Part 1: The Healing State Vector (Defining Health)
We cannot control what we cannot measure. This chapter defines the 10-dimensional state vector (SH) that mathematically distinguishes ‘Health’ from ‘Disease’.
TASK 1: The Healing State Vector (SH)
Version: 1.1 (Updated with Validation)
Status: DEFINED
Date: 2026-01-16
1. Definition
The Healing State Vector (SH) is a minimal, rigorous physical description of a biological region’s capacity to maintain non-equilibrium order. It contains exactly 10 variables that are measurable, bounded, and independent of biological labels (e.g., “inflammation”).
If a variable cannot be measured in SI units, it is excluded.
SH(t) = [ Φm, σdc, Δ μ, κan, Tnoise, εr, Jion, Γ ]}, ρS, Ψmech
2. The Variables
| Index | Symbol | Name | Physical Definition | SI Unit | Bound (Healthy) | Bound (Critical) |
|---|---|---|---|---|---|---|
| 1 | Φm | Membrane Potential Coherence | Spatial variance of transmembrane voltage field (Vmem) across the tissue patch. | V2 (Variance) | < 10-6 | > 10-3 |
| 2 | σdc | DC Conductivity | Bulk ionic conductivity of the extracellular matrix (ECM) at 0Hz. | S/m | 0.2 – 0.5 | > 1.0 (Leak) |
| 3 | Δ μ | Chemical Potential Gradient | Steepness of the primary morphogen/ion gradient (e.g., Ca2+). | J/mol · m | > 100 | ≈ 0 (Entropy max) |
| 4 | κan | Stiffness Anisotropy | Ratio of max/min Young’s modulus (Emax/Emin) along principal axes. | Dimensionless | 1.5 – 3.0 | ≈ 1.0 (Isotropic scar) |
| 5 | Tnoise | Thermal Noise Power | Local thermal fluctuations above background (Tbody). Proxy for metabolic turbulence. | W/Hz | Low | High (Inflammation) |
| 6 | εr | Dielectric Permittivity | Low-frequency relative permittivity (α-dispersion range). | Dimensionless | 104 – 106 | < 103 (Cell death) |
| 7 | Jion | Net Ionic Current Density | Vector sum of endogenous current flow through the boundary. | A/m2 | 1-10 μ A/cm2 | 0 or Reversal |
| 8 | Γbound | Boundary Continuity | Impedance mismatch at the wound edge (Zedge – Zcenter). | Omega | → 0 | High |
| 9 | ρS | Entropy Production Rate | Rate of local entropy generation (σ = J · vec{X). | W/K · m3 | Minimal | Maximal (Chaos) |
| 10 | Ψmech | Tensegrity Pre-stress | Resting mechanical tension stored in the cytoskeletal network. | Pa | 1-5 kPa | ≈ 0 (Collapse) |
3. Constraints & Invariants
3.1 The Measurability Constraint
For any proposed therapeutic intervention u(t), the effect must be observable in SH:
Δ SH = f(SH, u, t)
If u(t) claims to “heal” but does not move SH towards the Healthy Bound, it is rejected.
3.2 The Entropy Constraint
Healing is defined as the minimization of ρS (Variable 9) while maintaining Φm (Variable 1).
min intt0tfinal ρS(t) dt quad text{subject to} quad Φm < Φcritical
3.3 The Permissive Window
Regeneration is only possible when the state vector resides in the Permissive Hypervolume mathcal{V}{perm} subset mathbb{R}10.
* If SH notin mathcal{V}, the system falls into the Scar Attractor.
* The goal of the framework is to apply control forces (fields) to keep SH inside mathcal{V}perm.
4. Exclusion Notes
- Cell Count is NOT in the vector (it is a biological consequence, not a physical cause).
- “Growth Factors” are NOT in the vector (they are chemical potential carriers, covered by Δ μ).
- “Pain” is NOT in the vector (it is a subjective interpretation of Tnoise and Φm).
5. Correlations & Resolution (Validation Update)
5.1 Variable Independence
We acknowledge that SH is not an orthogonal basis set. The following variables are strongly coupled:
* Electrochemical Coupling: Φm (Coherence) ≤ftrightarrow Jion (Current).
* Maxwell-Wagner Coupling: σ (Conductivity) ≤ftrightarrow εr (Permittivity).
* Mechanotransduction: Ψmech (Tension) ≤ftrightarrow κan (Stiffness).
Validation Rule: When simulating, the covariance matrix Sigmacov must be included to avoid physically impossible states (e.g., high current with zero conductivity).
5.2 Spatial & Temporal Resolution
To be physically meaningful, SH is defined over specific scales:
* Spatial Voxel (Vvox): 1 mm3. This averages over ≈ 106 cells, smoothing out single-cell noise while capturing tissue-level gradients.
* Temporal Resolution (fs): 100 Hz. This is sufficient to capture ionic fluxes (<10 Hz) and mechanical creep, though it undersamples AP spikes (which are treated as time-averaged power in Tnoise).