Two Compartment Model Fitting From Dialysis Data

Abstract

Hemodialysis remains an under-appreciated opportunity to assess individual pharmacokinetics. As dialysis is started and stopped, drug clearance suddenly changes, thus disturbing drug equilibration between pharmacokinetic compartments and resulting in an observable change in the drug concentration of a patient’s blood. Such changes are not unlike the output response of a linear system when perturbed by an input signal. Indeed, commonly used pharmacokinetic modeling techniques involve injecting patients with a bolus drug infusion and observing the patient’s drug levels over time. In effect, such techniques aim to characterize the impulse response of a patient. However, such studies are expensive in terms of manpower and time, and are performed over many people to create a “one-size-fits-all” model for a population.

This thesis explores the idea of recasting pharmacokinetic modeling in the context of linear systems theory. In particular, we look to the dialysis machine as a means of creating an “input signal” to estimate the “filter coefficients” of a particular patient. We first show simulations where simple least squares techniques can accomplish this goal to any arbitrary accuracy, provided enough data exists in a noiseless environment. For real clinical data, we create a search procedure based on the linear systems representation of a two-compartment pharmacokinetic model. Our results on real patients show that good predictions of patient drug concentrations can be achieved from samples taken from only the first hour of dialysis. This is a significant improvement over normal pharmacokinetic studies that usually involve many more hours and samples.