Localizing Beta Synchronous Neurons in the STN Using Directional DBS Recordings and Patient-Specific Biophysical Models

Abstract

Objective:

Local field potentials (LFPs) exhibit abnormally elevated beta-band power in the subthalamic nucleus (STN) of patients with Parkinson’s disease (PD). To better understand these signals, we coupled advanced biophysical models with experimental LFP recordings to characterize the neural sources underlying beta oscillations in PD patients.

Methods:

Patient-specific biophysical models simulated LFPs with detailed representation of the directional DBS electrodes in the local neuroanatomy, as well as the ionic currents generated by STN neural activity. We then used the models to perform source localization of a beta synchronous volume of STN neurons in each patient. We also compared the utility of various referencing schemes for source localization.

Results:

The beta synchronous volumes typically localized to the posterior STN. We also identified a novel vertical-directional bipolar referencing scheme that demonstrated superior source localization.

Conclusions:

Our results support the hypothesis that beta synchronous STN neurons cluster into distinct focal areas, as opposed to being uniformly distributed throughout the nucleus.

Significance:

This proof-of-concept study demonstrates that patient-specific models characterizing the spatiotemporal characteristics of beta oscillations in the STN can be used to define a patient-specific target volume for DBS therapy.

Introduction

Subthalamic deep brain stimulation (DBS) improves motor symptoms and enhances quality of life in patients with Parkinson’s disease (PD) (Deuschl 2006). However, therapeutic improvements from DBS vary across individuals, and many patients still experience daily fluctuations in their motor symptoms (Deuschl & Agid 2013). Unfortunately, traditional DBS systems have lacked the capability to dynamically adjust stimulation parameters in response to these variations. As such, major research efforts over the last two decades have focused on developing DBS systems that can record local field potentials (LFPs) (Stanslaski 2018), with the goal of using those signals to guide adaptive stimulation strategies (Neumann 2023).

In PD, the subthalamic nucleus (STN) exhibits elevated spectral power in the beta frequency band (13–35 Hz) (Brown 2003). This beta signal is loosely correlated with disease severity (Neumann 2016, van Wijk 2023), and has been aggressively pursued as a biomarker to guide clinical adaptive DBS (Stanslaski 2024). However, the location, size, and consistency of the beta generating neural population within the STN remains relatively unknown.

Synchronous synaptic inputs to populations of neurons summate to generate the ionic currents responsible for the field potentials that can be measured in the brain with macroelectrodes (Jenkinson & Brown 2011). As such, we have previously used biophysical models of STN neurons to simulate LFPs recorded with DBS electrodes (Lempka & McIntyre 2013; Maling 2018; Noor & McIntyre 2021). However, those earlier modeling studies analyzed relatively brief recordings from a single canonical subject. Therefore, a major goal of this study was to apply our DBS LFP modeling methodology to multiple PD patients with goal of defining a unique beta synchronous volume in the STN of each patient that corresponded with their individual LFP recording data.

We coupled detailed patient-specific computational models with simultaneous broadband monopolar LFP recordings from 8-contact directional DBS leads. The models integrated image-based representations of the DBS electrode in each patient’s anatomy with biophysical models of the neural current sources. This framework allowed us to simulate LFPs while varying the size and position of a synchronous volume of neurons within the STN. We then identified a unique position and radius for the synchronous volume that produced simulated LFPs that matched the specific experimental recordings of each patient. We also assessed the stability of the LFP signals over time and examined how different bipolar referencing schemes influenced the model predictions.

The basic goal of this work was to use biophysical first principles, in combination with detailed anatomical models, to provide insight on the localization of beta sources within the STN of PD patients. The proof-of-concept patient-specific models also demonstrate a potential bridge between the current clinical tools of either image-guided or LFP-guided DBS programming, as the models integrate mutually beneficial aspects of both strategies. In turn, the methodological concepts of this study provide a foundation for the development of novel stimulation parameter selection algorithms that leverage modern advances clinical DBS technology.

Methods

This study utilized data from five patients with Parkinson’s disease (mean age: 66 ± 5.3 years; mean disease duration: 10.2 ± 2.6 years) who were part of an ongoing clinical study at the University of Alabama at Birmingham (NCT03343688) under an Investigational Device Exemption from the United States Food and Drug Administration (IDE# G170063). The supplementary materials provide additional information on the patient demographics (Table S1). This project was reviewed and approved by the Institutional Review Boards of both the University of Alabama at Birmingham and Duke University, and all participants provided written informed consent before engaging in any research activities.

We first acquired intraoperative LFP recordings obtained during each patient’s DBS surgery. We then used their imaging data to create patient-specific LFP models that simulated their LFPs for a range of synchronous neuron volume sizes and positions within the STN. Finally, we quantified the similarity between simulated and experimental LFPs to identify the location and volume of beta-synchronous STN neurons that best matched each patient’s experimental recordings.

