Computational Modeling of Tumor Response to Vascular-Targeting Therapies—Part I: Validation

Mathematical modeling techniques have been widely employed to understand how cancer grows, and, more recently, such approaches have been used to understand how cancer can be controlled. In this manuscript, a previously validated hybrid cellular automaton model of tumor growth in a vascularized environment is used to study the antitumor activity of several vascular-targeting compounds of known efficacy. In particular, this model is used to test the antitumor activity of a clinically used angiogenesis inhibitor (both in isolation, and with a cytotoxic chemotherapeutic) and a vascular disrupting agent currently undergoing clinical trial testing. I demonstrate that the mathematical model can make predictions in agreement with preclinical/clinical data and can also be used to gain more insight into these treatment protocols. The results presented herein suggest that vascular-targeting agents, as currently administered, cannot lead to cancer eradication, although a highly efficacious agent may lead to long-term cancer control

A Novel Three-Phase Model of Brain Tissue Microstructure

We propose a novel biologically constrained three-phase model of the brain microstructure. Designing a realistic model is tantamount to a packing problem, and for this reason, a number of techniques from the theory of random heterogeneous materials can be brought to bear on this problem. Our analysis strongly suggests that previously developed two-phase models in which cells are packed in the extracellular space are insufficient representations of the brain microstructure. These models either do not preserve realistic geometric and topological features of brain tissue or preserve these properties while overestimating the brain's effective diffusivity, an average measure of the underlying microstructure. In light of the highly connected nature of three-dimensional space, which limits the minimum diffusivity of biologically constrained two-phase models, we explore the previously proposed hypothesis that the extracellular matrix is an important factor that contributes to the diffusivity of brain tissue. Using accurate first-passage-time techniques, we support this hypothesis by showing that the incorporation of the extracellular matrix as the third phase of a biologically constrained model gives the reduction in the diffusion coefficient necessary for the three-phase model to be a valid representation of the brain microstructure

Mitigating non-genetic resistance to checkpoint inhibition based on multiple states of immune exhaustion

Abstract Despite the revolutionary impact of immune checkpoint inhibition on cancer therapy, the lack of response in a subset of patients, as well as the emergence of resistance, remain significant challenges. Here we explore the theoretical consequences of the existence of multiple states of immune cell exhaustion on response to checkpoint inhibition therapy. In particular, we consider the emerging understanding that T cells can exist in various states: fully functioning cytotoxic cells, reversibly exhausted cells with minimal cytotoxicity, and terminally exhausted cells. We hypothesize that inflammation augmented by drug activity triggers transitions between these phenotypes, which can lead to non-genetic resistance to checkpoint inhibitors. We introduce a conceptual mathematical model, coupled with a standard 2-compartment pharmacometric (PK) model, that incorporates these mechanisms. Simulations of the model reveal that, within this framework, the emergence of resistance to checkpoint inhibitors can be mitigated through altering the dose and the frequency of administration. Our analysis also reveals that standard PK metrics do not correlate with treatment outcome. However, we do find that levels of inflammation that we assume trigger the transition from the reversibly to terminally exhausted states play a critical role in therapeutic outcome. A simulation of a population that has different values of this transition threshold reveals that while the standard high-dose, low-frequency dosing strategy can be an effective therapeutic design for some, it is likely to fail a significant fraction of the population. Conversely, a metronomic-like strategy that distributes a fixed amount of drug over many doses given close together is predicted to be effective across the entire simulated population, even at a relatively low cumulative drug dose. We also demonstrate that these predictions hold if the transitions between different states of immune cell exhaustion are triggered by prolonged antigen exposure, an alternative mechanism that has been implicated in this process. Our theoretical analyses demonstrate the potential of mitigating resistance to checkpoint inhibitors via dose modulation

Fostering Diversity in Top-Rated Pure Mathematics Graduate Programs

The lack of a diverse student body continues to be a prob- lem among graduate programs in pure mathematics. This is true despite broad agreement among scholars that a more diverse student body would greatly improve the graduate experience, as well as overall professional productivity [1]. In an article entitled “Prioritizing Diversity in Graduate School,” Dr. Mark J. T. Smith, dean of the Graduate School and senior vice provost for academic affairs at The Univer- sity of Texas at Austin, noted, “Diversity is a strength we should fervently embrace, as it allows us to leverage the rich perspectives, experiences and talents of the full spectrum of groups in our society” [1]. In this article, we explore what some top-rated pure mathematics graduate programs are doing to make their programs more diverse and inclusive. Most of the infor- mation in this article was gleaned from discussions with representatives from Columbia University, Harvard Uni- versity, Massachusetts Institute of Technology, Princeton University, Stanford University, University of California Berkeley, and University of Chicago. Our aims are to report what these programs are doing, to give context to why these efforts are important, and to stimulate further discussion about diversity and inclusion in pure mathematics. This article is not directly applicable to related fields like applied mathematics and statistics (although trends in those fields are similar)