Avascular Tumor Research Articles

Nucleation of antagonistic organisms and cellular competitions on curved, inflating substrates.

We consider the dynamics of spatially distributed, diffusing populations of organisms with antagonistic interactions. These interactions are found on many length scales, ranging from kilometer-scale animal range dynamics with selection against hybrids to micron-scale interactions between poison-secreting microbial populations. We find that the dynamical line tension at the interface between antagonistic organisms suppresses survival probabilities of small clonal clusters: the line tension introduces a critical cluster size that an organism with a selective advantage must achieve before deterministically spreading through the population. We calculate the survival probability as a function of selective advantage δ and antagonistic interaction strength σ. Unlike a simple Darwinian selective advantage, the survival probability depends strongly on the spatial diffusion constant D_{s} of the strains when σ>0, with suppressed survival when both species are more motile. Finally, we study the survival probability of a single mutant cell at the frontier of a growing spherical cluster of cells, such as the surface of an avascular spherical tumor. Both the inflation and curvature of the frontier significantly enhance the survival probability by changing the critical size of the nucleating cell cluster.

The formation of cancer stem cells in EMT6/Ro tumor: Hybrid modeling within its micro-environment

Abstract We investigate the formation of cancer stem cells and their role in maintaining avascular solid tumors. For this purpose, we provide a mathematical framework to study the major biological interpretations on the stemness of cancerous cells (stochastic scheme) and the self-renewal ability of particular progenitor cells (hierarchical scheme). These interpretations are related to the genetic characteristics of cancer, which could be described by a set of mechanisms shared by all types of cancer, i.e., hallmarks of cancer. Hallmarks of cancer relate cellular genetics, differentiation and heterogeneity, and tumor micro-environment (TME). To reach our goal, based on hallmarks of cancer, we propose a hybrid discrete-continuous model that combines continual interactions of cellular genetics and tumor micro-environment. Using this model, we conduct computational experiments on EMT6/Ro tumor to study the possibility of stochastic and hierarchical schemes. Our experiments suggest that even in well-suited genomic and micro-environmental conditions, a tumor survives only when the majority of tumor cells are in the stemness state (stochastic approach), or progenitor to CSC transition exists (hierarchical approach). In the lack of progenitor to CSC transition, in the hierarchical scheme, the tumor fades away due to the CSCs malnutrition. These results are supported by a sensitivity analysis of the model parameters. Although our computational experiments are carried out for the EMT6/Ro tumor, due to the generic nature of this approach, we believe, this work could provide insights regarding similar behaviors in other tumors.

Three-Dimensional Modeling of Avascular Tumor Growth in Both Static and Dynamic Culture Platforms.

Microfluidic cell culture platforms are ideal candidates for modeling the native tumor microenvironment because they can precisely reconstruct in vivo cellular behavior. Moreover, mathematical modeling of tumor growth can pave the way toward description and prediction of growth pattern as well as improving cancer treatment. In this study, a modified mathematical model based on concentration distribution is applied to tumor growth in both conventional static culture and dynamic microfluidic cell culture systems. Apoptosis and necrosis mechanisms are considered as the main inhibitory factors in the model, while tumor growth rate and nutrient consumption rate are modified in both quiescent and proliferative zones. We show that such modification can better predict the experimental results of tumor growth reported in the literature. Using numerical simulations, the effects of the concentrations of the nutrients as well as the initial tumor radius on the tumor growth are investigated and discussed. Furthermore, tumor growth is simulated by taking into account the dynamic perfusion into the proposed model. Subsequently, tumor growth kinetics in a three-dimensional (3D) microfluidic device containing a U-shaped barrier is numerically studied. For this case, the effect of the flow rate of culture medium on tumor growth is investigated as well. Finally, to evaluate the impact of the trap geometry on the tumor growth, a comparison is made between the tumor growth kinetics in two frequently used traps in microfluidic cell culture systems, i.e., the U-shaped barrier and microwell structures. The proposed model can provide insight into better predicting the growth and development of avascular tumor in both static and dynamic cell culture platforms.

