Skull Modulated Strategy to Intensify Tumor Treating Fields on Brain Tumor: a Finite Element Study

Purpose Tumor treating elds (TTFields) are a breakthrough in treating glioblastoma (GBM). Whereas, the intensity cannot be further enhanced, due to the limitation of scalp lesions. Skull remodeling (SR) surgery can elevate the treatment dose of TTFields in the intracranial foci. This study was aimed at exploring the characteristics of SR surgery towards TTFields augmentation. Methods The simplied multiple-tissue-layer model (MTL) model and realistic head (RH) model were reconstructed through nite element methods (FEM), to simulate the remodeling of the skull, which included skull drilling, thinning, and cranioplasty with PEEK, titanium, cerebrospinal uid (CSF), connective tissue and autologous bone. Results Skull thinning could enhance the intensity of TTFields in the brain tumor, with a 10% of increase of average peritumoral intensity (API) by every 1 cm decrease in skull thickness. Cranioplasty with titanium accompanied the most enhancement of TTFields in the MTL model, but CSF was superior in TTFields enhancement when simulated in the RH model. Besides, API increased nonlinearly with the expansion of drilled burr holes. In comparison with the single drill replaced by titanium, 9 burr holes could reach 96.98% of enhancement in API, but it could only reach 63.08% of enhancement under craniectomy of 9-times skull defect area. Conclusion Skull thinning and drilling could enhance API, which was correlated with the number and area of skull drilling. Cranioplasty with highly conductive material could also augment API, but might not provide clinical benets as expected. This study investigated the effects of skull modulation on the enhancement of intracranial TTFields intensity, including adjusting different congurations of SR surgery or performing cranioplasty surgery with replaced materials. Skull thinning, drilling, and skull replacement with high-conductivity materials could all increase API.


Introduction
Glioblastoma (GBM) is the most prevalent and malignant type of primary brain tumor, and patients suffer from poor life quality and limited survival. Despite the extension of median overall survival (mOS) up to 16 months by STUPP protocol 1 . But the high recurrence rate usually leads to more restricted treatments and a worse prognosis 2 . Although many pieces of research have presented promising e cacy in their preliminary phases, the majority of phase III clinical trials have failed, including cytotoxic drugs 3, 4 , targeted therapies 5-7 , immunotherapies 8, 9 , and oncolytic viruses 10 .
Tumor treating elds (TTFields) apply external alternating electric elds of intermediate frequency and relatively low intensity to inhibit cytogenesis. The current researchers believe that TTFields can impair mitotic spindle microtubule formation and intervene mitosis through the dielectrophoretic effect. Some also proposed the in uence on the potential of the cell membrane, as well as cell migration and invasion 11 . TTFields can also exert anti-tumor effects through biological pathways as apoptosis, autophagy, DNA damage repair, molecule transportation, and angiogenesis 12 . To be noted, TTFields function extensively on solid tumors like ovarian cancer, breast cancer, lung cancer, mesothelioma, or even in the more malignant form like pancreatic cancer and GBM [13][14][15][16][17][18] . EF-11 is the rst phase III trial for TTFields on recurrent GBM patients, which presented comparable results between TTFields and standard care 19 . The following real-world study, PRiDe and EF-19 20,21 , testi ed their safety. In EF-14, TTFields combined with temozolomide (TMZ) further extended the mOS to 20.9 months in newly diagnosed GBM patients 22 , which directly led to the approval by the U.S. Food and Drug Administration (FDA) and enrollment in the guidance, becoming the "fourth modality" in GBM treatment 23 .
However, the clinical practice of TTFields is hindered by their thermal effects. The arrays of TTFields are required to closely adhere to the scalp of the patients to reach the maximal dosage of eld intensity intracranially. Prior studies have proved that the anti-tumor toxicity was positively correlated with the applied eld intensity 24 . Also as shown in the clinical trials, the higher compliance and local eld density accompanied better clinical bene ts 25,26 . Yet, skin lesions on the scalp are commonly observed in the TTFields users, and could cause reduction in the applicable dosage of TTFields and patients' compliance 19,22,26 . Currently, this is the most prominent impediment for TTFields practices.
Though researchers have reported the heat transfer pattern 27,28 , to our knowledge, therehas been no effective means of reducing heat production.  29 . Nevertheless, more detailed research on the modulations of SR surgery is required. Therefore, this research was aimed at exploring the relationships between the con gurations of SR surgery and TTFields enhancement. Also, the implant of other bio-compatible materials during cranioplasty was simulated, and its effects on TTFields penetration were analyzed.

