Combining cellular automata and Lattice Boltzmann method to model multiscale avascular tumor growth coupled with nutrient diffusion and immune competition

A decade of thermostatted kinetic theory models for complex active matter living systems

In the last decade, the thermostatted kinetic theory has been proposed as a general paradigm for the modeling of complex systems of the active matter and, in particular, in biology. Homogeneous and inhomogeneous frameworks of the thermostatted kinetic theory have been employed for modeling phenomena that are the result of interactions among the elements, called active particles, composing the system. Functional subsystems contain heterogeneous active particles that are able to perform the same task, called activity. Active matter living systems usually operate out-of-equilibrium; accordingly, a mathematical thermostat is introduced in order to regulate the fluctuations of the activity of particles. The time evolution of the functional subsystems is obtained by introducing the conservative and the nonconservative interactions which represent activity-transition, natural birth/death, induced proliferation/destruction, and mutation of the active particles. This review paper is divided in two parts: In the first part the review deals with the mathematical frameworks of the thermostatted kinetic theory that can be found in the literature of the last decade and a unified approach is proposed; the second part of the review is devoted to the specific mathematical models derived within the thermostatted kinetic theory presented in the last decade for complex biological systems, such as wound healing diseases, the recognition process and the learning dynamics of the human immune system, the hiding-learning dynamics and the immunoediting process occurring during the cancer-immune system competition. Future research perspectives are discussed from the theoretical and application viewpoints, which suggest the important interplay among the different scholars of the applied sciences and the desire of a multidisciplinary approach or rather a theory for the modeling of every active matter system.

Tumour growth: An approach to calibrate parameters of a multiphase porous media model based on in vitro observations of Neuroblastoma spheroid growth in a hydrogel microenvironment

To unravel processes that lead to the growth of solid tumours, it is necessary to link knowledge of cancer biology with the physical properties of the tumour and its interaction with the surrounding microenvironment. Our understanding of the underlying mechanisms is however still imprecise. We therefore developed computational physics-based models, which incorporate the interaction of the tumour with its surroundings based on the theory of porous media. However, the experimental validation of such models represents a challenge to its clinical use as a prognostic tool. This study combines a physics-based model with in vitro experiments based on microfluidic devices used to mimic a three-dimensional tumour microenvironment. By conducting a global sensitivity analysis, we identify the most influential input parameters and infer their posterior distribution based on Bayesian calibration. The resulting probability density is in agreement with the scattering of the experimental data and thus validates the proposed workflow. This study demonstrates the huge challenges associated with determining precise parameters with usually only limited data for such complex processes and models, but also demonstrates in general how to indirectly characterise the mechanical properties of neuroblastoma spheroids that cannot feasibly be measured experimentally.

Cellular-automaton model for tumor growth dynamics: Virtualization of different scenarios

Mathematical Oncology has emerged as a research field that applies either continuous or discrete models to mathematically describe cancer-related phenomena. Such methods are usually expressed in terms of differential equations, however tumor composition involves specific cellular structure and can demonstrate probabilistic nature, often requiring tailor-made approaches. In this context, cell-based models allow monitoring independent single parameters, which might vary in both time and space. By relying on extant tumor growth models in the literature, this study introduces cellular-automata simulation strategies that admit heterogeneous cell population while capturing both single-cell and cluster-cell behaviors. In this agent-based computational model, tumor cells are limited to follow four possible courses of action, namely: proliferation, migration, apoptosis or quiescence. Despite the apparent simplicity of those actions, the model can represent different complex tumor features depending on parameter settings. This study virtualized five different scenarios, showcasing model capabilities of representing tumor dynamics including alternate dormancy periods, cell death instability and cluster formation. Implementation techniques are also explored together with prospective model expansion towards deterministic features. The proposed stochastic cellular automaton model is able to effectively simulate different scenarios regarding tumor growth effectively, figuring as an interesting tool for in silico modeling, with promising capabilities of expansion to support research in mathematical oncology, thus improving diagnosis tools and/or personalized treatment.

