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Agent Based Modelling and Simulation of the Immune System: a Review



Computer simulations play an important role as a tool for predicting and understanding the behaviour of complex systems. The immune system is one such system, and it is feasible to expect that a well tuned model can provide qualitatively similar behaviour. Such models can have several applications, among which is its use as a virtual test bench in the first stages of drug testing. Most of the existing models are developed using a formal approach based on differential equations, which yields average behaviour and results for the total cellular population. This approach is not very intuitive, and though well formalized, can stray from biologic significance. In this paper we focus on cellular automata (CA) and agent-based models, that although poorly formalized, are more flexible and offer modelling possibilities close to biologic reality. We review and compare several models, discuss their methodologies and assumptions, and how these map on to plausible simulations. Finally we suggest a model based on those we consider the aspects of greater potential of the discussed solutions.
Agent Based Modelling and Simulation of the
Immune System: a Review
Nuno Fachada and Vitor V. Lopes and Agostinho Rosa
Evolutionary System and Biomedical Engineering Lab
Systems and Robotics Institute
Instituto Superior Técnico
Av. Rovisco Pais, 1049-001 Lisboa, Portugal
{nfachada, vlopes, acrosa}
Abstract. Computer simulations play an important role as a tool for
predicting and understanding the behaviour of complex systems. The
immune system is one such sys tem, and it is feasible to expect that a
well tuned model can provide qualitatively similar behaviour. Such mod-
els can have several applications, among which is its us e as a virtual test
b e nch in the first stages of drug testing. Most of the existing models
are developed using a formal approach based on differential equations,
which yields average behaviour and results for the total cellular popu-
lation. This approach is not very intuitive, and though well formalized,
can stray from biologic significance. In this paper we focus on cellular
automata (CA) and agent-based models, that although poorly formal-
ized, are more flexible and offer modelling possibilities close to biologic
reality. We review and compare several models, discuss their methodolo-
gies and assumptions, and how these map on to plausible simulations.
Finally we suggest a model based on those we consider the aspects of
greater potential of the discussed solutions. [1]
1 Introduction
In recent years, the advances in computational power have given us the possibil-
ity of implementing realistic low cost simulations of complex dynamic systems.
Complex systems consist of a large number of mutually interacting system enti-
ties, usually in a nonlinear fashion. Generally, analytic treatment does not yield a
complex system’s complete theory, and consequently c ompute r simulations have
been gaining widespread use and importance [2].
Computational models of the immune system (IS) can help us understand
its behaviour and test or validate theories. They are ideal for complementing ex-
perimental research and clinical observations, because experimental research is
expensive and its impossible to perform systematic tests in humans [3]. Nonethe-
less, in order to obtain relevant and useful information, models should be based
on recognized biological hypothesis and b e validated against real-world data.
IS modelling can be considered part of a broader discipline, the field of Ar-
tificial Immune Systems (AIS). However, Artificial Immune Systems in general
do not aim to reproduce a biological IS (which is the focus of this review); in-
stead, the goal of Artificial Immune Systems is to develop computational tools
for solving scienc e and engineering problems, using the IS powerful information
processing capabilities (such as feature extraction, pattern recognition, memory
and learning) as an inspiration. Computer security, fraud detection, machine
learning, data analysis an d optimization algorithms are examples of AIS appli-
cations (a general view of AIS is presented in [4]). As such, validation of AIS
based solutions is performed by comparing its perfomance with other approaches
to the same problem, with biological relevance becoming secondary. From this
perspective, AIS is a branch of Computational Intelligence where the computa-
tional properties of the IS are investigated [5]. It is emerging as an active and
attractive field involving models, techniques and applications of greater diversity,
but is out of the scop e of this review.
There are several approaches to model the IS or parts of the IS, among which
models based on differential equations are probably the most common [6]. These
models usually simulate how average conce ntrations of IS agents and substances
change over time, identifying key aspects of the immune response . However,
building and managing these equations, as well as changing them to incorporate
new aspects, is not trivial nor intuitive, leading to sometimes mathematically
sophisticated but biologically useless models or biologically realistic but mathe-
matically intractable models [7]. This approach also yields average behaviours,
characteristics or concentrations of the IS components, ignoring the important
aspects of the immune response, such as locality of responses and diversity of
repertoires. Nonetheless the y have had practical use regarding particular aspects
of IS modelling.
Agent-based and CA approaches are well suited for modelling complex sys-
tems in general and IS in particular, providing a way to represent the true
diversity of IS entities and substances. Other advantages include the possibil-
ity to determine behaviour distribution (and not just the average) [8], rapid
insertion of ne w entities or substances and natural consideration of non-linear
interactions between agents. This approach is not without problems of its own:
it lacks the formalism provided by differential equations, requires considerable
computational power to simulate individual agents, and parameter tuning is not
trivial. The success of any model based in these approaches depends on how
well these and other problems are solved. This paper describes the most signif-
icant p rogresses in this area, discuss ing the potential of individual features and
possible improvements.
In section 2 we present a short introduction the IS. In section 3 we discuss
the current state-of-the art in CA and agent-based simulations of the IS. A new
model, featuring some of the most promising ideas of section 3, is suggested in
section 4.
2 The i mmune system
The exact function of the IS is still is a source of active debate, but it can be
stated that its physiologic function is to protect individuals against infections
[9], which are caused by pathogenic agents that exist in many forms. At the
same time the IS must distinguish self from non-self, in order to avoid self in-
flicted damage. Auto-immune diseases are the consequence of failure to perform
such distinction. The IS is gifted with learning and memory features: it remem-
bers previous challenges with specific pathogens, and deals with them in a much
swifter fashion in subsequent encounters. The defense mechanism of an individ-
ual consists of innate and adaptive immunity, which work together to provide
protection against infections.
