Cancer Screening: A Mathematical Model Relating Secreted Blood Biomarker Levels to Tumor Sizes

Background: Increasing efforts and financial resources are being invested in early cancer detection research. Blood assays detecting tumor biomarkers promise noninvasive and financially reasonable screening for early cancer with high potential of positive impact on patients' survival and quality of life. For novel tumor biomarkers, the actual tumor detection limits are usually unknown and there have been no studies exploring the tumor burden detection limits of blood tumor biomarkers using mathematical models. Therefore, the purpose of this study was to develop a mathematical model relating blood biomarker levels to tumor burden. Methods and Findings: Using a linear one-compartment model, the steady state between tumor biomarker secretion into and removal out of the intravascular space was calculated. Two conditions were assumed: (1) the compartment (plasma) is well-mixed and kinetically homogenous; (2) the tumor biomarker consists of a protein that is secreted by tumor cells into the extracellular fluid compartment, and a certain percentage of the secreted protein enters the intravascular space at a continuous rate. The model was applied to two pathophysiologic conditions: tumor biomarker is secreted (1) exclusively by the tumor cells or (2) by both tumor cells and healthy normal cells. To test the model, a sensitivity analysis was performed assuming variable conditions of the model parameters. The model parameters were primed on the basis of literature data for two established and well-studied tumor biomarkers (CA125 and prostate-specific antigen [PSA]). Assuming biomarker secretion by tumor cells only and 10% of the secreted tumor biomarker reaching the plasma, the calculated minimally detectable tumor sizes ranged between 0.11 mm3 and 3,610.14 mm3 for CA125 and between 0.21 mm3 and 131.51 mm3 for PSA. When biomarker secretion by healthy cells and tumor cells was assumed, the calculated tumor sizes leading to positive test results ranged between 116.7 mm3 and 1.52 × 106 mm3 for CA125 and between 27 mm3 and 3.45 × 105 mm3 for PSA. One of the limitations of the study is the absence of quantitative data available in the literature on the secreted tumor biomarker amount per cancer cell in intact whole body animal tumor models or in cancer patients. Additionally, the fraction of secreted tumor biomarkers actually reaching the plasma is unknown. Therefore, we used data from published cell culture experiments to estimate tumor cell biomarker secretion rates and assumed a wide range of secretion rates to account for their potential changes due to field effects of the tumor environment. Conclusions: This study introduced a linear one-compartment mathematical model that allows estimation of minimal detectable tumor sizes based on blood tumor biomarker assays. Assuming physiological data on CA125 and PSA from the literature, the model predicted detection limits of tumors that were in qualitative agreement with the actual clinical performance of both biomarkers. The model may be helpful in future estimation of minimal detectable tumor sizes for novel proteomic biomarker assays if sufficient physiologic data for the biomarker are available. The model may address the potential and limitations of tumor biomarkers, help prioritize biomarkers, and guide investments into early cancer detection research efforts. Sanjiv Gambhir and colleagues describe a linear one-compartment mathematical model that allows estimation of minimal detectable tumor sizes based on blood tumor biomarker assays. Background.: Cancers—disorganized masses of cells that can occur in any tissue—develop when cells acquire genetic changes that allow them to grow uncontrollably and to spread around the body (metastasize). If a cancer (tumor) is detected when it is small, surgery can often provide a cure. Unfortunately, many cancers (particularly those deep inside the body) are not detected until they are large enough to cause pain or other symptoms by pressing against surrounding tissue. By this time, it may be impossible to remove the original tumor surgically and there may be metastases scattered around the body. In such cases, radiotherapy and chemotherapy can sometimes help, but the outlook for patients whose cancers are detected late is often poor. Consequently, researchers are trying to develop early detection tests for different types of cancer. Many tumors release specific proteins—“cancer biomarkers”—into the blood and the hope is that it might be possible to find sets of blood biomarkers that detect cancers when they are still small and thus save many lives. Why Was This Study Done?: For most biomarkers, it is not known how the amount of protein detected in the blood relates to tumor size or how sensitive the assays for biomarkers must be to improve patient survival. In this study, the researchers develop a “linear one-compartment” mathematical model to predict how large tumors need to be before blood biomarkers can be used to detect them and test this model using published data on two established cancer biomarkers—CA125 and prostate-specific antigen (PSA). CA125 is used to monitor the progress of patients with ovarian cancer after treatment; ovarian cancer is rarely diagnosed in its early stages and only one-fourth of women with advanced disease survive for 5 y after diagnosis. PSA is used to screen for prostate cancer and has increased the detection of this cancer in its early stages when it is curable. What Did the Researchers Do and Find?: To develop a model that relates secreted blood biomarker levels to tumor sizes, the researchers assumed that biomarkers mix evenly throughout the patient's blood, that cancer cells secrete biomarkers into the fluid that surrounds them, that 0.1%–20% of these secreted proteins enter the blood at a continuous rate, and that biomarkers are continuously removed from the blood. The researchers then used their model to calculate the smallest tumor sizes that might be detectable with these biomarkers by feeding in existing data on CA125 and on PSA, including assay detection limits and the biomarker secretion rates of cancer cells growing in dishes. When only tumor cells secreted the biomarker and 10% of the secreted biomarker reach the blood, the model predicted that ovarian tumors between 0.11 mm3 (smaller than a grain of salt) and nearly 4,000 mm3 (about the size of a cherry) would be detectable by measuring CA125 blood levels (the range was determined by varying the amount of biomarker secreted by the tumor cells and the assay sensitivity); for prostate cancer, the detectable tumor sizes ranged from similar lower size to about 130 mm3 (pea-sized). However, healthy cells often also secrete small quantities of cancer biomarkers. With this condition incorporated into the model, the estimated detectable tumor sizes (or total tumor burden including metastases) ranged between grape-sized and melon-sized for ovarian cancers and between pea-sized to about grapefruit-sized for prostate cancers. What Do These Findings Mean?: The accuracy of the calculated tumor sizes provided by the researchers' mathematical model is limited by the lack of data on how tumors behave in the human body and by the many assumptions incorporated into the model. Nevertheless, the model predicts detection limits for ovarian and prostate cancer that broadly mirror the clinical performance of both biomarkers. Somewhat worryingly, the model also indicates that a tumor may have to be very large for blood biomarkers to reveal its presence, a result that could limit the clinical usefulness of biomarkers, especially if they are secreted not only by tumor cells but also by healthy cells. Given this finding, as more information about how biomarkers behave in the human body becomes available, this model (and more complex versions of it) should help researchers decide which biomarkers are likely to improve early cancer detection and patient outcomes. Additional Information.: Please access these Web sites via the online version of this summary at http://dx.doi.org/10.1371/journal.pmed.0050170.