Effect of particularisation size on the accuracy and efficiency of a multiscale tumours' growth model

In silico, medicine models are frequently used to represent a phenomenon across multiples space-time scales. Most of these multiscale models require impracticable execution times to be solved, even using high performance computing systems, because typically each representative volume element in the upper scale model is coupled to an instance of the lower scale model; this causes a combinatory explosion of the computational cost, which increases exponentially as the number of scales to be modelled increases. To attenuate this problem, it is a common practice to interpose between the two models a particularisation operator, which maps the upper-scale model results into a smaller number of lower-scale models, and an operator, which maps the fewer results of the lower-scale models on the whole space-time homogenisation domain of upper-scale model. The aim of this study is to explore what is the simplest particularisation / homogenisation scheme that can couple a model aimed to predict the growth of a whole solid tumour (neuroblastoma) to a tissue-scale model of the cell-tissue biology with an acceptable approximation error and a viable computational cost. Using an idealised initial dataset with spatial gradients representative of those of real neuroblastomas, but small enough to be solved without any particularisation, we determined the approximation error and the computational cost of a very simple particularisation strategy based on binning. We found that even such simple algorithm can significantly reduce the computational cost with negligible approximation errors.

An Agent-Based Model of Combination Oncolytic Viral Therapy and Anti-PD-1 Immunotherapy Reveals the Importance of Spatial Location When Treating Glioblastoma

Simple Summary

A combination of oncolytic viral therapy and immunotherapy provides an alternative option to the standard of care for treating the lethal brain tumor glioblastoma (GBM). Although this combination therapy shows promise, there are many unknown questions regarding how the tumor landscape and spatial dosing strategies impact the effectiveness of the treatment. Our study aims to shed light on these questions using a novel spatially explicit computational model of GBM response to treatment. Our results suggest that oncolytic viral dosing in the location of highest tumor cell density leads to substantial tumor size reduction over viral dosing in the center of the tumor. These results can help to inform future clinical trials and more effective treatment strategies for oncolytic viral therapy in GBM patients.

Abstract

Oncolytic viral therapies and immunotherapies are of growing clinical interest due to their selectivity for tumor cells over healthy cells and their immunostimulatory properties. These treatment modalities provide promising alternatives to the standard of care, particularly for cancers with poor prognoses, such as the lethal brain tumor glioblastoma (GBM). However, uncertainty remains regarding optimal dosing strategies, including how the spatial location of viral doses impacts therapeutic efficacy and tumor landscape characteristics that are most conducive to producing an effective immune response. We develop a three-dimensional agent-based model (ABM) of GBM undergoing treatment with a combination of an oncolytic Herpes Simplex Virus and an anti-PD-1 immunotherapy. We use a mechanistic approach to model the interactions between distinct populations of immune cells, incorporating both innate and adaptive immune responses to oncolytic viral therapy and including a mechanism of adaptive immune suppression via the PD-1/PD-L1 checkpoint pathway. We utilize the spatially explicit nature of the ABM to determine optimal viral dosing in both the temporal and spatial contexts. After proposing an adaptive viral dosing strategy that chooses to dose sites at the location of highest tumor cell density, we find that, in most cases, this adaptive strategy produces a more effective treatment outcome than repeatedly dosing in the center of the tumor.

Overview of the modeling of complex biological systems and its role in neurosurgery

Biological systems are complex with distinct characteristics such as nonlinearity, adaptability, and self-organization. Biomedical research has helped in advancing our understanding of certain components the human biology but failed to illustrate the behavior of the biological systems within. This failure can be attributed to the use of the linear approach, which reduces the system to its components then study each component in isolation. This approach assumes that the behavior of complex systems is the result of the sum of the function of its components. The complex systems approach requires the identification of the components of the system and their interactions with each other and with the environment. Within neurosurgery, this approach has the potential to advance our understanding of the human nervous system and its subsystems.