Innate immunity is the first line of defense against infections (e.g., epithelial
barriers), and its performance does not depend of prior contact with potential
threats. Innate immunity mechanisms detect a vast group of potentially dan-
gerous agents, due to recognition of common molecular patterns in their sur-
face. In nate immunity agents, such as macrophages, recognize generic pathogen-
associated molecular patterns in the surface of other agents, and can phagocyte
and destroy them. The complement system
, due to the activation of the alter-
native pathway, also plays an important role in innate immune responses.
Microbial adversaries can rapidly evolve strategies to evade innate immunity
mechanisms. Adaptive immunity is the evolutionary answer of vertebrate ani-
mals, allowing the body to adapt to first time invasions and remember previous
ones, handling them more effectively in the future. Lymphocytes are adaptive
immunity agents which can challenge particular invaders through the recogni-
tion of the unique receptors they express, known as antigens. There are two main
types of lymphocytes, which differ in function and type of antigen receptor: B
cells and T cells.
The B cell produces antibo d y molecules complementary to a given antigen
in its native form; it plays a central role in humoral immunity, the protection
against extracellular microbes. When a macrophage detects an agent covered
with antibody, the probability of successful phagocytosis increases substantially.
Antigen-antibody complexes can also activate the classical pathway of the com-
plement system. The B cell receptor (BCR) is a superficial antibody, which
signals the B cell when antigen binding occurs.
The T ce ll is the main actor in cell-mediated immunity, which provides pro-
tection against intracellular microbes, complementing humoral immunity. T cells
are subdivided in Th (helper) cells, which assist macrophages an d B cells, and Tc
(cytotoxic) cells, which kill infected cells. Th cells may also help the activation of
Tc lymphocytes. The T cell receptor (TCR) is more complex, and will not bind
The process by which certain cells of the innate immune system, engulf large particles
(such as intact microbes) [9].
A group of serum proteins which can act in an enzymatic cascade, producing
molecules involved i n inflammation, phagocytosis and cell lysis [10]. Complement
activation can be initiated by classical, alternative or lectin pathways [9].
to native antigen; instead, it binds a complex formed by an MHC
molecule and
an antigen derived peptide. Cells that present antigenic peptides to Th cells via
MHC class II, such as macrophages and B cells, are known as Antigen Present-
ing Cells (APC). Macrophages process antigen for presentation after microbe
phagocytosis, while B cells do the same after engulfing BCRs binding antigen.
When a B cell presents antigen to a Th cell, the latter is stimulated to se-
crete cytokines
, which increase B cell proliferation and differentiation. B cells
either become plasma cells, which secrete antibody, or long-lived memory B cells,
which allow a more effective response in future challenges by the same intruder.
After a few days, some of the antigen activated B cells undergo a process called
somatic hypermutation, which consists of high-frequency mutations in antibody
specificity; B cells producing higher affinity antibodies after mutation have an
increased chance of survival, leading to affinity maturation of the humoral im-
mune response. When a Th cell recognizes the antigenic peptide + MHC class
II complex on the surface of a macrophage, it releases a cytokine which helps
the macrophage destroy phagocyted, but still living microbes.
These are important aspects of the IS, and illustrate the variety of ways in
which its components interact in order to eradicate infections. However, this
introduction does not reflect the true complexity of the IS, serving only to es-
tablish the underlying agent based structure, and therefore justifying why agent
based approaches for modeling are well suited for the task.
3 A Revie w
3.1 AbAIS
The AbAIS (Agent-based Artificial IS) framework uses a hybrid approach that
supports the evolving of an heterogeneous population of agents over a CA envi-
ronment [11, 12]; each cell on the CA may contain several agents and substances,
and serves as an indirect platform for agent communication, though agents can
also communicate directly.
Agents are mo d elled using a genetic approach where genotypes are formed
by tagged rules which express an agent’s behaviour, upon the interpretation of
an operator. These agent operators use no explicit fitness function; instead, they
use environment and genetic information as sensorial input for decision making.
The number of genes in each agent is not fixed, allowing dynamics during the
agent’s evolution. An agent can also present the environment and other agents
a set of external features, which are also encoded in the genetic code.
Major Histocompatibility Complex, a genetic receptor of body cells, uniq ue in each
p e rson, involved in antigen presentation to T cells. MHC class I is present in all nu-
cleated cells and is recognized by Tc cells; MHC class II exists on antigen-presenting
cells (mainly B cells, macrophages, dendritic cells), and is recognized by Th cells. It
is responsible for the most intense graft rejection within a species [10].
Secreted proteins that function as mediators of immune and inflammatory reactions
In [11, 12] the importance of cell coop eration and soluble mediators is as-
serted, mem ory effect on secondary immune responses is observed and HIV in-
fection caused immune cell depletion comp arable to the clinical course of the
disease. In [13] the framework was used to test a model for the ontogeny and
concomitant immune responses on Th cell subpopulations; results indicate that
Th cell dynamics appears to be one of the major regulatory mechanisms that
uphold the tolerance and rejection of the IS. The fact that different models were
simulated with plausible qualitative results is an indicator that the concepts used
to develop the AbAIS framework and the associated immune models are sound.
CAFISS presents a different approach on agent-based modelling of the IS. Like
most of agent-based models, CAFISS divides the simulation using a rectangu-
lar grid, where each division represents a spatial location; but what differenti-
ates CAFISS is the multithreaded asynchronous updating of the simulation [14],
where each IS cell instance runs in its own th read, communicating with other
cells using events. This approach is more line with the definition of Complex
Adaptive System (CAS) [15] than other frameworks.
Each cell has a bit string that acts as the cells sensorial input: specific sub-
strings may represent antigen receptors or receptors for stimulatory signals. Sub-
strings, or sensors, are activated with variable strength, depending on the number
of matching bits. Stronger rules have a greater chance of being selected when
several rules are in this s ituation. Antigen matching by B cells and antibody
is then part of a general rule bit matching mechanism instead of being the
mechanism itself. Each substring of bit detectors is associated to the activation
of one rule; each rule is associated with an action to be performed (reproduce,
die, etc. . . ), or to another rule, allowing the chaining of rules.
