PhotoA lot of attention is paid to early detection of cancer but Stanford University researchers have developed a new mathematical model that shows tumors can grow for 10 years or longer before currently available blood tests will detect them.

“The study’s results can be viewed as both bad and good news,” said Sanjiv “Sam” Gambhir, MD, PhD, professor and chair of radiology and the study’s senior author. 

The bad news, Gambhir said, is that by the time a tumor reaches a detectable size using today’s available blood tests, it is likely to have metastasized to other areas of the body, making it much more deadly than if it had been caught early on.

“The good news is that we have, potentially, 10 or even 20 years to find the tumor before it reaches this size, if only we can improve our blood-based methods of detecting tumors,” he said. “We think our mathematical model will help guide attempts to do that.”

The study advances previous research about the limits of current detection methods. For instance, it is strikingly consistent with a finding reported two years ago by Stanford biochemistry professor Patrick Brown, MD, PhD, that current ovarian cancer tests could not detect tumors early enough to make a significant dent in the mortality rate.

There is a push to develop more-sensitive diagnostic tests and find better biomarkers, and Gambhir’s new model could be an essential tool in this effort. It for the first time connects the size of a tumor with blood biomarker levels being shed by that tumor.

The analysis, which was restricted to ovarian tumors but is broadly applicable across all solid tumor types, published online Nov. 16 in Science Translational Medicine.

Mathematical model

To create their model, Gambhir and Hori used mathematical models originally developed to predict the concentration of drugs injected into the blood as they move in and out of the bloodstream. The investigators linked these to additional models of tumor cell growth.

Tumors don’t secrete drugs, but they can shed telltale molecules into surrounding tissue, from which those substances, known as biomarkers, diffuse into the blood. Some biomarkers may be made predominantly by tumor cells, while others exclusively by them. Either way, these substances can be measured in the blood as proxies for a tumor.

The new mathematical model employs separate equations, each governing the movement of a biomarker from one compartment into the next. Into these equations, one can plug known values — such as how fast a particular type of tumor grows, how much of the biomarker a tumor cell of this type sheds per hour and the minimum levels of the biomarker that must be present in the blood for a currently available assay to detect it.

In the last decade, many potential new biomarkers for different cancers have been identified. There’s no shortage of promising candidates — six for lung cancer alone, for example. But validating a biomarker in large clinical trials is a long, expensive process. So it is imperative to determine as efficiently as possible which, among many potential tumor biomarkers, is the best prospective candidate.

“This model could take some of the guesswork out of it,” Gambhir said. “It can be applied to all kinds of solid cancers and prospective biomarkers as long as we have enough data on, for instance, how much of it a tumor cell secretes per hour, how long the biomarker can circulate before it’s degraded and how quickly tumor cells divide."


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