Fractional Mathematical Oncology: On the potential of non-integer order calculus applied to interdisciplinary models

Mathematical Oncology investigates cancer-related phenomena through mathematical models as comprehensive as possible. Accordingly, an interdisciplinary approach involving concepts from biology to materials science can provide a deeper understanding of biological systems pertaining the disease. In this context, fractional calculus (also referred to as non-integer order) is a branch in mathematical analysis whose tools can describe complex phenomena comprising different time and space scales. Fractional-order models may allow a better description and understanding of oncological particularities, potentially contributing to decision-making in areas of interest such as tumor evolution, early diagnosis techniques and personalized treatment therapies. By following a phenomenological (i.e. mechanistic) approach, the present study surveys and explores different aspects of Fractional Mathematical Oncology, reviewing and discussing recent developments in view of their prospective applications.

In silico clinical trials: concepts and early adoptions

Innovations in information and communication technology infuse all branches of science, including life sciences. Nevertheless, healthcare is historically slow in adopting technological innovation, compared with other industrial sectors. In recent years, new approaches in modelling and simulation have started to provide important insights in biomedicine, opening the way for their potential use in the reduction, refinement and partial substitution of both animal and human experimentation. In light of this evidence, the European Parliament and the United States Congress made similar recommendations to their respective regulators to allow wider use of modelling and simulation within the regulatory process. In the context of in silico medicine, the term 'in silico clinical trials' refers to the development of patient-specific models to form virtual cohorts for testing the safety and/or efficacy of new drugs and of new medical devices. Moreover, it could be envisaged that a virtual set of patients could complement a clinical trial (reducing the number of enrolled patients and improving statistical significance), and/or advise clinical decisions. This article will review the current state of in silico clinical trials and outline directions for a full-scale adoption of patient-specific modelling and simulation in the regulatory evaluation of biomedical products. In particular, we will focus on the development of vaccine therapies, which represents, in our opinion, an ideal target for this innovative approach.

Modeling Living Cells Within Microfluidic Systems Using Cellular Automata Models

Several computational models, both continuum and discrete, allow for the simulation of collective cell behaviors in connection with challenges linked to disease modeling and understanding. Normally, discrete cell modelling employs quasi-infinite or boundary-less 2D lattices, hence modeling collective cell behaviors in Petri dish-like environments. The advent of lab- and organ-on-a-chip devices proves that the information obtained from 2D cell cultures, upon Petri dishes, differs importantly from the results obtained in more biomimetic micro-fluidic environments, made of interconnected chambers and channels. However, discrete cell modelling within lab- and organ-on-a-chip devices, to our knowledge, is not yet found in the literature, although it may prove useful for designing and optimizing these types of systems. Consequently, in this study we focus on the establishment of a direct connection between the computer-aided designs (CAD) of microfluidic systems, especially labs- and organs-on-chips (and their multi-chamber and multi-channel structures), and the lattices for discrete cell modeling approaches aimed at the simulation of collective cell interactions, whose boundaries are defined directly from the CAD models. We illustrate the proposal using a quite straightforward cellular automata model, apply it to simulating cells with different growth rates, within a selected set of microsystem designs, and validate it by tuning the growth rates with the support of cell culture experiments and by checking the results with a real microfluidic system.

Multiscale Agent-Based and Hybrid Modeling of the Tumor Immune Microenvironment

Multiscale systems biology and systems pharmacology are powerful methodologies that are playing increasingly important roles in understanding the fundamental mechanisms of biological phenomena and in clinical applications. In this review, we summarize the state of the art in the applications of agent-based models (ABM) and hybrid modeling to the tumor immune microenvironment and cancer immune response, including immunotherapy. Heterogeneity is a hallmark of cancer; tumor heterogeneity at the molecular, cellular, and tissue scales is a major determinant of metastasis, drug resistance, and low response rate to molecular targeted therapies and immunotherapies. Agent-based modeling is an effective methodology to obtain and understand quantitative characteristics of these processes and to propose clinical solutions aimed at overcoming the current obstacles in cancer treatment. We review models focusing on intra-tumor heterogeneity, particularly on interactions between cancer cells and stromal cells, including immune cells, the role of tumor-associated vasculature in the immune response, immune-related tumor mechanobiology, and cancer immunotherapy. We discuss the role of digital pathology in parameterizing and validating spatial computational models and potential applications to therapeutics.

