Cellular modeling of cancer invasion: integration of in silico and in vitro approaches

Molecular weight-dependent antitumor effects of prunes-derived type I arabinogalactan on human and murine triple wild-type melanomas

The regulation of metastasis-related cellular aspects of two structurally similar AGIs from prunes tea infusion, with different molar masses, was studied in vitro against Triple Wild-Type metastatic melanoma (TWM) from murine and human origin. The higher molar mass AGI (AGI-78KDa) induced TWMs cells death and, in murine cell line, it decreased some metastasis-related cellular processes: invasiveness capacity, cell-extracellular matrix interaction, and colonies sizes. The lower molar mass AGI (AGI-12KDa) did not induce cell death but decreased TWMs proliferation rate and, in murine cell line, it decreased cell adhesion and colonies sizes. Both AGIs alter the clonogenic capacity of human cell line. In spite to understand why we saw so many differences between AGIs effects on murine and human cell lines we performed in silico analysis that demonstrated differential gene expression profiles between them. Complementary network topological predictions suggested that AGIs can modulate multiple pathways in a specie-dependent manner, which explain differential results obtained in vitro between cell lines. Our results pointed to therapeutic potential of AGIs from prunes tea against TWMs and showed that molecular weight of AGIs may influence their antitumor effects.

Thinking in 3 dimensions: philosophies of the microenvironment in organoids and organs-on-chip

Organoids and organs-on-a-chip are currently the two major families of 3D advanced organotypic in vitro culture systems, aimed at reconstituting miniaturized models of physiological and pathological states of human organs. Both share the tenets of the so-called "three-dimensional thinking", a Systems Physiology approach focused on recapitulating the dynamic interactions between cells and their microenvironment. We first review the arguments underlying the "paradigm shift" toward three-dimensional thinking in the in vitro culture community. Then, through a historically informed account of the technical affordances and the epistemic commitments of these two approaches, we highlight how they embody two distinct experimental cultures. We finally argue that the current systematic effort for their integration requires not only innovative "synergistic" engineering solutions, but also conceptual integration between different perspectives on biological causality.

Integration of quantitative methods and mathematical approaches for the modeling of cancer cell proliferation dynamics

Physiological processes rely on the control of cell proliferation, and the dysregulation of these processes underlies various pathological conditions, including cancer. Mathematical modeling can provide new insights into the complex regulation of cell proliferation dynamics. In this review, we first examine quantitative experimental approaches for measuring cell proliferation dynamics in vitro and compare the various types of data that can be obtained in these settings. We then explore the toolbox of common mathematical modeling frameworks that can describe cell behavior, dynamics, and interactions of proliferation. We discuss how these wet-laboratory studies may be integrated with different mathematical modeling approaches to aid the interpretation of the results and to enable the prediction of cell behaviors, specifically in the context of cancer.

3D cancer models: One step closer to in vitro human studies

Cancer immunotherapy is the great breakthrough in cancer treatment as it displayed prolonged progression-free survival over conventional therapies, yet, to date, in only a minority of patients. In order to broad cancer immunotherapy clinical applicability some roadblocks need to be overcome, first among all the lack of preclinical models that faithfully depict the local tumor microenvironment (TME), which is known to dramatically affect disease onset, progression and response to therapy. In this review, we provide the reader with a detailed overview of current 3D models developed to mimick the complexity and the dynamics of the TME, with a focus on understanding why the TME is a major target in anticancer therapy. We highlight the advantages and translational potentials of tumor spheroids, organoids and immune Tumor-on-a-Chip models in disease modeling and therapeutic response, while outlining pending challenges and limitations. Thinking forward, we focus on the possibility to integrate the know-hows of micro-engineers, cancer immunologists, pharmaceutical researchers and bioinformaticians to meet the needs of cancer researchers and clinicians interested in using these platforms with high fidelity for patient-tailored disease modeling and drug discovery.

A simulation of parental and glycolytic tumor phenotype competition predicts observed responses to pH changes and increased glycolysis after anti-VEGF therapy

Clinical cancers are typically spatially and temporally heterogeneous, containing multiple microenvironmental habitats and diverse phenotypes and/or genotypes, which can interact through resource competition and direct or indirect interference. A common intratumoral evolutionary pathway, probably initiated as adaptation to hypoxia, leads to the "Warburg phenotype" which maintains high glycolytic rates and acid production, even in normoxic conditions. Since individual cancer cells are the unit of Darwinian selection, intraspecific competition dominates intratumoral evolution. Thus, elements of the Warburg phenotype become key "strategies" in competition with cancer cell populations that retain the metabolism of the parental normal cells. Here we model the complex interactions of cell populations with Warburg and parental phenotypes as they compete for access to vasculature, while subject to direct interference by Warburg-related acidosis. In this competitive environment, vasculature delivers nutrients, removes acid and necrotic detritus, and responds to signaling molecules (VEGF and TNF-α). The model is built in a nested fashion and growth parameters are derived from monolayer, spheroid, and xenograft experiments on prostate cancer. The resulting model of in vivo tumor growth reaches a steady state, displaying linear growth and coexistence of both glycolytic and parental phenotypes consistent with experimental observations. The model predicts that increasing tumor pH sufficiently early can arrest the development of the glycolytic phenotype, while decreasing tumor pH accelerates this evolution and increases VEGF production. The model's predicted dual effects of VEGF blockers in decreasing tumor growth while increasing the glycolytic fraction of tumor cells has potential implications for optimizing angiogenic inhibitors.