Experimental LFPs

Patients were implanted unilaterally with an 8-contact directional DBS lead (Boston Scientific, DB 2202) in the brain hemisphere most impacted by their Parkinson’s disease. Targeting was guided using standard stereotactic methods, intraoperative O-arm 2 CT imaging, microelectrode recordings, and trial macrostimulation with the implanted lead (Olson 2022). Each lead was intended to be positioned such that the two middle rows of directional contacts were equidistant from the dorsal STN border (Fig. 1A), which was based on the final microelectrode recording trajectory. Intra-operative monopolar LFP signals were recorded from all 8 electrodes simultaneously for 20 to 70 seconds with the patient awake, comfortable, and at rest using a BrainVision actiCHamp system at sampling rate of 25 kHz. The distant return electrode for the recordings was placed on the scalp.

Figure 1: Subthalamic DBS LFP.

(A) Coronal T1-weighted MR image of the brain, directional DBS lead, and 3D anatomical volumes representing the subthalamic nucleus (STN —green) and thalamus (yellow). (B) Left panel shows an 8-contact directional DBS lead (DB-2202) with labeled electrodes. Middle panel: 2-second monopolar LFP recorded from contact 1 (lower trace) and a bipolar LFP from contacts 1 and 4 (upper trace). Right panel: The normalized power spectral density of the bipolar LFP in the 5–35 Hz frequency range

Our LFP model system was designed to produce an STN peak beta power at 20 Hz (Lempka & McIntyre 2013) (see details below). Therefore, we selected study subjects with similar peak beta power to maximize the applicability of their electrophysiological data for analysis with this model system. We identified 5 participants for modeling from the larger UAB sample of 29 potential subjects based on the following requirements. First, each subject had high quality pre-operative MR and post-operative CT imaging datasets without motion artifacts. Second, minimal brain shift was noted on their immediate post-operative CT scan. Third, more than 20 seconds of continuous noise-free simultaneous 8-contact LFP recordings while the patient was awake and at rest to ensure a stable power spectral density. Fourth, their peak beta power occurred around 20 ± 2 Hz. The 5 selected participants were the only patients in the sample that fulfilled all the modeling inclusion criteria. However, these strict selection criteria ensured the highest possible confidence that both the anatomical data and LFP data of the subjects were suitable to justify the detailed modeling methods employed in this study.

Data Processing

The raw LFP data were down sampled to 1 kHz and filtered using a 2nd-order bandpass Butterworth filter with cutoff frequencies of 5 and 100 Hz. Bipolar LFPs were derived by selecting electrode pairs and calculating the difference between the filtered monopolar LFPs of the two electrodes. Power spectral densities (PSDs) were computed using the Welch method (Welch 1967), log-transformed, smoothed with a 5-point moving average filter, and normalized. The area under the PSD curves within the 13–25 Hz frequency range was calculated to quantify our definition of beta activity in each patient. The LFP time series durations for each patient were as follows: P1 – 31.5 s; P2 – 67.5 s; P3 – 69.5 s; P4 – 36.5 s; and P5 – 60.5 s.

The implanted DBS leads contained 8 electrode contacts (6 segmented and 2 ring) (Fig. 1B). Bipolar recording pairs were formed between either segmented only or ring only electrode contacts, avoiding pairing between segmented and ring electrodes because of different surface areas and impedances. The level numbers 1 to 4 correspond to different contact rows along the lead, while the letters “a,” “b,” and “c” represent different directional orientations around its circumference. Contacts labeled 2a and 3a, 2b and 3b, and 2c and 3c have the same spatial orientation, with a 120-degree angle separating adjacent electrodes within the same row.

In our definition of a traditional referencing scheme (Fig. 2A), three electrode pairs were formed within each row of segmented contacts (i.e., 2a-2b, 2a-2c, 2c-2b for row 2, and 3a-3b, 3a-3c, and 3c-3b for row 3). Additionally, three pairs were formed between vertically aligned segmented contacts across the two rows (i.e., 2a-3a, 2b-3b, 2c-3c). This yielded 9 segmented electrodes pairs plus one additional pairing between the two ring electrodes (1 and 4) (10 total pairs). We designated this bipolar referencing as “traditional” because it follows the native bipolar recording functionality of the Medtronic Percept device.

Figure 2: Directional DBS LFPs.

(A) Traditional referencing scheme, illustrating electrode pairs 2a-2b and 2a-3a. Three electrode pairs are formed within each row (i.e., 2a-2b, 2a-2c, 2c-2b for row 2, and 3a-3b, 3a-3c, and 3c-3b for row 3). Additionally, three pairs are formed between vertically aligned segmented electrodes across the two rows (i.e., 2a-3a, 2b-3b, 2c-3c). (B) Normalized Power Spectral Density (PSD) of 10 bipolar LFPs from the STN of a PD patient (upper panel). The lower panel shows the area under the PSD curve in the 13–25 Hz frequency range. (C) Vertical-directional referencing scheme, illustrating an electrode pair 2a-3b. Six electrode pairs are formed between segmented electrodes (D) Normalized Power Spectral Density (PSD) of 7 bipolar LFPs obtained using vertical-directional referencing (upper panel). The lower panel shows the area under the PSD curve in the 13–25 Hz frequency range.