The pivotal role of angiogenesis in a multi-scale modeling of tumor growth exhibiting the avascular and vascular phases

The mechanisms involved in tumor growth mainly occur at the microenvironment, where the interactions between the intracellular, intercellular and extracellular scales mediate the dynamics of tumor. In this work, we present a multi-scale model of solid tumor dynamics to simulate the avascular and vascular growth as well as tumor-induced angiogenesis. The extracellular and intercellular scales are modeled using partial differential equations and cellular Potts model, respectively. Also, few biochemical and biophysical rules control the dynamics of intracellular level. On the other hand, the growth of melanoma tumors is modeled in an animal in-vivo study to evaluate the simulation. The simulation shows that the model successfully reproduces a completed image of processes involved in tumor growth such as avascular and vascular growth as well as angiogenesis. The model incorporates the phenotypes of cancerous cells including proliferating, quiescent and necrotic cells, as well as endothelial cells during angiogenesis. The results clearly demonstrate the pivotal effect of angiogenesis on the progression of cancerous cells. Also, the model exhibits important events in tumor-induced angiogenesis like anastomosis. Moreover, the computational trend of tumor growth closely follows the observations in the experimental study.

The Lattice Boltzmann method and computational analysis of bone dynamics-I

Bone is comprised of an enormously hierarchical construction that promotes transportation of necessary fluids and solids, guaranteeing accurate function and growth. Bone remodeling is a combined process of bone creation and destruction. A number of mathematical models have been developed for the balanced and imbalanced bone remodeling. A brief overview regarding mathematical modeling of bone remodeling is provided. The Lattice Boltzmann method (LBM) has widely been implemented in CFD simulations, and it is becoming more suitable in the application of image processing amongst several others. Mainly, the LBM simulates the communication between synthetic particles dispersed in a lattice. Canaliculi and tortuous channels that have more or less roughly circular structure link among oval bodies identified as lacunae, and are vital to the function of bone. As there is a lack of equipment to inspect flow in channels on the order of measure of canaliculi, so the use of computational methods are more advantageous to give perceptivities into the nature of the flows. In this article, the computational fluid dynamics analysis is descried, using the Lattice Boltzmann method, to examine the result of the microscopic surface roughness of the canalicular wall, which is formed by collagen fibrils, on the flow profiles in the pericellular space.

Hybrid multiscale modeling and prediction of cancer cell behavior

Background

Understanding cancer development crossing several spatial-temporal scales is of great practical significance to better understand and treat cancers. It is difficult to tackle this challenge with pure biological means. Moreover, hybrid modeling techniques have been proposed that combine the advantages of the continuum and the discrete methods to model multiscale problems.

Methods

In light of these problems, we have proposed a new hybrid vascular model to facilitate the multiscale modeling and simulation of cancer development with respect to the agent-based, cellular automata and machine learning methods. The purpose of this simulation is to create a dataset that can be used for prediction of cell phenotypes. By using a proposed Q-learning based on SVR-NSGA-II method, the cells have the capability to predict their phenotypes autonomously that is, to act on its own without external direction in response to situations it encounters.

Results

Computational simulations of the model were performed in order to analyze its performance. The most striking feature of our results is that each cell can select its phenotype at each time step according to its condition. We provide evidence that the prediction of cell phenotypes is reliable.

Conclusion

Our proposed model, which we term a hybrid multiscale modeling of cancer cell behavior, has the potential to combine the best features of both continuum and discrete models. The in silico results indicate that the 3D model can represent key features of cancer growth, angiogenesis, and its related micro-environment and show that the findings are in good agreement with biological tumor behavior. To the best of our knowledge, this paper is the first hybrid vascular multiscale modeling of cancer cell behavior that has the capability to predict cell phenotypes individually by a self-generated dataset.

