Topological False Positives in Sciatic Localization: A Bayesian Failure Analysis of a 'Spine-First' Algorithm
Background: Sciatica is commonly attributed to lumbar radiculopathy; extra-spinal causes in the deep gluteal space are frequently overlooked, particularly after otherwise successful lumbar surgery. Computational Error: Contemporary spine surgery often operates on a deterministic heuristic: structural pathology dictates clinical presentation. However, in the aging spine, structural pathology is statistically ubiquitous, creating a "High-Noise Environment. Logic Trace: The initial surgeon fell into a "Base Rate Neglect" trap, conflating the high prevalence of asymptomatic spondylolisthesis (Background Noise) with the active pain generator. The "Null Result" of the spinal fusion forced a Bayesian Update of the diagnostic probability distribution. The Solution: High-resolution MR neurography identified the true high-entropy signal: a T2-hyperintense piriformis muscle.
Conclusion: "Failed Back Surgery Syndrome" is often a misnomer for "Failed Algorithm Syndrome." We propose a logic-gate protocol based on First-Principles Signal Tracing to mathematically decouple incidental spinal noise from extra-spinal entrapment.