Fundamental pharmacokinetic limits on the utility of using a sinusoidal drug delivery system to enhance therapy

Clinically, it is known that some disease states respond to drug treatment in a cyclic manner. This has resulted in qualitatively, or empirically, determined cyclically varying drug treatment studies which have been shown to improve therapeutic response in some cases. A theory is developed, for drugs that can be described by pure catenary pharmacokinetic models, which enables one to quantitatively determine at what time a cyclic infusion of drug should be initiated, what the frequency of infusion should be, and what the amplitude of the infusion should be to obtain maximum therapeutic benefit at steady state. Also, the theory allows one to determine quantitatively a priori if a drug's pharmacokinetics precludes the possibility of any real advantage to be gained by cyclically infusing the drug. To implement the theory, it is assumed that the drug obeys linear pharmacokinetics and that the desired pharmacological response is rapid and approximately proportional to a pharmacokinetic compartmental concentration. In particular, a linear system analysis approach is applied to drugs obeying linear pharmacokinetics. It is found that at steady state the amplitude of the sinusoidally varying component of drug's compartmental concentration can be expressed as the amplitude of the rate of infusion times the magnitude of the compartment's transfer function. In addition, an expression for the shift in phase (lag time) of the compartmental drug concentration, relative to the input infusion, is obtained. For a one-compartment model, or for a compartment containing the site of infusion, the amplitude of the sinusoidally varying component ultimately declines in direct proportion to the period (T) of oscillation and the lag time increases from 0 to -0.25T as the period decreases. At a short enough cyclic infusion period, the lag time increments by an additional value of -0.25T, and the attenuation in sinusoidal amplitude decreases by an additional factor of T, for each compartment sequentially connected down the chain from the compartment receiving the infusion. This theory is then applied to the drugs, 5-fluorouracil, KS1/4-DAVLB, theophylline, and adriamycin to see if sinusoidal modulation of the infusion rate would be of therapeutic benefit. The theoretical predictions are then compared to clinically determined empirical results and shown to be consistent. In general, it is shown that the micro rate constants describing the drug's pharmacokinetics must be large (i.e., the system must be able to respond rapidly) for sinusoidal infusion to be of value.