Simulation of Healing Threshold in Strain-Induced Inflammation Through a Discrete Informatics Model

Respiratory diseases such as asthma and acute respiratory distress syndrome as well as acute lung injury involve inflammation at the cellular level. The inflammation process is very complex and is characterized by the emergence of cytokines along with other changes in cellular processes. Due to the complexity of the various constituents that makes up the inflammation dynamics, it is necessary to develop models that can complement experiments to fully understand inflammatory diseases. In this study, we developed a discrete informatics model based on cellular automata (CA) approach to investigate the influence of elastic field (stretch/strain) on the dynamics of inflammation and account for probabilistic adaptation based on statistical interpretation of existing experimental data. Our simulation model investigated the effects of low, medium, and high strain conditions on inflammation dynamics. Results suggest that the model is able to indicate the threshold of innate healing of tissue as a response to strain experienced by the tissue. When strain is under the threshold, the tissue is still capable of adapting its structure to heal the damaged part. However, there exists a strain threshold where healing capability breaks down. The results obtained demonstrate that the developed discrete informatics based CA model is capable of modeling and giving insights into inflammation dynamics parameters under various mechanical strain/stretch environments.

Strain-induced inflammation in pulmonary alveolar tissue due to mechanical ventilation

Inflammation is the body's attempt at self-protection to remove harmful stimuli, including damaged cells, irritants, or pathogens and begin the healing process. In this study, strain-induced inflammation in pulmonary alveolar tissue under high tidal volume is investigated through a combination of an inflammation model and fluid structure interaction (FSI) analysis. A realistic three-dimensional organ model for alveolar sacs is built, and FSI is employed to evaluate strain distribution in alveolar tissue for different tidal volume (TV) values under the mechanical ventilation (MV) condition. The alveolar tissue is treated as a hyperelastic solid and provides the environment for the tissue constituents. The influence of different strain distributions resulting from different tidal volumes is investigated. It is observed that strain is highly distributed in the inlet area. In addition, strain versus time curves in different locations through the alveolar model reveals that middle layers in the alveolar region would undergo higher levels of strain during breathing under the MV condition. Three different types of strain distributions in the alveolar region from the FSI simulation are transferred to the CA model to study population dynamics of cell constituents under MV for different TVs; 200, 500 and 1000 mL, respectively. The CA model results suggests that strain distribution plays a significant role in population dynamics. An interplay between strain magnitude and distribution appears to influence healing capability. Results suggest that increasing TV leads to an exponential rise in tissue damage by inflammation.

Computational modeling in melanoma for novel drug discovery

INTRODUCTION

There is a growing body of evidence highlighting the applications of computational modeling in the field of biomedicine. It has recently been applied to the in silico analysis of cancer dynamics. In the era of precision medicine, this analysis may allow the discovery of new molecular targets useful for the design of novel therapies and for overcoming resistance to anticancer drugs. According to its molecular behavior, melanoma represents an interesting tumor model in which computational modeling can be applied. Melanoma is an aggressive tumor of the skin with a poor prognosis for patients with advanced disease as it is resistant to current therapeutic approaches.

AREAS COVERED

This review discusses the basics of computational modeling in melanoma drug discovery and development. Discussion includes the in silico discovery of novel molecular drug targets, the optimization of immunotherapies and personalized medicine trials.

EXPERT OPINION

Mathematical and computational models are gradually being used to help understand biomedical data produced by high-throughput analysis. The use of advanced computer models allowing the simulation of complex biological processes provides hypotheses and supports experimental design. The research in fighting aggressive cancers, such as melanoma, is making great strides. Computational models represent the key component to complement these efforts. Due to the combinatorial complexity of new drug discovery, a systematic approach based only on experimentation is not possible. Computational and mathematical models are necessary for bringing cancer drug discovery into the era of omics, big data and personalized medicine.

Modeling cell adhesion and proliferation: a cellular-automata based approach

BACKGROUND

Cell adhesion is a process that involves the interaction between the cell membrane and another surface, either a cell or a substrate. Unlike experimental tests, computer models can simulate processes and study the result of experiments in a shorter time and lower costs. One of the tools used to simulate biological processes is the cellular automata, which is a dynamic system that is discrete both in space and time.