Head model (simulated object)
To clarify the general distribution of intracranial electric elds under different skull thicknesses and implants, we generated a simpli ed multiple-tissue-layer (MTL) model in the shape of cuboid by COMSOL Multiphysics (see Figure 1). The MTL model reconstructed the multiple sectioned layers of the brain covered by TTFields, which were marked as the scalp, skull, cerebrospinal uid (CSF), grey matter (GM), and white matter (WM), regardless of the complex con gurations of gyri and sulci 30 . The tumor in this model was set parallel to the center of the arrays of TTFields according to prior studies [31][32][33] . The diameter of the tumor was 20 mm, the thickness of edema and invasion was 3mm, and the core represented necrosis.
The realistic head (RH) model was built from the head MRI data on the SimNIBS website (www.simnibs.org) 34 , which was scanned from a young healthy male subject through 3.0T Philips Achieva equipped with a 32-channel head coil, including the high-resolution T1, T2 weighted images and diffusion Magnetic Resonance Imaging (MRI). Written consent was acquired on the open access and publishment of his imaging data. We utilized the SimNIBS 3.0 to integrate the transformed imaging data.
The headreco command was run to establish the three-dimensional head model. Then MIMICS Research, 3-Matic Research, and Materialise Magics were applied for model smoothing and mesh optimization (see Figure 2). The brain tissue is of high complexity and the lower part of the head contributes minor in uence to studying the supratentorial brain tumor. Therefore, the RH model needed to be further simpli ed accordingly. Meanwhile, each layer was smoothed, avoiding the nonspeci c in uence and time-consuming brought by the complex con guration of WM and GM. The tumor was designed in the same way as that in the MTL model.

The settings of the numerical simulation
Although the TTFields devices consist of two pairs of electrodes in an orthogonal position, we applied only one pair as 3 3 arrays to exclude the in uences of anisotropy and focused mainly on the enhancement on the intensity of electric led. A total of 18 sites (C1-C6 FC1-FC6 CP1-CP6) were selected, which were all preset in SimNIBS (see Figure 1). The arrays were designed as cylinders with the diameter of 2cm, the thickness of 1mm, and the gel of 1mm thick. The current frequency was 200 kHz and the intensity was 100 mA in sin signal. Since the more aggressive cancer cells usually aggregate in the peritumoral region, we calculated the average eld intensity per volume in the peritumoral region, entitled "average peritumoral intensity (API)" as a representation of intracranial dosage of TTFields.
The thickness of the skull was adjusted in the simpli ed MTL model and the corresponding eld intensity was calculated to simulate the effects of skull thinning on TTFields enhancement. Moreover, in the RH model, the commonly used bio-compatible materials including titanium and polyetheretherketone (PEEK) were simulated as implants during cranioplasty. CSF, connective tissue, and autologous bone were also taken as control. The conductivity of titanium is 2.34 10 6 S/m with a relative dielectric constant of 10, the conductivity of PEEK is 1 10 -15 S/m with a relative dielectric constant of 3.2, and the conductivity of cortical bone is 1.0-2.1 10 -2 S/m with a relative dielectric constant of 200 35 . We also altered the arranged pattern and the size of skull drilling to explore the relationship between the con gurations of SR surgery and the effective dosage of TTFields in the peritumoral region.
The TTFields were solved using the COMSOL Multiphysics software. Domain Solver was applied to calculate the eld intensity. In addition, we conducted a sensitivity analysis to determine the variations in the conductivities of tissues, which affected the electric eld in the tumor. The electric parameters were listed in Supplementary Table 1 [34,35].

Validation of Finite Element Methods (FEM)
In order to verify the reliability of the FEM calculations, we conducted validation experiments using pork tissues (fatty and lean meat). A voltage signal was applied to the outside of the tissue, while the potentials at different sites in the tissue were measured using a differential probe, and the results were compared with those of the FEM calculations to plot the validation curves. In addition, for the materials, such as the bone, PEEK and titanium, which were involved in this study, a similar approach was applied to simulate the aforementioned cranioplasty surgery model in vitro. The potentials in the pork tissues were measured using a differential probe, compared with the FEM calculation results, and the validation curves were plotted.

