Modeling Longitudinal Preclinical Tumor Size Data to Identify Transient Dynamics in Tumor Response to Antiangiogenic Drugs

Abstract

Experimental evidence suggests that antiangiogenic therapy gives rise to a transient window of vessel normalization, within which the efficacy of radiotherapy and chemotherapy may be enhanced. Preclinical experiments that measure components of vessel normalization are invasive and expensive. We have developed a mathematical model of vascular tumor growth from preclinical time‐course data in a breast cancer xenograft model. We used a mixed‐effects approach for model parameterization, leveraging tumor size data to identify a period of enhanced tumor growth that could potentially correspond to the transient window of vessel normalization. We estimated the characteristics of the window for mice treated with an anti‐VEGF antibody (bevacizumab) or with a bispecific anti‐VEGF/anti‐angiopoietin‐2 antibody (vanucizumab). We show how the mathematical model could theoretically be used to predict how to coordinate antiangiogenic therapy with radiotherapy or chemotherapy to maximize therapeutic effect, reducing the need for preclinical experiments that directly measure vessel normalization parameters.

Revisiting Bevacizumab + Cytotoxics Scheduling Using Mathematical Modeling: Proof of Concept Study in Experimental Non‐Small Cell Lung Carcinoma

“…found that giving bevacizumab after targeted therapy in tumor‐bearing mice yielded better efficacy. Recently, Hutchinson et al . inferred (using a mathematical model and experimental data from breast cancer models) a vessel normalization window beginning 15 days after the start of anti‐angiogenics which is a much larger optimal delay compared to other studies .…”

“…In this respect, following previously published experimental studies, we have chosen the H460 model as a paradigm for mimicking NSCLC tumors. [36][37][38] Compared to our previous studies, 21,24 the mathematical model presented here was simplified to focus on a minimal number of equations and parameters. We abandoned a more mechanistic description of the vasculature quality in terms of stable and unstable vessels to the benefit of a more phenomenological but more parsimonious and robust model that implements normalization in terms of a simple delay from the bevacizumab concentration.…”

“…They demonstrated a possible synergistic interaction between sunitinib and irinotecan. 23 Recently, Hutchinson et al 24 developed a model of vascular tumor growth and normalization from breast cancer mice treated with bevacizumab alone. Still in breast cancer, our team tested multiple regimens for combining bevacizumab and paclitaxel.…”

Quantitative Systems Pharmacology: An Exemplar Model‐Building Workflow With Applications in Cardiovascular, Metabolic, and Oncology Drug Development

“…Capturing most mechanistic details of the cancer immunity cycle while preserving model identifiability, adequate parameter calibration, and predictive power would require an unrealistic amount of detailed molecular‐level and cellular‐level data next to longitudinal tumor‐size profiles. One approach we found actionable to overcome part of this enormous challenge is to use a population QSP modeling strategy, whereby the available mechanistic data, along with longitudinal tumor‐size data, are exploited at the individual animal‐level data in addition to NLME modeling . Population QSP modeling thus aims at remaining sufficiently mechanistic ( Figure a ) while minimizing the number of parameters to be calibrated to preserve model identifiability and predictive power—which can be achieved by taking interindividual variability into account in the model.…”

“…One approach we found actionable to overcome part of this enormous challenge is to use a population QSP modeling strategy, whereby the available mechanistic data, along with longitudinal tumor-size data, are exploited at the individual animal-level data in addition to NLME modeling. [82][83][84] Population QSP modeling thus www.psp-journal.com Helmlinger et al aims at remaining sufficiently mechanistic (Figure 5a) while minimizing the number of parameters to be calibrated to preserve model identifiability and predictive power-which can be achieved by taking interindividual variability into account in the model. Longitudinal tumorsize responses in syngeneic mice, in fact, display large interindividual variability in stark contrast to the tumorsize data typically seen in immuno-compromised mouse models.…”