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.

Predicting breast cancer response to neoadjuvant chemotherapy based on tumor vascular features in needle biopsies.

In clinical breast cancer intervention, selection of the optimal treatment protocol based on predictive biomarkers remains an elusive goal. Here, we present a modeling tool to predict the likelihood of breast cancer response to neoadjuvant chemotherapy using patient specific tumor vasculature biomarkers. A semi-automated analysis was implemented and performed on 3990 histological images from 48 patients, with 10-208 images analyzed for each patient. We applied a histology-based model to resected primary breast cancer tumors (n = 30), and then evaluated a cohort of patients (n = 18) undergoing neoadjuvant chemotherapy, collecting pre- and post-treatment pathology specimens and MRI data. We found that core biopsy samples can be used with acceptable accuracy (r = 0.76) to determine histological parameters representative of the whole tissue region. Analysis of model histology parameters obtained from tumor vasculature measurements, specifically diffusion distance divided by radius of drug source (L/rb) and blood volume fraction (BVF), provides a statistically significant separation of patients obtaining a pathologic complete response (pCR) from those that do not (Student's t-test; P < 0.05). With this model, it is feasible to evaluate primary breast tumor vasculature biomarkers in a patient specific manner, thereby allowing a precision approach to breast cancer treatment.

Understanding the Connection between Nanoparticle Uptake and Cancer Treatment Efficacy using Mathematical Modeling.

Nanoparticles have shown great promise in improving cancer treatment efficacy while reducing toxicity and treatment side effects. Predicting the treatment outcome for nanoparticle systems by measuring nanoparticle biodistribution has been challenging due to the commonly unmatched, heterogeneous distribution of nanoparticles relative to free drug distribution. We here present a proof-of-concept study that uses mathematical modeling together with experimentation to address this challenge. Individual mice with 4T1 breast cancer were treated with either nanoparticle-delivered or free doxorubicin, with results demonstrating improved cancer kill efficacy of doxorubicin loaded nanoparticles in comparison to free doxorubicin. We then developed a mathematical theory to render model predictions from measured nanoparticle biodistribution, as determined using graphite furnace atomic absorption. Model analysis finds that treatment efficacy increased exponentially with increased nanoparticle accumulation within the tumor, emphasizing the significance of developing new ways to optimize the delivery efficiency of nanoparticles to the tumor microenvironment.

Mechanistic modeling identifies drug-uptake history as predictor of tumor drug resistance and nano-carrier-mediated response.

A quantitative understanding of the advantages of nanoparticle-based drug delivery vis-à-vis conventional free drug chemotherapy has yet to be established for cancer or other diseases despite numerous investigations. Here, we employ first-principles cell biophysics, drug pharmaco-kinetics, and drug pharmaco-dynamics to model the delivery of doxorubicin (DOX) to hepatocellular carcinoma (HCC) tumor cells and predict the resultant experimental cytotoxicity data. The fundamental, mechanistic hypothesis of our mathematical model is that the integrated history of drug uptake by the cells over time of exposure, which sets the cell death rate parameter, and the uptake rate are the sole determinants of the dose response relationship. A universal solution of the model equations is capable of predicting the entire, nonlinear dose response of the cells to any drug concentration based on just two separate measurements of these cellular parameters. This analysis reveals that nanocarrier-mediated delivery overcomes resistance to the free drug because of improved cellular uptake rates, and that dose response curves to nanocarrier mediated drug delivery are equivalent to those for free-drug, but "shifted to the left;" that is, lower amounts of drug achieve the same cell kill. We then demonstrate the model's general applicability to different tumor and drug types, and cell-exposure time courses by investigating HCC cells exposed to cisplatin and 5-fluorouracil, breast cancer MCF-7 cells exposed to DOX, and pancreatic adenocarcinoma PANC-1 cells exposed to gemcitabine. The model will help in the optimal design of nanocarriers for clinical applications and improve the current, largely empirical understanding of in vivo drug transport and tumor response.