Optimal dynamic regimens with artificial intelligence: The case of temozolomide

We determine an optimal protocol for temozolomide using population variability and dynamic optimization techniques inspired by artificial intelligence. We use a Pharmacokinetics/Pharmacodynamics (PK/PD) model based on Faivre and coauthors (Faivre, et al., 2013) for the pharmacokinetics of temozolomide, as well as the pharmacodynamics of its efficacy. For toxicity, which is measured by the nadir of the normalized absolute neutrophil count, we formalize the myelosuppression effect of temozolomide with the physiological model of Panetta and coauthors (Panetta, et al., 2003). We apply the model to a population with variability as given in Panetta and coauthors (Panetta, et al., 2003). Our optimization algorithm is a variant in the class of Monte-Carlo tree search algorithms. We do not impose periodicity constraint on our solution. We set the objective of tumor size minimization while not allowing more severe toxicity levels than the standard Maximum Tolerated Dose (MTD) regimen. The protocol we propose achieves higher efficacy in the sense that –compared to the usual MTD regimen– it divides the tumor size by approximately 7.66 after 336 days –the 95% confidence interval being [7.36–7.97]. The toxicity is similar to MTD. Overall, our protocol, obtained with a very flexible method, gives significant results for the present case of temozolomide and calls for further research mixing operational research or artificial intelligence and clinical research in oncology.

• y 1 , y 2 : one-compartment model for the PK modelling of temozolomide; • y 2 is the temozolomide plasmatic concentration; • y 3 to y 7 model the PD for efficacy; • y 3 models the effect of temozolomide on cancer cells; • y 4 models effect of temozolomide on endothelial cells; • y 5 is the tumor size in grams; • y 6 models temozolomide anti-angionic effect; the effect is present when y 6 < 1 and absent when y 6 = 1; • y 7 represents the area under the curve of plasmatic concentration y 2 with a threshold c 1 ; • y 8 to y 11 model the PD for toxicity; • y 8 is the proliferating cell count in the bone marrow (all types combined); • y 9 is the non-proliferating cell count in the bone marrow in early maturation stages (metamylocytes); • y 10 is the non-proliferating cell count in the bone marrow in later maturation stages (bands and segmented); • y 11 is the neutrophil count (in % of the beginning-of-treatment neutrophil count).
Model calibration S1 Table 1 gathers the parameter values we consider. S1 Authors of [1] have set the parameters of the left column (except λ) to physiologically plausible values that enable to reproduce some stylized facts about the MTD protocol. However, these parameters have not actually been estimated based on clinical trials. The parameters in the right column, as well as the parameter λ, have been estimated in [2] on to match the outcomes of a clinical trial.
The population pharmacokinetics parameters are gathered in S1 Table 2. All parameters follow a log-normal distribution LN (µ, σ 2 ) and we report for each parameter the distribution parameters µ and σ 2 (the mean and variance of the logarithm of the parameter, respectively). We also report the mean and the standard error of the parameter. These latter quantities come from Panetta et al. [3], who have estimated population variability in temozolomide pharmacokinetics using results of a clinical trial. S1 The population of 3,200 patients that we consider in the paper differs along the values of their pharmacokinetic parameters. We have randomly drawn these values using the log-normal distributions that are specified in S1 Table 2, assuming that patients are independent from each other and that the different parameters of a given patient are also independent from each other. Because of space constraints, we cannot report here the 9,600 parameter values that we have drawn. However, they are not mandatory for replicating our study.
Indeed, given the size of the population, any other draw of 3,200 patients would enable to very closely replicate our results.
Finally, for the simulations with no variability, we use the parameter mean values.