Model validation
To validate the reliability of nite element calculation in the MTL model, a simpli ed experimental device was established. We put different types of pork tissues into special containers and applied voltage signals as Supplementary Figure 1A, 1B. The electrical potential at different locations was measured with differential probe and calculated in COMSOL using the electric parameters listed in Supplementary Table   1, to compare the calculation and experiment as Supplementary Figure 1C and 1D. The difference between the experimental results and the calculated results was within an acceptable range.
We then simulated the cranioplasty model in vitro with pork tissue, using bone plates, PEEK and titanium plates to ll the gap between the pork tissue and the electrodes. The parameters of each material used in the experiment were listed in Supplementary Table 3. A xed voltage of ±20 V was applied to both electrodes, and a differential probe was used to measure the potentials at speci c locations in the tissue, as shown in Supplementary  The effects of tissue conductivity on the API The primary hypothesis is that each layer with different conductivity might have the distinct in uence on the eld intensity. The simulation was performed in the established head model, with simpli ed 5 layers of tissue, including the scalp, skull, CSF, GM, and WM. ΔE/Δσ of each tissue was calculated to represent the direction and extent of in uence on TTFields ( Figure 3A). Among the investigated tissues, the skull showed the most prominent effects on TTFields, and the rest of those tissues might exert similar negligible effects on TTFields. Besides, only the conductivity of the skull presented a positive relationship with TTFields enhancement. In other words, the increase of skull conductivity could more e ciently enhance the intracranial treatment dosage of TTFields. We conducted sensitivity analysis by changing the conductivity of each tissue within speci c ranges listed in Supplementary Table 1. The skull conductivity had the greatest effect on the API, followed by the tumor itself. However, other tissues exhibited subtle effects on the API. And in accordance with the prior ndings, only the skull conductivity presented a positive effect on the API.
Skull thinning augmented the API When simulating skull thinning in the MTL model, we considered two conditions: group 1. the total size of the head remained the same, while the defect area was replaced by connective tissue, as seen in most patients who underwent a secondary resection for the recurrent brain lesions; group 2. the other tissues were not altered along with the skull thinning, and the total size of the head was reduced accordingly. The thickness of the skull was set as a decreasing sequence from 6mm to 0mm, and API was calculated separately for group 1 and group 2 (see Table 1). The results demonstrated that the extent of skull thinning correlated positively with the increase in API, with an average 10% enhancement in the eld intensity as every 1mm reduction of skull thickness. The difference between group 1 and group 2 remained minor (below 2%) before the complete removal of the skull, which meant that the total size of the head could be neglected during TTFields simulation on skull thinning. Cranioplasty with bio-compatible material and the con gurations of the burr holes affected the API First, we simulated a single burr hole in the MTL model, which was the same size as the electrode, and placed at the center of the 3 3 array. The electric parameters of PEEK and titanium were incorporated as the repairing material. Also based on our observation in patients under repeated brain surgeries, the defects of the skull would be lled by tissue uids shortly after surgeries, while could also be replaced by connective tissue. Thus, the data of CSF and connective tissue were also integrated as a simulation for the patients without skull repairing, and autologous bone was considered as the baseline. According to the FEM results, titanium contributed most to the enhancement of TTFields, followed by CSF, the connective tissue, autologous bone and PEEK (see Figure 4).
Furthermore, we explored whether the size of the burr holes could enhance API under the condition of cranioplasty surgery. When linearly increased the size of the burr holes replaced by different materials, we noticed that the more area implanted with high-conductivity materials, such as titanium, CSF, and connective tissue, the higher API could be reached. By contrast, API grew negatively with the increase of the implantation of PEEK. Besides, we created 9 burr holes corresponding to the size and locations of electrodes on the skull and calculated the alteration in API. The results presented a maximum enhancement of 96.98% with the implanted titanium, followed by CSF, connective tissue, and PEEK (see Supplementary Table 2).
Then, a similar simulation of the skull remodeling was conducted in the RH model, under a single burr hole and nine burr holes separately. In both patterns, however, the connective tissue offered the strongest enhancement to API, followed by the CSF, titanium, and PEEK (see Figure 5), which was contradicted the results in the MTL model. Moreover, compared to a single burr, nine burr holes in an array provided better augmentation in API, which was in accordance with that of the MTL model.
The skull drilling of a single hole compared to nine holes, and cranioplasty with different planted material were simulated in the RH model. In both drilling patterns, the connective tissue ranked the highest in TTFields enhancement, followed by CSF, the titanium, autologous bone, and PEEK. And nine burr holes in an array offered more enhancement to API, compared to a single burr hole in all models.

