The BG are a sub-cortical complex that consists of several nuclei, such as the subthalamic nucleus (STN) and the globus pallidus (Soghomonian and Jagaroo, 2016). Due to different synaptic projections, the latter is divided into internal (GPi) and external segments (GPe). The BG play an important role in decision-making, motor control, and motor learning. Several neurological disorders are associated with abnormal BG activity, such as excessive synchronization in Parkinson's disease, and alternations in synaptic connectivity (Hammond et al., 2007; Madadi Asl et al., 2022b). The STN and GPe circuit is in the center of the BG and is believed to be critical for the generation of oscillations (Plenz and Kital, 1999; Bevan et al., 2002; Crompe et al., 2020). Furthermore, the STN is a major target for high-frequency deep brain stimulation, the current standard of care for medically refractory Parkinson's disease (Krack et al., 2003).

The STN receives topographically organized glutamatergic inputs from the cerebral cortex via the cortico-STN hyperdirect pathway, and gamma-aminobutyric acid (GABA)ergic inputs from the GPe via the cortico-striato-GPe-STN indirect pathway (see Figure 1) (Jeon et al., 2022). Additionally, synaptic input to the BG nuclei is organized somatotopically (Nambu, 2011), i.e., motor cortical neurons in regions representing different body parts project to different regions in these nuclei (Monakow et al., 1978; Nambu et al., 1996, 2002; Miyachi et al., 2006). On the other hand, BG neurons respond to motor cortex stimulation (Nambu et al., 2000; Kita and Kita, 2011; Polyakova et al., 2020) and to active and passive movement of corresponding body parts (DeLong et al., 1985). These characteristics are harnessed during stereotaxic surgery for electrode placement for deep brain stimulation as a treatment for movement disorders such as Parkinson's disease (Kaplitt et al., 2003; Krack et al., 2003).

Experimental studies in primates and rodents analyzed the response of STN and GPe neurons to electrical stimulation of different cortical areas, including the limb regions of the motor cortex, the primary sensory cortex, and the supplementary motor area (Nambu et al., 2000; Kita et al., 2004; Kita and Kita, 2011; Polyakova et al., 2020). The effect of local injections of glutamate and GABA antagonists into the STN (Polyakova et al., 2020), the GPe (Kita et al., 2004) as well as into the putamen and the GPe (Polyakova et al., 2020) on evoked responses was studied to get further insight into the involved pathways (Kita et al., 2004; Jaeger and Kita, 2011; Polyakova et al., 2020). Responding STN neurons showed complex response patterns characterized by an early and a late excitation followed by a late inhibition. These patterns indicated that signals from the stimulated cortical region reach STN neurons via two pathways: the monosynaptic cortico-STN pathway and the polysynaptic cortico-striato-GPe-STN pathway (Nambu et al., 2000; Kita and Kita, 2011; Polyakova et al., 2020). Furthermore, responding GPe neurons show characteristic responses consisting of an early excitation, an inhibition, and a late excitation (Nambu et al., 2000; Jaeger and Kita, 2011; Kita and Kita, 2011). The analysis of these evoked responses revealed the complex interplay of synaptic pathways in the cortico-basal ganglia circuit.

Evidence from animal models suggests that Parkinson's disease is not only accompanied by abnormal neuronal synchrony (Hammond et al., 2007) but also by alterations of synaptic connectivity in the BG (Fan et al., 2012; Chu et al., 2015, 2017; Madadi Asl et al., 2022b) and impaired somatotopy (Filion et al., 1988; Boraud et al., 2000; Cho et al., 2002). Furthermore, characteristic features of cortically evoked responses change in 6-hydroxydopamine (6-OHDA) lesioned rats, an animal model for Parkinson's disease (Kita and Kita, 2011). Besides Parkinson's disease, abnormal alterations of the somatotopic organization of the BG and their cortical inputs have been observed in other movement disorders (Bronfeld and Bar-Gad, 2011), such as motor tics (McCairn et al., 2009), appearing as a symptom, for instance, in Tourette syndrome, and dystonia (Tamburin et al., 2002; Delmaire et al., 2005). This suggests that alterations of synaptic connectivity shape cortically evoked responses, and likely affect the processing of cortical stimuli.

