Modeling cancer blood biomarker dynamics in relation to tumor growth
Sharon Seiko Hori, Amelie M. Lutz, Ramasamy Paulmurugan, Sanjiv Sam Gambhir
Objectives: Cancer biomarkers, such as proteins that are shed (secreted or released) into the bloodstream from a tumor, may be useful for detecting early-stage cancers. However, it is not clear whether cancer blood biomarker levels correlate with tumor burden, especially for early-stage (sub-centimeter) tumors . The aim of this work was to apply an integrative modeling-experimental approach to investigate whether plasma levels of a cancer-specific biomarker could be used as a surrogate measure of tumor cell viability, as measured using preclinical (mouse) cancer models and in vivo imaging.
Methods: We engineered ovarian cancer cell lines to express both an artificial tumor-specific secreted biomarker and a bioluminescence imaging reporter and then implanted these cells into the mouse ovary. We monitored the resulting tumor growth for up to 28 days using biweekly plasma biomarker samples obtained just prior to in vivo bioluminescence imaging (to assess tumor viability). We extended our previous mathematical model of biomarker shedding  to account for biomarker present in the extravascular space and obtained estimates for individualized plasma biomarker shedding rates in relation to in vivo tumor growth. Model simulations and parameter estimates were obtained using Simulation and Analysis Software II (SAAM II).
Results: We showed that a model of biomarker shedding composed of two ordinary differential equations best fitted the preclinical plasma biomarker data for up to 15 days of early tumor growth in n = 18 mice. The fitted model provided a qualitatively excellent description of all individual mouse plasma biomarker kinetic data, with reasonably low standard errors on individual parameter estimates (< 25% CV). Furthermore, plasma biomarker levels correlated well with tumor cell viability as measured using bioluminescence imaging (R2 = 0.86). Of note, the in vivo tumor-specific biomarker shedding rate was estimated to be 7×10-5 ng/day/cell. This represents the first in vivo estimate of cancer biomarker shedding rates. We further explored a range of parameter values that may be exhibited by current clinical biomarkers by performing a 1-way sensitivity analysis by simulating plasma biomarker levels while increasing/decreasing the value of a single parameter estimate up to 1000-fold.
Conclusions: We showed that during early tumor growth, tumor-specific plasma biomarker levels correlate well with tumor viability. The mathematical model developed here can be extended to virtually any solid cancer and applied to the analysis of correlations between biomarker shedding and tumor size in other in vivo preclinical models.
 Hori SS and Gambhir SS. “Mathematical model identifies blood biomarker-based early cancer detection strategies and limitations.” Sci. Trans Med. Vol. 3, Issue 109, p. 109ra116, 2011.