Investigation of multicellular tumor spheroids enriched for a cancer stem cell phenotype

Cancer stem cells (CSCs) provide self-renewal of the tumor after radiation and chemotherapy. These cells are important during tumor development. The in vitro model of avascular tumor that enriched of cells with stem like characteristics is critical to understanding of the role CSCs in the tumor. Cell viability was evaluated by MTT assay. The expression of cancer stem cells markers (CD133, CD44, CD24 and bmi-1) in 2D cell culture and multicellular tumor spheroids (MCTS) of MCF-7 cells was evaluated. The Stemi2000 software AxioVisionRed 4.7 was used for image processing. The volume of spheroids was calculated by Bjerkvig formula. The highest expression of CD133, CD44, CD24 and bmi-1 receptors was detected in MCTS, enriched with cancer stem cells (eMCTS). Cell aggregates of eMCTS culture were returned from suspension to adhesive conditions. It was found that the cells of the MCTS surface layers were enriched with CD133, CD44, CD24, bmi-1, EpCAM, vim markers, but not adherent cells. eMCTS are less sensitive to anticancer drugs (cisplatin, methotrexate and doxorubicin), than adhesive cell culture and MCTS cultured under standard conditions in a complete nutrient medium (P<0.05). We observed that eMCTS population possesses aggressive phenotypic characteristics such as invasion, cancer stem cell markers and chemoresistance. eMCTS model could improve the screening efficiency of therapeutical agents against CSCs.

A cell-loss-free concave microwell array based size-controlled multi-cellular tumoroid generation for anti-cancer drug screening.

The 3D multi-cellular tumoroid (MCT) model is an in vivo-like, avascular tumor model that has received much attention as a refined screening platform for drug therapies. Several types of research have been efforted to improve the physiological characteristics of the tumor microenvironment (TME) of the in vivo-like MCTs. Size-controlled MCTs have received much attention for obtaining highly reproducible results in drug screening assays and achieving a homogeneous and meaningful level of biological activities. Here, we describe an effective method for fabricating the size-controlled in vivo-like MCTs using a cell-loss-free (CLF) microwell arrays. The CLF microwell arrays was fabricated by using the simple operation of laser carving of a poly (methyl methacrylate) (PMMA) master mold. We also demonstrated the biophysicochemical effect of tumor microenvironment (TME) resident fibroblasts through the expression of TGFβ, αSMA, Type I-, IV collagen, angiogenesis related markers on tumorigenesis, and confirmed the drug response of MCTs with anti-cancer agents. This technology for the fabrication of CLF microwell arrays could be used as an effective method to produce an in vitro tumor model for cancer research and drug discovery.

On a 2D Model of Avascular Tumor with Weak Allee Effect

Recent studies reveal that Allee effect may play important roles in the growth of tumor. We present one of the first mathematical models of avascular tumor that incorporates the weak Allee effect. The model considers the densities of tumor cells in three stages: proliferating cells, quiescent cells, and necrotic cells. We investigate how Allee effect impacts the growth of the avascular tumor. We also investigate the effect of apoptosis of proliferating cells and necrosis of quiescent cells. The system is numerically solved in 2D using different sets of parameters. We show that Allee effect and apoptosis play important roles in the growth of tumor and the formation of necrotic core.

Reduced CTL motility and activity in avascular tumor areas.

Patchy infiltration of tumors by cytotoxic T cells (CTLs) predicts poorer prognosis for cancer patients. The factors limiting intratumoral CTL dissemination, though, are poorly understood. To study CTL dissemination in tumors, we histologically examined human melanoma samples and used mice to image B16-OVA tumors infiltrated by OT-I CTLs using intravital two-photon microscopy. In patients, most CTLs concentrated around peripheral blood vessels, especially in poorly infiltrated tumors. In mice, OT-I CTLs had to cluster around tumor cells to efficiently kill them in a contact-and perforin-dependent manner and cytotoxicity was strictly antigen-specific. OT-I CTLs as well as non-specific CTLs concentrated around peripheral vessels, and cleared the tumor cells around them. This was also the case when CTLs were injected directly into the tumors. CTLs crawled rapidly only in areas within 50µm of flowing blood vessels and transient occlusion of vessels immediately, though reversibly, stopped their migration. In vitro, oxygen depletion and blockade of oxidative phosphorylation also reduced CTL motility. Taken together, these results suggest that hypoxia limits CTL migration away from blood vessels, providing immune-privileged niches for tumor cells to survive. Normalizing intratumoral vasculature may thus synergize with tumor immunotherapy.

