A global sensitivity analysis of a mechanistic model of neoadjuvant chemotherapy for triple negative breast cancer constrained by in vitro and in vivo imaging data.

Unlabelled: Neoadjuvant chemotherapy (NAC) is a standard-of-care treatment for locally advanced triple negative breast cancer (TNBC) before surgery. The early assessment of TNBC response to NAC would enable an oncologist to adapt the therapeutic plan of a non-responding patient, thereby improving treatment outcomes while preventing unnecessary toxicities. To this end, a promising approach consists of obtaining in silico personalized forecasts of tumor response to NAC via computer simulation of mechanistic models constrained with patient-specific magnetic resonance imaging (MRI) data acquired early during NAC.

Investigating tumor-host response dynamics in preclinical immunotherapy experiments using a stepwise mathematical modeling strategy.

Immunotherapies such as checkpoint blockade to PD1 and CTLA4 can have varied effects on individual tumors. To quantify the successes and failures of these therapeutics, we developed a stepwise mathematical modeling strategy and applied it to mouse models of colorectal and breast cancer that displayed a range of therapeutic responses. Using longitudinal tumor volume data, an exponential growth model was utilized to designate response groups for each tumor type.

Comparing mechanism-based and machine learning models for predicting the effects of glucose accessibility on tumor cell proliferation.

Glucose plays a central role in tumor metabolism and development and is a target for novel therapeutics. To characterize the response of cancer cells to blockade of glucose uptake, we collected time-resolved microscopy data to track the growth of MDA-MB-231 breast cancer cells. We then developed a mechanism-based, mathematical model to predict how a glucose transporter (GLUT1) inhibitor (Cytochalasin B) influences the growth of the MDA-MB-231 cells by limiting access to glucose.

Towards integration of time-resolved confocal microscopy of a 3D in vitro microfluidic platform with a hybrid multiscale model of tumor angiogenesis.

The goal of this study is to calibrate a multiscale model of tumor angiogenesis with time-resolved data to allow for systematic testing of mathematical predictions of vascular sprouting. The multi-scale model consists of an agent-based description of tumor and endothelial cell dynamics coupled to a continuum model of vascular endothelial growth factor concentration. First, we calibrate ordinary differential equation models to time-resolved protein concentration data to estimate the rates of secretion and consumption of vascular endothelial growth factor by endothelial and tumor cells, respectively.

Analysis of simplicial complexes to determine when to sample for quantitative DCE MRI of the breast.

Purpose: A method is presented to select the optimal time points at which to measure DCE-MRI signal intensities, leaving time in the MR exam for high-spatial resolution image acquisition.

Theory: Simplicial complexes are generated from the Kety-Tofts model pharmacokinetic parameters K and v . A geometric search selects optimal time points for accurate estimation of perfusion parameters.

Towards Patient-Specific Optimization of Neoadjuvant Treatment Protocols for Breast Cancer Based on Image-Guided Fluid Dynamics.

Objective: This study establishes a fluid dynamics model personalized with patient-specific imaging data to optimize neoadjuvant therapy (i.e., doxorubicin) protocols for breast cancers.

Quantitative multiparametric MRI predicts response to neoadjuvant therapy in the community setting.

Background: The purpose of this study was to determine whether advanced quantitative magnetic resonance imaging (MRI) can be deployed outside of large, research-oriented academic hospitals and into community care settings to predict eventual pathological complete response (pCR) to neoadjuvant therapy (NAT) in patients with locally advanced breast cancer.

Methods: Patients with stage II/III breast cancer (N = 28) were enrolled in a multicenter study performed in community radiology settings. Dynamic contrast-enhanced (DCE) and diffusion-weighted (DW)-MRI data were acquired at four time points during the course of NAT.

Quantitative magnetic resonance imaging and tumor forecasting of breast cancer patients in the community setting.

This protocol describes a complete data acquisition, analysis and computational forecasting pipeline for employing quantitative MRI data to predict the response of locally advanced breast cancer to neoadjuvant therapy in a community-based care setting. The methodology has previously been successfully applied to a heterogeneous patient population. The protocol details how to acquire the necessary images followed by registration, segmentation, quantitative perfusion and diffusion analysis, model calibration, and prediction.

Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data.

Tumor-associated vasculature is responsible for the delivery of nutrients, removal of waste, and allowing growth beyond 2-3 mm. Additionally, the vascular network, which is changing in both space and time, fundamentally influences tumor response to both systemic and radiation therapy. Thus, a robust understanding of vascular dynamics is necessary to accurately predict tumor growth, as well as establish optimal treatment protocols to achieve optimal tumor control.

A time-resolved experimental-mathematical model for predicting the response of glioma cells to single-dose radiation therapy.

Purpose: To develop and validate a mechanism-based, mathematical model that characterizes 9L and C6 glioma cells' temporal response to single-dose radiation therapy in vitro by explicitly incorporating time-dependent biological interactions with radiation.

Methods: We employed time-resolved microscopy to track the confluence of 9L and C6 glioma cells receiving radiation doses of 0, 2, 4, 6, 8, 10, 12, 14 or 16 Gy. DNA repair kinetics are measured by γH2AX expression via flow cytometry.

Towards an Image-Informed Mathematical Model of In Vivo Response to Fractionated Radiation Therapy.

Fractionated radiation therapy is central to the treatment of numerous malignancies, including high-grade gliomas where complete surgical resection is often impractical due to its highly invasive nature. Development of approaches to forecast response to fractionated radiation therapy may provide the ability to optimize or adapt treatment plans for radiotherapy. Towards this end, we have developed a family of 18 biologically-based mathematical models describing the response of both tumor and vasculature to fractionated radiation therapy.

Integrating Quantitative Assays with Biologically Based Mathematical Modeling for Predictive Oncology.

We provide an overview on the use of biological assays to calibrate and initialize mechanism-based models of cancer phenomena. Although artificial intelligence methods currently dominate the landscape in computational oncology, mathematical models that seek to explicitly incorporate biological mechanisms into their formalism are of increasing interest. These models can guide experimental design and provide insights into the underlying mechanisms of cancer progression.

Towards integration of Cu-DOTA-trastuzumab PET-CT and MRI with mathematical modeling to predict response to neoadjuvant therapy in HER2 + breast cancer.

While targeted therapies exist for human epidermal growth factor receptor 2 positive (HER2 +) breast cancer, HER2 + patients do not always respond to therapy. We present the results of utilizing a biophysical mathematical model to predict tumor response for two HER2 + breast cancer patients treated with the same therapeutic regimen but who achieved different treatment outcomes. Quantitative data from magnetic resonance imaging (MRI) and Cu-DOTA-trastuzumab positron emission tomography (PET) are used to estimate tumor density, perfusion, and distribution of HER2-targeted antibodies for each individual patient.

Integrating transcriptomics and bulk time course data into a mathematical framework to describe and predict therapeutic resistance in cancer.

A significant challenge in the field of biomedicine is the development of methods to integrate the multitude of dispersed data sets into comprehensive frameworks to be used to generate optimal clinical decisions. Recent technological advances in single cell analysis allow for high-dimensional molecular characterization of cells and populations, but to date, few mathematical models have attempted to integrate measurements from the single cell scale with other types of longitudinal data. Here, we present a framework that actionizes static outputs from a machine learning model and leverages these as measurements of state variables in a dynamic model of treatment response.

Evaluating patient-specific neoadjuvant regimens for breast cancer via a mathematical model constrained by quantitative magnetic resonance imaging data.

The ability to accurately predict response and then rigorously optimize a therapeutic regimen on a patient-specific basis, would transform oncology. Toward this end, we have developed an experimental-mathematical framework that integrates quantitative magnetic resonance imaging (MRI) data into a biophysical model to predict patient-specific treatment response of locally advanced breast cancer to neoadjuvant therapy. Diffusion-weighted and dynamic contrast-enhanced MRI data is collected prior to therapy, after 1 cycle of therapy, and at the completion of the first therapeutic regimen.

Optimal Control Theory for Personalized Therapeutic Regimens in Oncology: Background, History, Challenges, and Opportunities.

