Biophysical basis of subthalamic local field potentials recorded from deep brain stimulation electrodes

Abstract

Clinical deep brain stimulation (DBS) technology is evolving to enable chronic recording of local field potentials (LFPs) that represent electrophysiological biomarkers of the underlying disease state. However, little is known about the biophysical basis of LFPs, or how the patient's unique brain anatomy and electrode placement impact the recordings. Therefore, we developed a patient-specific computational framework to analyze LFP recordings within a clinical DBS context. We selected a subject with Parkinson's disease implanted with a Medtronic Activa PC+S DBS system and reconstructed their subthalamic nucleus (STN) and DBS electrode location using medical imaging data. The patient-specific STN volume was populated with 235,280 multicompartment STN neuron models, providing a neuron density consistent with histological measurements. Each neuron received time-varying synaptic inputs and generated transmembrane currents that gave rise to the LFP signal recorded at DBS electrode contacts residing in a finite element volume conductor model. We then used the model to study the role of synchronous beta-band inputs to the STN neurons on the recorded power spectrum. Three bipolar pairs of simultaneous clinical LFP recordings were used in combination with an optimization algorithm to customize the neural activity parameters in the model to the patient. The optimized model predicted a 2.4-mm radius of beta-synchronous neurons located in the dorsolateral STN. These theoretical results enable biophysical dissection of the LFP signal at the cellular level with direct comparison to the clinical recordings, and the model system provides a scientific platform to help guide the design of DBS technology focused on the use of subthalamic beta activity in closed-loop algorithms. NEW & NOTEWORTHY The analysis of deep brain stimulation of local field potential (LFP) data is rapidly expanding from scientific curiosity to the basis for clinical biomarkers capable of improving the therapeutic efficacy of stimulation. With this growing clinical importance comes a growing need to understand the underlying electrophysiological fundamentals of the signals and the factors contributing to their modulation. Our model reconstructs the clinical LFP from first principles and highlights the importance of patient-specific factors in dictating the signals recorded.

Keywords: Parkinson’s disease, patient specific; computational model; subthalamic nucleus.

Fig. 1.

Anatomical model. A and B: preoperative MRI and 3-dimensional brain atlas fit to the patient [green volume, subthalamic nucleus (STN); yellow volume, thalamus; other nuclei not shown for clarity]. C and D: postoperative CT coregistered to the MRI and used to define the deep brain stimulation (DBS) lead location (blue shaft, pink contacts). E: STN volume divided into 9 segments that represented different regions of neuron cell density. Each voxel in the STN volume was populated with grid of points for the location of the STN neuron cell bodies.

Fig. 2.

Neuron source models. A: relative positioning of the deep brain stimulation (DBS) electrode and subthalamic nucleus (STN) neuron models with 1 neuron represented in each voxel of the STN volume. Each neuron received inhibitory (GABA_A) and excitatory (AMPA) synaptic input currents. B: zoomed-in view of the full arborizations of the neuron models displayed at different densities. At the full model density, spheres represent the soma locations. C: each of the 235,280 STN neuron models received a time-varying oscillatory input pattern that triggered their synaptic currents. Inputs were either synchronous (top; green) or asynchronous (bottom; blue), with synchronous inputs designed to represent a 20-Hz beta pattern. D: transmembrane current traces from the soma of a single neuron receiving synchronous (top) or asynchronous (bottom) synaptic inputs. Insets show an overlay of 10 different neurons demonstrating highly correlated output for the synchronous case and no correlation for the asynchronous case.

Fig. 3.

Integrated subthalamic nucleus (STN) local field potential (LFP) model example. A: each STN neuron received either synchronous (green) or asynchronous (blue) synaptic inputs. This initial example model used a radius of 3 mm, centered on contact 1, to define the synchronous neurons. B: the voltage recorded on each deep brain stimulation (DBS) electrode contact was defined from the sum of all transmembrane currents generated by each compartment of each neuron using a reciprocity-based solution. Bipolar recording pairs were calculated as the difference between the appropriate monopolar recordings. C: comparison of the time-domain simulated LFP with the clinical LFP recorded from the 0–1 contact pair. Normalized amplitudes are expressed in arbitrary units. D: power spectra of the model and clinical LFPs show beta activity in both cases. The initial model example shows high-amplitude narrow peaks not only at 20 Hz but also at its harmonics (40, 60, and 80 Hz).

Fig. 4.

Radius of synchronous subthalamic nucleus (STN) neurons. A–D: patient-specific STN local field potential (LFP) model. A: variations in the size of the synchronous neural population centered on contact 1 within the STN volume. B: the root-mean-square (RMS) amplitude of the time-domain LFP recorded on each monopolar contact. Peaks at radius (R) = 0.75 and 2.75 mm reflect the envelope of the sphere of synchronous neurons passing the boundary of contact 1 and 0, respectively. C: the number of neurons in the model receiving synchronous input. D: beta power of the model LFP for each of the bipolar contact pairs showing a maxima on contact pair 0–1 at R = 2.75 mm. E–H: spherical STN LFP model. E: variations in the size of the synchronous neural population centered on contact 1 within a spherical volume. The sphere has a volume matched to the patient-specific STN (163 mm³). F: the RMS amplitude of the time-domain LFP recorded on each monopolar contact. Vertical lines represent R = 3 mm, where the amplitudes on contacts 2 and 3 are nearly identical, and R = 3.38 mm, where the radius of the synchronous population equals that of the volume-matched sphere. G: the number of synchronous neurons in the model increases with the cube of the radius until it fills the sphere. H: beta power for each bipolar contact pair. The case at R = 3 mm, where contacts 2 and 3 have nearly identical amplitude, is represented as an abrupt drop, a consequence of the bipolar referencing scheme subtracting one from the other. In A and E, the bold number below R indicates the radius of synchronous activity.

Fig. 5.

Location of synchronous subthalamic nucleus (STN) neurons. A–D: patient-specific STN local field potential (LFP) model. A: 3-mm radius of synchronous neurons in different positions along the long axis of the STN. B: the root-mean-square (RMS) amplitude of the time-domain model LFP on each of the monopolar contacts. C: the number of STN neurons in the model receiving synchronous input as the synchronous population is moved. D: beta power of the model LFP for each bipolar contact pair showing minima on contact pairs that correspond to positions where the monopolar amplitudes are similar. E–H: spherical STN LFP model. E: 3-mm radius of synchronous STN neurons in different positions within a spherical volume. The trajectory of the synchronous population, relative to the deep brain stimulation lead, had the same angle (θ = 8.75°) as the trajectory used in the patient-specific case. F: the RMS amplitude of the time-domain spherical model LFP on each of the monopolar contacts. G: the number of neurons in the spherical model receiving synchronous input as the synchronous population is moved. H: beta power for each bipolar contact pair in the idealized spherical model. Vertical lines show local minima where the monopolar channels are similar in amplitude. Pos, position.

Fig. 6.

Optimized subthalamic nucleus (STN) local field potential (LFP) model. A: search of the parameter space. The fitness metric incorporated coherence between the clinical and model power spectra, as well as the relative normalized beta power across the contact pairs. B: visual schematic of the optimized STN LFP model. The positions of synchronized and unsynchronized neurons are shown in green and blue, respectively. C: comparison of the time-domain results for the model and clinical LFPs. In both cases, the highest amplitude signals were recorded across contact pair 0–1. A.U., arbitrary units. D: comparison of the model and experimental power spectra. Both cases show high beta power for the contact pair 0–1. The optimized model shows much lower amplitude harmonics relative to the naive patient-specific model used in Fig. 3.