In a newly introduced vertical-directional referencing scheme (Fig. 2C), six pairs were formed between segmented contacts in a cross-row configuration (2a-3b, 2a-3c, 2b-3a, 2b-3c, 2c-3a, 2c-3b), providing a distinct approach to spatially resolving neural signals. Additionally, one pair was created between the two ring electrodes (1 and 4), resulting in a total of seven pairs. In this scheme, each segmented contact pair satisfied two conditions: the contacts were positioned in different rows (row 2 or 3) and were oriented in different directions. By utilizing segmented electrodes with maximum spatial separation, this scheme reduces common signal that would otherwise be cancelled if the paired electrodes were detecting the same synchronous neural source.

Simulated LFPs

We simulated the experimental LFP recordings using a patient-specific modeling system (Noor & McIntyre 2021). This system is comprised of two key components. One component was a volume conductor (VC) finite element model of the human head with a DBS lead. The other component was populations of multi-compartment cable models of individual STN neurons that simulate transmembrane current sources associated with their electrical activity. The neural source models were integrated with the VC model with a reciprocity-based solution, which enables simulation of the electrical voltage recorded at the DBS electrode contacts (Lempka & McIntyre 2013).

Volume Conductor Model

The publicly available MIDA human head model (Iacono 2015) served as the anatomical basis for our finite element VC model (Noor 2023). The VC model was created using COMSOL v5.5. The brain tissue was assigned a homogenous isotropic electrical conductivity of 0.215 S/m. Our previous methodological analyses have defined this relatively simplified VC model as the most useful balance of technical detail for STN LFP models, noting that complex tissue anisotropy and inhomogeneity factors are not relevant for these LFP simulations (Noor 2023). The location of the DBS electrode in each patient model was determined using StimVision (Noecker 2021). The post-operative CT, acquired immediately after the experimental LFP recordings, was co-registered with the pre-operative MRI to define the electrode contact locations relative to the brain anatomy. The LFP recording experiments were conducted immediately after DBS electrode implantation. In turn, the DBS VC models did not include a 0.1 mm interface layer that is typically used to mimic chronic tissue encapsulation around the implanted lead (Noor 2023).

Subthalamic Nucleus Model

The pre-operative surgical targeting T1-weighted MR image from each patient was processed in StimVision (Noecker 2021) to estimate their STN volume. The CIT168 brain atlas (Pauli 2018), which includes a model of the STN, was non-linearly warped into patient space using Advanced Normalization Tools (ANTs) (https://stnava.github.io/ANTs/). This approach for STN localization has been quantitatively validated as a highly accurate strategy for defining the borders of the STN in clinical MRI datasets from PD patients (Miller 2023). The STN atlas volumes, customized to each patient, then provided spatial boundaries to position multi-compartment cable models of STN neurons within the VC model (Fig 3A). The density and distribution of the neuron models in the STN volume were assigned to be consistent with human histological measurements (Levesque & Parent 2005) (243,320 ± 20,375 total neurons in various patients — details provided in Table S1). The STN neuron models were oriented parallel to the long axis of the nucleus (Hammond & Yelnik 1983, Yelnik & Percheron 1979).

Figure 3: Subthalamic Nucleus Model.

(A) Directional DBS lead and 3D anatomical volume representing the STN. (B) STN neuron models surrounding the lead; each STN neuron model is displayed with its complete 3D soma-dendritic architecture, with one model neuron shown in each voxel of the STN volume. (C) (i) View of a single STN neuron. (ii) Excitatory inputs theoretically originate from the cortex, while inhibitory inputs come from the GPe. (iii) Distribution of excitatory and inhibitory synapses across the soma-dendritic compartments. (D) Visualization of the distribution of ~240,000 neurons within the STN volume, with each gray dot representing an individual neuron. (E). Blue dots represent asynchronous STN neurons, while green dots indicate synchronous STN neurons. The large white dots indicate the normalized positions, ranging from 0.2 (0.0 is at the ventromedial tip of the STN) to 0.9 (1.0 at the dorsolateral tip of the STN), where the center of the beta synchronous volume could be positioned in the source localization search process.

The somatodendritic geometries of the neuron models were based on anatomical reconstructions of macaque STN neurons (Sato 2000) (Fig. 3B & C(i)). The electrical properties of the STN neurons were parameterized to mimic experimentally defined transmembrane currents and action potential firing characteristics of STN neurons (Gillies & Willshaw 2006, Miocinovic 2006). Each STN neuron model received 290 different synaptic input currents distributed over its structure (Fig. 3C(ii)) (Lempka & McIntyre 2013). The synaptic currents were intended to generically represent the thousands of synapses contributing to the neural activity of an individual STN neuron. The distal compartments received excitatory synaptic inputs, while the somatic and proximal dendritic compartments received inhibitory synaptic inputs, which were slightly delayed relative to the excitatory inputs (Baufreton 2005). Although not explicitly modeled as such, the excitatory and inhibitory synaptic inputs could be loosely considered to represent hyperdirect and pallidal input streams to STN neurons (Fig. 3C(iii)).

