Processes 2019, 7,37
From another standpoint, the models that describe the immune system can be broadly categorized
into top-down and bottom-up, and previous reviews have focused on computational modeling of the
immune system [44,54]. The top-down approach models populations of cells, not single entities, and
uses the mean behavior at the macroscopic level. ODE and PDE models are examples of this type of
modeling where individual interactions are not simulated. Stochastic differential equation models
are also a part of this class. On the other hand, the bottom-up approach focuses on the microscopic
level. The model tracks each agent (e.g., a cell) and its interactions with the surrounding environment,
and emergent behavior arises from all the entities and their local behavior. Features such as stochastic
behavior, spatial distribution, and heterogeneity of entities are inherent to bottom up models, and
thus, easier to capture with this approach. Drawbacks of these models are that they require more
computational power because they track individual agents and their interactions over time and space;
also, there are computational limitations on the number of agents that can be considered; it is thus
impossible to consider an entire organ or patient. Therefore, both approaches will need to be combined
to achieve both spatial cellular and sub-cellular resolutions and whole patient pharmacokinetics
and pharmacodynamics.
Agent-based models are an example of a bottom-up approach with applications in immunology
and immune related diseases such as cancer [55]. An agent-based model is a discrete mathematical
and computational framework that is capable of capturing emergent behavior of its interacting
agents, defined as large-scale spatio-temperal patterns resulting from local spatial interactions between
agents. The behavior and function of these agents are driven by the information they sense in their
local environment and the rules of the agent-based model. Some of the characteristics that separate
agent-based models apart from other rule-based modeling systems (in which outcomes are based on a
set of rules that govern decisions) are that (1) they are spatial, (2) they incorporate agents that interact
with other agents and their environment, (3) they may incorporate stochasticity, (4) they are modular,
and (5) they produce emergent behavior [56]. These models allow the individual agents to adapt to
their local environment (i.e., agents are adaptive instead of reactive), and take part in local interactions
with other agents [57]. These result in complex aggregate behavior stemming from simple rules and
emergent properties from agent interactions. Agent-based models can be lattice-based or lattice-free,
depending on whether agents reside and move on a (regular or irregular) spatially discretized lattice,
or have their locations and velocities represented by continuous variables, usually governed by forces
in the environment. For example, in lattice-based ABM, agents are placed on a lattice structure that
defines the locations of cells and their neighbors for cellular interactions. There are several model types
that, although they are not explicitly characterized as agent-based, are reviewed here for completeness;
those include cellular automata, Potts models, and Petri net models.
Agent-based models are particularly suitable for capturing spatially-varying events and
heterogeneities [58], and for understanding the immune system’s function. With this aim in mind,
several investigators have developed agent-based models of diseases with involvement of the immune
system. Several ABM have simulated the immune system’s involvement in maintaining homeostasis
and disease conditions, such as bacterial infections [59], fungal infections [60], abnormal systemic
inflammatory response [61], ulceration [62], allergens [63], ischemia [64], tuberculosis [65], sepsis [66],
and wound healing [67]. For cancers, such models include tumor growth and invasion [68], as well
as specific cancer types such as hepatocellular carcinoma [69], breast cancer [70], melanoma [71],
colorectal [72], lung cancer [73,74], and metastasis [75]. Software packages have been developed
based on the ABM framework to study the immune system; these include ImmSim [76–79],
Immunogrid [80,81], Simmune [82], Cycell [83], and PhysiCell [84].
Now we discuss the latest agent-based and hybrid models that investigate the effects of the
immune system on cancer progression and immunotherapy, see Table 1. In order to be included in the
review, the work needs to have an immune component, a tumor component, and include ABM. We
limited our focus to papers that were published within the last ten years. However, we also included
45
From another standpoint, the models that describe the immune system can be broadly categorized
into top-down and bottom-up, and previous reviews have focused on computational modeling of the
immune system [44,54]. The top-down approach models populations of cells, not single entities, and
uses the mean behavior at the macroscopic level. ODE and PDE models are examples of this type of
modeling where individual interactions are not simulated. Stochastic differential equation models
are also a part of this class. On the other hand, the bottom-up approach focuses on the microscopic
level. The model tracks each agent (e.g., a cell) and its interactions with the surrounding environment,
and emergent behavior arises from all the entities and their local behavior. Features such as stochastic
behavior, spatial distribution, and heterogeneity of entities are inherent to bottom up models, and
thus, easier to capture with this approach. Drawbacks of these models are that they require more
computational power because they track individual agents and their interactions over time and space;
also, there are computational limitations on the number of agents that can be considered; it is thus
impossible to consider an entire organ or patient. Therefore, both approaches will need to be combined
to achieve both spatial cellular and sub-cellular resolutions and whole patient pharmacokinetics
and pharmacodynamics.
Agent-based models are an example of a bottom-up approach with applications in immunology
and immune related diseases such as cancer [55]. An agent-based model is a discrete mathematical
and computational framework that is capable of capturing emergent behavior of its interacting
agents, defined as large-scale spatio-temperal patterns resulting from local spatial interactions between
agents. The behavior and function of these agents are driven by the information they sense in their
local environment and the rules of the agent-based model. Some of the characteristics that separate
agent-based models apart from other rule-based modeling systems (in which outcomes are based on a
set of rules that govern decisions) are that (1) they are spatial, (2) they incorporate agents that interact
with other agents and their environment, (3) they may incorporate stochasticity, (4) they are modular,
and (5) they produce emergent behavior [56]. These models allow the individual agents to adapt to
their local environment (i.e., agents are adaptive instead of reactive), and take part in local interactions
with other agents [57]. These result in complex aggregate behavior stemming from simple rules and
emergent properties from agent interactions. Agent-based models can be lattice-based or lattice-free,
depending on whether agents reside and move on a (regular or irregular) spatially discretized lattice,
or have their locations and velocities represented by continuous variables, usually governed by forces
in the environment. For example, in lattice-based ABM, agents are placed on a lattice structure that
defines the locations of cells and their neighbors for cellular interactions. There are several model types
that, although they are not explicitly characterized as agent-based, are reviewed here for completeness;
those include cellular automata, Potts models, and Petri net models.
Agent-based models are particularly suitable for capturing spatially-varying events and
heterogeneities [58], and for understanding the immune system’s function. With this aim in mind,
several investigators have developed agent-based models of diseases with involvement of the immune
system. Several ABM have simulated the immune system’s involvement in maintaining homeostasis
and disease conditions, such as bacterial infections [59], fungal infections [60], abnormal systemic
inflammatory response [61], ulceration [62], allergens [63], ischemia [64], tuberculosis [65], sepsis [66],
and wound healing [67]. For cancers, such models include tumor growth and invasion [68], as well
as specific cancer types such as hepatocellular carcinoma [69], breast cancer [70], melanoma [71],
colorectal [72], lung cancer [73,74], and metastasis [75]. Software packages have been developed
based on the ABM framework to study the immune system; these include ImmSim [76–79],
Immunogrid [80,81], Simmune [82], Cycell [83], and PhysiCell [84].
Now we discuss the latest agent-based and hybrid models that investigate the effects of the
immune system on cancer progression and immunotherapy, see Table 1. In order to be included in the
review, the work needs to have an immune component, a tumor component, and include ABM. We
limited our focus to papers that were published within the last ten years. However, we also included
45