Computational modeling of brain tumors: discrete, continuum or hybrid?

Prediction and validation of avascular tumor growth pattern in different metabolic conditions using in silico and in vitro models

Objectives: In recent years, scientists have taken many efforts for in vitro and in silico modeling of cancerous tumors. In fact, three-dimensional (3D) cultures of multicellular tumor spheroids (MCTSs) are good validators for computational results. The goal of this study is to simulate the 3D early growth of avascular tumors using MCTSs and to compare the in vitro models with the results and predictions of a specific computational modeling framework. Using these two types of models, the importance of metabolic condition on tumor growth behavior and necrosis could be predicted. Materials and methods: We took advantage of a previously developed computational model of tumor growth (constructed by integrating a generic metabolic network model of cancer cells with a multiscale agent-based framework). Among the computational predictions is the importance of glucose accessibility on tumor growth behavior. To study the effect of glucose concentration experimentally, MCTSs were grown in high and low glucose culture media. After that, tumor growth pattern was analyzed by MTT assay, cell counting and propidium iodide (PI) staining. Results: We obviously observed that the rate of necrosis increases and the rate of tumor growth and cell activity decreases as the glucose availability reduces, which is in line with the computational model prediction.

An on-lattice agent-based Monte Carlo model simulating the growth kinetics of multicellular tumor spheroids

PURPOSE

To develop an on-lattice agent-based model describing the growth of multicellular tumor spheroids using simple Monte Carlo tools.

METHODS

Cells are situated on the vertices of a cubic grid. Different cell states (proliferative, hypoxic or dead) and cell evolution rules, driven by 10 parameters, and the effects of the culture medium are included. About twenty spheroids of MCF-7 human breast cancer were cultivated and the experimental data were used for tuning the model parameters.

RESULTS

Simulated spheroids showed adequate sizes of the necrotic nuclei and of the hypoxic and proliferative cell phases as a function of the growth time, mimicking the overall characteristics of the experimental spheroids. The relation between the radii of the necrotic nucleus and the whole spheroid obtained in the simulations was similar to the experimental one and the number of cells, as a function of the spheroid volume, was well reproduced. The statistical variability of the Monte Carlo model described the whole volume range observed for the experimental spheroids. Assuming that the model parameters vary within Gaussian distributions it was obtained a sample of spheroids that reproduced much better the experimental findings.

CONCLUSIONS

The model developed allows describing the growth of in vitro multicellular spheroids and the experimental variability can be well reproduced. Its flexibility permits to vary both the agents involved and the rules that govern the spheroid growth. More general situations, such as, e. g., tumor vascularization, radiotherapy effects on solid tumors, or the validity of the tumor growth mathematical models can be studied.

Integrated Biophysical Modeling and Image Analysis: Application to Neuro-Oncology

Central nervous system (CNS) tumors come with vastly heterogeneous histologic, molecular, and radiographic landscapes, rendering their precise characterization challenging. The rapidly growing fields of biophysical modeling and radiomics have shown promise in better characterizing the molecular, spatial, and temporal heterogeneity of tumors. Integrative analysis of CNS tumors, including clinically acquired multi-parametric magnetic resonance imaging (mpMRI) and the inverse problem of calibrating biophysical models to mpMRI data, assists in identifying macroscopic quantifiable tumor patterns of invasion and proliferation, potentially leading to improved (a) detection/segmentation of tumor subregions and (b) computer-aided diagnostic/prognostic/predictive modeling. This article presents a summary of (a) biophysical growth modeling and simulation,(b) inverse problems for model calibration, (c) these models' integration with imaging workflows, and (d) their application to clinically relevant studies. We anticipate that such quantitative integrative analysis may even be beneficial in a future revision of the World Health Organization (WHO) classification for CNS tumors, ultimately improving patient survival prospects.