Heterotypic tumor models through freeform printing into photostabilized granular microgels

The tissue microenvironment contains a complex assortment of multiple cell types, matrices, and vessel structures, which is difficult to reconstruct in vitro. Here, we demonstrate model tumor microenvironments formed through direct writing of vasculature channels and tumor cell aggregates, within a cell-laden microgel matrix. Photocrosslinkable microgels provide control over local and global mechanics, while enabling the integration of virtually any cell type. Direct writing of a Pluronic sacrificial ink into a stromal cell-microgel suspension is used to form vessel structures for endothelialization, followed by printing of melanoma aggregates. Tumor cells migrate into the prototype vessels as a function of spatial location, thereby providing a measure of invasive potential. The integration of perfusable channels with multiple spatially defined cell types provides new avenues for modelling development and disease, with scope for both fundamental research and drug development efforts.

Beyond gold nanoparticles cytotoxicity: Potential to impair metastasis hallmarks

Gold nanoparticle (AuNP)-based systems have been extensively investigated as diagnostic and therapeutic agents due to their tunable properties and easy surface functionalization. Upon cell uptake, AuNPs present an inherent cell impairment potential based on organelle and macromolecules damage, leading to cell death. Such cytotoxicity is concentration-dependent and completely undesirable, especially if unspecific. However, under non-cytotoxic concentrations, internalized AuNPs could potentially weaken cells and act as antitumor agents. Therefore, this study aimed to investigate the antitumor effect of ultrasmall AuNPs (~3 nm) stabilized by the anionic polysaccharide gum arabic (GA-AuNPs). Other than intrinsic cytotoxicity, the focus was downregulation of cancer hallmarks of aggressive tumors, using a highly metastatic model of melanoma. We first demonstrated that GA-AuNPs showed excellent stability under biological environment. Non-cytotoxic concentrations to seven different cell lines, including tumorigenic and non-tumorigenic cells, were determined by standard 2D in vitro assays. Gold concentrations ≤ 2.4 mg L^-1 (16.5 nM AuNPs) were non-cytotoxic and therefore chosen for further analyses. Cells exposed to GA-AuNPs were uptaken by melanoma cells through endocytic processes. Next we described remarkable biological properties using non-cytotoxic concentrations of this nanomaterial. Invasion through an extracellular matrix barrier as well as 3D growth capacity (anchorage-independent colony formation and spheroids growth) were negatively affected by 2.4 mg L^-1 GA-AuNPs. Additionally, exposed spheroids showed morphological changes, suggesting that GA-AuNPs could penetrate into the preformed tumor and affect its integrity. All together these results demonstrate that side effects, such as cytotoxicity, can be avoided by choosing the right concentration, nevertheless, preserving desirable effects such as modulation of key tumor cell malignancy features.

A Lock Free Approach To Parallelize The Cellular Potts Model: Application To Ductal Carcinoma In Situ

In the field of computational biology, in order to simulate multiscale biological systems, the Cellular Potts Model (CPM) has been used, which determines the actions that simulated cells can perform by determining a hamiltonian of energy that takes into account the influence that neighboring cells exert, under a wide range of parameters. There are some proposals in the literature that parallelize the CPM; in all cases, either lock-based techniques or other techniques that require large amounts of information to be disseminated among parallel tasks are used to preserve data coherence. In both cases, computational performance is limited. This work proposes an alternative approach for the parallelization of the model that uses transactional memory to maintain the coherence of the information. A Java implementation has been applied to the simulation of the ductal adenocarcinoma of breast in situ (DCIS). Times and speedups of the simulated execution of the model on the cluster of our university are analyzed. The results show a good speedup.

A novel in silico platform for a fully automatic personalized brain tumor growth

Glioblastoma Multiforme is the most common and most aggressive type of brain tumors. Although accurate prediction of Glioblastoma borders and shape is absolutely essential for neurosurgeons, there are not many in silico platforms that can make such predictions. In the current study, an automatic patient-specific simulation of Glioblastoma growth would be described. A finite element approach is used to analyze the magnetic resonance images from patients in the early stages of their tumors. For segmentation of the tumor, the Support Vector Machine (SVM) method, which is an automatic segmentation algorithm, is used. Using in situ and in vivo data, the main parameters of tumor prediction and growth are estimated with high precision in proliferation-invasion partial differential equation, using the genetic algorithm optimization method. The results show that for a C57BL mouse, the differences between the area and perimeter of in vivo test and simulation prediction data, as the objective function, are 3.7% and 17.4%, respectively.

In vitro attenuation of classic metastatic melanoma‑related features by highly diluted natural complexes: Molecular and functional analyses

Metastasis is responsible for the majority of deaths among patients with malignant melanoma. Despite recent advances, the majority of current and modern therapies are ineffective and/or financially unfeasible. Thus, in this study, we investigated two low‑cost highly‑diluted natural complexes (HDNCs) that have been shown to be effective against malignant melanoma in a murine model in vivo. The aim of this study was to determine the mechanisms through which these HDNCs directly affect melanoma cells, either alone or in an artificial tumor microenvironment, suppressing the metastatic phenotype, thus explaining previous in vivo effects. For this purpose, HDNC in vitro treatments of B16‑F10 melanoma cells, alone or in co‑culture with Balb/3T3 fibroblasts, were carried out. Molecular biology techniques and standard functional assays were used to assess the changes in molecule expression and in cell behaviors related to the metastatic phenotype. Melanoma progression features were found to be regulated by HDNCs. Molecules related to cell adhesion (N‑cadherin, β1‑integrin and CD44), and migration, extracellular matrix remodeling and angiogenesis were modulated. The cell migratory, invasive and clonogenic capacities were reduced by the HDNCs. No loss of cell proliferation or viability were observed. On the whole, the findings of this study indicate that HDNCs directly reprogram, molecularly and functionally, melanoma cells in vitro, modulating their metastatic phenotype. Such findings are likely to be responsible for the attenuation of tumor growth and lung colonization previously observed in vivo.