Metabolic reprogramming dynamics in tumor spheroids: Insights from a multicellular, multiscale model.

Mathematical modeling provides the predictive ability to understand the metabolic reprogramming and complex pathways that mediate cancer cells’ proliferation. We present a mathematical model using a multiscale, multicellular approach to simulate avascular tumor growth, applied to pancreatic cancer. The model spans three distinct spatial and temporal scales. At the extracellular level, reaction diffusion equations describe nutrient concentrations over a span of seconds. At the cellular level, a lattice-based energy driven stochastic approach describes cellular phenomena including adhesion, proliferation, viability and cell state transitions, occurring on the timescale of hours. At the sub-cellular level, we incorporate a detailed kinetic model of intracellular metabolite dynamics on the timescale of minutes, which enables the cells to uptake and excrete metabolites and use the metabolites to generate energy and building blocks for cell growth. This is a particularly novel aspect of the model. Certain defined criteria for the concentrations of intracellular metabolites lead to cancer cell growth, proliferation or death. Overall, we model the evolution of the tumor in both time and space. Starting with a cluster of tumor cells, the model produces an avascular tumor that quantitatively and qualitatively mimics experimental measurements of multicellular tumor spheroids. Through our model simulations, we can investigate the response of individual intracellular species under a metabolic perturbation and investigate how that response contributes to the response of the tumor as a whole. The predicted response of intracellular metabolites under various targeted strategies are difficult to resolve with experimental techniques. Thus, the model can give novel predictions as to the response of the tumor as a whole, identifies potential therapies to impede tumor growth, and predicts the effects of those therapeutic strategies. In particular, the model provides quantitative insight into the dynamic reprogramming of tumor cells at the intracellular level in response to specific metabolic perturbations. Overall, the model is a useful framework to study targeted metabolic strategies for inhibiting tumor growth.

Pulsed Electric Field Treatment Enhances the Cytotoxicity of Plasma-Activated Liquids in a Three-Dimensional Human Colorectal Cancer Cell Model

Cold atmospheric plasma and more recently, plasma-activated liquids (culture media, water or buffered solutions previously exposed to plasma), are gathering momentum in cancer cells treatment. Nevertheless, in vitro tests show that this novel approach is sometimes less efficient than expected. We here evaluate the mechanisms of action of the plasma-activated PBS and suggest to use electropermeabilization (EP) in combination with the plasma-activated phosphate-buffered saline (PBS), in order to potentiate the cytotoxic effect of the plasma activated liquid. Human multicellular tumor spheroids (MCTS), a three-dimensional cell model, which resembles small avascular tumors, was used to define the optimal treatment conditions for single and dual-mode treatments. MCTS growth, viability, and global morphological changes were assessed by live cell video-microscopy. In addition, the induction of caspases activation, the appearance of DNA damages, and cell membrane permeabilization, as well as the early modifications in the cellular ultrastructure, were examined by immunofluorescence, propidium iodide staining, confocal fluorescence microscopy and transmission electron microscopy, respectively. Altogether, our results show that a combined treatment resulted in an earlier onset of DNA damage and caspases activation, which completely abolished MCTS growth. This report is a proof of concept study evidencing that electropermeabilization greatly potentiates the cytotoxic effect of plasma-activated PBS in vitro in a three-dimensional cancer cell model.

