Optimizing drug regimens in cancer chemotherapy: a simulation study using a PK–PD model

Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers

“…Following the modeling of [19] for the colonization rate β we take 6) with m the colonization coefficient and α the so-called fractal dimension of blood vessels infiltrating the tumour. The parameter α expresses the geometrical distribution of the vessels in the tumour.…”

“…We can distinguish between two classes of models: mechanistic models (see for instance [9,21]) try to integrate the whole biology of the processes and comprise a large number of parameters; on the other hand phenomenological models aim at describing the tumoural growth without taking into account all the complexity levels (see [25] for a review and [6,13,17]). Most of these models deal only with growth of the primary tumour but in 2000, Iwata et al [19] proposed a simple model for the evolution of the population of metastases, which was then further studied in [2,11].…”

Optimisation of Cancer Drug Treatments Using Cell Population Dynamics

“…The Gompertz model was initially developed in the context of insurance [62] and was first used in the nineties to fit experimental data of tumour growth [81]. A lot of studies on drug control are based on these models [14,15,35,96,97,98,106,107,108]. For instance, Murray [106,107] considered a two-population Gompertz growth model with a loss term to model the effect of the cytotoxic drug.…”

“…In the same work, the drug infusion schedule was optimised by determining drug infusion patterns that should maximise tumour cell death under the constraint of minimising healthy cell death. Barbolosi and Iliadis [14,70] coupled a Gompertz model of tumour growth, perturbed by a cytotoxic efficacy term, to a two-compartment model of the chemotherapy PK (plasmatic and active drug concentration). They investigated optimal drug delivery schedules under constraints of maximal allowed drug (single doses and cumulative dose) and leukopenia.…”

Mathematical model of cancer growth controled by metronomic chemotherapies

“…To optimize drug efficacy, both drug amounts (intensification) and administration schedule (densification) should be determined to ensure a desired rate of tumor cell kill with acceptable toxicity. Twenty years ago, the group of D. Barbolosi and A. Illiadis developed a mathematical model able to calculate densified administration protocols [3,34]. Their approach has been validated through two pioneer works; in [44] they illustrate how such approach may assist to design a phase I trial in oncology, in [58] they report a phase I clinical trial including twenty patients with metastatic breast cancer whose treatment were driven/optimized by a mathematical model.…”