METHOD

This work describes a computer model based on cellular automata for the adhesion process and cell proliferation to predict the behavior of a cell population in suspension and adhered to a substrate. The values of the simulated system were obtained through experimental tests on fibroblast monolayer cultures.

RESULTS

The results allow us to estimate the cells settling time in culture as well as the adhesion and proliferation time. The change in the cells morphology as the adhesion over the contact surface progress was also observed. The formation of the initial link between cell and the substrate of the adhesion was observed after 100 min where the cell on the substrate retains its spherical morphology during the simulation. The cellular automata model developed is, however, a simplified representation of the steps in the adhesion process and the subsequent proliferation.

CONCLUSION

A combined framework of experimental and computational simulation based on cellular automata was proposed to represent the fibroblast adhesion on substrates and changes in a macro-scale observed in the cell during the adhesion process. The approach showed to be simple and efficient.

A Lattice-Boltzmann scheme for the simulation of diffusion in intracellular crowded systems

Background

The intracellular environment is a complex and crowded medium where the diffusion of proteins, metabolites and other molecules can be decreased. One of the most popular methodologies for the simulation of diffusion in crowding systems is the Monte Carlo algorithm (MC) which tracks the movement of each particle. This can, however, be computationally expensive for a system comprising a large number of molecules. On the other hand, the Lattice Boltzmann Method (LBM) tracks the movement of collections of molecules, which represents significant savings in computational time. Nevertheless in the classical manifestation of such scheme the crowding conditions are neglected.

Methods

In this paper we use Scaled Particle Theory (SPT) to approximate the probability to find free space for the displacement of hard-disk molecules and in this way to incorporate the crowding effect to the LBM. This new methodology which couples SPT and LBM is validated using a kinetic Monte Carlo (kMC) algorithm, which is used here as our "computational experiment".

Results

The results indicate that LBM over-predicts the diffusion in 2D crowded systems, while the proposed coupled SPT-LBM predicts the same behaviour as the kinetic Monte Carlo (kMC) algorithm but with a significantly reduced computational effort. Despite the fact that small deviations between the two methods were observed, in part due to the mesoscopic and microscopic nature of each method, respectively, the agreement was satisfactory both from a qualitative and a quantitative point of view.

Conclusions

A crowding-adaptation to LBM has been developed using SPT, allowing fast simulations of diffusion-systems of different size hard-disk molecules in two-dimensional space. This methodology takes into account crowding conditions; not only the space fraction occupied by the crowder molecules but also the influence of the size of the crowder which can affect the displacement of molecules across the lattice system.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-015-0769-8) contains supplementary material, which is available to authorized users.

Multiscale modelling in immunology: a review

One of the greatest challenges in biomedicine is to get a unified view of observations made from the molecular up to the organism scale. Towards this goal, multiscale models have been highly instrumental in contexts such as the cardiovascular field, angiogenesis, neurosciences and tumour biology. More recently, such models are becoming an increasingly important resource to address immunological questions as well. Systematic mining of the literature in multiscale modelling led us to identify three main fields of immunological applications: host-virus interactions, inflammatory diseases and their treatment and development of multiscale simulation platforms for immunological research and for educational purposes. Here, we review the current developments in these directions, which illustrate that multiscale models can consistently integrate immunological data generated at several scales, and can be used to describe and optimize therapeutic treatments of complex immune diseases.

Bayesian immunological model development from the literature: example investigation of recent thymic emigrants

Bayesian estimation techniques offer a systematic and quantitative approach for synthesizing data drawn from the literature to model immunological systems. As detailed here, the practitioner begins with a theoretical model and then sequentially draws information from source data sets and/or published findings to inform estimation of model parameters. Options are available to weigh these various sources of information differentially per objective measures of their corresponding scientific strengths. This approach is illustrated in depth through a carefully worked example for a model of decline in T-cell receptor excision circle content of peripheral T cells during development and aging. Estimates from this model indicate that 21 years of age is plausible for the developmental timing of mean age of onset of decline in T-cell receptor excision circle content of peripheral T cells.