In the present paper, we build on these results and explore to which extent cortically evoked responses of STN and GPe neurons can be used to infer characteristics of the underlying synaptic network structure. In a computational model, we show that a characteristic width of parallel “functional channels” in the BG, which allow for parallel processing of multiple stimulation-induced cortical inputs, can be obtained based on the cortically evoked responses of STN and GPe neurons. Considering the underlying channel structure may be advantageous for the parameter adjustment and stimulation contact usage during multisite deep brain stimulation, for instance, for the delivery of coordinated reset stimulation in animal models for Parkinson's disease (Tass et al., 2012; Wang et al., 2016, 2022; Bore et al., 2022) or Parkinson's disease patients (Adamchic et al., 2014).

To study the relation between synaptic connectivity and cortically evoked responses, we developed a computational model of the BG that incorporates a simplified type of somatotopy (Nambu, 2011), where neurons tend to project to neurons that represent similar body parts characterized by similar (spatial) coordinates, as well as two modified somatotopy variants. Our model produces cortically evoked responses that mimic experimental data from rats (Kita and Kita, 2011). We analyzed the spatio-temporal pattern of cortically evoked responses and explored how it is affected by perturbations of the synaptic network structure. To quantify the width of parallel functional channels in the BG, we suggest a two-site stimulation approach in which two cortical stimuli cause two evoked responses in the STN and GPe. We quantify the modulation of the evoked response to a test stimulus by the presence of a priming stimulus and show how an approximate channel width can be inferred. The latter measures the minimum distance between cortical areas whose input to the BG is processed independently.

The present paper is organized as follows. First, we introduce our computational model and present details on the incorporated experimental data on synaptic connectivity as well as the suggested two-site stimulation technique. Next, we show that our computational model reproduces the experimentally observed characteristic sequence of excitations and inhibitions. Then, we analyze the spatio-temporal response pattern and study how it is affected by variations of the synaptic network structure. We present simulation results on evoked responses of STN and GPe neurons during two-site cortical stimulation and show how an estimate of the width of functional channels in the cortico-BG network can be obtained. Finally, we discuss our results.

We developed a computational model of the STN-GPe circuit that accounts for topographically organized synaptic connections. Following earlier studies, individual neurons were modeled by adaptive quadratic integrated-and-fire neurons to ensure low computational costs (Lindahl et al., 2013; Fountas and Shanahan, 2017). The organization of synaptic connections was partly motivated by earlier computational studies (Terman et al., 2002; Hahn and McIntyre, 2010; Kumaravelu et al., 2016), partly based on experimental data on the synaptic connectivity in the STN-GPe circuit (Oorschot, 1996; Sadek et al., 2007; Baufreton et al., 2009; Kita and Kita, 2011; Koshimizu et al., 2013; Ketzef and Silberberg, 2021), and partly obtained from parameter optimization to reproduce experimentally observed mean firing rates of the neurons (Fountas and Shanahan, 2017). Note that firing rates of BG neurons in rats vary depending on the state, e.g., awake, anesthetized, resting. Whenever possible, we considered the data from Kita and Kita (2011) in anesthetized rats, as they provide a detailed analysis of cortically evoked responses.

Responses of STN and GPe neurons evoked by cortical stimulation were studied in monkeys (Nambu et al., 2000; Kita et al., 2004; Polyakova et al., 2020) and in rodents (Kita and Kita, 2011). Electrical stimuli were delivered to the motor cortex (Nambu et al., 2000; Kita et al., 2004; Kita and Kita, 2011; Polyakova et al., 2020) and the primary sensory cortex (Nambu et al., 2000) and PSTHs of responding STN and GPe neurons were recorded.

Responses of STN neurons showed an early and a late excitation followed by a long inhibition, whereas responses of GPe neurons showed an early excitation, an inhibition, and a late excitation. These characteristics were observed in rodents and in monkeys. Combining cortical stimulation with local drug injection, experiments in monkeys revealed that these characteristic features result from the interplay of two pathways: the cortico-STN glutamatergic hyperdirect pathway and the cortico-striato-GPe-STN indirect pathway (Kita et al., 2004; Kita, 2007; Jaeger and Kita, 2011; Polyakova et al., 2020).

