The number of time steps s that inactivated cells move in that singular direction is given by the Lvy-Distribution: is the walk exponent, as described in (Harris et al

The number of time steps s that inactivated cells move in that singular direction is given by the Lvy-Distribution: is the walk exponent, as described in (Harris et al., 2012). M1 and M2 cells, is the density of non-immunogenic tumor cells, is activation rate of is modeled as follows: is tumor radius, is radial velocity, is proliferation rate, is oxygen level, is intracellular concentration of reactive oxygen species, is the fraction of the volume Varespladib methyl occupied by cells and is modeled as: (x, is macrophage level in the vessel after a single macrophage injection, is VEGF concentration at half of its max, is baseline extravasation rate, is increase in extravasation due to magnetic effects, vis macrophage velocity due to the magnetic field, (x, is the reference inflow of hematocrit. These mechanics were integrated in a complex multiscale model building on work in (Owen et al., 2009), in which vascular growth, drug, oxygen, and VEGF diffusion, tissue growth, and cell movement are modeled at different timescales. Recent work by (Leonard et al., 2017; Leonard et al., 2016) considered macrophages as both immune actors and vehicles for chemotherapeutic compound delivery. This model simulates macrophages as described in (Mahlbacher et al., 2018), in which the tumor tissue itself is divided into hypoxic, necrotic and proliferating regions based on oxygen availability (Macklin et al., 2009; Wu et al., 2013) coupled with a dynamically evolving vascular system (McDougall et al., 2006). In (Leonard et al., 2017; Leonard et al., 2016), experiments were Varespladib methyl performed with macrophages uptaking a silicon-based multistage vector (MSV) loaded with the GRIA3 chemotherapeutic agent albumin-bound paclitaxel (nab-PTX). Varespladib methyl Drug and macrophage effects were evaluated in the tumor model calibrated to the experimental data. In the model, monocytes extravasate from the vasculature and migrate semi-stochastically along chemokine gradients secreted from the hypoxic and normoxic tissue regions. Contact with M1- or M2-favoring chemokines causes differentiation to macrophages, upon which they take an active role Varespladib methyl in the model (Mahlbacher et al., 2018). The tumor boundary velocity as a function of the change in overall tumor tissue proliferation rate is defined as (Macklin et al., 2009): at the location of each macrophage(1and the diffusion of secreted growth factor is defined according to oxygen concentration at concentration s acts only on the proliferating tissue due to the cell-cycle targeting mechanism of nab-PTX. The tumor tissue native apoptosis rate is experiments (Leonard et al., 2017) in which M2 were repolarized to the M1 phenotype by their uptake of nab-PTX. Interestingly, it was found that the presence of M2 in addition to M1 might lead to a stronger tumor drug response than when only M1 were active, due to the M2 macrophages favoring tumor tissue proliferation and thus increasing tumor sensitivity to the cell-cycling action of nab-PTX. 2.2. Cytotoxic T Lymphocytes Cytotoxic T Lymphocytes (CTLs) have been a leading focus of onco-immunology in recent years (Fremd et al., 2013), being well known for antitumor activity by inducing apoptosis in an infected or cancerous cell with high specificity (Maher and Davies, 2004). Thus, CTLs are a frequent cell type represented in tumor-immune interaction models. (Kirschner and Panetta, 1998) was one of the first theoretical studies to investigate the role that CTLs may have on tumor growth and regression. The interactions between populations of effector cells are modeled as follows: is the effector cell population, is the tumors antigenicity, s1 is an external source of effector cells, is the tumor cell population, 1/is the immune response strength, is the concentration of IL-2 at a single tumor-site, is effector cells that enter the system with constant rate s, are recruited at rate at rate into the Kuznetsov model to simulate the interval in which the effector cells (such Varespladib methyl as CTLs) are recruited.