High-throughput cancer hypothesis testing with an integrated PhysiCell-EMEWS workflow

BACKGROUND

Cancer is a complex, multiscale dynamical system, with interactions between tumor cells and non-cancerous host systems. Therapies act on this combined cancer-host system, sometimes with unexpected results. Systematic investigation of mechanistic computational models can augment traditional laboratory and clinical studies, helping identify the factors driving a treatment's success or failure. However, given the uncertainties regarding the underlying biology, these multiscale computational models can take many potential forms, in addition to encompassing high-dimensional parameter spaces. Therefore, the exploration of these models is computationally challenging. We propose that integrating two existing technologies-one to aid the construction of multiscale agent-based models, the other developed to enhance model exploration and optimization-can provide a computational means for high-throughput hypothesis testing, and eventually, optimization.

RESULTS

In this paper, we introduce a high throughput computing (HTC) framework that integrates a mechanistic 3-D multicellular simulator (PhysiCell) with an extreme-scale model exploration platform (EMEWS) to investigate high-dimensional parameter spaces. We show early results in applying PhysiCell-EMEWS to 3-D cancer immunotherapy and show insights on therapeutic failure. We describe a generalized PhysiCell-EMEWS workflow for high-throughput cancer hypothesis testing, where hundreds or thousands of mechanistic simulations are compared against data-driven error metrics to perform hypothesis optimization.

CONCLUSIONS

While key notational and computational challenges remain, mechanistic agent-based models and high-throughput model exploration environments can be combined to systematically and rapidly explore key problems in cancer. These high-throughput computational experiments can improve our understanding of the underlying biology, drive future experiments, and ultimately inform clinical practice.

The biology and mathematical modelling of glioma invasion: a review

Adult gliomas are aggressive brain tumours associated with low patient survival rates and limited life expectancy. The most important hallmark of this type of tumour is its invasive behaviour, characterized by a markedly phenotypic plasticity, infiltrative tumour morphologies and the ability of malignant progression from low- to high-grade tumour types. Indeed, the widespread infiltration of healthy brain tissue by glioma cells is largely responsible for poor prognosis and the difficulty of finding curative therapies. Meanwhile, mathematical models have been established to analyse potential mechanisms of glioma invasion. In this review, we start with a brief introduction to current biological knowledge about glioma invasion, and then critically review and highlight future challenges for mathematical models of glioma invasion.

Organotypic three-dimensional assays based on human leiomyoma-derived matrices

Alongside cancer cells, tumours exhibit a complex stroma containing a repertoire of cells, matrix molecules and soluble factors that actively crosstalk between each other. Recognition of this multifaceted concept of the tumour microenvironment (TME) calls for authentic TME mimetics to study cancer in vitro. Traditionally, tumourigenesis has been investigated in non-human, three-dimensional rat type I collagen containing organotypic discs or by means of mouse sarcoma-derived gel, such as Matrigel^®. However, the molecular compositions of these simplified assays do not properly simulate human TME. Here, we review the main properties and benefits of using human leiomyoma discs and their matrix Myogel for in vitro assays. Myoma discs are practical for investigating the invasion of cancer cells, as are cocultures of cancer and stromal cells in a stiff, hypoxic TME mimetic. Myoma discs contain soluble factors and matrix molecules commonly present in neoplastic stroma. In Transwell, IncuCyte, spheroid and sandwich assays, cancer cells move faster and form larger colonies in Myogel than in Matrigel^®. Additionally, Myogel can replace Matrigel^® in hanging-drop and tube-formation assays. Myogel also suits three-dimensional drug testing and extracellular vesicle interactions. To conclude, we describe the application of our myoma-derived matrices in 3D in vitro cancer assays.

This article is part of the discussion meeting issue ‘Extracellular vesicles and the tumour microenvironment’.

Microenvironmental influence on microtumour infiltration patterns: 3D-mathematical modelling supported by in vitro studies

Mathematical modelling approaches have become increasingly abundant in cancer research. Tumour infiltration extent and its spatial organization depend both on the tumour type and stage and on the bio-physicochemical characteristics of the microenvironment. This sets a complex scenario that often requires a multidisciplinary and individually adjusted approach. The ultimate goal of this work is to present an experimental/numerical combined method for the development of a three-dimensional mathematical model with the ability to reproduce the growth and infiltration patterns of a given avascular microtumour in response to different microenvironmental conditions. The model is based on a diffusion-convection reaction equation that considers logistic proliferation, volumetric growth, a rim of proliferative cells at the tumour surface, and invasion with diffusive and convective components. The parameter values of the model were fitted to experimental results while radial velocity and diffusion coefficients were made spatially variable in a case-specific way through the introduction of a shape function and a diffusion-limited-aggregation (DLA)-derived fractal matrix, respectively, according to the infiltration pattern observed. The in vitro model consists of multicellular tumour spheroids (MTSs) of an epithelial mammary tumour cell line (LM3) immersed in a collagen I gel matrix with a standard culture medium ("naive" matrix) or a conditioned medium from adipocytes or preadipocytes ("conditioned" matrix). It was experimentally determined that both adipocyte and preadipocyte conditioned media had the ability to change the MTS infiltration pattern from collective and laminar to an individual and atomized one. Numerical simulations were able to adequately reproduce qualitatively and quantitatively both kinds of infiltration patterns, which were determined by area quantification, analysis of fractal dimensions and lacunarity, and Bland-Altman analysis. These results suggest that the combined approach presented here could be established as a new framework with interesting potential applications at both the basic and clinical levels in the oncology area.