Using our computational model, we explored how the characteristics of motor cortical stimulation-evoked responses depend on synaptic network connectivity. To this end, we mimicked the experimental setup in our computational model and studied PSTHs of STN and GPe neurons. We delivered cortical stimulation (Model and methods). Cortical stimuli were centered at s^CTX = 0, if not mentioned otherwise.

Cortically evoked responses of STN and GPe neurons exhibit characteristic sequences of excitations and inhibitions that were observed in rodents (Kita and Kita, 2011) and primates (Nambu et al., 2000; Kita, 2007; Jaeger and Kita, 2011; Polyakova et al., 2020). We developed a computational model of the STN-GPe circuit that reproduced these response characteristics and related them to aspects of the topology of synaptic connections. Furthermore, we presented a one- and a two-site stimulation technique to quantify the width of functional channels in the BG network. Our results suggest that details of the synaptic connectivity are critical for the processing of cortical signals. They further support the use of computational models that include synaptic connectivity that is derived from experimental findings rather than random connections. The presented one- and two-site stimulation protocols enable probing of connectivity patterns in preclinical experiments. Based on our computational results on the effect of alterations of network connectivity on cortically-evoked responses, one may design preclinical experiments to falsify or verify our predictions. With such a combined computational and experimental approach, one may reveal further characteristics of synaptic connectivity in the BG and may identify patterns of synaptic reorganization in neurological diseases, e.g., Parkinson's disease.

The characteristic pattern of excitations and inhibitions in cortically evoked responses of STN and GPe neurons was studied experimentally (Nambu et al., 2000; Kita et al., 2004; Kita, 2007; Kita and Kita, 2011; Polyakova et al., 2020). Cortical stimulation triggered characteristic responses of STN neurons that consisted of an early excitation and a late excitation, which were separated by a gap, and a long, late inhibition (Nambu et al., 2000; Polyakova et al., 2020). In GPe neurons, responses showed an early excitation that was followed by an inhibition and a late excitation (Nambu et al., 2000; Kita, 2007; Jaeger and Kita, 2011). These features were well reproduced by our computational model (Figure 3).

Polyakova et al. (2020) found that local injection of glutamate receptor antagonists into the STN diminished the early excitation, and that the injection of muscimol (a GABA receptor agonist) into the striatum or the GPe diminished the late excitation. Their results supported the suggestions of earlier studies that the early excitation in the evoked response of STN neurons is caused by glutamatergic input via the cortico-STN hyperdirect pathway and the late excitation results from disinhibition due to GABAergic input via the cortico-striato-GPe-STN indirect pathway (Nambu et al., 2000). In our computational model, we modeled these experiments by cutting glutamate inputs to single STN neurons (to mimic the local injection of glutamate receptor antagonists) and by cutting inhibitory inputs to STN neurons (to mimic the local injection of GABA antagonists) (Figure 4). In accordance with Polyakova et al. (2020) we observed a suppression of the early excitation in the former case (Figure 4A) and a suppression of the late excitation in the latter case (Figure 4C). However, in our computational model, the latter case also led to damped beta oscillations in the instantaneous firing rate of STN neurons (Figure 4C). Such damped oscillations were not reported by Polyakova et al. (2020). However, Polyakova et al. reported high variability in the amplitude of the early and late excitations in the responses of STN neurons after local injection of a GABA antagonist. In our computational model, cutting GPe inputs to STN neurons destabilized the characteristic response pattern of excitations and inhibitions in both responding STN and GPe neurons (Figures 4C, D). A similar destabilizing effect may occur in the experiments and may cause high variability of the amplitudes of excitations among responding STN neurons (Polyakova et al., 2020). Together, these findings suggest that the GPe → STN connections are critical for the GPe-STN network to process cortical input and stabilize baseline activity. The results from our computational model further suggest that cutting STR MSN inputs to single GPe neurons would diminish the inhibition in the GPe neurons' responses (Figure 4F) and also reduce the amplitude of the late excitation in the evoked response of STN neurons (Figure 4E). These results are in accordance with other experiments by Polyakova et al. (2020) in which the injection of muscimol into the putamen reduced the amplitude of the second excitation in STN neurons substantially. Our results on the effect of cutting STR MSN inputs to GPe neurons are also in line with the experimental results of Kita et al. (2004); however, Kita et al. injected a GABA antagonist locally into the GPe, which also reduced GABAergic input from other GPe neurons and not only STR MSN input. In our computational model, only STR MSN inputs were cut, which resulted in a substantial weakening of the inhibition in the response of GPe neurons (Figure 4F). Furthermore, our computational results suggest that the late excitation in the GPe may be partly due to excitatory input from the STN and partly due to disinhibition after striatal inhibition. This is in accordance with previous results by Kita and colleagues (Kita et al., 2004; Kita, 2007).

