Biophysical Foundations of the Healing Process. From the Perspective of the MRC Framework

The Multilevel Recursive Coherence (MRC) framework interprets healing not as mere structural repair but as restoration of oscillatory coherence across molecular, cellular, network and systemic scales. A companion clinical article applies this framework to perioperative medicine and bone healing; here we develop its biophysical foundations. We introduce three mathematical components. First, a Kuramoto‑type model of coupled cellular oscillators describes tissue repair as a resynchronization process that can be driven out of pseudoarthrosis‑like attractors by external forcing such as pulsed electromagnetic fields (PEMF) or controlled mechanical loading. Second, Gradient Indeterminacy (IG) is used to formalize the thermodynamic cost of repair, defining a time‑dependent window of tolerance that constrains how much gradient complexity a healing tissue can sustain without coherence collapse. Third, we define a tissue hash as a spectral fingerprint of oscillatory activity, and show how healing corresponds to a trajectory in hash space that restores both coherence and spectral distinguishability. Together, these elements provide a biophysical interpretation of healing that complements standard structural and biochemical accounts and yields concrete, testable predictions for regenerative medicine.