Mathematical modeling for novel cancer drug discovery and development

INTRODUCTION

Mathematical modeling enables: the in silico classification of cancers, the prediction of disease outcomes, optimization of therapy, identification of promising drug targets and prediction of resistance to anticancer drugs. In silico pre-screened drug targets can be validated by a small number of carefully selected experiments.

AREAS COVERED

This review discusses the basics of mathematical modeling in cancer drug discovery and development. The topics include in silico discovery of novel molecular drug targets, optimization of immunotherapies, personalized medicine and guiding preclinical and clinical trials. Breast cancer has been used to demonstrate the applications of mathematical modeling in cancer diagnostics, the identification of high-risk population, cancer screening strategies, prediction of tumor growth and guiding cancer treatment.

EXPERT OPINION

Mathematical models are the key components of the toolkit used in the fight against cancer. The combinatorial complexity of new drugs discovery is enormous, making systematic drug discovery, by experimentation, alone difficult if not impossible. The biggest challenges include seamless integration of growing data, information and knowledge, and making them available for a multiplicity of analyses. Mathematical models are essential for bringing cancer drug discovery into the era of Omics, Big Data and personalized medicine.

Agent-based modeling of the immune system: NetLogo, a promising framework

Several components that interact with each other to evolve a complex, and, in some cases, unexpected behavior, represents one of the main and fascinating features of the mammalian immune system. Agent-based modeling and cellular automata belong to a class of discrete mathematical approaches in which entities (agents) sense local information and undertake actions over time according to predefined rules. The strength of this approach is characterized by the appearance of a global behavior that emerges from interactions among agents. This behavior is unpredictable, as it does not follow linear rules. There are a lot of works that investigates the immune system with agent-based modeling and cellular automata. They have shown the ability to see clearly and intuitively into the nature of immunological processes. NetLogo is a multiagent programming language and modeling environment for simulating complex phenomena. It is designed for both research and education and is used across a wide range of disciplines and education levels. In this paper, we summarize NetLogo applications to immunology and, particularly, how this framework can help in the development and formulation of hypotheses that might drive further experimental investigations of disease mechanisms.

In silico modeling of the immune system: cellular and molecular scale approaches

The revolutions in biotechnology and information technology have produced clinical data, which complement biological data. These data enable detailed descriptions of various healthy and diseased states and responses to therapies. For the investigation of the physiology and pathology of the immune responses, computer and mathematical models have been used in the last decades, enabling the representation of biological processes. In this modeling effort, a major issue is represented by the communication between models that work at cellular and molecular level, that is, multiscale representation. Here we sketch some attempts to model immune system dynamics at both levels.

Current trends in cancer vaccines--a bioinformatics perspective

Cancer vaccine development is in the process of becoming reality in future, due to successful phase II/III clinical trials. However, there are still problems due to the specificity of tumor antigens and weakness of tumor associated antigens in eliciting an effective immune response. Computational models to assess the vaccine efficacy have helped to improve and understand what is necessary for personalized treatment. Further research is needed to elucidate the mechanisms of activation of antigen specific cytotoxic T lymphocytes, decreased TREG number functionality and antigen cascade, so that overall improvement in vaccine efficacy and disease free survival can be attained. T cell epitomic based in sillico approaches might be very effective for the design and development of novel cancer vaccines.

Agent based modeling of Treg-Teff cross regulation in relapsing-remitting multiple sclerosis

Background

Multiple sclerosis (MS) is a disease of central nervous system that causes the removal of fatty myelin sheath from axons of the brain and spinal cord. Autoimmunity plays an important role in this pathology outcome and body's own immune system attacks on the myelin sheath causing the damage. The etiology of the disease is partially understood and the response to treatment cannot easily be predicted.

Results

We presented the results obtained using 8 genetically predisposed randomly chosen individuals reproducing both the absence and presence of malfunctions of the Teff-Treg cross-balancing mechanisms at a local level. For simulating the absence of a local malfunction we supposed that both Teff and Treg populations had similar maximum duplication rates. Results presented here suggest that presence of a genetic predisposition is not always a sufficient condition for developing the disease. Other conditions such as a breakdown of the mechanisms that regulate and allow peripheral tolerance should be involved.