The suitability of liposomes for the delivery of hydrophobic drugs – A case study with curcumin

Liposomes are a popular formulation strategy for the delivery of anticancer drugs. While their benefits for formulating hydrophilic anticancer drugs have been clearly shown during the last decades, the suitability of liposomes for the delivery of hydrophobic drugs is questionable. Curcumin is a diphenolic plant compound that is extensively researched for its anticancer properties. It was chosen as a hydrophobic model drug in this study. Due to its low bioavailability, poor solubility and instability in aqueous media it is a highly problematic compound and requires particular formulation techniques. Curcumin liposomes with lipids of different rigidities were comprehensively investigated in respect to their physicochemical properties, their storage and serum stability. In vitro experiments were conducted with common 2D cell models and additionally with multicellular tumor spheroids (MCTS) as a more sophisticated tool to represent the physiology of avascular solid tumors. Our results indicate that liposomes containing the fluid phospholipid dioleoylphosphatidylcholine (DOPC) represent an excellent formulation to enhance the solubility and stability of curcumin. However, in presence of serum or cells, curcumin is rapidly released from the protecting and stabilizing lipid bilayer. Thus, improvement of the in vivo efficacy of curcumin is probably not achieved by using liposomes. Cytotoxicity and uptake experiments showed clearly a reduced effectivity of curcumin liposomes in the 3D cell model in comparison to the 2D model. This not only illustrates the limitations of monolayer cultures in predicting drug and nanocarrier interactions with solid tumors, but also further questions the use of liposomes as a formulation strategy in the treatment of solid tumors with curcumin.

Role of circulating tumor cell spheroids in drug resistance.

Cancer cell spheroids are used for drug screening as these three-dimensional (3D) assemblies recapitulate tumors more realistic than the widely employed 2D in vitro cultures. Limited drug diffusion and gradients of oxygen and nutrients in spheroids represent avascular tumor regions containing quiescent and hypoxic tumor cells with high drug resistance. Circulating tumor cells (CTCs) effect metastatic spread and are present in high numbers in malignant diseases such as small-cell lung cancer (SCLC) and in other cancer patients with high tumor load. CTCs are heterogeneous and only a small fraction of these cells survive in the circulation and cause distal lesions. CTCs may circulate as single cells but small CTC clusters or CTC spheroids have been detected in cancer patients and demonstrated to possess increased metastatic potential. At our lab we have obtained 9 permanent SCLC CTC cell lines (BHGc7, BHGc10, BHGc16, BHGc26, BHGc27, BHGc50, BHGc59, BHGc71, and UHGc5) of distinct patients exhibiting similar characteristics and spontaneous formation of large spheroids, termed tumorospheres. These aggregates were shown to exhibit high drug resistance compared to the corresponding single cell suspensions. The increased metastatic capability of small circulating tumor clusters/spheroids may be explained by their role as putative precursors of tumorospheres eventually trapped in capillaries. Limited drug penetration and the presence of hypoxic/quiescent cells can readily account for the global drug resistance of advanced SCLC which has resulted in clinical failure of a wide range of chemotherapeutics and low survival. Furthermore, we have detected such tumorospheres in non-small-cell lung cancer (NSCLC) patients progressing under EGFR-directed tyrosine kinase inhibitor therapy which had undergone NSCLC-SCLC transformation.

Modeling three-dimensional invasive solid tumor growth in heterogeneous microenvironment under chemotherapy.

A systematic understanding of the evolution and growth dynamics of invasive solid tumors in response to different chemotherapy strategies is crucial for the development of individually optimized oncotherapy. Here, we develop a hybrid three-dimensional (3D) computational model that integrates pharmacokinetic model, continuum diffusion-reaction model and discrete cell automaton model to investigate 3D invasive solid tumor growth in heterogeneous microenvironment under chemotherapy. Specifically, we consider the effects of heterogeneous environment on drug diffusion, tumor growth, invasion and the drug-tumor interaction on individual cell level. We employ the hybrid model to investigate the evolution and growth dynamics of avascular invasive solid tumors under different chemotherapy strategies. Our simulations indicate that constant dosing is generally more effective in suppressing primary tumor growth than periodic dosing, due to the resulting continuous high drug concentration. In highly heterogeneous microenvironment, the malignancy of the tumor is significantly enhanced, leading to inefficiency of chemotherapies. The effects of geometrically-confined microenvironment and non-uniform drug dosing are also investigated. Our computational model, when supplemented with sufficient clinical data, could eventually lead to the development of efficient in silico tools for prognosis and treatment strategy optimization.

Global asymptotic stability of positive steady states of a solid avascular tumor growth model with time delays

In this work, global stability of a free boundary problem modeling solid avascular tumor growth is studied. The model is considered with time delays during the proliferation process. We prove that the unique positive constant steady state is globally asymptotically stable under some assumptions. The proof uses the comparison principle and the iteration method.

