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Stanford Team Develops Mathematical Model to Assess Effectiveness of Early-Stage Cancer Biomarkers

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By Uduak Grace Thomas

Researchers at Stanford University have created a mathematical model that sheds light on the correlation between blood biomarker levels and tumor size — information that can determine how well certain biomarkers may be suited for early cancer detection.

As the developers note in a paper published this week in Science Translational Medicine, "it is not yet clear how early a clinical blood assay can be used to detect cancer or how biomarker-based strategies can be improved to enable earlier detection of smaller tumors."

The Stanford researchers said that they developed the modeling approach in order to address this issue, as well as to "motivate the design of new experiments that challenge current hypothesis regarding biomarker detectability," and to ascertain "whether blood detection of single cancer biomarkers can ever become a feasible end-all strategy for diagnosing early-stage cancers."

The model uses a set of equations that govern biomarker kinetics and builds a link between tumor growth rates, the rate at which biomarkers are shed by tumor cells, and the detection limits of available tests, Sanjiv "Sam" Gambhir, professor and chair of Stanford's radiology department and one of the study's authors, explained to BioInform this week.

Users can enter information such as how fast a particular type of cancer grows, how much of the biomarker a tumor cell sheds per hour, and the minimum level of the biomarker that must be present in the blood for a specific assay to detect it. The model then uses this data to calculate how early a given biomarker would be able to detect a particular type of tumor.

The approach "[quantif[ies] the time required for a growing malignant tumor ... to reach a sufficient size so that its shed blood biomarker levels were high enough to be detected by current clinical assays," the authors wrote in the paper.

These calculations, the researchers wrote, can be used to identify the most important biomarker parameters, as well as to "quantify how far each parameter value would need to change" in order to detect the disease earlier.

Gambhir likened the approach to models used by pharmacologists to determine drug dosing.

These models take into account information such as "the rate at which [the drug] will move from the blood to the kidneys," he explained. "Those same models are being used here but now instead of someone injecting a drug into you, the tumor from within you is injecting the biomarker into the blood."

He explained that the approach provides a framework for determining "what characteristics [are needed in] blood tests in order to detect a tumor of a certain size" — data that should aid in the development of assays that can detect tumors well before they spread.

No More Guessing

There are "thousands of potential biomarkers that are being reported and examined for diagnostic use, however few are routinely being used in the clinic," the authors note in the paper.

Furthermore, it is still unclear whether biomarkers from very small tumors — those that are smaller than a cubic centimeter in size — can be detected, the team said.

Part of the problem is that there is very little quantitative, in vivo data available for biological factors such as "the effects of cancer heterogeneity on tumor growth" and the rate at which tumors secrete biomarkers. As such, the correlation between blood biomarker levels and the growth of the cancer "is not well understood," they wrote

Furthermore, in some cases, healthy cells also secrete the same proteins at varying levels, which can result in false positives — particularly in studies involving large patient populations.

"This model could take some of the guesswork out of [developing early-stage cancer tests]," Gambhir said in a statement.

In their paper, the researchers describe how they applied the model to CA125 — an FDA-approved biomarker for ovarian cancer.

When the team considered blood biomarkers shed by both tumor cells and healthy cells, they determined that currently available tests would only be able to detect a tumor when it had grown to a size of about 1.7 billion cells, around the size of a 2 cm cube. Furthermore, they estimated that it could take the tumor more than 12 years to grow to this detectable level.

By shifting certain parameters of the model, they were able to demonstrate the features that would be necessary to detect tumors at a much smaller size. For example, they found that a hypothetical marker shed only by ovarian tumor cells would be able to detect a tumor around 10 millimeters in diameter, which would require around nine years of unnoticed growth.

A key finding of the paper is that even with current biomarker-based tests, tumors can go unnoticed for ten or more years, the researchers noted. By that time, the cancer 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," Gambhir said. "Our mathematical model will help guide attempts to do that."

He noted that the method could be applied to other cancer types beyond ovarian cancer provided there is enough data to feed the equations.

"We can tweak one or another variable — for instance, whether a biomarker is also made in healthy tissues or just the tumor, or assume we could manage to boost the sensitivity of our blood tests by 10-fold or 100-fold — and see how much it advances our ability to detect the tumor earlier on," he explained.

Gambhir added that the method can also identify biomarkers other than proteins, including DNA and microRNA markers.

Besides highlighting the limitations of current cancer clinical assays, the Stanford study discusses the need for more sensitive diagnostic tests.

The researchers note, for example, that a 10-fold improvement in assay detection limit could identify a 5 mm diameter tumor, which would be around eight years old.

Currently, the team is using mouse models to test whether the model's predictions hold up in vivo, Gambhir told BioInform.

He also said that since the method is fully described in the Science Translational Medicine paper, test developers should be able to use it as long as they have the requisite data about the properties of the biomarkers of the cancer in question.

Catch 'em Young

In the paper, the authors point out that although cancer can be treated effectively if caught early, the bulk of medical diagnoses are made when the disease is quite advanced.

As an example, the paper states that ovarian cancer patients diagnosed at stage I have 5-year survival rates of around 90 percent, but the reality is that "more than 80 percent of ovarian cancer patients are diagnosed when symptoms arise during stages III and IV, when 5-year survival rates become less than 30 percent."

"There aren't a lot of early cancer detection tests or ones that work," Gambhir told BioInform, adding that current tests monitor tumors' response to therapy in patients that have already been diagnosed with cancer or, as in the case of CA125, detect elevated levels of biomarkers that indicate that the disease has reached a relatively advanced stage.

He likened the problem to crab grass growing on a large field. "While its much easier to find the crab grass after its spread all over the field ... trying to find the crab grass when it first starts, when there is one patch … is very hard because there is less information and less evidence that it's there."


Have topics you'd like to see covered in BioInform? Contact the editor at uthomas [at] genomeweb [.] com.

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