Basic PK/PD principles of drug effects in circular/proliferative systems for disease modelling.

Disease progression modelling can provide information about the time course and outcome of pharmacological intervention on the disease. The basic PK/PD principles of proliferative and circular systems within the context of modelling disease progression and the effect of treatment thereupon are illustrated with the goal to better understand/predict eventual clinical outcome. Circular/proliferative systems can be very complex. To facilitate the understanding of how a dosing regimen can be defined in such systems we have shown the derivation of a system parameter named the Reproduction Minimum Inhibitory Concentration (RMIC) which represents the critical concentration at which the system switches from growth to extinction. The RMIC depends on two parameters (RMIC = (R(0) - 1) x IC(50)): the basic reproductive ratio (R(0)) a fundamental parameter of the circular/proliferative system that represents the number of offspring produced by one replicating species during its lifespan, and the IC(50), the potency of the drug to inhibit the proliferation of the system. The RMIC is constant for a given system and a given drug and represents the lowest concentration that needs to be achieved for eradication of the system. When exposure is higher than the RMIC, success can be expected in the long term. Time varying inhibition of replicating species proliferation is a natural consequence of the time varying inhibitor drug concentrations and when combined with the dynamics of the circular/proliferative system makes it difficult to predict the eventual outcome. Time varying inhibition of proliferative/circular systems can be handled by calculating the equivalent effective constant concentration (ECC), the constant plasma concentration that would give rise to the average inhibition at steady state. When ECC is higher than the RMIC, eradication of the system can be expected. In addition, it is shown that scenarios that have the same steady state ECC whatever the dose, dosage schedule or PK parameters have also the same average R (0) in the presence of the inhibitor (i.e. R (0-INH)) and therefore lead to the same outcome. This allows predicting equivalent active doses and dosing schedules in circular and proliferative systems when the IC(50) and pharmacokinetic characteristics of the drugs are known. The results from the simulations performed demonstrate that, for a given system (defined by its RMIC), treatment success depends mainly on the pharmacokinetic characteristics of the drug and the dosing schedule.