Mathematical estimates of recovery after loss of activity: II. Long-range connectivity facilitates rapid functional recovery

OBJECTIVE: To model the effects of system connectedness on recovery of dysfunctional tissues. DESIGN: One-dimensional elementary cellular automata models with small-world features, where the center-input for a few cells comes not from itself but, with a given probability, from another cell. This probability represents the connectivity of the network. The long-range connections are chosen randomly to survey the potential influences of distant information flowing into a local region. SETTING: MATLAB and Mathematica computing environments. PATIENTS: None. INTERVENTIONS: None. MEASUREMENTS AND MAIN RESULTS: We determined the recovery rate of the entropy after perturbing a uniformly dormant system. We observed that the recovery of normal activity after perturbation of a dormant system had the characteristics of an epidemic. Moreover, we found that the rate of recovery to normal steady-state activity increased rapidly even for small amounts of long-range connectivity. Findings obtained through numerical simulation were verified through analytical solutions. CONCLUSIONS: This study links our hypothesis that multiple organ function syndromes represent recoupling failure with a mathematical model showing the contribution of such coupling to reactivation of dormant systems. The implication is that strategies aimed not at target tissues or target organs but rather at restoring the quality and quantity of interconnections across those tissues and organs may be a novel therapeutic strategy.