Biophysics of Frequency-Dependent Variation in Paresthesia and Pain Relief during Spinal Cord Stimulation

Abstract

The neurophysiological effects of spinal cord stimulation (SCS) for chronic pain are poorly understood, resulting in inefficient failure-prone programming protocols and inadequate pain relief. Nonetheless, novel stimulation patterns are regularly introduced and adopted clinically. Traditionally, paresthetic sensation is considered necessary for pain relief, although novel paradigms provide analgesia without paresthesia. However, like pain relief, the neurophysiological underpinnings of SCS-induced paresthesia are unknown. Here, we paired biophysical modeling with clinical paresthesia thresholds (of both sexes) to investigate how stimulation frequency affects the neural response to SCS relevant to paresthesia and analgesia. Specifically, we modeled the dorsal column (DC) axonal response, dorsal column nucleus (DCN) synaptic transmission, conduction failure within DC fiber collaterals, and dorsal horn network output. Importantly, we found that high-frequency stimulation reduces DC fiber activation thresholds, which in turn accurately predicts clinical paresthesia perception thresholds. Furthermore, we show that high-frequency SCS produces asynchronous DC fiber spiking and ultimately asynchronous DCN output, offering a plausible biophysical basis for why high-frequency SCS is less comfortable and produces qualitatively different sensation than low-frequency stimulation. Finally, we demonstrate that the model dorsal horn network output is sensitive to SCS-inherent variations in spike timing, which could contribute to heterogeneous pain relief across patients. Importantly, we show that model DC fiber collaterals cannot reliably follow high-frequency stimulation, strongly affecting the network output and typically producing antinociceptive effects at high frequencies. Altogether, these findings clarify how SCS affects the nervous system and provide insight into the biophysics of paresthesia generation and pain relief.

Keywords: chronic pain; computer simulation; electric stimulation; paresthesia; somatosensation; spinal cord stimulation.

Figure 1.

Overview of the computational modeling study. We evaluated the effects of stimulation frequency on four relevant phenomena: (1) The DC fiber firing response (red box). (2) Synaptic transmission at the DC-to-DCN synapse (green box). (3) Action potential conduction failure at the axon terminals of DC fiber collaterals (blue box). (4) Output of the dorsal horn pain processing network (brown box).

Figure 2.

Comparison of the frequency-dependent EPSP amplitude between experimental data (left) and our computational model (right). Experimental data and figure are recreated from Nuñez and Buño (1999).

Figure 3.

Two-dimensional transverse cross section of the 25 stochastically generated collateral models. Scale bar, 100 µm.

Figure 4.

A raster plot showing firing behavior for two identical axons separated by 200 µm. The black spikes represent the firing of the original axon, whereas the red spikes are those for a second axon, located 200 µm ventral to the first axon. The top row corresponds to 2.4 mA stimulation, which is increased in 0.2 mA increments to a maximum of 3.2 mA.

Figure 5.

Top, A Scatterplot showing individual PTs for each participant. PTs are given as relative to the PT for conventional 50 Hz SCS for each participant to account for interparticipant variation in baseline thresholds and model activation thresholds. Red lines indicate the model PT when 10% of fibers fire at least one action potential. Bottom, Comparison of model PT predictions with clinical medians.

Figure 6.

A raster plot showing firing behavior of activated DC axons at model PT. Note that the highest frequencies produce highly asynchronous and more rapid firing than lower frequencies. At frequencies from 10 to 100 Hz, the population firing rate is highly synchronized with the SCS pulses, but each individual fiber does not respond one-to-one with each pulse.

Figure 7.

DCN projection neuron firing rates for DC fiber input spike trains of varying frequencies. Note, data are given as the ratio between the number of output spikes to the number of input spikes at a given frequency. Color-coded lines correspond to different strengths of the synaptic connection.

Figure 8.

A raster plot of DCN neuron firing patterns (n = 100) during SCS at frequencies between 2 and 1,000 Hz, using a stimulation amplitude of 5.0 mA (left) and 7.5 mA (right). Each row corresponds to the firing pattern of an individual DCN neuron. Green lines indicate the SCS pulses at the various frequencies.

Figure 9.

Frequency-following properties within 25 DC fiber collateral models. Output data represent the percentage of collateral models that were able to respond faithfully to a given spike train frequency. A collateral was considered to respond faithfully if each of its terminal nodes of Ranvier generated a spike in response to at least 90% of input spikes. The left figure shows the results for the base model (orange) as well as the model with a 25% decrease in fast sodium conductance at all nodes of Ranvier (decrease from 3.0 to 2.25 S/cm²). The right figure shows the results for the base model (orange) compared with those for a model in which the collateral diameters were either increased by 33% (red) or decreased by 33% (blue).

Figure 10.

Different firing patterns within an individual collateral model. This figure shows the response of one model collateral (using baseline model parameters) to a 250 Hz input spike train. The voltage traces at the bottom correspond to the time-dependent membrane voltage of the matching-color terminal nodes marked in the illustration of the collateral at the top.

Figure 11.

The dorsal horn network response is highly sensitive to DC fiber spike timing, and high-frequency conduction failure within primary afferent terminal fibers produces antinociceptive effects. A, The network architecture and biophysics were identical to that developed by Zhang et al. (2014). The network model output was the firing rate of the transmission neuron. B, Left, Dorsal horn network model output during SCS at frequencies between 2 and 1,000 Hz using spiking patterns sampled from DC fibers. In this model, all action potentials initiated in the DC fibers were faithfully transmitted into the dorsal horn pain network (i.e., “perfect fidelity”). Right, Dorsal horn network model output when randomly sampling from collateral terminal models (using DC spiking patterns as input), allowing realistic conduction failure. IN, inhibitory interneuron; EX, excitatory interneuron; T, transmission (output) neuron.