Identification of genes associated with matrix metalloproteinases in invasive lung adenocarcinoma

The aim of the present study was to identify genes with similar function to that of matrix metalloproteinases (MMPs) in invasive lung adenocarcinoma (AC) and to screen the transcription factors that regulate MMPs. The gene expression dataset GSE2514, including 20 invasive lung AC samples and 19 adjacent normal lung samples, was downloaded from the Gene Expression Omnibus database. Differentially expressed genes (DEGs) were screened using the limma package in R. Genes with similar function to MMPs were identified by K-means clustering. Their correlations with MMPs were validated using Pearson correlation analysis. The expression of MMPs in lung cancer and normal tissues was evaluated by western blot analysis. Protein-protein interaction (PPI) network and transcriptional regulatory network analyses were performed with Retrieval of Interacting Genes and Database for Annotation, Visualization and Integrated Discovery, respectively. As a result, 269 DEGs were identified between invasive lung AC samples and normal lung samples, including 78 upregulated and 191 downregulated genes. Four MMPs (MMP1, MMP7, MMP9 and MMP12), which were upregulated in lung AC, were clustered into one group with other genes, including NAD(P)H quinone oxidoreductase 1, claudin 3 (CLDN3), S100 calcium-binding protein P, serine protease inhibitor Kazal type 1, collagen type XI α 1 chain, periostin and desmoplakin (DSP), following cluster analysis. Pearson correlation analysis further confirmed correlations between MMP9-CLDN3, MMP9-DSP and MMP12-DSP. PPI network analysis also indicated multiple interactions between MMPs-associated genes. Furthermore, MMPs were commonly regulated by CCAAT/enhancer binding protein α transcription factor. These findings may provide further insight into the mechanisms of MMPs in invasive lung AC.

3D cellular invasion platforms: how do paper-based cultures stack up?

Cellular invasion is the gateway to metastasis, which is the leading cause of cancer-related deaths. Invasion is driven by a number of chemical and mechanical stresses that arise in the tumor microenvironment. In vitro assays are needed for the systematic study of cancer progress. To be truly predictive, these assays must generate tissue-like environments that can be experimentally controlled and manipulated. While two-dimensional (2D) monolayer cultures are easily assembled and evaluated, they lack the extracellular components needed to assess invasion. Three-dimensional (3D) cultures are better suited for invasion studies because they generate cellular phenotypes that are more representative of those found in vivo. This feature article provides an overview of four invasion platforms. We focus on paper-based cultures, an emerging 3D culture platform capable of generating tissue-like structures and quantifying cellular invasion. Paper-based cultures are as easily assembled and analyzed as monolayers, but provide an experimentally powerful platform capable of supporting: co-cultures and representative extracellular environments; experimentally controlled gradients; readouts capable of quantifying, discerning, and separating cells based on their invasiveness. With a series of examples we highlight the potential of paper-based cultures, and discuss how they stack up against other invasion platforms.

Combining radiation with hyperthermia: a multiscale model informed by in vitro experiments

Combined radiotherapy and hyperthermia offer great potential for the successful treatment of radio-resistant tumours through thermo-radiosensitization. Tumour response heterogeneity, due to intrinsic, or micro-environmentally induced factors, may greatly influence treatment outcome, but is difficult to account for using traditional treatment planning approaches. Systems oncology simulation, using mathematical models designed to predict tumour growth and treatment response, provides a powerful tool for analysis and optimization of combined treatments. We present a framework that simulates such combination treatments on a cellular level. This multiscale hybrid cellular automaton simulates large cell populations (up to 107 cells) in vitro, while allowing individual cell-cycle progression, and treatment response by modelling radiation-induced mitotic cell death, and immediate cell kill in response to heating. Based on a calibration using a number of experimental growth, cell cycle and survival datasets for HCT116 cells, model predictions agreed well (R2 > 0.95) with experimental data within the range of (thermal and radiation) doses tested (0-40 CEM43, 0-5 Gy). The proposed framework offers flexibility for modelling multimodality treatment combinations in different scenarios. It may therefore provide an important step towards the modelling of personalized therapies using a virtual patient tumour.

Growth of adult spinal cord in knifefish: Development and parametrization of a distributed model

The study of indeterminate-growing organisms such as teleost fish presents a unique opportunity for improving our understanding of central nervous tissue growth during adulthood. Integrating the existing experimental data associated with this process into a theoretical framework through mathematical or computational modeling provides further research avenues through sensitivity analysis and optimization. While this type of approach has been used extensively in investigations of tumor growth, wound healing, and bone regeneration, the development of nervous tissue has been rarely studied within a modeling framework. To address this gap, the present work introduces a distributed model of spinal cord growth in the knifefish Apteronotus leptorhynchus, an established teleostean model of adult growth in the central nervous system. The proposed model incorporates two mechanisms, cell proliferation by active stem/progenitor cells and cell drift due to population pressure, both of which are subject to global constraints. A coupled reaction-diffusion equation approach was adopted to represent the densities of actively-proliferating and non-proliferating cells along the longitudinal axis of the spinal cord. Computer simulations using this model yielded biologically-feasible growth trajectories. Subsequent comparisons with whole-organism growth curves allowed the estimation of previously-unknown parameters, such as relative growth rates.

