Optimal Drug Dosing to Achieve the Desired Actual Neutrophil Counts (ANC) in Chemotherapy Induced Myelosuppression

Abstract

In this paper we have first considered the well-known myelosuppression mathematical model of Lena Friberg and her coworkers from the system analysis point of view and study the linearized model steady state stability, controllability, observability, and scaling of model variables. We have found that the original model has poor stability properties at steady state since all its eigenvalues are very close to the imaginary axis. Using theory of multi-time scale systems, it was noticed that the linearized dynamics of two state variables is slow (corresponding to the numbers of maturing cells in the third compartment and the number of circulating cells) and that three remaining state variables display fast dynamics (corresponding to the number of proliferative cells and the number of maturing cells in the first and second compartments). In order to avoid numerical computations with large numbers scaling of system state variables by a factor of 109 has been utilized. In the second part of the paper, a method was proposed for optimal chemotherapy dosing using a result from optimal control theory in order to reduce the amount of administrated chemotherapy drugs and to keep the number of neutrophil cells above a pre-specified desired ANC (actual neutrophil count) level. It was shown that in the case of continuous dosing, the variable optimal amounts of the drug have to be administrated daily based on feedback information regarding the actual count of neutrophils. This result mathematically establishes that administrating constant amount of drugs daily cannot provide the optimal dosing schedule. The obtained results open a door for modern personalized and optimized medicine that requires daily monitoring of fundamental variables and daily drug administration in variable quantities based on the actual state of the patient's fundamental variables (parameters) for the considered decease.