Optimal control theory is branch of mathematics that aims to optimize a solution to a dynamical system. While the concept of using optimal control theory to improve treatment regimens in oncology is not novel, many of the early applications of this mathematical technique were not designed to work with routinely available data or produce results that can eventually be translated to the clinical setting. The purpose of this review is to discuss clinically relevant considerations for formulating and solving optimal control problems for treating cancer patients.

Anti-HER2 induced myeloid cell alterations correspond with increasing vascular maturation in a murine model of HER2+ breast cancer.

Background: Therapy targeted to the human epidermal growth factor receptor type 2 (HER2) is used in combination with cytotoxic therapy in treatment of HER2+ breast cancer. Trastuzumab, a monoclonal antibody that targets HER2, has been shown pre-clinically to induce vascular changes that can increase delivery of chemotherapy. To quantify the role of immune modulation in treatment-induced vascular changes, this study identifies temporal changes in myeloid cell infiltration with corresponding vascular alterations in a preclinical model of HER2+ breast cancer following trastuzumab treatment.

Forecasting tumor and vasculature response dynamics to radiation therapy via image based mathematical modeling.

Background: Intra-and inter-tumoral heterogeneity in growth dynamics and vascularity influence tumor response to radiation therapy. Quantitative imaging techniques capture these dynamics non-invasively, and these data can initialize and constrain predictive models of response on an individual basis.

Methods: We have developed a family of 10 biologically-based mathematical models describing the spatiotemporal dynamics of tumor volume fraction, blood volume fraction, and response to radiation therapy.

Experimentally-driven mathematical modeling to improve combination targeted and cytotoxic therapy for HER2+ breast cancer.

The goal of this study is to experimentally and computationally investigate combination trastuzumab-paclitaxel therapies and identify potential synergistic effects due to sequencing of the therapies with in vitro imaging and mathematical modeling. Longitudinal alterations in cell confluence are reported for an in vitro model of BT474 HER2+ breast cancer cells following various dosages and timings of paclitaxel and trastuzumab combination regimens. Results of combination drug regimens are evaluated for drug interaction relationships based on order, timing, and quantity of dose of the drugs.

The 2019 mathematical oncology roadmap.

Whether the nom de guerre is Mathematical Oncology, Computational or Systems Biology, Theoretical Biology, Evolutionary Oncology, Bioinformatics, or simply Basic Science, there is no denying that mathematics continues to play an increasingly prominent role in cancer research. Mathematical Oncology-defined here simply as the use of mathematics in cancer research-complements and overlaps with a number of other fields that rely on mathematics as a core methodology. As a result, Mathematical Oncology has a broad scope, ranging from theoretical studies to clinical trials designed with mathematical models.

Calibrating a Predictive Model of Tumor Growth and Angiogenesis with Quantitative MRI.

The spatiotemporal variations in tumor vasculature inevitably alters cell proliferation and treatment efficacy. Thus, rigorous characterization of tumor dynamics must include a description of this phenomenon. We have developed a family of biophysical models of tumor growth and angiogenesis that are calibrated with diffusion-weighted magnetic resonance imaging (DW-MRI) and dynamic contrast-enhanced (DCE-) MRI data to provide individualized tumor growth forecasts.

Magnetization Transfer MRI of Breast Cancer in the Community Setting: Reproducibility and Preliminary Results in Neoadjuvant Therapy.

Repeatability and reproducibility of magnetization transfer magnetic resonance imaging of the breast, and the ability of this technique to assess the response of locally advanced breast cancer to neoadjuvant therapy (NAT), are determined. Reproducibility scans at 3 different 3 T scanners, including 2 scanners in community imaging centers, found a 16.3% difference (n = 3) in magnetization transfer ratio (MTR) in healthy breast fibroglandular tissue.

Mechanism-Based Modeling of Tumor Growth and Treatment Response Constrained by Multiparametric Imaging Data.

Multiparametric imaging is a critical tool in the noninvasive study and assessment of cancer. Imaging methods have evolved over the past several decades to provide quantitative measures of tumor and healthy tissue characteristics related to, for example, cell number, blood volume fraction, blood flow, hypoxia, and metabolism. Mechanistic models of tumor growth also have matured to a point where the incorporation of patient-specific measures could provide clinically relevant predictions of tumor growth and response.