7,923 research outputs found
Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies
Resistance to chemotherapies, particularly to anticancer treatments, is an
increasing medical concern. Among the many mechanisms at work in cancers, one
of the most important is the selection of tumor cells expressing resistance
genes or phenotypes. Motivated by the theory of mutation-selection in adaptive
evolution, we propose a model based on a continuous variable that represents
the expression level of a resistance gene (or genes, yielding a phenotype)
influencing in healthy and tumor cells birth/death rates, effects of
chemotherapies (both cytotoxic and cytostatic) and mutations. We extend
previous work by demonstrating how qualitatively different actions of
chemotherapeutic and cytostatic treatments may induce different levels of
resistance. The mathematical interest of our study is in the formalism of
constrained Hamilton-Jacobi equations in the framework of viscosity solutions.
We derive the long-term temporal dynamics of the fittest traits in the regime
of small mutations. In the context of adaptive cancer management, we also
analyse whether an optimal drug level is better than the maximal tolerated
dose
Minimizing Metastatic Risk in Radiotherapy Fractionation Schedules
Metastasis is the process by which cells from a primary tumor disperse and
form new tumors at distant anatomical locations. The treatment and prevention
of metastatic cancer remains an extremely challenging problem. This work
introduces a novel biologically motivated objective function to the radiation
optimization community that takes into account metastatic risk instead of the
status of the primary tumor. In this work, we consider the problem of
developing fractionated irradiation schedules that minimize production of
metastatic cancer cells while keeping normal tissue damage below an acceptable
level. A dynamic programming framework is utilized to determine the optimal
fractionation scheme. We evaluated our approach on a breast cancer case using
the heart and the lung as organs-at-risk (OAR). For small tumor
values, hypo-fractionated schedules were optimal, which is consistent with
standard models. However, for relatively larger values, we found
the type of schedule depended on various parameters such as the time when
metastatic risk was evaluated, the values of the OARs, and the
normal tissue sparing factors. Interestingly, in contrast to standard models,
hypo-fractionated and semi-hypo-fractionated schedules (large initial doses
with doses tapering off with time) were suggested even with large tumor
/ values. Numerical results indicate potential for significant
reduction in metastatic risk.Comment: 12 pages, 3 figures, 2 table
The effects of time valuation in cancer optimal therapies: a study of chronic myeloid leukemia
Background
The mathematical design of optimal therapies to fight cancer is an important research field in today’s Biomathematics and Biomedicine given its relevance to formulate patient-specific treatments. Until now, however, cancer optimal therapies have considered that malignancy exclusively depends on the drug concentration and the number of cancer cells, ignoring that the faster the cancer grows the worse the cancer is, and that early drug doses are more prejudicial. Here, we analyze how optimal therapies are affected when the time evolution of treated cancer is envisaged as an additional element determining malignancy, analyzing in detail the implications for imatinib-treated Chronic Myeloid Leukemia.
Methods
Taking as reference a mathematical model describing Chronic Myeloid Leukemia dynamics, we design an optimal therapy problem by modifying the usual malignancy objective function, unaware of any temporal dimension of cancer malignance. In particular, we introduce a time valuation factor capturing the increase of malignancy associated to the quick development of the disease and the persistent negative effects of initial drug doses. After assigning values to the parameters involved, we solve and simulate the model with and without the new time valuation factor, comparing the results for the drug doses and the evolution of the disease.
Results
Our computational simulations unequivocally show that the consideration of a time valuation factor capturing the higher malignancy associated with early growth of cancer and drug administration allows more efficient therapies to be designed. More specifically, when this time valuation factor is incorporated into the objective function, the optimal drug doses are lower, and do not involve medically relevant increases in the number of cancer cells or in the disease duration.
Conclusions
In the light of our simulations and as biomedical evidence strongly suggests, the existence of a time valuation factor affecting malignancy in treated cancer cannot be ignored when designing cancer optimal therapies. Indeed, the consideration of a time valuation factor modulating malignancy results in significant gains of efficiency in the optimal therapy with relevant implications from the biomedical perspective, specially when designing patient-specific treatments.This work was supported by projects MTM2014-56022-C2-2-P and MTM2017-85476-C2-1-P of the Spanish Office of Innovation and Competitiveness and European FEDER Funds, and by projects of the Castile and León Autonomous Government: VA041P17 (with European FEDER Funds), VA138G18 and VA148G18
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