Interesting concepts are introduced with CAFISS, and realistic results re-
garding HIV dynamics are achieved. The negative aspect of this framework is
that using a separate thread for each cell in order to achieve a CAS-like ap-
proach, results in a large overhead; consequently, simulations necessarily have
limited dimension. The ques tion remains if the gains of using a faithful CAS ap-
proach outcome limits in simulation size. Antibodies are also modelled as a cell
running in their own thread, adding to the already large overhead; given that
antibodies are basically molecules, thus not possessing an “intelligent” behaviour,
one can question the scalability of the model.
3.3 ImmSim
ImmSim is one of the most referenced and peer reviewed IS simulators available
[16, 5], and many of the underlying ideas have been us ed in other models and
frameworks. The first version of the model was developed by Celada and Seiden
[17, 18], and was limited to the humoral response of the IS; its basic idea cons isted
in the capture and processing of antigens and how that p rocessing affects the
various cell populations [19]. As the framework matured, the initial core concept
proved the models capability to represent several different scenarios. ImmSim has
been used to reprod uce and analyze immunological memory, affinity maturation,
effects of hypermutation, autoimmune responses and competitive tolerance [19,
20]. ImmSim3 is currently the most advanced version of this framework [20].
ImmSim is based on a CA with p robabilistic rules, representing an average
piece of the IS, like a section of a lymph node [8]. At each time step, cellular and
molecular entities in the same CA site can interact with each other and diffuse
through the lattice. Entities consider all possible interactions, and choose one
stochastically, with probability given by the respective interaction rule. Entities
take on a number of states based on their repertoire, which also influence the
chosen interaction and the respective action. The entities receptors are modelled
using bit strings, where the MHC receptor is included, if applicable; this means
that for an n-bit string, there are 2
specificities. Affinity between entities is
given by the Hamming distance between their receptors. The specific interaction
rules in the model can depend on the bit string receptor matching of two entities.
In ImmSim there is no distinction between antigens and the micro-organisms
themselves, like viruses and bacteria. Besides expressing epitopes and peptides
(that compose the antigen repertoire), the antigen model in ImmSim possesses
several parameters: speed of growth, infectivity and lethality. Antigen also has
the ability to produce a toxin, for example to produce a ‘danger’ s ignal. In
[8], vaccine efficiency is tested against 64 viruses, determined by a combination
of four values for each of the given parameters. The effects of vaccination are
evaluated by comparing the progress of the same infection with and without
vaccine. Vaccine is made antigenically equal to the virus, but infectivity is set
to 0 and doesn’t produce a danger signal. This inactive virus cannot infect cells,
but with the presenc e of a danger signal, it can be ingested by APC’s and have
the respective peptides displayed on both MHC I and II. The danger signal is
included in the vaccine by means of a model adjuvant. This methodology mimics
the use of nonliving organisms as vaccines, which frequently require am adjuvant
to provide prophylactic immunization [10]. Each simulation run is considered to
have three possible outcomes: cure, death or chronic infection. With vaccination,
there is a general improvement in the immune response, and its capacity to cure
In [21] and [8] the effects of viral attack are studied, considering humoral and
cellular immunity working both individually and simultaneously, in order to as-
sert the efficiency of each response to different types of viruses. Naturally, results
pointed to a generally superior immune efficiency when both kinds of response
are activated; in some cases though, an isolated humoral response proved best, in-
dicating that the usually collaborative cell-mediated and humoral responses can
potentially inhibit effectiveness of the global response regarding certain types of
Simulating the immune response to viruses with parameters like speed of
growth, infectivity and lethality, can be somewhat reductive when compared
to the true diversity of viral behaviour, namely antigen change, interference
with immune effector mechanisms, evasion of MHC Class I antigen presentation,
among many others [9, 22, 23, 10].
ImmSim3, like its predecessors, is developed in APL2, an interpreted lan-
guage that imposes constraints on the maximum system size; thus all performed
simulations are relatively small scale. The same group also maintains other ver-
sions of the framework, of which ImmSim-C is the most relevant, though it has a
reduced feature set, and doesn’t really take advantage of the C programming lan-
guage. Independently of the programming language, ImmSim has a very rigid
structure, that considers only one possible antigen. Due to hard-wired rules,
users can only change parameters, and not the rules themselves [24], unless they
change the source code. Nonetheless it is a model that has been very use ful for
experimenting on a wide range of parameters, providing some results that were
realistic and others that led investigators to pose new hypothesis. It also proved
itself as a good didactic tool [20]. It seems that since 2002 no more work is pub-
lished based on the original ImmSim group; yet, the ideas of Celada and Seiden
continue to be very prolific, specifically in the form of C-ImmSim, and generally
in almost every other agent based immune simulations.
3.4 C-ImmSim, ParImm, ImmunoGrid
C-ImmSim and the correspondent parallel variant, ParImm, are versions of Imm-
Sim developed by F. Castiglione and M. Bernaschi in the C programming lan-
guage, with focus on improved effic iency and simulation size and complexity [25].
In these adaptations of the Celada-Se iden model, the IS response is designed and
coded to allow simulations considering millions of cells with a very high degree
of complexity. The co de can resort to parallel processing to run faster; optimized
data structures and I/O have allowed stretching the limits of available memory
and disk space. The design is open and modular, which allows smooth upgrades
and addition of new features (cells, molecules, interactions and so on) for future
investigations; however, new modules must conform to the pre-defined structure
of the model.
Currently, C-ImmS im is the most advanc ed IS simulator based on the original
Celada-Seiden automaton, with consistent publication throughput. Regarding
the model itself, the most recent upgrades include, among other features, the
use of three-dimensional shapes, inclusion of the chemotaxis phenomen a and
consideration of different cell speeds [26]. C-ImmSim based simulations have been
yielding results with interesting potential. Some examples are work regarding
progression of the HIV-1 infection in untreated host organisms [27], scheduling
of Highly Active Anti-Retroviral (HAART) for HIV-1 infection [26], simulation
of cancer immunoprevention vaccine concerning its effectiveness and scheduling
[28, 29] and the modelling of Epstein-Barr virus infection [30]. In the correct
context, these results have biological relevance, motivating further experiments
with the framework.
