A mathematical model of low grade gliomas treated with temozolomide and its therapeutical implications

Abstract

Low grade gliomas (LGGs) are infiltrative and incurable primary brain tumours with typically slow evolution. These tumours usually occur in young and otherwise healthy patients, bringing controversies in treatment planning since aggressive treatment may lead to undesirable side effects. Thus, for management decisions it would be valuable to obtain early estimates of LGG growth potential.Here we propose a simple mathematical model of LGG growth and its response to chemotherapy which allows the growth of LGGs to be described in real patients. The model predicts, and our clinical data confirms, that the speed of response to chemotherapy is related to tumour aggressiveness. Moreover, we provide a formula for the time to radiological progression, which can be possibly used as a measure of tumour aggressiveness.Finally, we suggest that the response to a few chemotherapy cycles upon diagnosis might be used to predict tumour growth and to guide therapeutical actions on the basis of the findings.

Non-standard radiotherapy fractionations delay the time to malignant transformation of low-grade gliomas

“…Indeed a model based on previous ideas for RT [39] has been recently developed providing an excellent description of the response of individual LGG patients to temozolomide [54]. Recent observations using vinblastine with a limited number of LGG patients may be related to our analysis [55], their observations suggest the use of a metronomic chemotherapy with weekly vinblastine after an induction by irinotecan-bevacizumab in order to improve progression-free survival in children with LGG.…”

Optimal control problems for differential equations applied to tumor growth: state of the art

“…There are many mathematical models that deal with the different aspects of the growth of a tumor. They use ordinary differential equations [2,6,13,54], partial differential equations [1,3,34], stochastic processes [38], game theory [52], etc.…”

Computational design of improved standardized chemotherapy protocols for grade II oligodendrogliomas

“…To calculate the rate of drug decay 82 λ we followed the same methodology as in Ref. [34], using values of TMZ half-life 83 clearance time t 1/2 for doses of 150 mg/m 2 . From the definition of t 1/2 and since Eq.…”

“…Since time to reach peak drug concentration in 91 brain is smaller than two hours and thus negligible in comparison with the other time 92 scales in the model, we chose to set the initial drug concentration C 0 to the value 93 C max = 0.6 µg/ml as in Ref. [34].…”

“…This is in striking contrast with 212 the value used here inferred from realistic data of a few hours. Bogdanska et al [34] 213 used a minimal mathematical model incorporating death only through mitotic 214 catastrophe [32], what forced the parameter κ to have values beyond the biologically 215 feasible range. Our approach achieved better quantitative fittings than those in 216 Ref.…”