As an emerging neuromodulation technique, transcranial direct current stimulation (tDCS) has been shown to have therapeutic effects for a wide range of neurological disorders such as major depression (Bikson et al., 2008), epilepsy (Fregni et al., 2006b; Auvichayapat et al., 2013), Parkinson’s disease (Fregni et al., 2006a), chronic pain (Fregni et al., 2007), and stroke (Meinzer et al., 2016). It is shown that tDCS has the potential to promote motor recovery and improve cognitive functions after traumatic brain injury (TBI) (Kim et al., 2019; Schwertfeger et al., 2023; Ziesel et al., 2023). High-definition (HD) tDCS leverages several small disc electrodes (~6 mm radius) to achieve better focality compared to conventional pad electrodes (Datta et al., 2009). We have previously developed algorithms to optimally guide electrode placement so that a specific brain region can be stimulated with HD-tDCS with either maximal intensity or maximal focality (Dmochowski et al., 2011; Huang et al., 2018). However, all these studies are based on intact skulls. Skull defects and use of skull plates can significantly alter the injected electric current, as shown in previous computational studies (Datta et al., 2010; Sun et al., 2021). To the best of our knowledge, there is still no data reported in the literature that shows if we can efficiently stimulate brain regions below the skull defects or skull plates by optimizing the electrode montages. This is important for patients with TBI as they usually have defects in their skull (also known as the decompressive craniectomy), and tDCS has shown benefits to recovery after TBI (Kim et al., 2019; Schwertfeger et al., 2023; Ziesel et al., 2023). In this study, we aim to computationally investigate how skull defects or plates affect the current flow induced by optimized HD-tDCS. Specifically, we built a realistic, high-resolution computational model following previous methodology (Huang et al., 2019). To find out how different sizes and electrical conductivities of skull defects / plates affect the patterns of current flow, we altered the original model of normal anatomy into four variants that modeled a larger and a smaller skull defect with different conductivities. As the most common locations of the skull defect are unilateral with an opening on the left or right hemisphere (Fatima et al., 2019; Lambride et al., 2020), we modeled the skull defect above the right primary motor cortex. We then performed optimized HD-tDCS (Dmochowski et al., 2011) targeting the right primary motor cortex and compared the achieved electric field at the target with those from an intact skull anatomy. We found that optimization always increases the stimulation at the target below the skull defects. Large skull defects reduce the stimulation intensity while small defects increase the intensity. We hope that our results will provide some general guidelines for future tDCS on patients with skull defects and skull plates.

To the best of our knowledge, this work is the first computational study to compare optimized HD-tDCS with conventional electrode montages on a head model with a skull defect. Existing work in the literature mostly focus on how the forward models of electroencephalogram (EEG) is affected by skull defects (Lau et al., 2016), skull segmentation (Lanfer et al., 2012), skull conductivity (Antonakakis et al., 2019b), and skull suture (McCann and Beltrachini, 2022). The only work we found that studied how skull defects affect optimized tDCS is Antonakakis et al. (2019a), but it only looked at small burr holes on the skull instead of skull plates. Our previous work (Datta et al., 2010) studied how skull defects affect the current flow but did not compare between un-optimized and optimized montage stimulating the cortex under the defect. Here we investigated how different sizes and conductivities of skull defects affect the current flow on the cortex beneath the defects, for both un-optimized and optimized stimulation. We found that large defects with titanium or acrylic plates significantly reduces the electric current reaching the target area beneath the defect by about 80%, while small defects with CSF or scar tissue significantly increases the stimulation by about 200%. Optimization always increases the stimulation intensities at the target area, no matter if the skull has a defect or not, even though this increase is not significant when a large defect with titanium plate or a small defect with scar tissue is present on the skull.

From the safety standpoint, the increase in electric field by 200% does not raise any potential theoretical safety issue. Using epicranial electrode stimulation in rats, Liebetanz and colleagues demonstrated that the threshold for tissue damage is at least two orders of magnitude away from the scalp charge density applied in humans (Liebetanz et al., 2009). Further, one may expect similar electric field deviation even in intact anatomy across individual heads (Datta et al., 2012). If the study objective requires maintaining the same electric field magnitude, a simple abating strategy would be to reduce the scalp injected current in proportion to the increase. Finally, optimized HD-tDCS has already been safely delivered to stroke subjects including cases where the cortical electric field was found to triple in comparison to conventional tDCS delivery (Dmochowski et al., 2013; Richardson et al., 2015).

To address the 80% decrement, a compelling clinical strategy would be to increase the scalp injected current. Higher intensity tDCS (i.e., delivery of 3–4 mA scalp current) has been recently shown to be safe (Workman et al., 2020; Hsu et al., 2023). While doubling the scalp intensity would only cover for the 50% decrement, what is clear is that scaling scalp current offers an option to get closer to what may be considered as “efficacious dose.” Ultimately, clinicians would have to make the decision based on the potential risk–benefit, as tDCS may be one of the few interventions available considering the high vulnerability of patients with skull defects and plates.

Note that the strategies above are only general guidelines on tDCS on patients with skull defects or plates, as they are only based on the results from the single subject model we obtained here. Future modeling studies leveraging individualized geometry of the skull defects/plates obtained from patients MRI and CT scans will be needed to further provide personalized guidelines and plans on improving the outcomes from tDCS therapy.

Besides the average of 0.3 V/m increase of stimulation intensities at the target compared to un-optimized montages, the utility of optimization is best exemplified by targeting a region directly under the large skull acrylic plate. In general, the very low conductivity of acrylic makes it difficult to deliver meaningful electric field intensity directly underneath the plate (Datta et al., 2010). However, using optimized HD-tDCS, we are able to obtain ~0.18 V/m and as mentioned above, potentially deliver an efficacious dose by a simple scaling of scalp current. This is in stark contrast to the traditional montages, where the very low induced target electric field makes pursuing them unworthy.

There are some limitations of this work. First, we only modeled the skull defect at one single location which is mostly motivated by the clinical scenario (Fatima et al., 2019; Lambride et al., 2020). However, the same physics and optimization algorithm apply to defects at other locations on the skull. Second, we simplified the shape of the defect, while in reality the defect could have a complicated shape. Future work will collect image data from patients with skull defects to model the actual geometry of skull defects. Third, only one individual head was modeled. Considering inter-individual variability, future work will repeat the modeling process on more heads with skull defects to confirm if the results are replicable on other individual heads. Lastly, all the results were obtained from computational models, which need to be confirmed by experimental measurements following previous methodology (Huang et al., 2017).

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

AG contributes to build the initial head model and draft of the manuscript. DT contributes to build the initial head model and editing of the manuscript. AD contributes to the concept of this work, and editing of the manuscript. YH contributes to the concept of this work, implementation of the model optimization, analysis of results, and editing of the manuscript. All authors contributed to the article and approved the submitted version.