ImmunoGrid is a European Union funded project to establish an infrastruc-
ture f or the simulation of the IS at the molecular, cellular and organ levels [3].
ImmunoGrid uses C-ImmSim as the underlying framework, further establishing
the Celada-Seiden model and C-ImmSim as references regarding the simulation
of the IS. Design of vaccines, immunotherapies and optimization of immunization
protocols are some of the applications for this project. Grid technologies are used
in order to perform simulations orders of magnitude more complex than current
models, with the final objective of matching a real size IS. Separate nodes in the
grid can simulate different tissues or even organs. Simulator validation is to be
performed by pre-clinical trials in mice.
The C-ImmSim framework shares some of the basic problems of ImmSim in
particular, and of the Celada-Seiden model in general. It is an experimentally
driven approach, and may lack the formal theoretical structure present in models
like SIS (discussed next). Its rigid structure, where each entity performs actions
based on rules that depend on its state and environmental input, prevents the
model from being a true evolving system.
3.5 Simmune
Simmune, developed by Meier-Schellersheim and Mack, is a tool to investigate
how context adaptive behaviour of the IS might e merge from local cell-cell and
cell-molecule interactions [31]. It is based on molecule interactions on a cell’s
surface. Cells don’t have states like in the Celada-Seiden model, instead they have
behaviours that depend on rules based on cellular response to external stimuli,
usually external molecule interactions. Cells can have intracellular compartments
with connections between them, and perform actions like secretion of molecules,
expression of receptors, etc., that depend on the number of stimulated superficial
receptors or the presence of intracellular molecules [32]. Modification of cell
mechanisms during simulation, through viral attack for example, is also possible
(a feature shared by AbAIS).
Molecules can form aggregates according to their mutual binding possibil-
ities, defined by their binding sites. Molecules have a typical lifetime before
disintegrating into fragment molecules, and indication of the types of fragments
that are produ ced upon disintegration. Cells and molecules are spread across a
3D environment, where they interact in specific compartments. These compart-
ments can be considered specific body sections (like lymph nodes, for example),
and have editable properties like diffusion rate and type and size of agents that
can enter and leave. The properties of cells, molecules and compartments are
user-definable, thus making Simmune capable of, accordingly to the authors, “to
simulate populations of cells of any kind” [31]. Besides the IS model described in
[31], Simmune was more recently used to build a molecular signalling model for
the study of the role of local regulation in chemosensing [33], thus substantiating
the author’s affirmation. The potential of the Simmune framework, especially its
behaviour-based model, seems to be far reaching. Nonetheless, compared with
the Celada-Seiden model, publications and respective peer analysis, have had an
inferior impact.
Regarding the s imulation of the IS, results obtained by this framework are
essentially proof of concept. In [31], a demonstration of a simple IS is p resented,
which includes several IS cell types and a virus. B-cell activation through direct
antigen dose-dependent response is also modeled.
The Simmune model is focused on representational acc uracy, with little con-
cern for performance [34]. Detailed molecular interactions are computationally
expensive and und ermine the scalability of this model. However, the concepts
introduced here are worth further investigation, and with the advent of multi-
processor systems and grid computing, could be explored in a distributed fashion
(just like ImmunoGrid and ParImm are doing with the Celada-Seiden model).
3.6 SIS
SIS is developed by the Conceptual Immunology Group at the Salk Institute,
and in contrast with most of the models presented here, is more theoretically
driven and less of an experimentalist tool. It is based on a cellular automaton,
with descriptive cellular states and rules that define transitions between those
states, and aims to provide a larger picture of the IS, including self-nonself
discrimination [24]. Each cell has state, type, age and specificity and responds to
stimuli from surroundings. The cellular response to stimuli depends on cellular
states. Cell-cell interactions have a 100 cell scope in the CA; interleukins have
10,000 cell scop e; and antigen has a “visible to all” scope.
SIS is capable of performing simulations with large number of cells (in the
order of 10
to 10
cells), with linear correlation between simulation size and
time. SIS-I, the first iteration of this system, started development in the early
1980’s, and only recently has been abandoned in favour of SIS-II, though it still
can be used through a web interface. It has many hardwired values, a pre-defined
keyword language for writing of rules and is based on a two-dimensional CA.
SIS-II is based on SIS-I, but uses a three-dimensional CA, and allows user defined
rules, thus being much more flexible, allowing the testing and simulation of a
wider variety of IS models. It can also be used through a web interface. SIS-III
is already on a planning phase, and several extensions are being considered; an
interesting one is the use of a XML backbone to describe s imulations, cells, rules
and so on. The developers expect SIS-III to more generalist, and to be able to
simulate other types of complex systems.
SIS is based on the Protecton Theory [35] and the Theory of Associative
Antigen Recognition [36]; the former addresses the problem of specificity and
repertoire dimension, while the later concerns the problem of self-nonself dis-
tinction. However, these theories are not consensual among investigators. In [37,
38] the Protecton Theory is questioned, while in [39, 40] the effective validity
of the Theory of Associative Antigen Recognition is discussed and compared
with other studie s. Therefore, results produced by SIS should be analyzed in
this specific context, and SIS should be considered more of a study tool for these
theories, and less of a general immune system simulator; these usually assume
recognized textbook biological hypothesis to start with. While SIS appears to
be more efficient performing simulations, it effectively does much less than other
models presented he re [5].
3.7 Sentinel Models
Sentinel is a complex system simulation platform, designed for immunology and
AIS research [5]. The design principles are similar to the Celada-Seiden model,
with the environment divided into a discrete grid of locations, where entities can
move from on location to the other, responding to events that occur in the same
or nearby locations. One of the novel approaches of the Sentinel system consists
in the use of specialized engines to manage physical and chemical interactions.