Dynamic Targeting in Cancer Treatment

With the advent of personalized medicine, design and development of anti-cancer drugs that are specifically targeted to individual or sets of genes or proteins has been an active research area in both academia and industry. The underlying motivation for this approach is to interfere with several pathological crosstalk pathways in order to inhibit or at the very least control the proliferation of cancer cells. However, after initially conferring beneficial effects, if sub-lethal, these artificial perturbations in cell function pathways can inadvertently activate drug-induced up- and down-regulation of feedback loops, resulting in dynamic changes over time in the molecular network structure and potentially causing drug resistance as seen in clinics. Hence, the targets or their combined signatures should also change in accordance with the evolution of the network (reflected by changes to the structure and/or functional output of the network) over the course of treatment. This suggests the need for a "dynamic targeting" strategy aimed at optimizing tumor control by interfering with different molecular targets, at varying stages. Understanding the dynamic changes of this complex network under various perturbed conditions due to drug treatment is extremely challenging under experimental conditions let alone in clinical settings. However, mathematical modeling can facilitate studying these effects at the network level and beyond, and also accelerate comparison of the impact of different dosage regimens and therapeutic modalities prior to sizeable investment in risky and expensive clinical trials. A dynamic targeting strategy based on the use of mathematical modeling can be a new, exciting research avenue in the discovery and development of therapeutic drugs.

System Dynamics versus Agent-Based Modeling: A Review of Complexity Simulation in Construction Waste Management

The environmental impacts caused by construction waste have attracted increasing attention in recent years. The effective management of construction waste is essential in order to reduce negative environmental influences. Construction waste management (CWM) can be viewed as a complex adaptive system, as it involves not only various factors (e.g., social, economic, and environmental), but also different stakeholders (such as developers, contractors, designers, and governmental departments) simultaneously. System dynamics (SD) and agent-based modeling (ABM) are the two most popular approaches to deal with the complexity in CWM systems. However, the two approaches have their own advantages and drawbacks. The aim of this research is to conduct a comprehensive review and develop a novel model for combining the advantages of both SD and ABM. The research findings revealed that two options can be considered when combining SD with ABM; the two options are discussed.

Integrating Multiscale Modeling with Drug Effects for Cancer Treatment

In this paper, we review multiscale modeling for cancer treatment with the incorporation of drug effects from an applied system's pharmacology perspective. Both the classical pharmacology and systems biology are inherently quantitative; however, systems biology focuses more on networks and multi factorial controls over biological processes rather than on drugs and targets in isolation, whereas systems pharmacology has a strong focus on studying drugs with regard to the pharmacokinetic (PK) and pharmacodynamic (PD) relations accompanying drug interactions with multiscale physiology as well as the prediction of dosage-exposure responses and economic potentials of drugs. Thus, it requires multiscale methods to address the need for integrating models from the molecular levels to the cellular, tissue, and organism levels. It is a common belief that tumorigenesis and tumor growth can be best understood and tackled by employing and integrating a multifaceted approach that includes in vivo and in vitro experiments, in silico models, multiscale tumor modeling, continuous/discrete modeling, agent-based modeling, and multiscale modeling with PK/PD drug effect inputs. We provide an example application of multiscale modeling employing stochastic hybrid system for a colon cancer cell line HCT-116 with the application of Lapatinib drug. It is observed that the simulation results are similar to those observed from the setup of the wet-lab experiments at the Translational Genomics Research Institute.

Integrated PK-PD and agent-based modeling in oncology

Mathematical modeling has become a valuable tool that strives to complement conventional biomedical research modalities in order to predict experimental outcome, generate new medical hypotheses, and optimize clinical therapies. Two specific approaches, pharmacokinetic-pharmacodynamic (PK-PD) modeling, and agent-based modeling (ABM), have been widely applied in cancer research. While they have made important contributions on their own (e.g., PK-PD in examining chemotherapy drug efficacy and resistance, and ABM in describing and predicting tumor growth and metastasis), only a few groups have started to combine both approaches together in an effort to gain more insights into the details of drug dynamics and the resulting impact on tumor growth. In this review, we focus our discussion on some of the most recent modeling studies building on a combined PK-PD and ABM approach that have generated experimentally testable hypotheses. Some future directions are also discussed.

Simulating cancer growth with multiscale agent-based modeling

There have been many techniques developed in recent years to in silico model a variety of cancer behaviors. Agent-based modeling is a specific discrete-based hybrid modeling approach that allows simulating the role of diversity in cell populations as well as within each individual cell; it has therefore become a powerful modeling method widely used by computational cancer researchers. Many aspects of tumor morphology including phenotype-changing mutations, the adaptation to microenvironment, the process of angiogenesis, the influence of extracellular matrix, reactions to chemotherapy or surgical intervention, the effects of oxygen and nutrient availability, and metastasis and invasion of healthy tissues have been incorporated and investigated in agent-based models. In this review, we introduce some of the most recent agent-based models that have provided insight into the understanding of cancer growth and invasion, spanning multiple biological scales in time and space, and we further describe several experimentally testable hypotheses generated by those models. We also discuss some of the current challenges of multiscale agent-based cancer models.