The variability of the STN and GPe neurons' baseline firing rates contributed to the variability of single-neuron responses to cortical stimuli in our computational model. In more detail, the characteristic features of neuronal responses were most pronounced among neurons with high baseline activity (see Figures 5, 7). Unfortunately, it is difficult to compare the responses of STN or GPe neurons with low mean firing rates to cortical stimuli to experimental data, because such neurons were often excluded from the analysis in experimental studies (Kita et al., 2004; Kita and Kita, 2011; Polyakova et al., 2020).

N-networks and S-networks resulted in unimodal distributions of single-neuron mean firing rates for STN and GPe neurons (Figure 6). In contrast, in D-networks, baseline firing rates of GPe neurons showed a multimodal distribution (Figure 6B). The shapes of these distributions obtained from our computational model reproduced experimental data for STN neurons as observed in studies in rat brain slices qualitatively; a histogram of single-neuron firing rates of tonically spiking STN neurons in rat brain slices can be found in Beurrier et al. (1999). However, the mean firing rate in that study was higher than in our model, as our model was fitted to experimental data from anesthetized rats presented in Kita and Kita (2011). A histogram of single-neuron mean firing rates of GPe neurons can be found in Figure 8B of Miguelez et al. (2012). There, a significant portion of GPe neurons did not spike (≈25% in Miguelez et al., 2012), and the broad distribution of single-neuron mean firing rates of GPe neurons suggests high variability of single-neuron mean firing rates. In our model, GPe neurons with a small number of incoming STN connections possessed very low firing rates (Figure 6B). High variability of single-neuron mean firing rates occurred due to variability in the number of incoming STN → GPe connections, which was only realized in D-networks for a small number of STN → GPe connections, N^{STN, GPe} = 3. For the latter, individual connections were substantially stronger than for N^{STN, GPe} = 30 because parameters were adjusted to fit the STN and GPe firing rates to experimental data (Figure 5B). The random displacement of connections in D-networks led to broader distributions of single-neuron mean firing rates in D-networks than in N-networks or in S-networks.

Our results suggest that cortical stimulation results in complex spatio-temporal response patterns in the STN and GPe. These patterns result from the propagation of signals along the cortico-STN hyperdirect pathway and along the cortico-striato-GPe-STN indirect pathway (Figure 1B), and the convergence of these pathways onto the same regions in the STN and the GPe. In our computational model, these patterns strongly depended on the underlying structure of synaptic connections (Figure 7). Evidence from animal models suggests that the synaptic network structure in the BG nuclei is impaired in the dopamine-depleted state in animal models for Parkinson's disease (Fan et al., 2012; Miguelez et al., 2012; Chu et al., 2015; Pamukcu et al., 2020). Modulation of evoked responses of individual BG neurons in the dopamine-depleted state has been reported and analyzed by Kita and Kita (2011) in a rodent model for Parkinson's disease. The authors observed that the characteristic patterns of excitations and inhibitions were strongly affected by dopamine depletion. Our results suggest that dopamine depletion may also affect the spatio-temporal pattern of evoked responses and affect the structure of parallel functional channels in the BG.

