Mathematical Modeling for Neuropathic Pain: Bayesian Linear Regression and Self-Organizing Maps Applied to Carpal Tunnel Syndrome

Abstract

A better understanding of the connection between risk factors associated with pain and function may assist therapists in optimizing therapeutic programs. This study applied mathematical modeling to analyze the relationship of psychological, psychophysical, and motor variables with pain, function, and symptom severity using Bayesian linear regressions (BLR) and self-organizing maps (SOMs) in carpal tunnel syndrome (CTS). The novelty of this work was a transfer of the symmetry mathematical background to a neuropathic pain condition, whose symptoms can be either unilateral or bilateral. Duration of symptoms, pain intensity, function, symptom severity, depressive levels, pinch tip grip force, and pressure pain thresholds (PPTs) over the ulnar, radial, and median nerve trunks, the cervical spine, the carpal tunnel, and the tibialis anterior were collected in 208 women suffering from CTS. The first BLR model revealed that symptom severity, PPTs over the radial nerve, and function had significant correlations with pain intensity. The second BLR showed that symptom severity, depressive levels, pain intensity, and years with pain were associated with function. The third model demonstrated that pain intensity and function were associated with symptom severity. The SOMs visualized these correlations among variables, i.e., clinical, psychophysical, and physical, and identified a subgroup of women with CTS exhibiting worse clinical features, higher pressure sensitivity, and lower pinch tip grip force. Therefore, the application of mathematical modeling identified some interactions among the intensity of pain, function, and symptom severity in women with CTS.

Keywords

• carpal tunnel syndrome
• Bayesian linear regression
• self-organizing maps
• mathematical modeling