Each STN neuron model received unique, time varying, synaptic currents. The synaptic input models were previously parameterized to generate electrical sources that mimic beta activity in the human STN (Maling 2018). Each STN neuron in the model system received either a synchronous beta pattern of synaptic inputs or an asynchronous pattern of synaptic inputs. The beta synchronous population received synaptic inputs that were generated every 50 ms (i.e. 20 Hz) with temporal jitter randomly chosen from a normal distribution with a standard deviation of 6.25 ms. The asynchronous population received synaptic inputs at a rate randomly sampled from an exponential distribution with a mean and standard deviation of 50 ms (i.e. 20 Hz). Neurons in the beta synchronous population exhibited highly correlated activity, while neurons in the asynchronous population exhibited uncorrelated activity (Maling 2018). Consequently, the simulated LFP signals primarily result from the beta synchronous neural activity, while the asynchronous neurons primarily contribute to noise (Lempka & McIntyre 2013). The specific locations of the synchronous and asynchronous neurons within the STN volume are represented in the figures by green and blue dots, respectively (Fig. 3E).

Simulated LFP Computation

The LFP simulations were computed by coupling the VC model with the individual neural currents using a reciprocity-based approach (Lempka & McIntyre 2013). In the coupled model system, each compartment (365 compartments) of each neuron model (~240,000 neurons in each STN) was represented by an independent time-varying current source (~88M total sources) positioned at the appropriate spatial location within the VC model. The transmembrane currents from these sources generate voltages at each DBS electrode contact, which sum to create the simulated LFP signal. Differential recordings for any pair of electrodes were obtained by subtracting the voltage time series recorded at one electrode from the voltage time series recorded at the other electrode.

We computed LFPs for a range of synchronous neuron volume sizes and positions within the STN. The radius of the synchronous volume was varied from 1.0 mm to 2.8 mm in increments of 0.2 mm. The center of the synchronous volume was moved from a normalized position of 0.2 (near ventromedial corner) to 0.9 (dorsolateral corner) in steps of 0.1 (Fig. 3). LFPs were calculated for every combination of volume radius and position (8 positions × 10 radii = 80 conditions). Computations were performed on an Apple M1 Pro with 32 GB of RAM, running native MATLAB 2023b (64-bit, maca64), as well as on the Duke Computing Cluster. On the laptop, each LFP simulation took approximately 12 minutes, resulting in a total computation time of about 960 minutes (16 hours) per subject for the 80 evaluated conditions.

Model Fitness

We determined the similarity between the experimental and simulated LFPs for each patient using a fitness function. This function compared two key metrics between the experimental and simulated LFPs for each bipolar electrode pair: 1) the normalized peak-to-peak amplitudes (p2p Amp) from all bipolar LFPs, and 2) the normalized area under the PSD from all bipolar LFPs. The fitness score was the average of the amplitude fitness and PSD fitness, providing an overall measure of how well the simulated LFPs matched the experimental data.

$$\left[\text{fitness}=\frac{\text{amp}\text{fitness}+\text{psd}\text{fitness}}{2}\right]$$

where amplitude fitness was calculated as follows,

$$\left[{\text{norm}\text{Experimental}\text{p2p}\text{Amp}}_c=\frac{{\text{Experimental}\text{p2p}\text{Amp}}_c}{\underset{i=1,\dots ,7}{\text{max}}\left({\text{Experimental}\text{p2p}\text{Amp}}_i\right)}\right]$$

where the subscript c denotes one of the seven bipolar electrode pairs, with c = 1,…,7, and the subscript i in the denominator indicates that the maximum is taken over all pairs.

$$\left[{\text{norm}\text{Model}\text{p2p}\text{Amp}}_c=\frac{{\text{Model}\text{p2p}\text{Amp}}_c}{\underset{i=1,\dots ,7}{\text{max}}\left({\text{Model}\text{p2p}\text{Amp}}_i\right)}\right]$$

$$\left[{\text{Amp}\text{normalizer}}_{\text{c}}=\text{max}\left({\text{norm}\text{Experimental}\text{p2p}\text{Amp}}_{\text{c}}{,\text{norm}\text{Model}\text{p2p}\text{Amp}}_{\text{c}}\right)\right]$$

$$\left[{\text{normalized}\text{Amp}\text{difference}}_c=\frac{\left|{\text{norm}\text{Experimental}\text{p2p}\text{Amp}}_{\text{c}}-{\text{norm}\text{Model}\text{p2p}\text{Amp}}_{\text{c}}\right|}{{\text{Amp}\text{normalizer}}_c}\right]$$

$$\left[\text{Amp}\text{fitness}=1-\frac{{\sum }_{c=1}^7{\text{normalized}\text{Amp}\text{difference}}_c}{7}\right]$$