Discussion
This study investigated the effects of skull modulation on the enhancement of intracranial TTFields intensity, including adjusting different con gurations of SR surgery or performing cranioplasty surgery with replaced materials. Skull thinning, drilling, and skull replacement with high-conductivity materials could all increase API.
The distribution of TTFields was predominantly determined by the local conductivities of brain tissues, which was also the prerequisite hypothesis of this research 36 . The dense skull offered the toughest impediment to the penetration of the external electric elds. Interestingly, other brain tissues except for the skull presented negative relationships with TTFields. This phenomenon might be due to "the charge shielding effects" that induced converse electric elds against the external TTFields. Therefore, the elevation of conductivity within these tissues could cause a decrease in the intracranial dosage of electric elds. As Lang S et al reported that peritumoral edema could hinder the TTFields penetration, and 6mm of edema blocked 52% of intracranial electric eld intensity 37 . Hence manipulating the conductivity of the brain and skull could be a potential facilitation to TTFields, for instance, alleviating the brain edema through Bevacizumab and steroids, or alternating the con gurations and materials of the skull.
In comparison between the two commonly implanted materials, titanium and PEEK, the former offered more intracranial augmentation to TTFields, and the intensity was elevated as the increase of the replaced area, but the growth rate of API declined as the skull defects further expanded. And we considered that the excessive implantation not only accompanied higher risks of infection, and might not provide clinical bene ts as expected. Parameters of the CSF and connective tissue were also incorporated as reference models, because the resected lesions would soon be lled with uid, and a stepwise reorganization by connective tissues. The conductivity of titanium is far larger than that of CSF, and the titanium implant offered much stronger augmentation to TTFields in the MTL model. However, their differences in the intensity of intracranial electric elds were only about 3% in the RH model. The distinction might lie in the complex con gurations of gyri and sulci, which could generate more shielding charges against the external electric elds. Therefore, theoretically, titanium might not be as effective as what was observed in the RH model, but it requires further evidences in real patients.
Korshoej AR reported in 2016 that SR surgery could enhance electric elds in the tumor regions 38 . Based on the MRI data of two patients with super cial or deep brain tumors, they stated that craniectomy could elevate the dosage of TTFields in both models, especially for the super cial tumor, and the size and shape of the burr holes affected the peritumoral electric intensity 38 . The primary results further supported their following clinical trials 39 . In the phase I clinical trial OptimalTTF-1, 15 GBM patients with the rst recurrence were enrolled. They all received a second brain tumor debulk surgery and other physician's choices of therapy 39 . The tumors were all near the surface of the brain and 4 patients did not receive TTFields due to personal reasons. Three drilling patterns were applied with signi cantly prolonged median progression free survival (mPFS) and mOS (mPFS, 4.6 months; 6-month PFS rate, 36%; mOS, 15.5 months) 29 . To clarify the exact augmentation of SR surgery to TTFields, one phase II clinical trial (NCT04223999) is ongoing.
Admittedly, the authenticity was compromised by the simpli ed MTL model and RH model. In particular, the RH model was constructed based on the imaging data of a healthy subject, and we simpli ed the model to eliminate as many individualized features as possible, then a virtual tumor was manually placed to shape a relatively standardized realistic head model 40,41 . This was mainly for avoiding the confounding factors that affected TTFields dosimetry other than electric eld strength, such as head shape and tumor morphology 42 . Nevertheless, due to the complex anatomy of the head, variations in neuro-ber topology, and the isotropic conductivity distribution, orthogonal electric elds with 2 pairs of transducer arrays might introduce considerable correlations which were indexed as fractional anisotropy (FA) 40,42 . Even at the optimal electrode position with maximum TTFields intensity, FA could still bias the pattern of the electric elds 36 . Thus, we applied only 1 pair of 3 3 transducer arrays in the left-right eld direction parallel to the tumor. Diffusion tensor imaging (DTI) was not available for the subject, and detailed simulation concerning FA could not be acquired. Moreover, only one RH model might not be representative for all patients. These limitations all indicated an urgent need for prospective simulation studies on real patients.
Another limitation was the lack of thermal simulation on the head model. Despite broad clinical applications in cranioplasty, titanium is notorious for its skin burnt under heat or direct sunlight exposure. The alternating electric elds might also increase the heat produced by titanium. Also, the skull drilling is an invasive procedure, which warrants precise scheme and design, but we only simulated some of the occasions where the burr holes were set corresponding to the electrodes. Further exploration on the con gurations of skull drilling and the safety of cranioplasty with other replaced materials are still required for further clinical applications.
Besides, considering the edge effect of the transducer array, our research did not involve the in uence of the relative position of electrodes and the tumor on the peritumoral eld intensity. In our simulation, we set the tumor xed deeply and directly below the center of the electrode array, in which case we believed that the edge effect of electrodes had subtle impact on the peritumoral electrical elds 40 .
Our research was aimed at the clinical optimization of TTFields. Except for the method of altering skull conductivity as mentioned above, reducing the heat produced by electrodes are also essential (see Fig. 6), which is the key problem hindering its usage. Researches have focused on simulating the heat transfer pattern of TTFields 28 , but to our knowledge, none reported feasible solutions. Further studies might overcome this issue from the perspective of materials. Besides, although the new version of TTFields has facilitated patients' life, many still complained about carrying the battery 43 . From the perspective of thermal effects and life quality, implantable electrodes embedded in the skull or brain parenchyma, and the implantable batteries, which are similar to the design of cardiac pacemakers or deep brain stimulation × with batteries placed in the chest, could both increase the compliance of patients. As for the clinical practices, the current application of TTFields urgently requires appropriate criteria for evaluation. The clinical trials of TTFields mainly used scales like Mini-Mental Status Exam (MMSE), EORTC quality-of-life questionnaire core-30 (QLQ-C30), and BN20 to assess life quality and functions, and used Macdonald, or RANO criteria to assess the radiological progression of GBM patients treated with TTFields 44,45 . But there were reports of delayed response to TTFields as well 45 . It is still required to verify in an extended population whether the established evaluation scales could represent the responses to TTFields, whether there is also pseudoprogression during the treatment, and whether there are other predictive factors, such as blood or imaging biomarkers and local minimum dose density (LMiDD) 25 . Finally, as more studies attempting to reveal the anti-tumor mechanisms of TTFields, combinatory treatment regimens are also under consistent investigation 46 . The upcoming studies could be focused on answering these questions.
The design of current TTFields that are applied in the clinic warrants further optimization, including better temperature control of the electrodes, performing SR surgery to enhance TTFields, and managing peritumoral edema to minimize its blocking effects. The devices also warrant further optimizing so that they can be lighter to carry, have implantable generators and electrodes, and be more durable in usage. Predictive factors from serum biomarkers and imaging markers are also required, and more combinatory regimens to augment TTFields should be further explored.