Calibration of Multi-Parameter Models of Avascular Tumor Growth Using Time Resolved Microscopy Data

Two of the central challenges of using mathematical models for predicting the spatiotemporal development of tumors is the lack of appropriate data to calibrate the parameters of the model, and quantitative characterization of the uncertainties in both the experimental data and the modeling process itself. We present a sequence of experiments, with increasing complexity, designed to systematically calibrate the rates of apoptosis, proliferation, and necrosis, as well as mobility, within a phase-field tumor growth model. The in vitro experiments characterize the proliferation and death of human liver carcinoma cells under different initial cell concentrations, nutrient availabilities, and treatment conditions. A Bayesian framework is employed to quantify the uncertainties in model parameters. The average difference between the calibration and the data, across all time points is between 11.54% and 14.04% for the apoptosis experiments, 7.33% and 23.30% for the proliferation experiments, and 8.12% and 31.55% for the necrosis experiments. The results indicate the proposed experiment-computational approach is generalizable and appropriate for step-by-step calibration of multi-parameter models, yielding accurate estimations of model parameters related to rates of proliferation, apoptosis, and necrosis.

On the avascular ellipsoidal tumour growth model within a nutritive environment

The present work is part of a series of studies conducted by the authors on analytical models of avascular tumour growth that exhibit both geometrical anisotropy and physical inhomogeneity. In particular, we consider a tumour structure formed in distinct ellipsoidal regions occupied by cell populations at a certain stage of their biological cycle. The cancer cells receive nutrient by diffusion from an inhomogeneous supply and they are subject to also an inhomogeneous pressure field imposed by the tumour microenvironment. It is proved that the lack of symmetry is strongly connected to a special condition that should hold between the data imposed by the tumour’s surrounding medium, in order for the ellipsoidal growth to be realizable, a feature already present in other non-symmetrical yet more degenerate models. The nutrient and the inhibitor concentration, as well as the pressure field, are provided in analytical fashion via closed-form series solutions in terms of ellipsoidal eigenfunctions, while their behaviour is demonstrated by indicative plots. The evolution equation of all the tumour’s ellipsoidal interfaces is postulated in ellipsoidal terms and a numerical implementation is provided in view of its solution. From the mathematical point of view, the ellipsoidal system is the most general coordinate system that the Laplace operator, which dominates the mathematical models of avascular growth, enjoys spectral decomposition. Therefore, we consider the ellipsoidal model presented in this work, as the most general analytic model describing the avascular growth in inhomogeneous environment. Additionally, due to the intrinsic degrees of freedom inherited to the model by the ellipsoidal geometry, the ellipsoidal model presented can be adapted to a very populous class of avascular tumours, varying in figure and in orientation.

Model for breast cancer diversity and spatial heterogeneity

We present and analyze a growth model of an avascular tumor that considers the basic biological principles of proliferation, motility, death, and genetic mutations of the cell. From an analysis of genomic data and considering the results of a regulatory network analysis we identify two sets of genes---a set of sixteen and six genes---that are believed to play an important role in the evolution of breast cancer. Considering that cancer cells shape the tissue microenvironment and niches to their competitive advantage, the model assumes that cancer and normal cells compete for essential nutrients and that the rate of mutations is affected by nutrients availability. To this end, we propose a coupling between the transport of nutrients and gene mutations dynamics. Gene mutation dynamics are modeled as a Yule-Furry Markovian process, while transport of nutrients is described with a system of reaction-diffusion equations. For each representative tumor we calculate its diversity, represented by the Shannon index, and its spatial heterogeneity, measured by its fractal dimension. These quantities are important in the clinical diagnosis of tumor malignancy. A tumor malignancy diagram, obtained by plotting diversity versus fractal dimension, is calculated for different values of a parameter $\ensuremath{\beta}$, that modulate proliferation rate. It is found that, when $\ensuremath{\beta}l1$, tumors show greater diversity and more spatial heterogeneity as compared with $\ensuremath{\beta}g1$. More importantly, it is found that the results and conclusions are similar when we use the six-gene set versus the sixteen-gene set.