A Screening System for Evaluating Cell Extension Formation, Collagen Compaction, and Degradation in Drug Discovery

The generation of cell extensions is critical for matrix remodeling in tissue invasion by cancer cells, but current methods for identifying molecules that regulate cell extension formation and matrix remodeling are not well adapted for screening purposes. We applied a grid-supported, floating collagen gel system (~100 Pa stiffness) to examine cell extension formation, collagen compaction, and collagen degradation in a single assay. With the use of cultured diploid fibroblasts, a fibroblast cell line, and two cancer cell lines, we found that compared with attached collagen gels (~2800 Pa), the mean number and length of cell extensions were respectively greater in the floating gels. In assessing specific processes in cell extension formation, compared with controls, the number of cell extensions was reduced by latrunculin B, β1 integrin blockade, and a formin FH2 domain inhibitor. Screening of a kinase inhibitor library (480 compounds) with the floating gel assay showed that compared with vehicle-treated cells, there were large reductions of collagen compaction, pericellular collagen degradation, and number of cell extensions after treatment with SB431542, SIS3, Fasudil, GSK650394, and PKC-412. These data indicate that the grid-supported floating collagen gel model can be used to screen for inhibitors of cell extension formation and critical matrix remodeling events associated with cancer cell invasion.

Multiscale biphasic modelling of peritumoural collagen microstructure: The effect of tumour growth on permeability and fluid flow

We present an in-silico model of avascular poroelastic tumour growth coupled with a multiscale biphasic description of the tumour–host environment. The model is specified to in-vitro data, facilitating biophysically realistic simulations of tumour spheroid growth into a dense collagen hydrogel. We use the model to first confirm that passive mechanical remodelling of collagen fibres at the tumour boundary is driven by solid stress, and not fluid pressure. The model is then used to demonstrate the influence of collagen microstructure on peritumoural permeability and interstitial fluid flow. Our model suggests that at the tumour periphery, remodelling causes the peritumoural stroma to become more permeable in the circumferential than radial direction, and the interstitial fluid velocity is found to be dependent on initial collagen alignment. Finally we show that solid stresses are negatively correlated with peritumoural permeability, and positively correlated with interstitial fluid velocity. These results point to a heterogeneous, microstructure-dependent force environment at the tumour–peritumoural stroma interface.

Are Tumor Cell Lineages Solely Shaped by Mechanical Forces?

This paper investigates cell proliferation dynamics in small tumor cell aggregates using an individual-based model (IBM). The simulation model is designed to study the morphology of the cell population and of the cell lineages as well as the impact of the orientation of the division plane on this morphology. Our IBM model is based on the hypothesis that cells are incompressible objects that grow in size and divide once a threshold size is reached, and that newly born cell adhere to the existing cell cluster. We performed comparisons between the simulation model and experimental data by using several statistical indicators. The results suggest that the emergence of particular morphologies can be explained by simple mechanical interactions.

Exosomal miRs in Lung Cancer: A Mathematical Model

Lung cancer, primarily non-small-cell lung cancer (NSCLC), is the leading cause of cancer deaths in the United States and worldwide. While early detection significantly improves five-year survival, there are no reliable diagnostic tools for early detection. Several exosomal microRNAs (miRs) are overexpressed in NSCLC, and have been suggested as potential biomarkers for early detection. The present paper develops a mathematical model for early stage of NSCLC with emphasis on the role of the three highest overexpressed miRs, namely miR-21, miR-205 and miR-155. Simulations of the model provide quantitative relationships between the tumor volume and the total mass of each of the above miRs in the tumor. Because of the positive correlation between these miRs in the tumor tissue and in the blood, the results of the paper may be viewed as a first step toward establishing a combination of miRs 21, 205, 155 and possibly other miRs as serum biomarkers for early detection of NSCLC.

Multi-scale Modeling in Clinical Oncology: Opportunities and Barriers to Success

Hierarchical processes spanning several orders of magnitude of both space and time underlie nearly all cancers. Multi-scale statistical, mathematical, and computational modeling methods are central to designing, implementing and assessing treatment strategies that account for these hierarchies. The basic science underlying these modeling efforts is maturing into a new discipline that is close to influencing and facilitating clinical successes. The purpose of this review is to capture the state-of-the-art as well as the key barriers to success for multi-scale modeling in clinical oncology. We begin with a summary of the long-envisioned promise of multi-scale modeling in clinical oncology, including the synthesis of disparate data types into models that reveal underlying mechanisms and allow for experimental testing of hypotheses. We then evaluate the mathematical techniques employed most widely and present several examples illustrating their application as well as the current gap between pre-clinical and clinical applications. We conclude with a discussion of what we view to be the key challenges and opportunities for multi-scale modeling in clinical oncology.

Multiscale modelling of solid tumour growth: the effect of collagen micromechanics

Here we introduce a model of solid tumour growth coupled with a multiscale biomechanical description of the tumour microenvironment, which facilitates the explicit simulation of fibre-fibre and tumour-fibre interactions. We hypothesise that such a model, which provides a purely mechanical description of tumour-host interactions, can be used to explain experimental observations of the effect of collagen micromechanics on solid tumour growth. The model was specified to mouse tumour data, and numerical simulations were performed. The multiscale model produced lower stresses than an equivalent continuum-like approach, due to a more realistic remodelling of the collagen microstructure. Furthermore, solid tumour growth was found to cause a passive mechanical realignment of fibres at the tumour boundary from a random to a circumferential orientation. This is in accordance with experimental observations, thus demonstrating that such a response can be explained as purely mechanical. Finally, peritumoural fibre network anisotropy was found to produce anisotropic tumour morphology. The dependency of tumour morphology on the peritumoural microstructure was reduced by adding a load-bearing non-collagenous component to the fibre network constitutive equation.