WITHDRAWN: Cancer modeling: The holonic agent-based approach

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Pathological neural attractor dynamics in slowly growing gliomas supports an optimal time frame for white matter plasticity

Neurological function in patients with slowly growing brain tumors can be preserved even after extensive tumor resection. However, the global process of cortical reshaping and cerebral redistribution cannot be understood without taking into account the white matter tracts. The aim of this study was to predict the functional consequences of tumor-induced white matter damage by computer simulation. A computational model was proposed, incorporating two cortical patches and the white matter connections of the uncinate fasciculus. Tumor-induced structural changes were modeled such that different aspects of the connectivity were altered, mimicking the biological heterogeneity of gliomas. The network performance was quantified by comparing memory pattern recall and the plastic compensatory capacity of the network was analyzed. The model predicts an optimal level of synaptic conductance boost that compensates for tumor-induced connectivity loss. Tumor density appears to change the optimal plasticity regime, but tumor size does not. Compensatory conductance values that are too high lead to performance loss in the network and eventually to epileptic activity. Tumors of different configurations show differences in memory recall performance with slightly lower plasticity values for dense tumors compared to more diffuse tumors. Simulation results also suggest an optimal noise level that is capable of increasing the recall performance in tumor-induced white matter damage. In conclusion, the model presented here is able to capture the influence of different tumor-related parameters on memory pattern recall decline and provides a new way to study the functional consequences of white matter invasion by slowly growing brain tumors.

Dealing with diversity in computational cancer modeling

This paper discusses the need for interconnecting computational cancer models from different sources and scales within clinically relevant scenarios to increase the accuracy of the models and speed up their clinical adaptation, validation, and eventual translation. We briefly review current interoperability efforts drawing upon our experiences with the development of in silico models for predictive oncology within a number of European Commission Virtual Physiological Human initiative projects on cancer. A clinically relevant scenario, addressing brain tumor modeling that illustrates the need for coupling models from different sources and levels of complexity, is described. General approaches to enabling interoperability using XML-based markup languages for biological modeling are reviewed, concluding with a discussion on efforts towards developing cancer-specific XML markup to couple multiple component models for predictive in silico oncology.

Accelerating cancer systems biology research through Semantic Web technology

Cancer systems biology is an interdisciplinary, rapidly expanding research field in which collaborations are a critical means to advance the field. Yet the prevalent database technologies often isolate data rather than making it easily accessible. The Semantic Web has the potential to help facilitate web-based collaborative cancer research by presenting data in a manner that is self-descriptive, human and machine readable, and easily sharable. We have created a semantically linked online Digital Model Repository (DMR) for storing, managing, executing, annotating, and sharing computational cancer models. Within the DMR, distributed, multidisciplinary, and inter-organizational teams can collaborate on projects, without forfeiting intellectual property. This is achieved by the introduction of a new stakeholder to the collaboration workflow, the institutional licensing officer, part of the Technology Transfer Office. Furthermore, the DMR has achieved silver level compatibility with the National Cancer Institute's caBIG, so users can interact with the DMR not only through a web browser but also through a semantically annotated and secure web service. We also discuss the technology behind the DMR leveraging the Semantic Web, ontologies, and grid computing to provide secure inter-institutional collaboration on cancer modeling projects, online grid-based execution of shared models, and the collaboration workflow protecting researchers' intellectual property.

Multiscale cancer modeling

Simulating cancer behavior across multiple biological scales in space and time, i.e., multiscale cancer modeling, is increasingly being recognized as a powerful tool to refine hypotheses, focus experiments, and enable more accurate predictions. A growing number of examples illustrate the value of this approach in providing quantitative insights in the initiation, progression, and treatment of cancer. In this review, we introduce the most recent and important multiscale cancer modeling works that have successfully established a mechanistic link between different biological scales. Biophysical, biochemical, and biomechanical factors are considered in these models. We also discuss innovative, cutting-edge modeling methods that are moving predictive multiscale cancer modeling toward clinical application. Furthermore, because the development of multiscale cancer models requires a new level of collaboration among scientists from a variety of fields such as biology, medicine, physics, mathematics, engineering, and computer science, an innovative Web-based infrastructure is needed to support this growing community.

