Fig 1.
Mathematical modeling reveals differential effects of neoadjuvant sunitinib treatment on primary tumor and metastatic growth.
(A) Schematic of the study. Data from an ortho-surgical, human xenograft animal model of neoadjuvant sunitinib breast cancer treatment were fitted using a mixed-effects statistical framework. This provided calibrated parameters for each animal. Machine learning algorithms were used to assess the predictive power of molecular and cellular biomarkers to predict the metastatic dissemination parameter μ and quantify metastatic aggressiveness. (B) Schematic of tested hypotheses of the effect of neoadjuvant sunitinib Tx on primary tumor and metastatic growth and dissemination through mechanistic mathematical modeling. Scenario A = growth arrest on both primary and secondary tumors. Scenario B = growth arrest on primary tumor only. (C) Predicted simulations of Scenarios A and B using parameters calibrated from a previous study involving untreated (vehicle) animals only [4]. Data plotted here (LM2-4LUC+ bioluminescent human breast cancer cells orthotopically injected in mice) was not used to estimate the model parameters. Tx, treatment; PT, primary tumor; MB, metastatic burden. *See methods for additional details on animal experiments, treatment dose and duration, and mechanistic model. The mouse images were drawn using Biorender.
Table 1.
Parameter estimates of the metastatic and survival models obtained by likelihood maximization via the SAEM algorithm.
Fig 2.
Calibration and validation of a kinetics-pharmacodynamics (K-PD) mathematical model for neoadjuvant sunitinib treatment effect on pre- and post-surgical tumor growth.
Pre- and postsurgical growth of LM2-4LUC+ human metastatic breast carcinomas were measured in multiple groups involving different neoadjuvant treatment modalities (doses and durations). The mathematical model was fitted to the experimental data using a mixed-effects population approach (n = 104 animals in total). (A) Comparison of the simulated model population distribution (visual predictive check) for vehicle and neoadjuvant sunitinib treatment (60mg/kg/day) 14 days before surgery. (B) Examples of individual dynamics. Tx, treatment; PT, primary tumor; MB, metastatic burden.
Fig 3.
Simulations of varying neoadjuvant treatment duration quantify contrasted impact on primary tumor size reduction and risk of metastatic relapse.
Using model parameters calibrated from data of our ortho-surgical animal model of breast cancer neoadjuvant targeted treatment, simulations were conducted for treatment durations varying between 0 (light color) and 18 (dark color) days, for three dose levels (60 mg/kg, 120 mg/kg and 240 mg/kg). (A) Predicted simulations of pre-surgical primary tumor and post-surgical metastatic kinetics. Note: for the 240 mg/kg plot, the metastatic burden growth curves with the three longest treatment durations are superimposed and not distinguishable. (B) Population-level predictions of final primary tumor size (solid line and grey area) and probability of metastatic relapse as functions of the duration of neoadjuvant treatment, which delays surgical removal of the primary tumor (circled line). Inter-individual variability simulated from the population distribution of the parameters learned from the data (n = 1000 virtual subjects). Tx, treatment; PT, primary tumor; MB, metastatic burden.
Fig 4.
Use of machine learning algorithms based on presurgical molecular and cellular markers to predict metastatic dissemination parameter ‘μ’.
(A-C) Examples of molecular and cellular biomarker analysis. (A) Proliferating endothelial cell identification by immunofluorescence. Tissue sections from resected tumors were stained with antibodies against mouse CD31 (red) and mouse Ki67 (green) and counterstained with DAPI (blue). Single channel and merged images are shown. Yellow arrows show proliferating endothelial cells which were counted manually. (B) Myeloid-Derived Suppressor Cells (MDSC) quantification by flow cytometry. Whole blood was stained with anti-mouse antibodies for CD45, CD11b, and Gr1. After selection of CD45-positive cells, MDSCs were analyzed based on CD11b and Gr1 levels. Monocytic-MDSC (M-MDSC) are CD11b+/Gr1 high and granulocytic-MDSC (G-MDSC) are CD11b+/Gr1Medium. Examples of MDSC in untreated and treated animals are shown. (C) CTC quantification by flow cytometry. CTCs for xenografts were identified using anti-human HLA. Blood was stained with anti-mouse CD45 and anti-human HLA. Blood and LM2-4 cell samples were overlaid in a dot plot to identify and create the gates for CTCs. Once the gates were created CTC were identified in the blood of tumor-bearing mice. (D) Pearson correlation coefficients between biomarkers. Blue (resp. red) color indicates a positive (resp. negative) correlation, with the size of the circle being proportional to the R2 correlation coefficient. * p<0.05, ** p<0.01, *** p<0.001. (E) Univariate correlations between the biomarkers and the mathematical parameters. DT = doubling time. (F) Cross-validated Root Mean Square Error (RMSE) across different machine learning regression models (see methods) utilizing the values of the biomarkers for predicting log(μ). To assess the significance of the covariate in the models, RMSEs were compared against the value of this metric obtained using the intercept-only model. Bars are 95% confidence intervals. Shown in red is the model with the lowest RMSE. PLS = Partial Least Squares. SVM = Support Vector Machines. (G) Cross-validated R2 with 95% confidence intervals. (H) Predictions versus observations for the conditional random forest algorithm.