A Mathematical Biologist Against Cancer

More sophisticated approaches to improve the efficacy of anticancer arsenal

Patients have long received cancer treatments at the maximum tolerated dose on a regular schedule. An article published online on 7 May 2014 in the Nature Medicine features an interview with one mathematical biologist whose theories are now being tested in the clinic to see if they can improve the efficacy of today's anticancer arsenal.

The way in which people receive cancer therapy is pretty much the same as it's been for decades: researchers determine the highest dose of a drug or treatment that does not cause unacceptable side effects; oncologists then administer that dose to patients on a standard timetable. Almost all current cancer therapies are given this way. And although the approach has undoubtedly extended patients' lives, given the level of health expenditure on cancer care, it's worth asking: are these schedules really yielding the best results for patients?

Could alternative timetables produce better outcomes?

Franziska Michor hopes to answer this question. She is 31-year-old mathematical biologist from the Dana-Farber Cancer Institute in Boston, USA. She has turned to math and evolutionary theory to determine whether clinicians can make existing therapies work better simply by altering the time course by which they are administered. Her models are now being put to the test in prospective human clinical trials. This is something that few mathematical biologists see in their entire careers and her career in particular is barely a decade old.

Lung cancer

Last autumn, oncologists at the Memorial Sloan Kettering Cancer Center (MSKCC) in New York launched a phase I trial that aims to test the safety of an unconventional dosing schedule proposed by Michor and her colleagues for the treatment of non–small cell lung cancer.

The trial involves erlotinib. For patients with lung cancer, the recommended dose of erlotinib is 150 milligrams taken daily on an empty stomach. Clinicians arrived at this dosing schedule largely on the basis of its safety profile and how quickly the drug is metabolised. Back in 2008, when she and William Pao were both at MSKCC, they teamed up to determine the best way to delay the onset of drug resistance and, thus, prolong the impact of erlotinib.

They first quantified differences in the growth kinetics of lung cancer cells that respond to treatment and those that have mutated to become drug resistant. They repeated these in vitro measurements at varying concentrations of erlotinib. Using a type of mathematical formula known as a continuous-time Markov chain to model cell birth and death dynamics, Michor and her then-postdoc Jasmine Foo next considered various time-dependent dosing strategies to arrive at a predicted optimum.

The math suggested that occasional high-dose pulses of erlotinib, on top of low-dose administrations of the drug the rest of the time, impeded the outgrowth of drug-resistant cells to the maximum extent. Laboratory studies led by Pao, who had moved to the Vanderbilt-Ingram Cancer Center in Nashville, Tennessee, bore out this prediction.

According to Michor, the approach proved optimal because the continuous low-dose drug levels inhibit drug-sensitive cells, while the high doses slow down the overall growth of the resistant cell population. What's more, the absence of treatment breaks prevents selection for further drug resistance. “It makes sense, and it's certainly worth exploring,” according to MSKCC oncologist Gregory Riely, who is co-leading the phase I trial, the first prospective study of this dosing strategy in humans.

Instead of receiving 150 milligrams of erlotinib daily, the 58 participants in the trial are taking high-dose erlotinib two days a week and 50 milligrams the other five days. In March, the trial completed enrollment for the last of four planned high-dose levels (all of which doctors have previously tested in weekly 'pulsatile' treatment regimens but not in combination with continuous low-dose administration).

Since the trial participants tolerated the highest pulse dose—1,050 milligrams—and the responses looked favourable, Riely and his colleagues are now considering whether to modify the study protocol to add an even higher dose level.

Glioblastoma

A paper published earlier this year in Cell could prompt the next human study of Michor's theories. In that paper, Michor and her collaborators started with a simple question: is there a better way to give radiation therapy for glioblastoma? The standard schedule for glioblastoma treatment involves 2 Gray given once a day, Monday to Friday, for six weeks, for a total of 60 Grays. Alternative schedules have been tried, but none have led to improved results.

Michor decided to revisit the scheduling question after scientists recently discovered subtypes of glioblastoma distinguished by unique molecular patterns. Perhaps, Michor thought, different subtypes could benefit from different radiation schedules. She and her then-postdoc Kevin Leder chose to focus on the proneural form of glioblastoma, a subtype that contains a small population of tumour cells with stem cell–like properties. These radiation-resistant stem-like cells can arise either through self-renewal or from radiation-sensitive cells through a process known as dedifferentiation. This cellular transformation is accelerated by radiation, but it takes a few hours to complete, during which time another dose of radiation could help kill the cells.

Since the parameters involved in these cellular dynamics would be impossible to obtain in humans, Michor joined forces with her former MSKCC colleague Eric Holland, a brain tumour researcher and neurosurgeon now at the Fred Hutchinson Cancer Research Center in Seattle. Together, they obtained the molecular metrics from a mouse model of proneural glioblastoma. Mice can't handle as much total radiation as people can, so Michor and Holland just modeled how best to administer one week's worth of human treatment: 10 Grays. To keep the model realistic, the researchers limited themselves to a Monday to Friday, 8 am to 5 pm schedule—after all, radiation oncologists are known to maintain fairly regular office hours.

The math ultimately spit out a survival-maximising schedule that looked nothing like the clinical standard of 2 Gray per day. It involved 3 Gray up front on Monday morning, 1 Gray on Tuesday afternoon, nothing on Wednesday and then three doses of 1 Gray each spaced evenly over would-be business hours on Thursday and Friday. When the researchers experimentally tested the optimised schedule in their mouse model they found a significant improvement in survival outcomes. In fact, half the mice treated with the optimised schedule lived beyond 50 days, the longest life span displayed by any mouse on the standard schedule.

Michor is now in active discussions with physicians at MSKCC about clinically testing a version of this model adapted for use in humans.

Reference

Dolgin E. The mathematician versus the malignancy. Nature Medicine 2014; 20(5): 460–463. doi:10.1038/nm0514-460.