Fig 1.
Typical testosterone profile after administration of triptorelin.
TSTmax refers to the maximal testosterone concentrations, tcast indicates the time where testosterone levels fall below 0.5ng/ml (castration limit of prostate cancer patients, marked with an horizontal dashed line in the figure) and teffect indicates the castration period of the patients.
Fig 2.
Schematic representation of the state variables and control input for the pharmakinetic-pharmacodynamic model of the testosterone effects of Triptorelin (left) and model parameter estimates (right).
CTRP, serum concentrations of Triptorelin; CL, apparent total clearance; Vc, VT1, and VT2, apparent volumes of distribution of the central, shallow, and deep peripheral compartments, respectively; CLD1 and CLD2, distribution clearances between the central and peripheral compartments; RT, total receptors; RT0, total receptors at baseline; TST0, baseline testosterone level; KD, receptor equilibrium dissociation constant of triptorelin; DR, down-regulation process; DR_50, the value that elicits a 50% maximal reduction in kS_R for a given amount of total receptors; kS_R, zero-order rate constants of receptor synthesis; kD_R, first-order rate constants of degradation; kS_R, zero-order rate constants of testosterone synthesis; kD_T, first-order rate constants of testosterone degradation; kin, zero-order rate production of testosterone independent from gonadotropins; AGN, ratio between the endogenous agonist concentration and its receptor equilibrium dissociation constant; FDB, feedback.
Fig 3.
Principal steps implemented in our methodology.
Table 1.
Summary of the setup of the different components of the optimal control problem.
Fig 4.
Optimal testosterone (TST) profiles for 1000 simulated individuals.
Solid circles represent optimal TST observations obtained after the optimal control approach, solid line represent the median tendency of the data and red dashed line indicates the castration limit (0.5ng/ml) of prostate cancer patients.
Table 2.
Population absorption parameters estimated for the optimal triptorelin profiles.
The median values and the 95% confidence intervals (CI%) are shown for a population of 1000 patients.
Fig 5.
Optimal testosterone profiles of the 1000 virtual patients.
Optimal testosterone observations (solid circles) with individual predictions (solid blue lines) of the pharmacokinetic/pharmacodynamic model and a red dashed line indicating the castration limit (0.5ng/ml) of prostate cancer patients.
Fig 6.
Optimal drug release characteristics following each of the absorption mechanisms.
Fig 7.
Comparison of the three therapeutic objectives between the optimal control strategy (salmon) and the pharmacokinetic/pharmacodynamic modeling approach (blue) for 1000 individuals.
A) Distribution of tcast (time to obtain testosterone levels below castration limit) values. B) Distribution of the values of the testosterone flare-up (maximum testosterone level/baseline testosterone level). C) Distribution of tcast + teffect (castration time after injection of the drug) time values of the modelling approach.