Theory and Experimental Validation of a Spatio-temporal Model of Chemotherapy Transport to Enhance Tumor Cell Kill.

AUTHOR SUMMARY: Cancer treatment efficacy can be significantly enhanced through the elution of drug from nano-carriers that can temporarily stay in the tumor vasculature. Here we present a relatively simple yet powerful mathematical model that accounts for both spatial and temporal heterogeneities of drug dosing to help explain, examine, and prove this concept. We find that the delivery of systemic chemotherapy through a certain form of nano-carriers would have enhanced tumor kill by a factor of 2 to 4 over the standard therapy that the patients actually received. We also find that targeting blood volume fraction (a parameter of the model) through vascular normalization can achieve more effective drug delivery and tumor kill. More importantly, this model only requires a limited number of parameters which can all be readily assessed from standard clinical diagnostic measurements (e.g., histopathology and CT). This addresses an important challenge in current translational research and justifies further development of the model towards clinical translation.

A hybrid agent-based model of the developing mammary terminal end bud.

Mammary gland ductal elongation is spearheaded by terminal end buds (TEBs), where populations of highly proliferative cells are maintained throughout post-pubertal organogenesis in virgin mice until the mammary fat pad is filled by a mature ductal tree. We have developed a hybrid multiscale agent-based model to study how cellular differentiation pathways, cellular proliferation capacity, and endocrine and paracrine signaling play a role during development of the mammary gland. A simplified cellular phenotypic hierarchy that includes stem, progenitor, and fully differentiated cells within the TEB was implemented. Model analysis finds that mammary gland development was highly sensitive to proliferation events within the TEB, with progenitors likely undergoing 2-3 proliferation cycles before transitioning to a non-proliferative phenotype, and this result is in agreement with our previous experimental work. Endocrine and paracrine signaling were found to provide reliable ductal elongation rate regulation, while variations in the probability a new daughter cell will be of a proliferative phenotype were seen to have minimal effects on ductal elongation rates. Moreover, the distribution of cellular phenotypes within the TEB was highly heterogeneous, demonstrating significant allowable plasticity in possible phenotypic distributions while maintaining biologically relevant growth behavior. Finally, simulation results indicate ductal elongation rates due to cellular proliferation within the TEB may have a greater sensitivity to upstream endocrine signaling than endothelial to stromal paracrine signaling within the TEB. This model provides a useful tool to gain quantitative insights into cellular population dynamics and the effects of endocrine and paracrine signaling within the pubertal terminal end bud.

Predictive Modeling of Drug Response in Non-Hodgkin's Lymphoma.

We combine mathematical modeling with experiments in living mice to quantify the relative roles of intrinsic cellular vs. tissue-scale physiological contributors to chemotherapy drug resistance, which are difficult to understand solely through experimentation. Experiments in cell culture and in mice with drug-sensitive (Eµ-myc/Arf-/-) and drug-resistant (Eµ-myc/p53-/-) lymphoma cell lines were conducted to calibrate and validate a mechanistic mathematical model. Inputs to inform the model include tumor drug transport characteristics, such as blood volume fraction, average geometric mean blood vessel radius, drug diffusion penetration distance, and drug response in cell culture. Model results show that the drug response in mice, represented by the fraction of dead tumor volume, can be reliably predicted from these inputs. Hence, a proof-of-principle for predictive quantification of lymphoma drug therapy was established based on both cellular and tissue-scale physiological contributions. We further demonstrate that, if the in vitro cytotoxic response of a specific cancer cell line under chemotherapy is known, the model is then able to predict the treatment efficacy in vivo. Lastly, tissue blood volume fraction was determined to be the most sensitive model parameter and a primary contributor to drug resistance.