As such, agents can move according to chemotaxis (a very important factor in
the real IS), motor capabilities and external forces acting on th em. Chemicals
diffuse, react and degrade in order to model chemotaxis and cytokines. Rules
define the nature of interactions between cells, and how cells release chemicals,
or other entities.
An evaluation of several immunological memory theories is performed in [5].
To validate the Sentinel framework, three theories, that were previously tested
in a simpler simulator [41], are evaluated again. Apart from some differences in
details, results where similar enough, con firming Sentinel can reproduce previous
simulations. After simulator validation, an evaluation of Polyclonal Activation
Memory theory [42] was performed. Simulation results were qualitatively con-
sistent with in vivo experiments, though with a clear need for further parame-
ter adjustment. Nonetheless, simulation results point that Polyclonal Activation
Memory theory can b e qualitatively reasonable.
This kind of approach, the testing and evaluation of theories, is undoubtedly
one of the main practical uses of IS simulation. Certain assumptions have nec-
essarily to be made; in these models, assumptions are clearly described, which
is always useful when analyzing possibly related artifacts in simulation results.
The physical and chemical engines are probably the most interesting part of the
framework itself, while the “experiment on theories” path of investigation has
also much practical use.
3.8 Jacob et al. model
In [43] Jacob et al. present a swarm and agent-based, continuous three-dimensional
model of the IS, using the multi-agent simulator Breve [44]. Both humoral and
cell-mediated immunity are modelled in order to ascertain the global immune
response to primary and secondary viral antigen exposure. In sum, this model
tries to offer a highly visual, intuitive and user-friendly investigation tool to
Agents are spheres of different sizes and colours that move around randomly
in the continuous three-dimensional environment; they interact with each other
due to proximity, considering a spherical neighbourhood. The fact that agents
move in a continuous environment differentiates this mode l from the usual CA
based approach seen in other models discu ss ed here. In spite of this, cells are
state-based like in the Celada-Seiden model; consequently, rules that control
interactions can depend on cellular states (as well as on the neighbourhood
situation). These if-then-else rules can produce actions like the killing of another
agent, cellular division, antibody secretion, and so on.
The presented simulation concerns immune response to primary and sec-
ondary viral antigen exposure; results have qualitative resemblance with what
happens in the real IS.
The novelty of this model lies in the continuous environment approach, which
is undoubtedly more faithful to reality than explicitly discrete space approach.
It is also a very interesting visualization tool, but there are a few problems. The
continuous and visual three-dimensional paradigm can impose serious processing
load, restricting simulation size. As a consequence, this model can support very
few agents when compared to other frameworks. A possible solution could be
the direct use of a GPU (Graphics Processing Unit) to perform physical and
environmental calculations (an interesting analysis is performed in [45]). Other
features of the model are still underdeveloped, like the random movement of cells
(ignoring the important chemotaxis factor), and the simplicity of the simulations
themselves (similar results where obtained by Celada and Seiden in 1992 [17, 18]).
3.9 CyCells
CyCells was designed for studying intercellular interactions, allowing to define
cell behaviours and molecular properties, as well as having features to represent
intracellular infection [46]. The beh aviour-based approach is similar to Simmune.
The author claims CyCells is not a general-purpose agent-based development
framework, but states that it could be used to model a broad variety of multi-
cellular systems (a similar claim to the one made by the Simmune authors).
CyCless uses a hybrid model that represents molecular conc entrations con-
tinuously and cells discretely. Each type of molecular signal (e.g. cytokines) is
given a decay and diffusion rate. Cell behaviour is based on a ‘sense-p rocess-act’
agent model. Each agent has its own attributes; these attributes (e.g. cell diam-
eter) can be associated with sensing, processing and action protocols. A sensing
protocol can, for example, respond to a specific substance concentration; a pro-
cessing procedure acknowledges the sensing protocol, which could lead to cell
activation; several types of action can take place due to a processing procedure,
for example, death or production of a molecular substance. A similar approach
is used in SimulIm [16], though CyCells is implemented on a three-dimensional
square grid, while SimulIm uses a two-dimensional hexagonal grid.
Several investigations were performed with CyCells. In [46] three studies are
presented. The first concerns two theories about the maintenance of peripheral
macrophage population sizes in the lung. Macrophage-Pathogen interactions,
more specifically initial macrophage interactions with bacteria, were the topic of
investigation in the second study. Infection dynamics of pulmonary tuberculosis
was also modeled.
The realistic treatment of cytokines and the other molecular players in the
immune response was the principal feature in CyCells, and one that is worth
pursing further. Developed in C++, CyCells presents relatively good perfor-
mance. In spite of being well documented, this framework as some limitations
in terms of accessibility when compared to generic agent-based platforms. The
author states that “A number of ‘general-purpose’ frameworks (..) are often too
general to be of much use in a particular scientific discipline” [46]; in spite of
this affirmation, it is our belief, after a similar experience developing a simulator
from scratch, that the use of certain generic platforms can spare much time with
model development.
3.10 Other models
There are several other CA and / or agent-based models in literature. We present
some of them, in our opinion not as relevant or as general as those already
ImmunoSim is a customizable modelling environment with several interesting
features and a purely visual interface. It received the Fulton Roberts Immunology
prize from Cambridge University (twice), but apparently hasn’t been published
Ballet et al. developed a multi-agent system to model humoral immunity
[47], using a platform named oRis. Results include the observation of immuno-
logical response to four types of antigenic substance: dead, proliferating, poorly
recognizable proliferating and directed against Th cells.
CA are especially useful for modelling tummor growth. An interesting pro-
posal is made in [48]; in [49] these ideas are taken even further, and the resulting
solutions are in qualitative agreement with both the experimental and theoretical
In [50] Beauchemin et al. present a simple two-dimensional CA model for
influenza infections, based on the ma_immune framework. Localized tissue in-
fection is the specific area of investigation in this framework: infected cells are
tightly packed and don’t move, the infection spreads to immediate neighbours
and immune cells move randomly in the grid. This approach proved more con-
sistent with experimental data than an equivalent non-spatial model, asserting
the effects of spatial lo calization in influenza infections [6].
