the current that is injected into one pair will not only increase the temperature in scalp regions underneath that pair but also contribute to increasing the temperature underneath the complimentary pair. This can be seen quantitively in the data presented in Table 2, where an increase of 200 mA in pair 75 led to an increase of 0.4 °C underneath pair 0.

In particular, two pairs in layouts 0/75, 15/105 and 0/90 created a temperature hotspot near the two closest transducers of different arrays, as shown in Fig. 6. In the first two layouts the shortest distance between transducers of two different pairs was 2.2 mm. In layout 0/90, this distance was 10.0 mm, which created a weaker but still significant hotspot.

Fig. 6
An image where temperature layouts are illustrated in three different layouts. The highest is 38 degree Celsius and the lowest is 35 degree Celsius.

Temperature distribution at the end of the simulation (t = 5 minutes) in layouts 0/75 (left), 15/105 (middle) and 0/90 (right), when 400/600 mA were injected in the first, 400/575 mA in the second and 410/625 mA in the third. Due to the proximity of some transducers of different pairs in these three layouts temperature hotspots occurred (black arrows) which limited how much current could be injected into each pair. In the first two the shortest distance between transducers of different pairs was 2.2 mm, whereas in the third it was 10.0 mm. Temperature scale is in oC

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This highlights the importance of considering scalp’s temperature during TTFields planning, especially in patients with smaller heads in which there is a high probability for the transducers of different pairs being very close to each other.

The average value of the LMiPD across layouts decreased from 6.59 mW/cm3, when only the electric field in the tumor was considered, to 1.51 mW/cm3, when information concerning the temperature of the scalp was also included, a reduction of 77% on the average LMiPD predicted in the tumor. This is due to the large reduction in injected current imposed by the limit on the scalp temperature.

This simplified head model allowed us to gain important insights on some of the most important parameters when planning TTFields. However, the conclusions drawn from it might only be useful qualitatively due to some limitations such as the small variation in the values of the metrics used and the fact that the temperature threshold had to be increased from 39.5 °C to 40.5 °C. The latter might suggest that the heat mechanisms, mainly the Joule heating term, is overcontributing to the temperature increases as this threshold was reached for low values of injected current compared to what is typically seen in patients. In the next section, we present a preliminary study where we performed the same type of analysis using a realistic head model.

3.2 Realistic Head Model

3.2.1 LMiPD vs. T + LMiPD

In the realistic head model, the LMiPD in the tumor was also first calculated by injecting 900 mA into each pair, which yielded 0.81 mW/cm3. This value is below the 1.15 mW/cm3, reported by Ballo et al. [7], which is the threshold that best divides GBM patients into two groups with the most significant differences in the overall survival. One important factor limiting the LMiPD in this head model is the electric field produced by the anterior-posterior (AP) configuration. The power density in the tumor induced by this pair was 0.88 mW/cm3, a value far below the 3.32 mW/cm3 induced by the left-right (LR) configuration. The virtual lesion was placed in the right hemisphere of the brain, close to the lateral ventricles but midway between the anterior and posterior arrays, where the electric field produced by the AP pair was much lower than to the one induced by the LR pair. In general, tumors located in deeper regions of the brain, as in this case, require a more robust placement of the layouts as clearly shown in the work by Korshoej et al. [9]. According to the results of the latter work, a layout that might yield a higher LMiPD in our head model could be one in which all pairs are maintained at the same height, but rotated by 45°. This would decrease the power density induced by the LR pair but increase the one produced by the AP pair, which is the pair that is strongly limiting the LMiPD.

We then included information regarding the temperature of the scalp in the simulations. We followed the same approach as before and our results indicated that if 580 mA were injected into the AP pair and 850 mA in the LR pair alternately, the maximum temperature that the scalp would reach underneath both pairs would be 39.5 °C. The lowest A-R2 obtained for the data used to drawn these conclusions was 0.998.

More current could be injected in the left-right configuration because the head is less resistive in this direction than in the AP direction. Figure 7, shows the temperature distribution in scalp’s surface at the end of the simulation (t = 5 minutes). As expected, heating was very localised, and it occurred mainly underneath the regions where the arrays were placed. Contrary to what occurred with layouts 0/75, 15/105 and 0/90 in the SHM (Fig. 6), in this model the two pairs were relatively far from each other, and thus common temperature hotspots did not occur.

Fig. 7
An image depicts temperature layouts in two skull models. The highest achieved temperature is 38 degree Celsius and the lowest is 34 degree Celsius.

Scalp surface temperature after the first 5 minutes of treatment when 580 mA of current were injected into the AP pair and 850 mA into the LR pair, alternately with a switching time of 1 second. The maximum temperature predicted in the scalp under these conditions is 39.5 °C underneath both pairs. As it can be seen, heating is very localised, and the temperature increases underneath one pair do not significantly affect the increases underneath the complimentary pair. Temperature scale is in oC

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The LMiPD was then calculated for these conditions (T + LMiPD) and compared with the values obtained when only the electric field was used as a criterion. The LMiPD induced by the AP configuration decreased from 0.88 to 0.36 mW/cm3 and the one produced by the LR pair decreased from 3.32 to 2.96 mW/cm3. The overall LMiPD predicted in the tumor decreased from 0.81 mW/cm3 to 0.36 mW/cm3, when the temperature was also included in treatment planning, a 56% reduction. This suggests that taking the scalp’s temperature into account is likely to introduce large variations in the LMiPD also when using realistic head models.

4 Conclusions and Future Studies

The results obtained using the SHM model suggested that the best treatment layout in terms of LMiPD was not necessarily the best one when the temperature was included in treatment planning. In some cases, layouts in which two array pairs were close to each other yielded the highest average EF in the tumor, but the occurrence of a common temperature hotspot significantly limited the current that could be injected into each array pair, and thus the predicted treatment efficacy when the temperature was accounted for. However, adding this additional step during TTFields treatment planning might be very time-consuming. In our workstation, it took 10 hours to compute each time-dependent simulation. The process of fine-tuning the values of the injected current and of testing several layouts for each model might lead to computational times that are unfeasible from a practical point of view. Thus, further investigation is needed to include thermal studies in the treatment planning workflow. One important consideration that might be helpful is to define a minimum distance between the arrays to prevent the occurrence of temperature hotspots.

The results obtained with the RHM are a part of a preliminary study that is under investigation. The data presented here were intended to show that the LMiPD predicted in the tumor can also significantly decrease in realistic head models when the temperature of the scalp is considered during treatment. We are currently evaluating the impact of these decreases using different array layouts obtained through the NovoTAL system. In some of them, transducers of different pairs are also very close to each other, as it occurred with the SHM, and thus significant decreases in the predicted LMiPD are expected. Furthermore, we are also investigating different metrics that could be used alongside LMiPD to predict more realistically treatment effectiveness.