In the present paper, we studied three types of networks: a base case with an intact functional channel structure and two cases in which this structure was perturbed. In the base case, neurons projected to neurons expressing similar features. This was realized in N-networks by connecting neurons with similar (spatial) coordinates s^X (Figure 1C1). This mimicked an intact somatotopic organization of synaptic connections (Nambu, 2011) and precise reciprocal loops between STN and GPe (Kita, 2007). In addition, we considered two types of altered network structures: First, in D-networks a shift in synaptic connectivity was induced for a fraction of the neurons such that they would connect to neurons with shifted (spatial) coordinates s^X+d (Figure 1C2). Second, in S-networks, neurons projected to an enlarged area in the postsynaptic nucleus such that neurons with less similar coordinates were also targeted (Figure 1C3). The described changes in the network structure had a strong impact on cortically evoked spatio-temporal responses of STN and GPe neurons. While cortical stimulation in N-networks only triggered responses of neurons with similar coordinates, a second neuronal population expressing different features responded in D-networks. Interpreting these results, stimulation or activation of a cortical region corresponding to a certain body part or motor program would also activate neuronal populations representing different body parts or motor programs in D-networks. Such a perturbation of the BG structure may lead to the inability to activate these body parts independently. In contrast, in S-networks, cortical stimuli triggered less pronounced responses but of a bigger neuronal population. Such an alteration of the BG structure may correspond to less coordinated motor movements in response to cortical activation. Evidence from animal models suggests that a reorganization of network connectivity emerges in several BG related movement disorders, e.g., Parkinson's disease (Bronfeld and Bar-Gad, 2011). Experimental studies in the MPTP monkey model suggest that both types of impairment, i.e., responses to different body parts (D-network) and broadening of the projection region (S-network), may occur in the BG in Parkinson's disease. Boraud et al. (2000) reported that, under normal conditions, arm- and leg-related GPi neurons occurred in clusters and were linked to a single joint. In contrast, in the MPTP monkey model for Parkinson's disease, the overall number of responding neurons increased, and most responding neurons were linked to multiple joints (Boraud et al., 2000). Filion et al. (1988) reported that in MPTP monkeys, more globus pallidus neurons responded to the movement of a certain body part. Also, neuronal responses were elicited by the movement of more than one joint and by movements in different directions. Furthermore, some neurons responded to the movement of both upper and lower limbs on both the ipsi- and the contralateral sides. In contrast, in healthy animals, responses were only caused by the movement of a single joint on the contralateral side and in one direction (Filion et al., 1988). In rats, Cho et al. (2002) analyzed the reorganization in the lateral striatum (sensorimotor striatum) following 6-OHDA lesion. In controls, STR neurons that responded to the same body part were organized in clusters. However, after 6-OHDA lesion, the cluster size was reduced, and the portion of STR neurons that responded to more than one body part increased by a factor of 16 (Cho et al., 2002). These findings supported a hypothesis advanced by Mink (1996) that the BG's primary role may be the focused selection of the “correct” motor program and inhibition of competing ones. Synaptic reorganization in disorders such as Parkinson's disease would diminish action selection and cause motor symptoms.

Of particular interest for further analysis of the synaptic network structure of the BG would be to measure aspects of the synaptic connectivity in experiments. In earlier studies, the organization of cortico-STN connections was analyzed in tracer studies in monkeys (Monakow et al., 1978; Nambu et al., 1996). Furthermore, in Jeon et al. (2022), neuroanatomical techniques were used to construct 3D connectivity maps in mice and compare them to results from 7T MRI and tractography studies in humans. In the present study, we suggested a two-site stimulation protocol in which a test and a priming stimulus are delivered to two cortical stimulation sites at a certain distance and with a certain inter-stimulus interval. Analyzing how the priming stimulus influences the response of neurons to the test stimulus, we found that if the priming stimulus is applied long (>100 ms) before the test stimulus, varying the spatial distance between cortical stimulation sites yields an approximate “channel width,” characterizing the width of the cortical area in which stimulation activates the considered area in the STN or GPe (Figures 9A, C). This method may be used to analyze the spatial characteristics of the somatotopic organization in the BG. To realize two-site stimulation in an experiment, the response of single BG neurons to cortical stimuli would be measured, similar to the experiments performed by Nambu et al. (2000); Kita et al. (2004); Jaeger and Kita (2011); Kita and Kita (2011); and Polyakova et al. (2020). Then a priming stimulus would be administered with a time lag Δt and at a distance Δs from the original, test stimulus. Measuring the BG neuron's PSTH for a long sequence of stimuli and comparing it to the one in the absence of the priming stimulus yields estimates of the quantities Lbasex(Δt,Δs) and Lrex(Δt,Δs). Evaluating, these quantities for different Δt and Δs yields similar data as the one shown in Figure 9 for each responding BG neuron.