SimulIm was a generic complex system simulator developed in 2005 by the
authors [16]. Its goal was to perform distributed simulations and allow the easy
development of specific simulations packages , that were transparent regarding
the distribution process. A specific package for IS simulation was also developed,
based on concepts presented by the AbAIS framework. At the time we stated
that “it is (...) curious to observe that there are practically no IS models based
on a generic modelling package. (...) the very specific IS intricacies (...) can be
difficult to model using one of these packages”. After the development of SimulIm,
a more profound discussion to ok place, and with the posterior experience of using
the generic agent-based platform Repast [51], we retract that statement, and can
affirm that much time can be saved in using such package. One has the full power
of a programming language (Java in this case) without worrying with specific
details like scheduling, visualization, charting and data output.
4 Future Work
Practically all of the mode ls presented here contain useful concepts. We are re-
implementing SimulIm on Repast, and though the main concepts are based on
AbAIS, we will try to incorporate some of the more interesting ideas discussed
in this paper.
The majority of the models have an underlying CA, being discrete in space
and time; though Jacob et al. and Cafiss models display novel approaches
regarding space and time, respectively, we think that for now the associated
computational cost implies that we continue to use the discrete approach
used in the Celada-Seiden and AbAIS models, without much loss in mod-
elling fidelity.
In order to represent cellular and molecular repertoires and determine affin-
ity, the concept of complementing bit strings used in many models seems a
good choice, in spite of Mata and Cohn’s criticism [24].
The exchange of genetic code introduced in AbAIS, and also used in Sim-
mune, is a very important factor in developing a model that is truly evolving
and that can realistically mimic the biological IS.
Detailed molecular interactions on the cellular surface and on the environ-
ment (Simmune and CyCells) are a computationally expensive premise, but
offer the possibility of observing pure emergent behaviour.
We consider that the use of an established agent-based simulation framework
allows modellers to concentrate on the model rather than on programming
details. Jacob et al. mo d el follows this path by using the breve multi-agent
simulator. The use of an established object oriented paradigm can also facil-
itate development; Cafiss, a Java based model, is a good example. The best
of both worlds can be achieved if Repast [51] or Mason [52] are used, both
established agent-based toolkits using Java, an established object oriented
programming language. Our choice falls on Repast, a more stable and widely
reviewed framework [53, 54].
The physics and chemical engines of Sentinel are important for realistic simu-
lation of chemotaxis and cell movement. SimulIm also had a chemical engine
for substance diffusion and decay, and a simpler physics engine that incor-
porated inertial cell movement. As such, our new mod el should continue to
have such features.
Accessible simulation setup is required if a given tool is to be used by non-
programmers. SimulIm, and eventually SIS-III, use a XML backbone to de-
scribe simulations. While this facilitates the process, it can be impractical
for large simulations. We suggest a graphical user interface in order to auto-
matically prod uc e XML simulation descriptions.
To perform realistically sized simulations, it is necessary to use distributed
computation. ParImm and ImmunoGrid are specialized versions of the Celada-
Seiden model that are focused on this objective. Nonetheless, the initial
premise of SimulIm of offering a transparent framework for distributed sim-
ulations (within the principles we define here), is still a goal to achieve. RMI
and other Java distribution packages can surely facilitate this task.
5 Conclusions
In order to develop new models it is important to know what has been done
before, and this is the primary purpose of this paper. Practically all IS models
presented here contain interesting, usable concepts. Armed with this knowledge,
investigators can focus on new concepts and avoid reinventing the wheel.
This paper also discusses work in progress concerning the development of a
“new” simulation framework. Though based on known concepts, this framework
hopes to offer investigators an accessible and powerful tool of research for IS
This work was partially supported by Fundação para a Ciência e a Tecnologia
(ISR/IST plurianual funding) through the POS_Conhecimento Program that
includes FEDER funds. The author V. V. Lopes acknowledge its grant SFRH/
BPD/20735-2004 to Fundação para a Ciência e Tecn ologia (FCT).
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... One main advantage of continuous-time models is that they have been studied exhaustively in the last centuries, leading to many well-known numerical methods to determine their solutions, such as the finite element (FE) method (Zienkiewicz et al., 1977, used e.g. in Zysset et al., 2013Coquim et al., 2018), the finite difference method (Liszka andOrkisz, 1980, used e.g. in Nagatani et al., 2006) and the method of lines (Hundsdorfer andVerwer, 2003, used e.g. in Geris et al., 2008). Some main disadvantages are that they usually fail to capture heterogeneous behaviors (Van Dyke Parunak et al., 1998;Wilkinson, 2009) and that the incorporation of new biological aspects is often not trivial (Yates et al., 2001;Fachada et al., 2007). ...
... Within in silico models of tissue-specific immune responses, the popularity of AB methods is clear (Fachada et al., 2007;Shi et al., 2016). Several AB models of the immune system can be found in the literature, together with a large variety of simulators to develop them. ...
... Some models are implemented in custom AB simulators, such as ImmSim Seiden and Celada, 1992) and UISS (Pappalardo et al., 2010), whereas other models use generic open-source simulators that allow for the implementation of AB models such as NetLogo (Mi et al., 2007;Brown et al., 2011;Pennisi et al., 2013;Shi et al., 2016). ImmSim was the first AB model and framework to simulate the immune system, focusing on the processing of antigens and their effects on the different cell types Seiden and Celada, 1992;Fachada et al., 2007). Mi et al. (2007) presented an AB model focused on the interrelation between inflammation and skin wound healing in a physical domain. ...
