A system approach to pharmacodynamics. I: Theoretical framework

A general theoretical framework is constructed for the relationship between a pharmacokinetic response r (e.g., systemic drug concentration or input rate), and an observed pharmacologic effect response E. The overall relationship may be described mathematically by E = omega(r) = omega p(omega b(omega r(r))) where omega is an operator that describes the overall relationship, and omega r, omega b, and omega p are operators that describe the contributions of components of the pharmacodynamic system. The kinetic basis for applying certain general mathematical properties such as linearity are discussed. The result is the introduction of various specific mathematical structures that may be applied to pharmacodynamic systems [e.g., E = phi t(r), E = phi t(psi r*r), E = phi p(psi p*phi b(r)), and E = phi p(psi p*phi b(psi r*r))].