title: Mathematical model of nerve fiber activation during low back peripheral nerve field stimulation: analysis of electrode implant depth.
abstract: OBJECTIVE
  The lower back is the most common location of pain experienced by one-fifth of the European population reporting chronic pain. A peripheral nerve field stimulation system, which involves electrodes implanted subcutaneously in the painful area, has been shown to be efficacious for low back pain. Moreover, the predominant analgesic mechanism of action is thought to be via activation of peripheral Aβ fibers. Unfortunately, electrical stimulation also might coactivate Aδ fibers, causing pain or unpleasantness itself. The aim of this study was to investigate at which implant depth Aβ-fiber stimulation is maximized, and Aδ-fiber minimized, which in turn should lead to therapy optimization.
  
  
  METHODS
  A finite element model was used to estimate the electrical potential generated by a bipolar single-lead electrode implanted in the subcutaneous adipose tissue at depths of 5 mm to 30 mm below the skin surface. The model includes low back tissue; the epidermis, dermis, adipose, and muscle layers, and nerve fibers, which were programmed to branch randomly in the model in a fiber type-specific manner. Likewise, activation thresholds were specific to Aβ- and Aδ-fiber types and were estimated using a passive cable model.
  
  
  RESULTS
  The stimulus-response functions showed that the skin area covered by Aβ-fiber activation was larger than the area covered by Aδ-fiber activation at all depths and all intensities. The skin area covered by Aδ-fiber activation was largest when the electrode was modeled to have a superficial location (5 mm below the skin surface), while the skin area covered by Aβ-fiber activation was largest at lower depths.
  
  
  CONCLUSIONS
  The present mathematical model predicts an optimal implantation depth of 10 to 15 mm below the skin surface to achieve activation of the greatest area of Aβ fibers and the smallest area of Aδ fibers. This finding may act as a guide for peripheral nerve field stimulation implant depth to treat low back pain.
authors.affiliation: Integrative Neuroscience group, Center for Sensory Motor Interaction, Department of Health Science and Technology, Aalborg University, Aalborg, Denmark.
authors.forename: Carsten Dahl
authors.initials: CD
authors.lastname: Mørch
authors.forename: Giang P
authors.initials: GP
authors.lastname: Nguyen
authors.forename: Paul W
authors.initials: PW
authors.lastname: Wacnik
authors.forename: Ole Kæseler
authors.initials: OK
authors.lastname: Andersen
mesh_terms: D000200:Action Potentials; D003198:Computer Simulation; D004553:Electric Conductivity; D004599:Electric Stimulation Therapy / Q000009:adverse effects / Q000379:methods; D004567:Electrodes, Implanted; D006801:Humans; D017116:Low Back Pain / Q000628:therapy*; D008959:Models, Neurological; D009413:Nerve Fibers, Myelinated / Q000145:classification / Q000502:physiology*; D009431:Neural Conduction; D010146:Pain / Q000209:etiology; D012867:Skin / Q000294:innervation; D013127:Spinal Nerves / Q000503:physiopathology*; D013269:Stochastic Processes; D050151:Subcutaneous Fat; D040521:Subcutaneous Tissue
keywords: Low back pain; nerve fiber modeling; subcutaneously implanted lead