Similarly,

$$\left[{\text{norm}\text{Experimental}\text{PSD}}_c=\frac{{\text{Area}\text{under}\text{Experimental}\text{PSD}}_c}{\underset{i=1,\dots ,7}{\text{max}}\left({\text{Area}\text{under}\text{Experimental}\text{PSD}}_i\right)}\right]$$

$$\left[{\text{norm}\text{Model}\text{PSD}}_{\text{c}}=\frac{{\text{Area}\text{under}\text{Model}\text{PSD}}_c}{\underset{i=1,\dots ,7}{\text{max}}\left({\text{Area}\text{under}\text{Model}\text{PSD}}_i\right)}\right]$$

$$\left[{\text{PSD}\text{normalizer}}_{\text{c}}=\text{max}\left({\text{norm}\text{Experimental}\text{PSD}}_{\text{c}},{\text{norm}\text{Model}\text{PSD}}_{\text{c}}\right)\right]$$

$$\left[{\text{normalized}\text{PSD}\text{difference}}_c=\frac{\left|{\text{norm}\text{Experimental}\text{PSD}}_c-{\text{norm}\text{Model}\text{PSD}}_c\right|}{{\text{PSD}\text{normalizers}}_c}\right]$$

$$\left[\text{PSD}\text{fitness}=1-\frac{{\sum }_{c=1}^7{\text{normalized}\text{PSD}\text{difference}}_c}{7}\right]$$

The model fitness was calculated for each combination of beta synchronous volume size and position for each patient.

Model Validation

We evaluated the ability of our fitness method to identify known source parameters from synthetically generated LFPs in each subject (Fig. S2). For each subject, we created a population of synchronous neurons with a known size and position within their STN to produce a synthetic LFP. The size and position of this known synchronous volume was randomly assigned in each subject. The fitness function was able to accurately identify the positions and radii of the beta-synchronous volumes across subjects (Fig. S2). This test provided confidence that the method can correctly identify a known beta-synchronous source in the STN model.

Statistical Testing

Significant differences between the fitness matrices obtained from the two referencing schemes (traditional vs. vertical-directional) were assessed using permutation testing on both synthetic (Fig. S3) and patient datasets (Fig. S4). Since the purpose of the fitness matrices was to determine the size and location of the synchronous volume that best matched the experimental LFPs, the analysis focused on comparing the most prominent cluster in each matrix rather than the entire matrices.

To define this cluster, a threshold was first applied to all pixels in each fitness matrix, and the MATLAB function bwconncomp was used to identify connected groups of above-threshold pixels as clusters. Rather than using a fixed threshold, we began with the maximum fitness value in each matrix and gradually lowered it until at least one cluster containing three or more pixels was identified in that matrix. From the identified clusters in each matrix, the cluster containing the pixel with the highest fitness value was selected from that matrix. This approach focused the analysis on the most prominent region in the data, ensuring that the chosen cluster was both sufficiently large (≥3 pixels) and included the maximum-value pixel.

Permutation testing was then performed on the selected clusters from the matrices generated by the two referencing schemes (traditional vs. vertical-directional). All values from the two different clusters were pooled, shuffled, and repeatedly split into two groups. For each shuffle, the difference in group means was calculated, forming a null distribution. The observed difference was compared against this distribution to obtain a p-value and evaluate whether the result could be explained by chance. If the p-value was ≤ 0.05, the fitness matrices from the two referencing schemes were considered to differ significantly.

Results

Our previous LFP modeling work quantified how varying the location and size of a beta synchronous volume of STN neurons theoretically affects the signals recorded with clinical DBS electrodes (Maling 2018; Noor & McIntyre 2021). The present study extends those concepts to high-density intraoperative LFP data recorded with directional DBS electrodes in multiple PD patients. Simultaneous LFP recordings from all of the DBS electrode contacts facilitated opportunities to perform source localization analyses in each patient-specific model. Therefore, we systematically investigated the size and position of a beta synchronous volume of STN neurons within each patient-specific model to find the best match with their unique experimental recordings.

Figure 4 demonstrates the source localization optimization process for a representative patient (P1). The color-coded fitness matrix (Fig. 4A) displays the fitness values computed for various combinations of a beta synchronous volume radius and position within their STN model. For example, at position 0.7 and radius 1.4 mm, the model-derived PSDs and the area under the curve in the 13–25 Hz range (Fig. 4B, second column) show a good match with the experimental data (Fig. 4B, first column). In contrast, the model outputs at position 0.3 and radius 1.0 mm (Fig. 4B, third column) align poorly with the experimental data. These metrics were quantified using the peak-to-peak amplitude and AUC of the PSDs across seven bipolar electrode pairs of the vertical-directional referencing scheme. Figure 4C visualizes the optimized synchronous neuron volume within the STN anatomical model of the patient, noting that contact 2a was closest to the estimated beta source volume.

Figure 4: Patient-Specific LFP Model.

(A) A color-coded matrix displays fitness values for each combination of volume radius and position for patient P1. The black rectangle highlights a combination of volume radius and position yielding a good fit, while the white rectangle marks one resulting in a poor fit. (B) PSDs (top row) and area under the curve in the 13–25 Hz range (bottom row) for the experimental PSDs (first column), and representative model PSDs with a good vs. poor match to the experimental data. (C) The synchronous neuron volume is visualized within the anatomical model of the patient. The inset indicates that electrode 2a is closest to the center of the beta synchronous volume.

