Mathematical model identifies blood biomarker-based early cancer detection strategies and limitations

Abstract

Most clinical blood biomarkers lack the necessary sensitivity and specificity to reliably detect cancer at an early stage, when it is best treatable. 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. To address these issues, we developed a mathematical model describing dynamic plasma biomarker kinetics in relation to the growth of a tumor, beginning with a single cancer cell. To exemplify a realistic scenario in which biomarker is shed by both cancerous and noncancerous cells, we primed the model on ovarian tumor growth and CA125 shedding data, for which tumor growth parameters and shedding rates are readily available in published literature. We found that a tumor could grow unnoticed for more than 10.1 years and reach a volume of about π/6(25.36 mm)(3), corresponding to a spherical diameter of about 25.36 mm, before becoming detectable by current clinical blood assays. Model parameters were perturbed over log orders of magnitude to quantify ideal shedding rates and identify other blood-based strategies required for early submillimeter tumor detectability. The detection times we estimated are consistent with recently published tumor progression time lines based on clinical genomic sequencing data for several cancers. Here, we rigorously showed that shedding rates of current clinical blood biomarkers are likely 10(4)-fold too low to enable detection of a developing tumor within the first decade of tumor growth. The model presented here can be extended to virtually any solid cancer and associated biomarkers.

Fig. 1. One-compartment model for plasma biomarker kinetics

The change in the amount (mass) of plasma biomarker with respect to time is equal to the difference between the influx of biomarker into plasma, as shed by tumor cells and healthy cells, u_T(t) + u_H(t), and the outflux of biomarker from plasma, k_ELq_PL(t). See “Derivation of Model Equations” in the Supplementary Material.

Fig. 2. Model-predicted detection capability of current and potential strategies for earlier cancer detection using blood biomarker assays

See Table 2 for baseline parameter values. Dashed horizontal lines indicate the mean (42 mm) and minimum (10 mm) tumor diameters detected by transvaginal ultrasound (TVUS) in a study of 1,094 women with adnexal mass (30). Detection capability using: (A) current clinical ELISA assays (assuming baseline parameter values); (B) a biomarker that has 100% vascular permeability (f_PL,T = 1); (C) a biomarker not shed by healthy cells; (D) a biomarker shed by tumor cells at a rate 10³-fold higher than baseline; (E) a biomarker not shed by healthy cells, and decreasing assay detection limit 10³-fold relative to baseline; (F) a biomarker not shed by healthy cells, and decreasing assay detection limit 10⁵-fold relative to baseline.