Modular model of TNFalpha cytotoxicity

MOTIVATION

Tumour Necrosis Factor alpha (TNF) initiates a complex series of biochemical events in the cell upon binding to its type R1 receptor (TNF-R1). Recent experimental work has unravelled the molecular regulation of the signalling complexes that lead either to cell survival or death. Survival signals are activated by direct binding of TNF to TNF-R1 at the cell membrane whereas apoptotic signals by endocytosed TNF/TNF-R1 complexes. Here we describe a reduced, effective model with few free parameters, where we group some intricate mechanisms into effective modules, that successfully describes this complex set of actions. We study the parameter space to show that the model is structurally stable and robust over a broad range of parameter values.

RESULTS

We use state-of-the-art Bayesian methods (a Sequential Monte Carlo sampler) to perform inference of plausible values of the model parameters from experimental data. As a result, we obtain a robust model that can provide a solid basis for further modelling of TNF signalling. The model is also suitable for inclusion in multi-scale simulation programs that are presently under development to study the behaviour of large tumour cell populations.

AVAILABILITY

We provide supplementary material that includes all mathematical details and all algorithms (Matlab code) and models (SBML descriptions).

CONTACT

edoardo.milotti@ts.infn.it

Discovering Molecular Targets in Cancer with Multiscale Modeling

Multiscale modeling is increasingly being recognized as a promising research area in computational cancer systems biology. Here, exemplified by two pioneering studies, we attempt to explain why and how such a multiscale approach paired with an innovative cross-scale analytical technique can be useful in identifying high-value molecular therapeutic targets. This novel, integrated approach has the potential to offer a more effective in silico framework for target discovery and represents an important technical step towards systems medicine.

In-silico oncology: an approximate model of brain tumor mass effect based on directly manipulated free form deformation

PURPOSE

The present work introduces a novel method for approximating mass effect of primary brain tumors.

METHODS

The spatio-temporal dynamics of cancerous cells are modeled by means of a deterministic reaction-diffusion equation. Diffusion tensor information obtained from a probabilistic diffusion tensor imaging atlas is incorporated into the model to simulate anisotropic diffusion of cancerous cells. To account for the expansive nature of the tumor, the computed net cell density of malignant cells is linked to a parametric deformation model. This mass effect model is based on the so-called directly manipulated free form deformation. Spatial correspondence between two successive simulation steps is established by tracking landmarks, which are attached to the boundary of the gross tumor volume. The movement of these landmarks is used to compute the new configuration of the control points and, hence, determines the resulting deformation. To prevent a deformation of rigid structures (i.e. the skull), fixed shielding landmarks are introduced. In a refinement step, an adaptive landmark scheme ensures a dense sampling of the tumor isosurface, which in turn allows for an appropriate representation of the tumor shape.

RESULTS

The influence of different parameters on the model is demonstrated by a set of simulations. Additionally, simulation results are qualitatively compared to an exemplary set of clinical magnetic resonance images of patients diagnosed with high-grade glioma.

CONCLUSIONS

Careful visual inspection of the results demonstrates the potential of the implemented model and provides first evidence that the computed approximation of tumor mass effect is sensible. The shape of diffusive brain tumors (glioblastoma multiforme) can be recovered and approximately matches the observations in real clinical data.

Nonlinear modelling of cancer: bridging the gap between cells and tumours

Despite major scientific, medical and technological advances over the last few decades, a cure for cancer remains elusive. The disease initiation is complex, and including initiation and avascular growth, onset of hypoxia and acidosis due to accumulation of cells beyond normal physiological conditions, inducement of angiogenesis from the surrounding vasculature, tumour vascularization and further growth, and invasion of surrounding tissue and metastasis. Although the focus historically has been to study these events through experimental and clinical observations, mathematical modelling and simulation that enable analysis at multiple time and spatial scales have also complemented these efforts. Here, we provide an overview of this multiscale modelling focusing on the growth phase of tumours and bypassing the initial stage of tumourigenesis. While we briefly review discrete modelling, our focus is on the continuum approach. We limit the scope further by considering models of tumour progression that do not distinguish tumour cells by their age. We also do not consider immune system interactions nor do we describe models of therapy. We do discuss hybrid-modelling frameworks, where the tumour tissue is modelled using both discrete (cell-scale) and continuum (tumour-scale) elements, thus connecting the micrometre to the centimetre tumour scale. We review recent examples that incorporate experimental data into model parameters. We show that recent mathematical modelling predicts that transport limitations of cell nutrients, oxygen and growth factors may result in cell death that leads to morphological instability, providing a mechanism for invasion via tumour fingering and fragmentation. These conditions induce selection pressure for cell survivability, and may lead to additional genetic mutations. Mathematical modelling further shows that parameters that control the tumour mass shape also control its ability to invade. Thus, tumour morphology may serve as a predictor of invasiveness and treatment prognosis.