Full-text available
In silico modeling is a powerful strategy to investigate the biological events occurring at tissue, cellular and subcellular level during bone fracture healing. However, most current models do not consider the impact of the inflammatory response on the later stages of bone repair. Indeed, as initiator of the healing process, this early phase can alter the regenerative outcome: if the inflammatory response is too strongly down- or upregulated, the fracture can result in a non-union. This review covers the fundamental information on fracture healing, in silico modeling and experimental validation. It starts with a description of the biology of fracture healing, paying particular attention to the inflammatory phase and its cellular and subcellular components. We then discuss the current state-of-the-art regarding in silico models of the immune response in different tissues as well as the bone regeneration process at the later stages of fracture healing. Combining the aforementioned biological and computational state-of-the-art, continuous, discrete and hybrid modeling technologies are discussed in light of their suitability to capture adequately the multiscale course of the inflammatory phase and its overall role in the healing outcome. Both in the establishment of models as in their validation step, experimental data is required. Hence, this review provides an overview of the different in vitro and in vivo set-ups that can be used to quantify cell- and tissue-scale properties and provide necessary input for model credibility assessment. In conclusion, this review aims to provide hands-on guidance for scientists interested in building in silico models as an additional tool to investigate the critical role of the inflammatory phase in bone regeneration.
... The challenge for simulation is, therefore, to generate novel insights that cannot be uncovered just by looking at a phenomena using reductionism. Examples of successful simulation approaches that helped advance immunological research were introduced in [7]. The models reviewed simulate interactions of immune cells and chemical substances, humoral responses and drug testing. ...
... This rule defines the next state of each cell according to its current state and its neighbourhood states. Examples of several applications for the immune system are found in [7]. ...
... By reviewing the simulation methods and some of their applications to immune problems, such as those from [7,[23][24][25]29], it is possible to outline the benefits of simulation to immunology and, therefore, achieve our first objec-tive of this work. Compared with real-world experimentation, simulation is time and cost-effective. ...
... Agents move randomly in the continuous space and only interact with those within their local radius. The visualisation and continuous space approach impose constraints on the simulation size [31]. Generally, simulating large scale complex models is computationally expensive.A possible solution is the use of Graphic Processing Units (GPUs). ...
Full-text available
Background: In recent years, the study of immune response behaviour using bottom up approach, Agent Based Modeling (ABM), has attracted considerable efforts. The ABM approach is a very common technique in the biological domain due to high demand for a large scale analysis tools for the collection and interpretation of information to solve biological problems. Simulating massive multi-agent systems (i.e. simulations containing a large number of agents/entities) requires major computational effort which is only achievable through the use of parallel computing approaches. Results: This paper explores different approaches to parallelising the key component of biological and immune system models within an ABM model: pairwise interactions. The focus of this paper is on the performance and algorithmic design choices of cell interactions in continuous and discrete space where agents/entities are competing to interact with one another within a parallel environment. Conclusions: Our performance results demonstrate the applicability of these methods to a broader class of biological systems exhibiting typical cell to cell interactions. The advantage and disadvantage of each implementation is discussed showing each can be used as the basis for developing complete immune system models on parallel hardware.
... In highly nonlinear systems, however, the formulation of realistic mean-field models can be challenging. Such scenarios (e.g. at the complex cellular level) highlight the advantages of agent-based models, where the local cooperation, based on self-state, of many separate agents yields an 'emergent behaviour' of the system as a whole [4,5,7,8]. ...
Predictive modelling of complex biological systems and biophysical interactions requires the inclusion of multiple nano- and micro-scale events. In many scenarios, however, numerical solutions alone do not necessarily enhance the understanding of the system. Instead, this work explores the use of an agent-based model with visualization capabilities to elucidate interactions between single cells. We present a model of juxtacrine signalling, using Cell Studio, an agent-based modelling system, based on gaming and three-dimensional visualization tools. The main advantages of the system are its ability to apply any cell geometry and to dynamically visualize the diffusion and interactions of the molecules within the cells in real time. These provide an excellent tool for obtaining insight about different biological scenarios, as the user may view the dynamics of a system and observe its emergent behaviour as it unfolds. The agent-based model was validated against the results of a mean-field model of Notch receptors and ligands in two neighbouring cells. The conversion to an agent-based model is described in detail. To demonstrate the advantages of the model, we further created a filopodium-mediated signalling model. Our model revealed that diffusion and endocytosis alone are insufficient to produce significant signalling in a filopodia scenario. This is due to the bottleneck at the cell-filopodium contact region and the long distance to the end of the filopodium. However, allowing active transport of ligands into filopodia enhances the signalling significantly compared with a face-to-face scenario. We conclude that the agent-based approach can provide insights into mechanisms underlying cell signalling. The open-source model can be found in the Internet hosting service GitHub.
... The agent-based modeling approach [11] is a useful method applied in many areas where an interaction of multiple autonomous individuals (agents) is simulated. In biology, this method is used, for example, in epidemiological modeling [12], cellular modeling (eg, immune system [13] or tumor growth [14]), or molecular modeling [15]. We focus mainly on physiological models of organs or their systems where traditional modeling based on mathematical relations is predominant. ...
... The agent-based modeling approach [11] is a useful method applied in many areas where an interaction of multiple autonomous individuals (agents) is simulated. In biology, this method is used, for example, in epidemiological modeling [12], cellular modeling (eg, immune system [13] or tumor growth [14]), or molecular modeling [15]. We focus mainly on physiological models of organs or their systems where traditional modeling based on mathematical relations is predominant. ...