The presented two-site stimulation protocol also allowed us to measure the displacement of synaptic connections in D-networks. In these networks, neurons in the considered region of the STN or GPe responded to stimulation of two distinct cortical regions (Figures 9E–H). Our computational results suggest that this method is most sensitive when the modulation of the evoked response of STN neurons by an earlier cortical stimulus rather than the modulation of their baseline activity is considered (Figures 9B, F, J), in particular for an inter-stimulus interval of about 30 − 40 ms. This time interval may be affected by synaptic transmission delays and needs to be verified experimentally. In our computational model, an approximate of the width of functional channels was also obtained if the modulation of the baseline activity of STN or GPe neurons by the presence of the cortical priming stimulus was studied (Figures 9A, E, I). This approach may also be realized by applying only one cortical stimulus and studying variations of neuronal activity from their baseline activity. However, the baseline activity may vary over time, whereas evoked responses possess characteristic features. In general, two-site stimulation may help to get a deeper understanding of the topology of synaptic connections in the BG, the somatotopic organization of the cortico-BG circuits, and to which extent this structure is impaired in animal models of neurological disorders, e.g., Parkinson's disease.

More detailed information on the organization of synaptic connections could inform future computational models. Current computational models often either consider random connectivity between nuclei, e.g., Lindahl et al. (2013); Ebert et al. (2014); Madadi Asl et al. (2022a); Adam et al. (2022); Salehi et al. (2023), or they incorporate parallel channels either by considering macroscopic parallel circuits of randomly connected subpopulations, e.g., Leblois et al. (2006); Fountas and Shanahan (2017), or by constructing parallel channels on the scale of the individual neurons, e.g., Terman et al. (2002); Hahn and McIntyre (2010); Lourens et al. (2015). The latter is somewhat comparable to the synaptic connectivity used in the present study. Our results suggest that differences in the organization of synaptic connections in computational models strongly impact cortically evoked responses and likely affect other characteristics of neuronal activity, such as synchronization or the existence of pathological oscillations. An accurate implementation of synaptic connections may be critical for generating clinically relevant hypotheses, e.g., about the response to brain stimulation.

Recently, Schmidt et al. (2020) related the shape of deep brain stimulation-evoked potentials to the involved pathways. While no information on somatotopic maps was revealed, the authors suggested that the shape of deep brain stimulation-evoked potentials may serve as a biomarker for adaptive deep brain stimulation, or may guide parameter selection and electrodes placement for deep brain stimulation in Parkinson's disease (Schmidt et al., 2020; Dale et al., 2022). Our results may motivate preclinical and clinical studies to use cortical as well as BG one- or two-site stimulation to analyze the spatial arrangement of synaptic connections between BG nuclei. Such insight may help to improve computational models of the BG and models on high-frequency deep brain stimulation as a treatment for medically refractory Parkinson's disease significantly.

