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 mm(3) and 3,610.14 mm(3) for CA125 and between 0.21 mm(3) and 131.51 mm(3) 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 mm(3) and 1.52 × 10(6) mm(3) for CA125 and between 27 mm(3) and 3.45 × 10(5) mm(3) 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.