Investigation of avascular tumor–immune system interactions using a CA–PDE model

Abstract We report on investigations that illustrate the interaction between the specific immune system and a young avascular tumor growing due to a diffusive nutrient supply. We formulate a hybrid cellular automata-partial differential equation (CA-PDE) model which includes cell cycle dynamics and allows for tracking the spatial and temporal evolution of this elaborate biological system. We present results of two dimensional numerical simulations that, specifically in this work, include special cases of the spherical and papillary tumor growth, the infiltration of immune system cells into the tumor and the escape of tumor cells from the regime of the immune cells.

Modeling Avascular Tumor Growth: Approach with an Adaptive Grid Numerical Technique

The mathematical modeling of complex biological systems leads to system of coupled nonlinear partial differential equations (PDEs). In this paper, we present a short review on the interaction of the urokinase plasminogen activator (uPA) system with a model for cancer cell in the avascular phase, faced using the moving mesh PDE/(MMPDE) numerical technique. The dynamical evolution of the system as a function of the diffusion properties of cancer cells has been considered, as well as the effect of hypoxia to the cancer evolution, introducing a model equation for the nutrient oxygen. The model parameters have been taken from the data existing in the literature, in particular to gauge the oxygen supply, data determined from in vivo experiments on human tumors have been used. The numerical results obtained simulating a one-dimensional portion of the biological tissue are consistent with the data existing in the literature. Our high-resolution computations show that cancer proliferation begins through highly irregular spatio-temporal pattern, which depends on cancer motility characteristics. In presence of hypoxia, the cancer proliferation patterns are still characterized by an inhomogeneous pattern, but other effects are present which depend on the model parameters, triggered by the oxygen.

Self-influenced growth through evolving material inhomogeneities

We reformulate a model of avascular tumour growth in which the tumour tissue is studied as a biphasic medium featuring an interstitial fluid and a solid phase. The description of growth relies on two fundamental features: one of those is given by the mass transfer among the constituents of the phases, which is taken into account through source and sink terms; the other one is the multiplicative decomposition of the deformation gradient tensor of the solid phase, with the introduction of a growth tensor, which represents the growth-induced structural changes of the tumour. In general, such tensor is non-integrable, and it may allow to define a Levi-Civita connection with non-trivial curvature. Moreover, its evolution is related to the source and sink of mass of the solid phase through an evolution equation. Our goal is to study how growth can be influenced by the inhomogeneity of the growth tensor. To this end, we study the evolution of the latter, as predicted by two different models. In the first one, the dependence of the growth tensor on the tumour’s material points is not explicitly considered in the evolution equation. In the second model, instead, the inhomogeneity of the growth tensor is resolved explicitly by introducing the curvature associated with it into the evolution equation. We perform numerical simulations to compare the results produced by these two models, and evaluate a possible role of the material inhomogeneities on growth.

Oxygen diffusion in ellipsoidal tumour spheroids.

Oxygen plays a central role in cellular metabolism, in both healthy and tumour tissue. The presence and concentration of molecular oxygen in tumours has a substantial effect on both radiotherapy response and tumour evolution, and as a result the oxygen micro-environment is an area of intense research interest. Multi-cellular tumour spheroids closely mimic real avascular tumours, and in particular they exhibit physiologically relevant heterogeneous oxygen distribution. This property has made them a vital part of in vitro experimentation. For ideal spheroids, their heterogeneous oxygen distributions can be predicted from theory, allowing determination of cellular oxygen consumption rate (OCR) and anoxic extent. However, experimental tumour spheroids often depart markedly from perfect sphericity. There has been little consideration of this reality. To date, the question of how far an ellipsoid can diverge from perfect sphericity before spherical assumptions break down remains unanswered. In this work, we derive equations governing oxygen distribution (and, more generally, nutrient and drug distribution) in both prolate and oblate tumour ellipsoids, and quantify the theoretical limits of the assumption that the spheroid is a perfect sphere. Results of this analysis yield new methods for quantifying OCR in ellipsoidal spheroids, and how this can be applied to markedly increase experimental throughput and quality.