(253b) Sparse Grid-Based Adaptive Nonlinear Model Predictive Control for Personalizing Drug Regimes

Nonlinear model predictive control with sparse grid-based optimization is applied to personalize the scheduled dosing of pharmaceuticals based on recurrent observations. A mathematical model is used to describe the patient response to the drug(s), with some model parameters being patient-specific and therefore unknown. During the course of treatment, the uncertainty in the patient parameters will become sufficiently constrained by the recurrent observations to support customized adjustments of the drug dose and scheduling. The sparse grid-based optimization identifies disjoint acceptable clusters of parameter values that could have given rise to the data measured from the patient. Unlike other parameter identification routines that select only one acceptable parameter set, we consider all acceptable parameter subset(s) for the controller design. Representative parameter values from each disjoint acceptable cluster are selected and used to support the controller design. Nonlinear model predictive control produces a set of potential controller parameters (drug doses) based upon all of the representative patient parameters. This provides a subset of potential doses based on all possible patient responses. The administered dose is selected through a majority rule, and is applied to the plant (patient). Following this process, additional measurements are collected over the course of treatment, and the uncertainty in the patient-specific parameters is reduced as more information becomes available.

As an example, maintenance chemotherapy for childhood acute lymphoblastic leukemia (ALL) was tuned using routine mean corpuscular volume (MCV) measurements. A delay differential equation model that reflects the action of 6-MP on the proliferation and differentiation of hematopoietic stem cells into circulating red blood cells was developed. The model parameters for an average patient were identified using previously published time-course MCV data [1] and steady-state erythrocyte counts [2]. Patient specific parameters are unknown at the onset of maintenance chemotherapy so initial dosing was based on the average patient response. Through simulation studies, the controller-derived dosing strategy successfully achieved and maintained the target MCV in the presence of uncertain patient-specific parameters and measurement noise. Additionally, it achieved the target MCV faster and with less overshoot than a more intuitive constant-dose strategy.

This adaptive model predictive control approach to customizing drug treatments is applicable for systematically adjusting the treatments for many types of chronic and acute diseases provided an appropriate mathematical model and recurrent measurements. The output of the controller design process provides a recommended course of action for the physician along with a prediction of the patient's response and may help provide insight into the individual's disease and response to treatment based upon the patient-specific parameters that emerge.

References:

[1] Decaux, G., et al., Relationship between red cell mean corpuscular volume and 6-thioguanine nucleotides in patients treated with azathioprine. Journal of Laboratory Clinical Medicine, 2000. 135: p. 256-262.

[2] Innocenti, F., et al., Variable Correlation Between 6-Mercaptopurine Metabolites in Erythrocytes and Hematologic Toxicity: Implications for Drug Monitoring in Children With Acute Lymphoblastic Leukemia. Therapeutic Drug Monitoring, 2000. 22(4): p. 375-382.