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The Load-Bearing Threshold: A Quality-Gated Saddle-Node Hypothesis for Skeletal and Cardiac Failure in Duchenne Muscular Dystrophy

Authors: Pan, Mu-Hsun Moses;

The Load-Bearing Threshold: A Quality-Gated Saddle-Node Hypothesis for Skeletal and Cardiac Failure in Duchenne Muscular Dystrophy

Abstract

Duchenne muscular dystrophy (DMD) destroys two load-bearing muscles — the skeletal muscle that moves the body and the cardiac muscle that maintains circulation — and it is cardiac failure that proves fatal. This paper argues that both organs fail through the same structure: a saddle-node bifurcation in functional load-bearing capacity, gated by the fidelity with which a repair process renews itself. As capacity falls, mechanical load redistributes onto fewer contractile units, raising stress per unit and accelerating their loss — a self-amplifying loop established at the single-fiber level in skeletal muscle and following from Laplace's law in the heart. Against this loop runs repair, gated by a quality parameter κ. We derive a closed-form threshold, κ* = 4βL/(ρC²max), separating a sustainable load-bearing state from runaway collapse, and show the same form governs both organs under one disease. Three consequences follow. First, a symptom–ramp–collapse distinction: visible symptom onset is upstream of the fold, which is why a window for intervention remains open at first symptom. Second, treatment predictions: renewal-preserving interventions outperform output-forcing ones; the framework retrodicts the clinical failure of myostatin inhibitors as satellite-cell pool depletion; a partial-unloading optimum exists for the limb; and a discontinuous therapeutic window closes at the fold. Third, the cardiac instantiation is the cleaner instrument — cardiac output cannot be behaviorally renegotiated, making the threshold a single measurable quantity. The fold's existence is conditional on the stress–capacity relationship being sufficiently convex; this is the decisive empirical question. The discriminating test is critical slowing in longitudinal capacity data, which has not been performed and which we identify as the key open experiment. This paper is part of a program on formal frameworks for biological compensation. The companion framework paper is posted at DOI: 10.5281/zenodo.20515948.

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