A Nonlinear Dynamical Theory of Cell Injury

Multifactorial injuries, such as ischemia, trauma, etc., have proven stubbornly elusive to clinical therapeutics, in spite of the binary outcome of recovery or death. This may be due, in part, to the lack of formal approaches to cell injury. We present a minimal system of nonlinear ordinary differential equations describing a theory of cell injury dynamics. A mutual antagonism between injury-driven total damage and total induced stress responses gives rise to attractors representing recovery or death. Solving across a range of injury magnitudes defines an 'injury course' containing a well-defined tipping point between recovery and death. Via the model, therapeutics is the diverting of a system on a pro-death trajectory to a pro-survival trajectory on bistable phase planes. The model plausibly explains why laboratory-based therapies have tended to fail clinically. A survival outcome is easy to achieve when lethal injury is close to the tipping point, but becomes progressively difficult as injury magnitudes increase, and there is an upper limit to salvageable injuries. The model offers novel insights into cell injury that may assist in overcoming barriers that have prevented development of clinically effective therapies for multifactorial conditions, as exemplified by brain ischemia.