Mathematics helps cure leukemia

When children complain that math homework will not help them in real life, a recent answer may suggest that math can help cure cancer.

In a recent study of mathematics and medicine, researchers showed that patients with chronic myeloid leukemia (CML) can be treated with an anti-cancer vaccine. The letter is calculated optimally in time, in which time calculation is determined based on the immune response of each person.

In the issue on June 20, the biology journal PloS, mathematics professor Doron Levy of the University of Maryland, associate professor of medical doctor Peter P. Lee of Stanford Medical School and Dr. Peter S.Kim of the École Supérieure d'Électricité described their success in creating a predictive mathematical model that the anti-leukemia immune response in CML patients using imatinib may stimulated by a method that can provide a treatment for this disease.

Levy, of the University of Maryland's Center for Mathematical and Scientific Computation, said: 'By combining new biological data with mathematical models, we have found the rules of the design of the directions. Adaptive treatment for each specific patient. With this mathematical model, please give me 1000 patients, I can give you 1000 different customized treatment plans'.

Mathematics and leukemia

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While the harmonious combination of mathematics and biology has only begun to become popular in science, people have tried to use equations to understand how leukemia develops and how it progresses over time. . The study of Levy, Lee and Kim differs in noting the patient's immune response along with the effects of imatinib - a drug that has succeeded in relieving disease in CML patients.

They want to know if they can develop a mathematical model or a set of laws that will increase the likelihood of long-term remission in each patient. In the past four years, Lee's lab has collected data from CML patients, measuring the length of each patient's immune response in terms of the number and activity of T-cells against leukemia. Various times during treatment with imatinib.

Levy said: 'The results show that not only do drugs relieve leukemia but also the natural immune response. After starting imatinib, the anti-leukemia immune response gradually increased. However, this reaction begins to weaken after reaching the peak. "

Leukemia cells remain but the number is quite low, causing the immune response to decrease. Unfortunately, this is the ideal time for cancer cells to develop resistance and make the treatment ineffective.

The best time for an immune response

Combined with Lee's clinical data on the immune response, Levy's model shows that patients' immune responses should be elevated when they begin to weaken.

The authors showed that such stimulation can be provided in the form of 'anti-cancer vaccine', in which blood is taken from the patient to be irradiated to kill activated cancer cells, then is brought back to the patient's body. It has been shown that a strong immune system stimulation is within the test tube in Lee's experiments.

Mathematical methods show that, it is imperative to link the calculation of the time of the anti-cancer vaccine with the personal profile of each patient's immune response, Levy said. Math simulations show that a vaccine used during the first months of treatment will not affect the progression of the disease. On the other hand, a carefully timed vaccine can treat this disease.

Individual treatment plan

But the motivation for each patient's immune response is different. That's the reason mathematically interferes, Levy said. We can find the rules to apply for each specific patient, we can measure the parameters of each patient to see when this dose is most effective. Mathematics provides the necessary tools to make treatments suitable for each patient.

Levy said: 'While some parameters can be measured in the laboratory, the mathematical model helps us understand the mechanisms that control this disease and show how to apply this knowledge. to our advantage '.

Levy and Lee are currently conducting further research to expand the results of this study, to prepare experiments on animal models and to conduct clinical trials.

The research was funded by the American Cancer Society, the National Cancer Research Institute and the National Science Foundation.