Fig 1.
A general framework for model-based individualized dosing of chemotherapeutic drugs.
Pharmacokinetic and pharmacodynamic models are formulated based on underlying physiology. With extensive data from a large cohort of patients, a population model is formulated based on the Bayesian approach. A few measurements from a new patient, collected at optimal time points, enables the adaptation of the population model to an individual behavior. Patient models are used to optimize the dose based on model predictive control to maintain the drug concentration within the therapeutic window. In this work, only pharmacokinetic aspects of 6-MP are considered.
Fig 2.
Schematic representation of 6-MP metabolism.
The model equations for 6-MP metabolism based on mass-action kinetics are shown in Eq (7).
Table 1.
Glossary of state variables and parameters for 6-MP model.
Fig 3.
Marginal parameter distribution with correlation matrix estimated through Bayesian approach.
The diagonal cells show the marginal distribution for individual parameters. The off-diagonal cells show the pairwise joint distribution of parameters and their corresponding correlation coefficient.
Table 2.
Parameter statistics for prior distribution in Bayesian calculations.
Fig 4.
Population prior distribution for model and error parameters.
Blue solid line indicates the actual distribution formulated by sampling individual patient distribution. The red dashed lines show the approximation by multivariate normal distribution.
Fig 5.
Comparison of concentration confidence region predicted using Bayesian approach for 6-MP model.
The red region shows the prediction with non-informative prior. The gray region shows the improved CR with informative population prior formulated using several patient data. The solid dots represent the data collected from an individual patient.
Fig 6.
Marginal distribution of parameters showing correlation between kcm and kme.
Only kcm and kme are estimated, with all other parameters fixed at population mean, to reveal the correlation between them.
Fig 7.
Evolution of information as a function of time and parameter set determined via optimal DoE technique.
Table 3.
List of parameters identified for deriving patient-specific model (bold face) together with other fixed parameters (regular face).
Cumulative error, calculated at 1, 10, 20, 50, 75 and 100 days according to Eq 30, is given in column 2. % error is given in column 3.
Fig 8.
Comparison of 95% CR predicted using different information on biological chain-of-response for two representative patients.
The black region represents the population. The gray region shows the prediction when only TPMT enzyme activity is measured. The red region shows the 95% CR predicted when just one measurement of 6-TGN is available (the solid dot).
Fig 9.
Optimal 6-MP dosing and corresponding optimal 6-TGN concentration profile for two representative patients.
The red region is the 95% CR of concentration optimized for the group. Green region is 95% CR back calculated until the 6-TGN measurement is taken. Black region is the optimized profile with patient-specific model after 6-TGN measurement on the 35th day. Blue and pink stems represent 6-MP doses before and after 6-TGN measurement respectively. The blue dashed line designates the concentration target. See text for details.