An in silico model to demonstrate the effects of Maspin on cancer cell dynamics

Most cancer treatments efficacy depends on tumor metastasis suppression, where tumor suppressor genes play an important role. Maspin (Mammary Serine Protease Inhibitor), an non-inhibitory serpin has been reported as a potential tumor suppressor to influence cell migration, adhesion, proliferation and apoptosis in in vitro and in vivo experiments in last two decades. Lack of computational investigations hinders its ability to go through clinical trials. Previously, we reported first computational model for maspin effects on tumor growth using artificial neural network and cellular automata paradigm with in vitro data support. This paper extends the previous in silico model by encompassing how maspin influences cell migration and the cell-extracellular matrix interaction in subcellular level. A feedforward neural network was used to define each cell behavior (proliferation, quiescence, apoptosis) which followed a cell-cycle algorithm to show the microenvironment impacts over tumor growth. Furthermore, the model concentrates how the in silico experiments results can further confirm the fact that maspin reduces cell migration using specific in vitro data verification method. The data collected from in vitro and in silico experiments formulates an unsupervised learning problem which can be solved by using different clustering algorithms. A density based clustering technique was developed to measure the similarity between two datasets based on the number of links between instances. Our proposed clustering algorithm first finds the nearest neighbors of each instance, and then redefines the similarity between pairs of instances in terms of how many nearest neighbors share the two instances. The number of links between two instances is defined as the number of common neighbors they have. The results showed significant resemblances with in vitro experimental data. The results also offer a new insight into the dynamics of maspin and establish as a metastasis suppressor gene for further molecular research.

The Importance of Neighborhood Scheme Selection in Agent-based Tumor Growth Modeling

Modeling tumor growth has proven a very challenging problem, mainly due to the fact that tumors are highly complex systems that involve dynamic interactions spanning multiple scales both in time and space. The desire to describe interactions in various scales has given rise to modeling approaches that use both continuous and discrete variables, known as hybrid approaches. This work refers to a hybrid model on a 2D square lattice focusing on cell movement dynamics as they play an important role in tumor morphology, invasion and metastasis and are considered as indicators for the stage of malignancy used for early prognosis and effective treatment. Considering various distributions of the microenvironment, we explore how Neumann vs. Moore neighborhood schemes affects tumor growth and morphology. The results indicate that the importance of neighborhood selection is critical under specific conditions that include i) increased hapto/chemo-tactic coefficient, ii) a rugged microenvironment and iii) ECM degradation.

Tumor growth prediction with reaction-diffusion and hyperelastic biomechanical model by physiological data fusion

The goal of tumor growth prediction is to model the tumor growth process, which can be achieved by physiological modeling and model personalization from clinical measurements. Although image-driven frameworks have been proposed with promising results, several issues such as infinitesimal strain assumptions, complicated personalization procedures, and the lack of functional information, may limit their prediction accuracy. In view of these issues, we propose a framework for pancreatic neuroendocrine tumor growth prediction, which comprises a FEM-based tumor growth model with coupled reaction-diffusion equation and nonlinear biomechanics. Physiological data fusion of structural and functional images is used to improve the subject-specificity of model personalization, and a derivative-free global optimization algorithm is adopted to facilitate the complicated model and accommodate flexible choices of objective functions. With this flexibility, we propose an objective function accounting for both the tumor volume difference and the root-mean-squared error of intracellular volume fractions. Experiments were performed on synthetic and clinical data to verify the parameter estimation capability and the prediction performance. Comparisons of using different biomechanical models and objective functions were also performed. From the experimental results of eight patient data sets, the average recall, precision, Dice coefficient, and relative volume difference between predicted and measured tumor volumes were 84.5 ± 6.9%, 85.8 ± 8.2%, 84.6 ± 1.7%, and 14.2 ± 8.4%, respectively.

Tumor growth in complex, evolving microenvironmental geometries: a diffuse domain approach

We develop a mathematical model of tumor growth in complex, dynamic microenvironments with active, deformable membranes. Using a diffuse domain approach, the complex domain is captured implicitly using an auxiliary function and the governing equations are appropriately modified, extended and solved in a larger, regular domain. The diffuse domain method enables us to develop an efficient numerical implementation that does not depend on the space dimension or the microenvironmental geometry. We model homotypic cell-cell adhesion and heterotypic cell-basement membrane (BM) adhesion with the latter being implemented via a membrane energy that models cell-BM interactions. We incorporate simple models of elastic forces and the degradation of the BM and ECM by tumor-secreted matrix degrading enzymes. We investigate tumor progression and BM response as a function of cell-BM adhesion and the stiffness of the BM. We find tumor sizes tend to be positively correlated with cell-BM adhesion since increasing cell-BM adhesion results in thinner, more elongated tumors. Prior to invasion of the tumor into the stroma, we find a negative correlation between tumor size and BM stiffness as the elastic restoring forces tend to inhibit tumor growth. In order to model tumor invasion of the stroma, we find it necessary to downregulate cell-BM adhesiveness, which is consistent with experimental observations. A stiff BM promotes invasiveness because at early stages the opening in the BM created by MDE degradation from tumor cells tends to be narrower when the BM is stiffer. This requires invading cells to squeeze through the narrow opening and thus promotes fragmentation that then leads to enhanced growth and invasion. In three dimensions, the opening in the BM was found to increase in size even when the BM is stiff because of pressure induced by growing tumor clusters. A larger opening in the BM can increase the potential for further invasiveness by increasing the possibility that additional tumor cells could invade the stroma.

