Processes 2019, 7,37
growth. In a further study, they found that the macrophage/tumor cell ratio was most sensitive to the
strength of EGF signaling, but usually maintained a 1:3 ratio [133].
Another ABM of triple-negative breast cancer examined the tumor enhancing effects of
macrophages [134]. Norton et al. investigated the interplay between tumor growth, blood vessel
recruitment and macrophage recruitment through tumor vasculature. They observed that while
macrophages increase tumor growth, excessive macrophage recruitment conversely leads to a decrease
in tumor growth due to the inhibition of proliferation resulting from overcrowding.
3.6. Models Focusing on Intra-Tumor Heterogeneity
Intra-tumor heterogeneity and the characteristics of the tumor microenvironment are found to
have important implications in the outcome of disease progression [135]. Patients often have varied
responses to treatment because each patient is unique in their genome, microbiome, disease history,
lifestyle, and environment. The case of tumors is especially complex, because this heterogeneity is
observed not only between tumors, but also between subpopulations of cells from the same tumor,
resulting in different response to drugs [136]. While capturing this degree of heterogeneity may be
difficult in experiments and clinical trials, especially the temporal dynamics of spatial heterogeneity,
computational models are especially suited to tackling this challenge. This section focuses on the
models that have aimed to capture intra-tumor heterogeneity.
A 2D agent-based model was used to study the interactions between an avascular tumor
and immune cells (NK cells and cytotoxic T-cells) [137]. They examined the effects of cancer cell
proliferation on overall tumor growth under two conditions: the first, where cancer cells do not
consider the microenvironment when deciding when to proliferate, and the second, where they
proliferate based on the number of healthy cells surrounding them. Tumor-immune cell interaction
can have three outcomes: tumor cell death, immune cell death, or no cell death based on the state
of the tumor. The predicted growth of the tumor was then compared to a xenograft tumor growth.
Spatial heterogeneity was also examined in a different model where cancer cells use glycolysis instead
of oxidative phosphorylation to increase their energy production. In order to study how this increased
energy production affects the surrounding stroma, a combination of computational modeling and
in vitro/in vivo experiments was used [138]. They used agent-based modeling to understand tumor
growth in a vascularized area of the tumor. They found that tumors develop spatial patterns where
macrophages and tumor cells coexisted in areas with high levels of oxygen, but that only tumor cells
survived in ischemic regions. They then used an in vitro tissue-mimetic system to create the directional
gradients for oxygen and lactate, which also allowed for the co-culture of tumor cells and macrophages.
Figueredo et al. created a series of hybrid models to study the interplay between the immune
system (including macrophages) and tumor cells [139,140]. An agent-based on-lattice model for
tumors was created using Chaste (Cancer, Heart and Soft Tissue Environment), part of the Virtual
Physiological Human (VPH) Toolkit; the model consists of three layers: a diffusible layer, a cellular
layer, and a subcellular layer [141]. The diffusible layer consists of diffusible species such as oxygen,
the cellular layer consists of normal cells, tumor cells, and macrophages, and the subcellular layer
governs apoptosis and cell-cycle in each cell. In this model, macrophages were M1-like, they supported
the immune system, and aided immunotherapies. They investigated the growth of the tumor under
oxygen-dependent proliferation. They found that the emergent behavior of agent-based models
allowed for the generation of additional tumor architectures over other modeling methodologies [142].
50
growth. In a further study, they found that the macrophage/tumor cell ratio was most sensitive to the
strength of EGF signaling, but usually maintained a 1:3 ratio [133].
Another ABM of triple-negative breast cancer examined the tumor enhancing effects of
macrophages [134]. Norton et al. investigated the interplay between tumor growth, blood vessel
recruitment and macrophage recruitment through tumor vasculature. They observed that while
macrophages increase tumor growth, excessive macrophage recruitment conversely leads to a decrease
in tumor growth due to the inhibition of proliferation resulting from overcrowding.
3.6. Models Focusing on Intra-Tumor Heterogeneity
Intra-tumor heterogeneity and the characteristics of the tumor microenvironment are found to
have important implications in the outcome of disease progression [135]. Patients often have varied
responses to treatment because each patient is unique in their genome, microbiome, disease history,
lifestyle, and environment. The case of tumors is especially complex, because this heterogeneity is
observed not only between tumors, but also between subpopulations of cells from the same tumor,
resulting in different response to drugs [136]. While capturing this degree of heterogeneity may be
difficult in experiments and clinical trials, especially the temporal dynamics of spatial heterogeneity,
computational models are especially suited to tackling this challenge. This section focuses on the
models that have aimed to capture intra-tumor heterogeneity.
A 2D agent-based model was used to study the interactions between an avascular tumor
and immune cells (NK cells and cytotoxic T-cells) [137]. They examined the effects of cancer cell
proliferation on overall tumor growth under two conditions: the first, where cancer cells do not
consider the microenvironment when deciding when to proliferate, and the second, where they
proliferate based on the number of healthy cells surrounding them. Tumor-immune cell interaction
can have three outcomes: tumor cell death, immune cell death, or no cell death based on the state
of the tumor. The predicted growth of the tumor was then compared to a xenograft tumor growth.
Spatial heterogeneity was also examined in a different model where cancer cells use glycolysis instead
of oxidative phosphorylation to increase their energy production. In order to study how this increased
energy production affects the surrounding stroma, a combination of computational modeling and
in vitro/in vivo experiments was used [138]. They used agent-based modeling to understand tumor
growth in a vascularized area of the tumor. They found that tumors develop spatial patterns where
macrophages and tumor cells coexisted in areas with high levels of oxygen, but that only tumor cells
survived in ischemic regions. They then used an in vitro tissue-mimetic system to create the directional
gradients for oxygen and lactate, which also allowed for the co-culture of tumor cells and macrophages.
Figueredo et al. created a series of hybrid models to study the interplay between the immune
system (including macrophages) and tumor cells [139,140]. An agent-based on-lattice model for
tumors was created using Chaste (Cancer, Heart and Soft Tissue Environment), part of the Virtual
Physiological Human (VPH) Toolkit; the model consists of three layers: a diffusible layer, a cellular
layer, and a subcellular layer [141]. The diffusible layer consists of diffusible species such as oxygen,
the cellular layer consists of normal cells, tumor cells, and macrophages, and the subcellular layer
governs apoptosis and cell-cycle in each cell. In this model, macrophages were M1-like, they supported
the immune system, and aided immunotherapies. They investigated the growth of the tumor under
oxygen-dependent proliferation. They found that the emergent behavior of agent-based models
allowed for the generation of additional tumor architectures over other modeling methodologies [142].
50