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Does Cancer Follow The Rules Of Math?

by — 2015-09-18 in Cancer
Thirty-two year-old Austrian-born biomathematician Franziska Michor believes that cancer cells may behave in predictable ways that can be understood with advances in mathematics.

Evolutionary biologist Franziska Michor, who earned her Ph.D. in evolutionary biology at Harvard University in 2005 at the age of 22, knew from childhood that she wanted to be a mathematician.

It was that or marry a mathematician. Her mathematician father and nurse mother had decreed that she and her sister must either become mathematicians or marry one. "Marry? Anything but that!" she is quoted as saying in a 2007 interview with Esquire, and at a very tender age Michor earned her doctoral degree at one of the most prestigious universities in the world. This began her career looking at cancer as an evolutionary process.

What Does It Mean To Say Cancer "Evolves"?

Cancer, Dr Michor explains, doesn't really evolve in the sense that humans evolved from earlier hominids or land creatures evolved from sea creatures. It isn't a natural progression from normal cell to cancer cell, as if the cancer cell were, in the sense most people understand it, "more evolved." Instead, the evolution of cancer recapitulates what really happens in the evolution of organisms.
 
The human body contains trillions of cells. Most of them function normally. Of those trillions of cells, however, millions or even billions carry mutated DNA. Cells sometimes can repair mutated DNA, and go back to normal function. Cells sometimes die because of errors in their genetic code, and are removed the immune system with inflammation. A few cells with mutated DNA become cancerous, and multiply to cause the disease.
 
If cancer cells are allowed to multiply unchecked, in most cases they form tumors, invade neighboring tissues, grow their own blood vessels, and enter the sto attach to new organs.
 
The end result of unfettered cancer growth is death. Treatments for cancer, understandably, focus on killing cancer cells. However, imprecise treatments like chemotherapy kill both cancer cells and healthy cells, rolling the dice that they will kill more cancer cells than healthy cells and result in net benefit to the patient. More precise treatments like modern radiation therapy kill cancer cells and sometimes only cancer cells, but the body still has to remove the debris with inflammation. Even the most modern immunotherapies cause temporary enlargment of tumors (which can put pressure on blood vessels and adjacent organs) as they knock out the disease.

Dr Michor's Innovation

Franziska Michor's work focuses on using modern methods to refine commonly available cancer treatments. Chemotherapy, despite its many detractors, tends to do more good than harm, at least the first few times it is used, and it is relatively inexpensive and widely available. Michor uses mathematics to calculate the least harmful doses of chemotherapy used at the optimal time to interrupt the orderly and predictable multiplication of cancer cells using modern math. Her approach has found some major successes, which will be discussed on the next page.
For her innovations, Michor received the Vilcek Prize for Creative Promise in Biomedical Science, awarded to immigrants to the United States who make noteworthy contributions to "immigrants who have made lasting contributions to American society through their extraordinary achievements in biomedical research and the arts and humanities." Using math to minimize chemotherapy certainly falls into this category.

Making Gleevec More Effective Against Leukemia

Dr Michor's prize-winning work focused on dosing and timing Gleevec, the main treatment for chronic myeloid leukemia. As chemotherapies go, Gleevec is probably the best that modern medicine has. Because it is keyed to compensating for a single defect in a single gene, rather than a complex series of mutations, it brings most cases of chronic myeloid leukemia into remission. The problem is, as soon as the treatment is stopped, the cancer returns, sometimes even more severely than before treatment.
 
Michor realized that the problem probably was that the right dose of Gleevec was not being delivered at the right time. To finesse dosing regimens, she took a look at a massive amount of bloodwork data provided by a colleague in Australia. 
 
 
What the Harvard-trained scientist discovered was that:
  • Gleevec kills leukemia cells, but has no effect on the stem cells from which they originate.
  • Gleevec is superbly suited for treating this form of leukemia, but it can never bring about a cure.
  • Even though Gleevec is a "smart" drug for this form of cancer, the cancer is smarter.
This led Michor to a question that just about every cancer specialist considers for every patient, which is better, continuous low doses of chemotherapy spread over time, or high doses of chemotherapy interspersed with "chemotherapy vacations" to minimize toxic side effects. The answer, Michor has computed, is that high-dose Gleevec interrupted by breaks to give the body a chance to recover from side effects actually works better at keeping the cancer at bey. 
 
Michor, however, is the first person to have reached this conclusion from cold, hard, factual data, rather than clinical experience.
 
It turns out that many doctors don't like the idea of an algorithm's doing their work. Rather than being hailed for her innovative work in the mathematics of cancer, Michor was attacked. Most investigators refused to share data with her for analysis. However, Michor was offered a position at New York City's Sloan-Kettering cancer center, where she now has access to massive amounts of data about multiple cancers and how they respond to conventional treatments.
 
Since Michor left Harvard (and later returned to Harvard), her research has focused on some very basic, patient-centered questions:
  • When treating patients for glioblastoma, a particularly aggressive form of brain cancer, it is necessary to wheel them into radiation in the middle of the night, so as not to waste even part of a single day before initiating treatment? Michor and her colleagues found that sticking to an 8 a.m. to 5 p.m. schedule worked just as well (and certainly gave patients and their families more opportunities to rest).
  • Is one kind of chemotherapy enough, or should cancers be attacked with multiple chemotherapy drugs? Michor and her colleagues have developed a concept of "stochastic tunneling," in which cancers caused by one mutation may develop a second mutation before the first mutation can be addressed by treatment. The implication is that one kind of chemo usually will not bring a cancer into remission.
  • Does the five-year survival rate tell us anything about how well patients feel in the years after they are diagnosed with cancer? Michor and her colleagues determined that the data indicate that survival is an indicator of how well patients feel, not just how late they die.
Michor has collaborated on over 100 studies of the mathematics of cancer. Her non-invasive conceptual tools may lead to better treatments with fewer side effects for millions of people who have cancer.

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