BACKGROUND Simulators for use in teaching are interactive applications composed of a mathematical model of the system under study and a graphical user interface that allows the user to control the model inputs and visualize the model results in an intuitive and educational way. Well-designed simulators promote active learning, enhance problem-solving skills, and encourage collaboration and small group discussion. However, creating simulators for teaching purposes is a challenging process that requires many contributors including educators, modelers, graphic designers and programmers. The availability of a toolchain of user-friendly software tools for building simulators can facilitate this complex task. OBJECTIVE The purpose of this work is to develop an open source toolchain of software tools termed Bodylight.js that will facilitate the creation of browser-based, client-side simulators for teaching purposes which are platform independent, do not require any installation, and can work offline. The toolchain interconnects state-of-the-art modeling tools with current web technologies and is designed to be resilient to future changes in the software ecosystem. METHODS We utilized several open source web technologies, namely WebAssembly and JavaScript, combined with the power of the Modelica modelling language and deployed them on the web with interactive animations built with Adobe Animate. RESULTS Models are implemented in Modelica language using either OpenModelica or Dymola and exported to a standardised Functional Mock-up Unit (FMU) to ensure future compatibility. The C code from the FMU is further compiled to WebAssembly using Emscripten. Industry standard Adobe Animate is used to create interactive animations. A new tool called Bodylight.js Composer was developed for the toolchain that enables one to create the final simulator by composing the graphical user interface using animations, plots and control elements in a drag-and-drop style, and bind them to the model variables. The resulting simulators are standalone HTML files including Javascript and WebAssembly. Several simulators for use in physiology education were created using the Bodylight.js toolchain and have been received with general acclaim by teachers and students alike, thus validating our approach. One of simulators, the Nephron simulator, is presented in this paper. Bodylight.js is licensed under GPL 3.0 and is free for anyone to use. CONCLUSIONS Bodylight.js enabled us to effectively develop teaching simulators. Armed with this technology we intend to focus on the development of new simulators and interactive textbooks for educating medical students. Bodylight.js usage is not constrained to developing simulators for teaching physiology and can facilitate development of simulators for teaching complex topics in a variety of different fields.
... Note this model is different from all other mentioned above due to the fact that is continuous based. The visualisation and continuous space approach impose constraints on the simulation size [26] which could be improved by employing parallel processing techniques [27]. Generally, simulating large scale complex models is computationally expensive. ...
Conference Paper
Agent Based Modelling (ABM), is an approach for modelling dynamic systems and studying complex and emergent behaviour. ABM approach is a very common technique in biological domain due to high demand for a large scale analysis tool to collect and interpret information to solve biological problems. However, simulating large scale cellular level models (i.e. large number of agents/entities) require a high degree of computational power which is achievable through parallel computing methods such as Graphics Processing Units (GPUs). The use of parallel approaches in ABMs is growing rapidly specifically when modelling in continuous space system (particle based). Parallel implementation of particle based simulation within continuum space where agents contain quantities of chemicals/substances is very challenging. Pair-wise interactions are different abstraction to continuous space (particle) models which is commonly used for immune system modelling. This paper describes an approach to parallelising the key component of biological and immune system models (pair-wise interactions) within an ABM model. Our performance results demonstrate the applicability of this method to a broader class of biological systems with the same type of cell interactions and that it can be used as the basis for developing complete immune system models on parallel hardware.
... To advance our study, we have two research objectives. Nuno et al. [7] mention that most of what has been done in simulation of the immune system is based on differential equations, which can be easily implemented using SDS, as long as feedback loops are expressed in the equations. We believe that the conversion of current well established mathematical or SDS models into ABS would be a first step to investigate individual behaviour and emergence on the existing models. ...
In this review paper, we discuss graphical dynamical systems (GDSs) and their applications to biological and social systems (bio-social systems). Traditionally, differential equation-based models have been central in modeling bio-social systems. GDSs provide an alternate modeling framework. This framework explicitly represents individual components of the system and captures the interactions among them via a network. The purpose of this review is to enable modelers to obtain an understanding of this basic mathematical and computational framework so that it can be used to study specific bio-social applications. The work covers the range from computational theory to simulation-based analysis. We also provide some directions for future work.
Full-text available
This work consists in the study and implementation of a software application for complex system modelling and simulation. The human immune system is used as a case study for demonstrating the developed application capabilities; more specifically, the expected results are the replication of dynamics of the active components in the immune system. The development of software specifically designed for such a particular system, constrains its use in the modelling and simulation of other, possibly uncorrelated, complex systems. Thus, the developed simulation engine has been made to be as generic as possible, yet reasonably powerful. Generality is obtained by specifying that the simulation classes themselves must simply obey to a predefined and flexible programming interface; in this way, there is almost no limit to what can be done, as long as it’s based on the simulation engine basic premise: a multi-agent system over a discrete space. Power is obtained by making the simulation engine distributed: each block of the discrete space is an independent simulation unit, which can be processed remotely. At this stage, the application allows the user to perform simulations in a vast number of contexts, even by just using the supplied simulation package (biased towards the immune system); nonetheless, the application also gives the freedom to extend or completely rewrite simulation classes, in order to best model the desired complex system. The developed immune system simulation package is a proof of concept of the application’s potential as a generic complex system distributed simulator. Future results of performed simulations should conform to qualitative data retrieved from immunology textbooks in an early phase, and from real data at a more advanced stage.
Human immune system simulation can serve several purposes. Medical researchers can use immune system simulation in drug research or to test hypotheses about the infection process. Distributed systems researchers can use immune algorithms to build robust, fault tolerant networks. Given the wide range of uses for immune simulation and the difficulty of the task, it is useful to know what research has been conducted in this area. This paper attempts to provide a comprehensive survey of the literature in this field.
We simulate the progression of the HIV-1 infection in untreated host organisms. The phenotype features of the virus are represented by the replication rate, the probability of activating the transcription, the mutation rate and the capacity to stimulate an immune response (the so-called immunogenicity). It is very difficult to study in-vivo or in-vitro how these characteristics of the virus influence the evolution of the disease. Therefore we resorted to simulations based on a computer model validated in previous studies. We observe, by means of computer experiments, that the virus continuously evolves under the selective pressure of an immune response whose effectiveness downgrades along with the disease progression. The results of the simulations show that immunogenicity is the most important factor in determining the rate of disease progression but, by itself, it is not sufficient to drive the disease to a conclusion in all cases.
The immune system protects our organisms against pathogens and aberrant cells. It achieves this capability by processing and evaluating a wide variety of molecular signals many of which are generated by its own agents.