Investigation of the essential role of platelet-tumor cell interactions in metastasis progression using an agent-based model

BACKGROUND

Metastatic tumors are a major source of morbidity and mortality for most cancers. Interaction of circulating tumor cells with endothelium, platelets and neutrophils play an important role in the early stages of metastasis formation. These complex dynamics have proven difficult to study in experimental models. Prior computational models of metastases have focused on tumor cell growth in a host environment, or prediction of metastasis formation from clinical data. We used agent-based modeling (ABM) to dynamically represent hypotheses of essential steps involved in circulating tumor cell adhesion and interaction with other circulating cells, examine their functional constraints, and predict effects of inhibiting specific mechanisms.

METHODS

We developed an ABM of Early Metastasis (ABMEM), a descriptive semi-mechanistic model that replicates experimentally observed behaviors of populations of circulating tumor cells, neutrophils, platelets and endothelial cells while incorporating representations of known surface receptor, autocrine and paracrine interactions. Essential downstream cellular processes were incorporated to simulate activation in response to stimuli, and calibrated with experimental data. The ABMEM was used to identify potential points of interdiction through examination of dynamic outcomes such as rate of tumor cell binding after inhibition of specific platelet or tumor receptors.

RESULTS

The ABMEM reproduced experimental data concerning neutrophil rolling over endothelial cells, inflammation-induced binding between neutrophils and platelets, and tumor cell interactions with these cells. Simulated platelet inhibition with anti-platelet drugs produced unstable aggregates with frequent detachment and re-binding. The ABMEM replicates findings from experimental models of circulating tumor cell adhesion, and suggests platelets play a critical role in this pre-requisite for metastasis formation. Similar effects were observed with inhibition of tumor integrin αV/β3. These findings suggest that anti-platelet or anti-integrin therapies may decrease metastasis by preventing stable circulating tumor cell adhesion.

CONCLUSION

Circulating tumor cell adhesion is a complex, dynamic process involving multiple cell-cell interactions. The ABMEM successfully captures the essential interactions necessary for this process, and allows for in-silico iterative characterization and invalidation of proposed hypotheses regarding this process in conjunction with in-vitro and in-vivo models. Our results suggest that anti-platelet therapies and anti-integrin therapies may play a promising role in inhibiting metastasis formation.

The formation of tight tumor clusters affects the efficacy of cell cycle inhibitors: a hybrid model study

Cyclin-dependent kinases (CDKs) are vital in regulating cell cycle progression, and, thus, in highly proliferating tumor cells CDK inhibitors are gaining interest as potential anticancer agents. Clonogenic assay experiments are frequently used to determine drug efficacy against the survival and proliferation of cancer cells. While the anticancer mechanisms of drugs are usually described at the intracellular single-cell level, the experimental measurements are sampled from the entire cancer cell population. This approach may lead to discrepancies between the experimental observations and theoretical explanations of anticipated drug mechanisms. To determine how individual cell responses to drugs that inhibit CDKs affect the growth of cancer cell populations, we developed a spatially explicit hybrid agent-based model. In this model, each cell is equipped with internal cell cycle regulation mechanisms, but it is also able to interact physically with its neighbors. We model cell cycle progression, focusing on the G1 and G2/M cell cycle checkpoints, as well as on related essential components, such as CDK1, CDK2, cell size, and DNA damage. We present detailed studies of how the emergent properties (e.g., cluster formation) of an entire cell population depend on altered physical and physiological parameters. We analyze the effects of CDK1 and CKD2 inhibitors on population growth, time-dependent changes in cell cycle distributions, and the dynamic evolution of spatial cell patterns. We show that cell cycle inhibitors that cause cell arrest at different cell cycle phases are not necessarily synergistically super-additive. Finally, we demonstrate that the physical aspects of cell population growth, such as the formation of tight cell clusters versus dispersed colonies, alter the efficacy of cell cycle inhibitors, both in 2D and 3D simulations. This finding may have implications for interpreting the treatment efficacy results of in vitro experiments, in which treatment is applied before the cells can grow to produce clusters, especially because in vivo tumors, in contrast, form large masses before they are detected and treated.

Evolution of intratumoral phenotypic heterogeneity: the role of trait inheritance

A tumour is a heterogeneous population of cells that competes for limited resources. In the clinic, we typically probe the tumour by biopsy, and then characterize it by the dominant genetic clone. But genotypes are only the first link in the chain of hierarchical events that leads to a specific cell phenotype. The relationship between genotype and phenotype is not simple, and the so-called genotype to phenotype map is poorly understood. Many genotypes can produce the same phenotype, so genetic heterogeneity may not translate directly to phenotypic heterogeneity. We therefore choose to focus on the functional endpoint, the phenotype as defined by a collection of cellular traits (e.g. proliferative and migratory ability). Here, we will examine how phenotypic heterogeneity evolves in space and time and how the way in which phenotypes are inherited will drive this evolution. A tumour can be thought of as an ecosystem, which critically means that we cannot just consider it as a collection of mutated cells but more as a complex system of many interacting cellular and microenvironmental elements. At its simplest, a growing tumour with increased proliferation capacity must compete for space as a limited resource. Hypercellularity leads to a contact-inhibited core with a competitive proliferating rim. Evolution and selection occurs, and an individual cell's capacity to survive and propagate is determined by its combination of traits and interaction with the environment. With heterogeneity in phenotypes, the clone that will dominate is not always obvious as there are both local interactions and global pressures. Several combinations of phenotypes can coexist, changing the fitness of the whole. To understand some aspects of heterogeneity in a growing tumour, we build an off-lattice agent-based model consisting of individual cells with assigned trait values for proliferation and migration rates. We represent heterogeneity in these traits with frequency distributions and combinations of traits with density maps. How the distributions change over time is dependent on how traits are passed on to progeny cells, which is our main enquiry. We bypass the translation of genetics to behaviour by focusing on the functional end result of inheritance of the phenotype combined with the environmental influence of limited space.