An agent-based model identifies MRI regions of probable tumor invasion in a patient with glioblastoma

We present an application of a previously developed agent-based glioma model (Chen et al 2009 Biosystems 95 234-42) for predicting spatio-temporal tumor progression using a patient-specific MRI lattice derived from apparent diffusion coefficient (ADC) data. Agents representing collections of migrating glioma cells are initialized based upon voxels at the outer border of the tumor identified on T1-weighted (Gd+) MRI at an initial time point. These simulated migratory cells exhibit a specific biologically inspired spatial search paradigm, representing a weighting of the differential contribution from haptotactic permission and biomechanical resistance on the migration decision process. ADC data from 9 months after the initial tumor resection were used to select the best search paradigm for the simulation, which was initiated using data from 6 months after the initial operation. Using this search paradigm, 100 simulations were performed to derive a probabilistic map of tumor invasion locations. The simulation was able to successfully predict a recurrence in the dorsal/posterior aspect long before it was depicted on T1-weighted MRI, 18 months after the initial operation.

Hybrid mathematical model of glioma progression

OBJECTIVES

Gliomas are an important form of brain cancer, with high mortality rate. Mathematical models are often used to understand and predict their behaviour. However, using current modeling techniques one must choose between simulating individual cell behaviour and modeling tumours of clinically significant size.

MATERIALS AND METHODS

We propose a hybrid compartment-continuum-discrete model to simulate glioma growth and malignant cell invasion. The discrete portion of the model is capable of capturing intercellular interactions, including cell migration, intercellular communication, spatial cell population heterogeneity, phenotype differentiation, epigenetic events, proliferation, and apoptosis. Combining this with a compartment and continuum model allows clinically significant tumour sizes to be evaluated.

RESULTS AND CONCLUSIONS

This model is used to perform multiple simulations to determine sensitivity to changes in important model parameters, specifically, the fundamental length parameter, necrotic cell degradation rate, rate of cell migration, and rate of phenotype transformation. Using these values, the model is able to simulate tumour growth and invasion behaviour, observed clinically. This mathematical model provides a means to simulate various tumour development scenarios, which may lead to a better understanding of how altering fundamental parameters can influence neoplastic progression.

Cross-scale, cross-pathway evaluation using an agent-based non-small cell lung cancer model

We present a multiscale agent-based non-small cell lung cancer model that consists of a 3D environment with which cancer cells interact while processing phenotypic changes. At the molecular level, transforming growth factor beta (TGFbeta) has been integrated into our previously developed in silico model as a second extrinsic input in addition to epidermal growth factor (EGF). The main aim of this study is to investigate how the effects of individual and combinatorial change in EGF and TGFbeta concentrations at the molecular level alter tumor growth dynamics on the multi-cellular level, specifically tumor volume and expansion rate. Our simulation results show that separate EGF and TGFbeta fluctuations trigger competing multi-cellular phenotypes, yet synchronous EGF and TGFbeta signaling yields a spatially more aggressive tumor that overall exhibits an EGF-driven phenotype. By altering EGF and TGFbeta concentration levels simultaneously and asynchronously, we discovered a particular region of EGF-TGFbeta profiles that ensures phenotypic stability of the tumor system. Within this region, concentration changes in EGF and TGFbeta do not impact the resulting multi-cellular response substantially, while outside these concentration ranges, a change at the molecular level will substantially alter either tumor volume or tumor expansion rate, or both. By evaluating tumor growth dynamics across different scales, we show that, under certain conditions, therapeutic targeting of only one signaling pathway may be insufficient. Potential implications of these in silico results for future clinico-pharmacological applications are discussed.