Conclusion
This research established the simpli ed MTL model and RH model through FEM analysis to simulate the process of SR surgery. This was the rst research to propose the possibility of utilizing high-conductivity material like titanium in cranioplasty surgery to facilitate TTFields, but the results still needed to be further validated in terms of safety and applicability. Also, skull thinning and drilling could both enhance the electric eld intensity in the peritumoral region. The larger number and area of burr holes could elevate the API. Future studies should be more focused on the clinical optimization of TTFields, including speci cally altering the conductivity of skull and brain tissue, reducing thermal effects of electrodes, optimizing the clinical evaluation of patients treated with TTFields, and exploring more potentials in combinatory therapies. The scheme of constructing the MTL model. A. The patient's MRI data was measured for the design of MTL model. B. MTL model was constructed based on the patient's imaging data, and tumor was planted parallel to the center of TTFields array Figure 2 The establishment of head and brain tumor model by the nite element methods. MRI data was collected and extracted. Head model was constructed by SimNIBS and TTFields array was placed at the speci c sites. Then the head model was further optimized and smoothened. Skull remodeling was simulated in different con gurations accordingly, and tumor was implanted parallel to the center of TTFields array. Abbreviation: FEM, nite element methods; MRI, magnetic resonance imaging. The size of single burr hole replaced by different material in uenced the peritumoral eld intensity. A. The simulated MTL model, where the different color pattern represents the distribution of the electrical intensity (red means higher intensity and blue means lower intensity). B. The change in API as altering the planted material and the size of the burr hole, where the titanium was superior in TTFields enhancement.

Figure 5
The implantation of bio-compatible materials and the pattern of the burr holes in uenced the peritumoral eld intensity The skull drilling of a single hole compared to nine holes, and cranioplasty with different planted material were simulated in the RH model. In both drilling patterns, the connective tissue ranked the highest in TTFields enhancement, followed by CSF, the titanium, autologous bone, and PEEK. And nine burr holes in an array offered more enhancement to API, compared to a single burr hole in all models.

Figure 6
Potential perspective of TTFields optimization The design of current TTFields that are applied in the clinic warrants further optimization, including better temperature control of the electrodes, performing SR surgery to enhance TTFields, and managing peritumoral edema to minimize its blocking effects. The devices also warrant further optimizing so that they can be lighter to carry, have implantable generators and electrodes, and be more durable in usage. Predictive factors from serum biomarkers and imaging markers are also required, and more combinatory regimens to augment TTFields should be further explored.

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