We examined the stability of the beta synchronous neuron volumes over time by computing fitness matrices using 10-second-long LFP time series segments (Fig. S1). The matrices consistently showed that the size and position of the synchronous volume remained stable across these intervals. These results demonstrated temporal stability of the model predictions with the patient at rest.

Figure 5 provides the LFP model optimization results for the additional patients (P2–P5). The fitness matrix for each patient highlights the combinations of radius and position for a beta synchronous volume that yielded their best fitness values (Fig. 5A). The area under the PSDs in the 13–25 Hz range for the experimental LFPs (Fig. 5B, upper panels) and the best-matched model LFPs (lower panels) are highly similar, indicating a strong alignment between the experimental and model-derived signals. Similarly, the peak-to-peak amplitudes for the experimental LFPs (Fig. 5C, upper panels) and the best-matched model LFPs (lower panels) are similar. Figure 5C visualizes the synchronous neuron volume that best matched the experimental LFP recordings for each patient, within their corresponding STN anatomical model.

Figure 5: Patient-Specific LFP Models.

(A) Fitness matrices for patients P2-P5 across various combinations of beta synchronous volume radii and positions. Black squares indicate the radius and position combination that yielded the best fitness values for each subject. (B) Area under the PSD curves in the 13–25 Hz frequency range for both experimental and the best-matched model-derived LFPs. C) Peak-to-peak amplitudes for both experimental and the best-matched model-derived LFPs. (D) Synchronous neuron volume that produced the best match with the experimental LFPs for each patient, within their corresponding STN anatomical model. Inset highlights the contact closest to the center of the beta synchronous volume.

We computed fitness matrices using both vertical-directional and traditional referencing schemes to compare their relative performance in localizing the synchronous neuronal volume within the STN (Fig. 6). The traditional referencing scheme resulted in lower fitness values (Fig. 6B vs 6C, Figs. S4–S5) across all subjects, except P3 (Fig. S4). More generally, the area under the PSD curves and peak-to-peak amplitude for all ten bipolar LFPs with the traditional referencing scheme (Fig. 6B) exhibited an inferior match between the experimental and model-derived data, compared to the match observed with the vertical-directional scheme (Fig. 6A). These results suggest a reduced accuracy for the traditional referencing scheme in performing source localization of beta-band activity in the STN. We then assessed whether the fitness matrices obtained with the two referencing schemes differed significantly. Permutation tests were performed on both the synthetic LFP and experimental LFP datasets from each patient. For the synthetic datasets, the permutation tests revealed significant differences for all subjects except P4 (Fig. S3). When using the experimental datasets, significant differences were noted for all subjects except P3 (Fig. S4).

Figure 6: Comparison of Bipolar Referencing Schemes.

(A) Fitness matrix using the vertical-directional referencing scheme. Example data from P1. The black rectangle indicates the position and radius of the synchronous volume that yields a good fit. The right panel displays the area under the PSDs in the 13–25 Hz range for all seven bipolar LFPs, comparing experimental and best-matched model LFPs (position 0.7, radius 1.4 mm). (B) Fitness matrix generated using the traditional referencing scheme, with the color bar set to the same range as in A. The right panel shows the area under the PSDs in the 13–25 Hz range for all ten bipolar LFPs, comparing experimental and model LFPs for a synchronous volume of radius 1.4 mm, located at position 0.7.

The results of this study were generated from experimental data with simultaneous monopolar recordings (i.e., a common distant return electrode) across all 8 contacts, collected with a 25 kHz sampling frequency, and then down-sampled to 1 kHz for computational efficiency. However, the currently available commercial DBS systems that are only capable of acquiring LFPs with a 256 Hz sampling rate. In addition, these systems employ a traditional referencing scheme and record bipolar LFPs in three separate passes (1 - ring electrodes referenced to other ring electrodes, 2 - segmented electrodes paired within the same row, and 3 - segmented electrodes paired with vertically aligned electrodes across rows). Our results suggest that accurately localizing a beta synchronous volume under those conditions would be challenging. Nonetheless, adoption of the vertical-directional referencing scheme could facilitate a more robust source localization with clinical DBS devices (Fig. S6). We found that down-sampling our data to 256 Hz, and only using 6 bipolar pairs from the directional contacts (which could in theory be simultaneously recorded in a single pass by the current clinical DBS devices) yielded fitness matrices that resembled those obtained using all seven bipolar LFPs sampled at 1 kHz, albeit with lower localization specificity (Fig S6).