Microengineered tumor models: insights & opportunities from a physical sciences-oncology perspective

Prevailing evidence has established the fundamental role of microenvironmental conditions in tumorigenesis. However, the ability to identify, interrupt, and translate the underlying cellular and molecular mechanisms into meaningful therapies remains limited, due in part to a lack of organotypic culture systems that accurately recapitulate tumor physiology. Integration of tissue engineering with microfabrication technologies has the potential to address this challenge and mimic tumor heterogeneity with pathological fidelity. Specifically, this approach allows recapitulating global changes of tissue-level phenomena, while also controlling microscale variability of various conditions including spatiotemporal presentation of soluble signals, biochemical and physical characteristics of the extracellular matrix, and cellular composition. Such platforms have continued to elucidate the role of the microenvironment in cancer pathogenesis and significantly improve drug discovery and screening, particularly for therapies that target tumor-enabling stromal components. This review discusses some of the landmark efforts in the field of micro-tumor engineering with a particular emphasis on deregulated tissue organization and mass transport phenomena in the tumor microenvironment.

Modeling the mechanics of cancer: effect of changes in cellular and extra-cellular mechanical properties

Malignant transformation, though primarily driven by genetic mutations in cells, is also accompanied by specific changes in cellular and extra-cellular mechanical properties such as stiffness and adhesivity. As the transformed cells grow into tumors, they interact with their surroundings via physical contacts and the application of forces. These forces can lead to changes in the mechanical regulation of cell fate based on the mechanical properties of the cells and their surrounding environment. A comprehensive understanding of cancer progression requires the study of how specific changes in mechanical properties influences collective cell behavior during tumor growth and metastasis. Here we review some key results from computational models describing the effect of changes in cellular and extra-cellular mechanical properties and identify mechanistic pathways for cancer progression that can be targeted for the prediction, treatment, and prevention of cancer.

The effects of stenting on shear stress: relevance to endothelial injury and repair

Stent deployment following balloon angioplasty is used routinely to treat coronary artery disease. These interventions cause damage and loss of endothelial cells (EC), and thus promote in-stent thrombosis and restenosis. Injured arteries are repaired (intrinsically) by locally derived EC and by circulating endothelial progenitor cells which migrate and proliferate to re-populate denuded regions. However, re-endothelialization is not always complete and often dysfunctional. Moreover, the molecular and biomechanical mechanisms that control EC repair and function in stented segments are poorly understood. Here, we propose that stents modify endothelial repair processes, in part, by altering fluid shear stress, a mechanical force that influences EC migration and proliferation. A more detailed understanding of the biomechanical processes that control endothelial healing would provide a platform for the development of novel therapeutic approaches to minimize damage and promote vascular repair in stented arteries.

A multiscale road map of cancer spheroids – incorporating experimental and mathematical modelling to understand cancer progression

Computational models represent a highly suitable framework, not only for testing biological hypotheses and generating new ones but also for optimising experimental strategies. As one surveys the literature devoted to cancer modelling, it is obvious that immense progress has been made in applying simulation techniques to the study of cancer biology, although the full impact has yet to be realised. For example, there are excellent models to describe cancer incidence rates or factors for early disease detection, but these predictions are unable to explain the functional and molecular changes that are associated with tumour progression. In addition, it is crucial that interactions between mechanical effects, and intracellular and intercellular signalling are incorporated in order to understand cancer growth, its interaction with the extracellular microenvironment and invasion of secondary sites. There is a compelling need to tailor new, physiologically relevant in silico models that are specialised for particular types of cancer, such as ovarian cancer owing to its unique route of metastasis, which are capable of investigating anti-cancer therapies, and generating both qualitative and quantitative predictions. This Commentary will focus on how computational simulation approaches can advance our understanding of ovarian cancer progression and treatment, in particular, with the help of multicellular cancer spheroids, and thus, can inform biological hypothesis and experimental design.

The mechanics of metastasis: insights from a computational model

Although it may seem obvious that mechanical forces are required to drive metastatic cell movements, understanding of the mechanical aspects of metastasis has lagged far behind genetic and biochemical knowledge. The goal of this study is to learn about the mechanics of metastasis using a cell-based finite element model that proved useful for advancing knowledge about the forces that drive embryonic cell and tissue movements. Metastasis, the predominant cause of cancer-related deaths, involves a series of mechanical events in which one or more cells dissociate from a primary tumour, migrate through normal tissue, traverse in and out of a multi-layer circulatory system vessel and resettle. The present work focuses on the dissemination steps, from dissociation to circulation. The model shows that certain surface tension relationships must be satisfied for cancerous cells to dissociate from a primary tumour and that these equations are analogous to those that govern dissociation of embryonic cells. For a dissociated cell to then migrate by invadopodium extension and contraction and exhibit the shapes seen in experiments, the invadopodium must generate a contraction equal to approximately twice that produced by the interfacial tension associated with surrounding cells. Intravasation through the wall of a vessel is governed by relationships akin to those in the previous two steps, while release from the vessel wall is governed by equations that involve surface and interfacial tensions. The model raises a number of potential research questions. It also identifies how specific mechanical properties and the sub-cellular structural components that give rise to them might be changed so as to thwart particular metastatic steps and thereby block the spread of cancer.