Conclusions

The presented model allows to capture the essential dynamics of relapsing-remitting MS despite its simplicity. It gave useful insights that support the hypothesis of a breakdown of Teff-Treg cross balancing mechanisms.

Cancer vaccines: state of the art of the computational modeling approaches

Cancer vaccines are a real application of the extensive knowledge of immunology to the field of oncology. Tumors are dynamic complex systems in which several entities, events, and conditions interact among them resulting in growth, invasion, and metastases. The immune system includes many cells and molecules that cooperatively act to protect the host organism from foreign agents. Interactions between the immune system and the tumor mass include a huge number of biological factors. Testing of some cancer vaccine features, such as the best conditions for vaccine administration or the identification of candidate antigenic stimuli, can be very difficult or even impossible only through experiments with biological models simply because a high number of variables need to be considered at the same time. This is where computational models, and, to this extent, immunoinformatics, can prove handy as they have shown to be able to reproduce enough biological complexity to be of use in suggesting new experiments. Indeed, computational models can be used in addition to biological models. We now experience that biologists and medical doctors are progressively convinced that modeling can be of great help in understanding experimental results and planning new experiments. This will boost this research in the future.

Modeling innate immune response to early Mycobacterium infection

In the study of complex patterns in biology, mathematical and computational models are emerging as important tools. In addition to experimental approaches, these modeling tools have recently been applied to address open questions regarding host-pathogen interaction dynamics, including the immune response to mycobacterial infection and tuberculous granuloma formation. We present an approach in which a computational model represents the interaction of the Mycobacterium infection with the innate immune system in zebrafish at a high level of abstraction. We use the Petri Net formalism to model the interaction between the key host elements involved in granuloma formation and infection dissemination. We define a qualitative model for the understanding and description of causal relations in this dynamic process. Complex processes involving cell-cell or cell-bacteria communication can be modeled at smaller scales and incorporated hierarchically into this main model; these are to be included in later elaborations. With the infection mechanism being defined on a higher level, lower-level processes influencing the host-pathogen interaction can be identified, modeled, and tested both quantitatively and qualitatively. This systems biology framework incorporates modeling to generate and test hypotheses, to perform virtual experiments, and to make experimentally verifiable predictions. Thereby it supports the unraveling of the mechanisms of tuberculosis infection.

Optimal vaccination schedule search using genetic algorithm over MPI technology

BACKGROUND

Immunological strategies that achieve the prevention of tumor growth are based on the presumption that the immune system, if triggered before tumor onset, could be able to defend from specific cancers. In supporting this assertion, in the last decade active immunization approaches prevented some virus-related cancers in humans. An immunopreventive cell vaccine for the non-virus-related human breast cancer has been recently developed. This vaccine, called Triplex, targets the HER-2-neu oncogene in HER-2/neu transgenic mice and has shown to almost completely prevent HER-2/neu-driven mammary carcinogenesis when administered with an intensive and life-long schedule.

METHODS

To better understand the preventive efficacy of the Triplex vaccine in reduced schedules we employed a computational approach. The computer model developed allowed us to test in silico specific vaccination schedules in the quest for optimality. Specifically here we present a parallel genetic algorithm able to suggest optimal vaccination schedule.

RESULTS & CONCLUSIONS

The enormous complexity of combinatorial space to be explored makes this approach the only possible one. The suggested schedule was then tested in vivo, giving good results. Finally, biologically relevant outcomes of optimization are presented.

Mathematical modeling of biological systems

Mathematical and computational models are increasingly used to help interpret biomedical data produced by high-throughput genomics and proteomics projects. The application of advanced computer models enabling the simulation of complex biological processes generates hypotheses and suggests experiments. Appropriately interfaced with biomedical databases, models are necessary for rapid access to, and sharing of knowledge through data mining and knowledge discovery approaches.