Discussion

The goal of this study was to use high-quality well-controlled patient-specific datasets to perform source localization analyses of beta synchronous STN neurons with directional DBS electrodes. The results demonstrate the feasibility of performing patient-specific source localization in the STN (Figs. 4, 5). We found that the beta synchronous volume was generally located in the posterior STN, as anticipated based on previous electrophysiological studies (Zaidel 2009). We also demonstrated a bipolar referencing scheme (vertical-directional) that maximized spatial separation between the paired DBS contacts, which helped to minimize their common signal from the assumed focal beta synchronous volume in the STN, and thus improve source localization specificity. This finding differentiating traditional and vertical-directional referencing also supports the hypothesis that beta synchronous STN neurons cluster into distinct focal areas, as opposed to being uniformly distributed throughout the nucleus. Therefore, if beta synchronous STN neurons are indeed an important therapeutic target of DBS, we propose that patient-specific source localization can aid in DBS contact selection, as well as the titration of stimulation parameters to focus the modulation on these LFP-derived target volumes.

Beta-band LFP recordings have become ubiquitous in PD research (Kühn 2006), and are readily measurable from current clinical DBS devices (Stanslaski 2018). However, the robustness of STN beta activity as a biomarker of PD symptoms has been questioned (van Wijk 2023), and clinical interpretation of LFP signals from directional DBS electrodes is at a relatively early stage of biophysical understanding (Marmor 2017, Noor & McIntyre 2021). Technically, the 8-contact directional leads have 28 possible bipolar pairs, but in practice, referencing schemes only use a subset of those pairs (Fig. 2). Nonetheless, domain experts still find difficulty in estimating the size and location of beta synchronous activity in the STN. In turn, computational algorithms have been derived to help identify a contact associated with the highest beta power and then use it for therapeutic stimulation (Tinkhauser 2018). These LFP-guided DBS programming strategies have generally been successful at selecting a good contact for therapy, but they are only slightly better than chance at identifying the clinically optimal therapeutic contact (Busch 2023). The results of this study suggest that transitioning to vertical-directional referencing, coupled with source localization modeling, has potential to improve specificity in defining the electrode contact most associated with beta synchronous STN neural activity (Figs. 4, 5).

Image-guided DBS programming, an alternative to LFP-guided DBS programming, has demonstrated substantial clinical success by focusing contact selection on anatomical targets derived from patient-specific MRI data (Frankemolle 2010, Pourfar 2015). This approach has good reliability in generating therapeutic outcomes that rival traditional DBS programming performed with a monopolar review (Hines 2024, Waldthaler 2021). However, a logical step forward would be to devise programming strategies that integrate the complementary advantages of both LFP-guided and image-guided algorithms to customize DBS therapy for individual patients. Our approach to this challenge has been the development of patient-specific DBS LFP simulation concepts (Maling 2018, Noor & McIntyre 2021), which are analogous to the models presented in this study (Figs. 4, 5). One application of patient-specific DBS LFP models would be to simulate the spatial localization of beta synchronous STN neurons, thereby defining an electrophysiology-based target volume for DBS therapy. This patient-specific target volume could then be coupled with image-guided DBS programming algorithms to determine optimal stimulation parameter settings for that target (Malekmohammadi 2022).

Prior to making the jump to a fully integrated LFP-guided + image-guided DBS programming strategy, this study lays the groundwork for beginning to address the likelihood of success for such an approach. Table 1 provides a comparison of the clinically-defined therapeutic DBS contact(s) for each subject in this study at 2 and 12 months after their DBS surgery. In addition, the directional DBS contact closest to the center of their beta synchronous STN volume (Figs. 4, 5) is listed alongside the DBS contact closest to the centroid of an established image-based “sweet spot” for subthalamic DBS (Dembek 2019). We generally found good consistency between the contact closest to the centroids of the beta synchronous volumes and the image-based “sweet spots” (Table 1). However, these model-based predictions did not always align with the clinical programming, which often undergoes substantial adjustments over the first year of DBS therapy.

Table 1.

Therapeutic Contacts and Synchronization Volume: Stimulation contacts used for DBS therapy at the 2- and 12-month time points alongside the contact closest to the synchronous volume centroid and the contact closest to the ‘sweet spot’ centroid for each patient.

Subject	Therapeutic contacts at 2 months	Therapeutic contacts at 12 months	Contact Closest to Sync Volume Centroid	Contact Closest to Sweet Spot Centroid
P1	2a, 2b, 3b	2a, 3a	2a	2a
P2	2a, 2c	2b, 2c, 3c	2b	3b
P3	1	2a, 2b, 2c	2a	3a
P4	3a, 3b, 3c	2c, 3b, 3c	3a	3a
P5	4	2c, 3a, 3c	1	3c

Several challenges remain for developing integrated model-based DBS programming algorithms. First, many different stimulation parameter settings, often through different contacts, can provide ~equivalent therapeutic benefits to the patient (Butson 2011). As such, the concept of a single “optimal” DBS setting is likely a fallacy for many patients. Second, image-based DBS analyses are fundamentally limited by the accuracy of co-registering the various imaging datasets, and so there will always be geometric error in the patient model (Bower 2023). Third, the hypothesis that beta synchronous STN neurons are the primary therapeutic target of the stimulation is tenuous, as there are several other neural targets of interest in the subthalamic region (Hines 2024). Along this line, multiple groups have found that clinically optimized contacts are often not submerged within the STN, and as such not likely to be directly stimulating beta synchronous STN neurons (Bower 2024). Fourth, while we noted stability in our LFP source localization over the course of seconds to minutes (Fig. S1), clinical experience suggests that STN LFP signals exhibit significant fluctuations in the early post-operative months (Behnke 2025). Despite these various complexities and challenges, the comparisons of Table 1 suggest at least some promise for future research into an integrated LFP-guided + image-guided DBS programming strategy.

