Mathematical modeling approaches to understanding pain processing and chronic pain therapies

Wednesday, June 16 at 09:30am (PDT)
Wednesday, June 16 at 05:30pm (BST)
Thursday, June 17 01:30am (KST)

SMB2021 SMB2021 Follow Wednesday (Thursday) during the "MS13" time block.
Share this


Jennifer Crodelle (Middlebury College, USA), Kevin Hannay (University of Michigan, USA), Victoria Booth (University of Michigan, USA)


Chronic pain affects approximately 20% of US adults and is one of the most common reasons adults seek medical care [1]. Spinal-cord stimulation (SCS) is a widely used therapy to alleviate chronic pain. However, details of how pain is processed in the spinal cord and the mechanisms by which SCS modulates sensory signals from the periphery have not been completely determined. Recent mathematical modeling approaches have focused on illuminating these mechanisms. In this minisymposium, speakers will present diverse physiologically-based mathematical modeling studies addressing the processing of pain signaling in spinal-cord circuits, as well as modulation of that processing by SCS.  [1] Dahlhamer J, Lucas J, Zelaya, C, et al. Prevalence of Chronic Pain and High-Impact Chronic Pain Among Adults — United States, 2016. MMWR Morb Mortal Wkly Rep 2018;67:1001–1006.

Jennifer Crodelle

(Middlebury College, USA)
"Firing-rate models for analyzing spinal circuit motifs underlying chronic pain"
Neuronal circuitries underlying the processing of pain signaling in the dorsal horn of the spinal cord are complex and not yet completely understood. In addition, changes induced in those circuitries due to nerve injury in chronic pain patients have been attributed to multiple pathologies at the cellular and synaptic levels. Using a firing-rate model formalism for activity of projection and interneuron neuronal populations, we construct models of multiple identified microcircuits that process mechanical sensory and nociceptive input to analyze how their parallel filtering of incoming signals affects projection neuron responses. We use the model to investigate how different proposed chronic pain pathologies disrupt and distort microcircuit processing to result in allodynia and hyperalgesia.

Warren Grill

(Department of Biomedical Engineering, Duke University, USA)
"Network Models to Analyze and Design Spinal Cord Stimulation for Chronic Pain"
Spinal cord stimulation (SCS) is an established treatment for chronic pain, but neither the neural mechanisms underlying SCS nor the relationship between the applied parameters of SCS and its clinical efficacy have been fully characterized. We developed and validated biophysical models of dorsal column axons as well as the dorsal horn neural circuit that processes peripheral sensory inputs, including nociceptive information. We simulated the effects of SCS across a range of frequencies and amplitudes on the activity of model dorsal column axons and model wide dynamic range projection neurons. SCS applied at amplitudes as low as 60% of the predicted sensory threshold activated model dorsal column axons, and the pattern of resulting activity was irregular and strongly dependent on the stimulation amplitude. These model-based predictions were validated with in vivo recordings from single dorsal column axons in anesthetized rats. The increased activity in dorsal column axons generated by SCS drove activity in model inhibitory interneurons and subsequently reduced model wide dynamic range neuron firing rates. Changes in model wide dynamic range neuron firing rate varied non-monotonically with stimulation amplitude and rate, and maximum inhibition occurred at 75-85% of sensory threshold and at rates between 50-90 Hz. Further in vivo recordings showed that net inhibition of putatively excitatory neurons was maximal at 80% of the predicted sensory threshold. The new understanding resulting from the implementation and validation of biophysically-based computations models provides a platform to guide the design of novel methods of stimulation

Steven A Prescott

(Neurosciences and Mental Health, The Hospital for Sick Children; Department of Physiology and Institute of Biomedical Engineering, University of Toronto , Canada)
"Altered processing of tactile input due to chloride dysregulation in the spinal dorsal horn "
Synaptic inhibition in the dorsal horn of the spinal cord plays a key role in processing somatosensory input. Weakened inhibition can cause light touch to be mistakenly perceived as painful – a phenomenon known as mechanical allodynia, which is common after nerve injury. Nerve injury induces many changes in the spinal dorsal horn, including weakened inhibition. This disinhibition is due primarily to chloride dysregulation caused by downregulation of the potassium-chloride co-transporter KCC2. KCC2 normally keeps intracellular chloride at a low concentration, thus maintaining the chloride driving force that GABAA and glycine receptors rely on to mediate inhibition. Weakened inhibition causes receptive fields to expand, which in turn affects spatial summation. Weakened inhibition also ungates polysynaptic pathways, allowing low-threshold inputs to activate projection neurons that are normally activated exclusively by high-threshold inputs. In this talk, I will discuss experimental data and our efforts to incorporate those data into a circuit-level model of the spinal dorsal horn. 

Scott Lempka

(Department of Biomedical Engineering, University of Michigan; Department of Anesthesiology, University of Michigan; Biointerfaces Institute, University of Michigan, USA)
"Computational modeling of neural recruitment during spinal cord stimulation for pain"
Spinal cord stimulation (SCS) is a popular neurostimulation therapy for severe chronic pain. To improve stimulation efficacy, multiple modes are now used in the clinic. Clinical observations have produced speculation that these modes target different neural elements and/or work via distinct mechanisms of action. However, in humans, these hypotheses cannot be conclusively answered via experimental methods. Therefore, we utilized computational modeling to assess the response of primary afferents, interneurons, and projection neurons to multiple forms of SCS. We used this modeling approach to understand how various technical and physiological factors, such as neuron geometry and waveform patterns (e.g., burst and kilohertz-frequency SCS), affect the cellular response to SCS. In our simulations, local cell thresholds were always higher than afferent thresholds, arguing against direct recruitment of these interneurons and projection neurons. Furthermore, all of the clinical SCS waveforms had the same relative neural recruitment order, albeit with different absolute thresholds. This result suggests that these SCS modalities do not exert differential effects through distinct recruitment profiles. These results motivate future work to contextualize clinical observations across conventional and emerging SCS paradigms.

Hosted by SMB2021 Follow
Virtual conference of the Society for Mathematical Biology, 2021.