To reduce complexity, we did not consider some aspects of the STN and GPe nuclei during the derivation of our computational model. For instance, recent experimental studies reported the existence of multiple neuron types with distinct functionality in the STN (Jeon et al., 2022) and the GPe (Mallet et al., 2012; Abdi et al., 2015; Mastro et al., 2017), which may affect network functionality such as the processing of cortical responses and rhythm generation (Suryanarayana et al., 2019; Gast et al., 2021). Neuron types in the GPe include prototypic neurons and arkypallidal neurons (Mallet et al., 2012; Abdi et al., 2015). While prototypic neurons have been found to project mainly to the STN and down-stream nuclei, arkypallidal neurons project to the striatum thereby providing feedback to this upstream nucleus. Anatomical studies also reported projections of STN neurons to the striatum (Beckstead, 1983; Kita and Kitai, 1987). Here, we neglected upstream synaptic connections of the STN-GPe circuit and focused on the most common neuron type in the GPe, i.e., prototypic neurons. There is also evidence from anatomical studies that STN neurons form local axon collaterals suggesting recurrent STN connections (Hammond and Yelnik, 1983; Gouty-Colomer et al., 2018); However, recent studies performing simultaneous multi-cell recordings in rat brain slices reported the absence of functional intra-STN connectivity (Steiner et al., 2019). Therefore, we did not consider synaptic connections between STN neurons in our computational model. Another simplification is the assumption of a one-dimensional arrangement of the neurons along the s^X-axes. The STN and GPe are three-dimensional structures and evidence from experimental studies suggests non-homogeneous synaptic connectivity along different directions. For instance, STN axons form band-like terminal fields in the globus pallidus that are aligned with those of striatal axons (Hazrati and Parent, 1992). This would likely impact spatio-temporal characteristics of cortically evoked responses and the orientation of functional channels. Furthermore, the somatotopic organization of STN and GPe nuclei are more complex. For instance it includes multiple body maps for inputs from the primary motor cortex and the supplementary motor area, respectively (Nambu, 2011). Some experimental evidence also suggests that within regions that represent a certain body part neurons encoding similar motor features are sometimes spread out across a larger area instead of clustering together (DeLong et al., 1985). Further studies are required to understand how these factors impact the spatio-temporal response patterns evoked by cortical stimulation studied in the present paper.

As explained above, the functional channels used in this study are related to the impact, specifically spatial range and coverage of electrical stimuli on parts of brain circuits (see Figure 2). These functional channels are not meant to be building blocks of a neural code as, e.g., activity sequences corresponding to sub-second behavioral motifs (Markowitz et al., 2018). However, disease-related changes as reflected by the width of these functional channels may impact behaviorally relevant activity sequences. Accordingly, functional channels may help elucidate neuronal information processing under physiological as well as pathological conditions.

In a future study, we want to address how characteristic measures, such as the width of functional channels, can be harnessed to calibrate multisite deep brain stimulation, for instance, coordinated reset stimulation (Tass, 2003; Tass et al., 2012; Adamchic et al., 2014; Wang et al., 2016, 2022; Bore et al., 2022), random reset stimulation (Kromer and Tass, 2020; Khaledi-Nasab et al., 2021a), and other multisite stimulation protocols (Khaledi-Nasab et al., 2021b, 2022; Weerasinghe et al., 2021; Kromer and Tass, 2022) for improving desynchronizing effects, especially in the presence of reorganized somatotopic maps. In computational studies, the desynchronization effect of coordinated reset stimulation was more pronounced when individual stimuli were delivered to segregated neuronal subpopulations (Popovych and Tass, 2012; Lysyansky et al., 2013; Ebert et al., 2014; Zeitler and Tass, 2015) suggesting that effective stimulation requires appropriate spacing of stimulation sites, e.g., minimal distances between the latter. This is in accordances with results from preclinical studies on coordinated reset deep brain stimulation in the MPTP monkey model, where weaker stimulation led to more pronounced long-lasting effects (Tass et al., 2012), and findings obtained in a clinical study on acoustic coordinated reset stimulation in tinnitus patients, where larger gaps between stimulus frequencies were correlated with better acute reduction of tinnitus loudness and annoyance after 16 min of sound treatment (Tass et al., 2019; Munjal et al., 2021). Future computational and pre-clinical studies might use the functional channel width, as introduced here, to determine optimal stimulation site spacing.

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

JK, HB, and PT conceived the idea and designed the study, analyzed and interpreted the numerical data, and revised and finalized the manuscript. JK performed the numerical simulations and prepared the initial draft. All authors contributed to the article and approved the submitted version.