The patient-specific models of this study are the most technically advanced and anatomically detailed simulations of STN LFPs ever assembled. Even still, patient-specific model development is always a balance between detail and interpretability, and this study employed several simplifications to make the models more tractable. One example was our use of a single spherical volume of beta synchronous STN neurons. This simplification provides an easily transferrable representation of a “target volume” for DBS therapy that could guide stimulation parameter selection. However, it is highly unlikely that beta synchronous STN neurons are so ideally organized in vivo.

Another limitation of this study was our idealized representation of generic beta activity in the STN with a peak at ~20 Hz. This simplification facilitated a proof-of-concept demonstration of the patient-specific source localization process within our existing LFP modeling infrastructure (Noor & McIntyre 2021). However, it should be noted that the exact frequency band of interest simulated by the models could be customized to any value in future research. For example, recent electrophysiology studies suggest functional distinctions between low-beta (13–20 Hz) and high-beta (21–35 Hz) sub-bands (Mathiopoulou 2024). These different sub-bands are potentially linked to different motor symptoms in PD (Oswal 2016), which may also be relevant to the different subtypes of PD (i.e. tremor dominant or postural instability gait difficulty) (Telkes 2018).

This study ignored the network origins of how various synaptic inputs to the STN generate beta synchrony. Our representation of synaptic currents on the individual STN neuron models condensed the thousands of pre-synaptic inputs from many different brain regions into generic representations of a few hundred inhibitory and excitatory currents (Lempka & McIntyre 2013). These synaptic currents were parameterized to generate activity patterns in the STN neuron models that correspond with experimental recordings, but the true magnitude and temporal characteristics of the in vivo synaptic currents are unknown. Nonetheless, one future scientific opportunity for the models is to use them to interrogate how the balance of excitatory and inhibitory inputs, as well as their relative distribution across different sections of the STN, can shape the LFP power spectrum (Noor 2023).

This study relied on relatively simple VC models of the patient head, which was done for computational efficiency. This decision was supported by our previous methodological analyses (Noor 2023) documenting that complex tissue anisotropy and inhomogeneity factors are not relevant to the STN LFP calculations performed in this study. This is because the fitness function focused on the peak-to-peak amplitude of the LFP simulations, which were highly consistent with our intra-operative STN recordings from recording rigs with known amplifier and filter settings (Fig. 1). Nonetheless, if we were explicitly concerned with detailed representation of the 1/f distribution across the power spectrum we would have needed to use more detailed models (Noor 2023).

Possibly the most important limitation of this study was the small number of patients analyzed. However, we elected to present results that follow a quality over quantity philosophy. It is especially challenging to create patient-specific models with the highest levels of scientific quality from clinical datasets. In our experience, finding subjects from intra-operative experiments that have the combination of excellent imaging data, excellent electrophysiological data, and no evidence of brain shift during the procedure, has a realistic yield for detailed patient-specific modeling of ~25%, which is aligned with the yield of this study (i.e. 5 of 29). Alternatively, we see little value in attempting to generate highly detailed proof-of-concept models with less than optimal datasets. Nonetheless, the small number of patient examples limits generalizability of the findings.

Finally, even with all of the simplifications and limitations listed above, these LFP models are far too complicated and cumbersome to be practical in a clinical DBS programming product. However, the developmental point of this study was to establish a baseline for what is theoretically achievable when research grade electrophysiology and highly detailed biophysical models are coupled together. In turn, our goal with the next paper in this series will be to demonstrate how much reduction / simplification to the biophysical models can be tolerated and still enable reasonable source localization estimation on a patient-specific basis.

In summary, the goal of this study was to create patient-specific models for source localization of beta synchronous STN neurons with directional DBS electrodes. The results demonstrate that the concept is feasible and that models of LFP biophysics can be used to predict a DBS contact for therapy. As such, the study represents an early step toward devising strategies that integrate the complementary advantages of LFP-guided and image-guided programming to customize DBS therapy to the individual patient.

HIGHLIGHTS.

• Detailed patient-specific models of local field potentials (LFPs) from deep brain stimulation (DBS) electrodes.

• Volume of beta synchronous neurons typically localized to the posterior subthalamic nucleus (STN).

• Identified vertical-directional referencing as the best strategy for STN source localization.

Data Sharing

The data and models of this study can be accessed via the online repository figshare.com. The repository includes the experimental electrophysiology and model simulation data, along with MATLAB scripts for reproducing the figures.

The permanent DOI is: doi.org/10.6084/m9.figshare.28828409