Weizmann Institute's Mathematical Model May Lead to Safer Chemotherapy

Cancer chemotherapy can be a life-saver, but it is fraught with severe side effects, among them an increased risk of infection. Until now, the major criterion for assessing this risk has been the blood cell count: if the number of white blood cells falls below a critical threshold, the risk of infection is thought to be high. A new model built by Weizmann Institute mathematicians in collaboration with physicians from the Meir Medical Center in Kfar Saba and from the Hoffmann-La Roche research center in Basel, Switzerland, suggests that for proper risk assessment, it is essential to evaluate not only the quantity of these blood cells, but also their quality, which varies from one person to another.

This research may represent an important step in the emerging field of personalized medicine, leading to a more individualized approach to chemotherapy. In particular, better precautions might need to be taken to prevent infection in high-risk patients whereas those at a low risk could be spared unnecessary preventive treatments.

The study, recently published in the Journal of Clinical Investigation, brought together the expertise of researchers from such diverse disciplines as applied mathematics, electrical engineering, oncology, immunology and pediatrics.

The new model reveals how the immune system functions under conditions of neutropenia – dangerously low levels of white blood cells, mainly neutrophils. In this condition, which often emerges after chemotherapy or bone marrow transplant, severe infections can develop if the immune system fails to perform the crucial function of devouring and destroying bacteria.

“Our mathematical model has revealed previously unknown mechanisms responsible for the variability in the vulnerability of neutropenia patients to infections,” says research leader Prof. Vered Rom-Kedar of the Weizmann Institute’s Computer Science and Applied Mathematics Department.

The model suggests that in neutropenia, the tug of war between the blood cells and the bacteria cannot be explained away by the simple bacteria-to-cell ratio, nor by the threshold that the blood cell count must exceed. Rather, when neutrophil counts are low, the patient’s immune system enters a fragile equilibrium – described as “bistability” in mathematical terms – which can easily be disrupted, with dramatic consequences, by even minute changes in bacterial concentration or neutrophil numbers. Other factors that can radically affect this equilibrium include the effectiveness of the neutrophil functioning and the permeability of tissues to bacteria, which can increase due to cancer therapy.

Thus according to the model, in healthy people, the fact that the effectiveness of neutrophils varies from one person to another usually has no significant consequences. In contrast, in patients with neutropenia, this individual variability can make a difference between life and death. This conclusion is drawn from the study based upon the blood analysis of four healthy volunteers. To use the model in the clinic, such analysis should be applied to large populations.