A reaction-diffusion model for the growth of avascular tumor

A nutrient-limited model for avascular cancer growth including cell proliferation, motility and death is presented. The model qualitatively reproduces commonly observed morphologies for primary tumors, and the simulated patterns are characterized by its gyration radius, total number of cancer cells, and number of cells on tumor periphery. These very distinct morphological patterns follow Gompertz growth curves, but exhibit different scaling laws for their surfaces. Also, the simulated tumors incorporate a spatial structure composed of a central necrotic core, an inner rim of quiescent cells and a narrow outer shell of proliferating cells in agreement with biological data. Finally, our results indicate that the competition for nutrients among normal and cancer cells may be a determinant factor in generating papillary tumor morphology.Comment: 9 pages, 6 figures, to appear in PR

Establishment of Highly Tumorigenic Human Colorectal Cancer Cell Line (CR4) with Properties of Putative Cancer Stem Cells

BACKGROUND: Colorectal cancer (CRC) has the third highest mortality rates among the US population. According to the most recent concept of carcinogenesis, human tumors are organized hierarchically, and the top of it is occupied by malignant stem cells (cancer stem cells, CSCs, or cancer-initiating cells, CICs), which possess unlimited self-renewal and tumor-initiating capacities and high resistance to conventional therapies. To reflect the complexity and diversity of human tumors and to provide clinically and physiologically relevant cancer models, large banks of characterized patient-derived low-passage cell lines, and especially CIC-enriched cell lines, are urgently needed. PRINCIPAL FINDINGS: Here we report the establishment of a novel CIC-enriched, highly tumorigenic and clonogenic colon cancer cell line, CR4, derived from liver metastasis. This stable cell line was established by combining 3D culturing and 2D culturing in stem cell media, subcloning of cells with particular morphology, co-culture with carcinoma associated fibroblasts (CAFs) and serial transplantation to NOD/SCID mice. Using RNA-Seq complete transcriptome profiling of the tumorigenic fraction of the CR4 cells in comparison to the bulk tumor cells, we have identified about 360 differentially expressed transcripts, many of which represent stemness, pluripotency and resistance to treatment. Majority of the established CR4 cells express common markers of stemness, including CD133, CD44, CD166, EpCAM, CD24 and Lgr5. Using immunocytochemical, FACS and western blot analyses, we have shown that a significant ratio of the CR4 cells express key markers of pluripotency markers, including Sox-2, Oct3/4 and c-Myc. Constitutive overactivation of ABC transporters and NF-kB and absence of tumor suppressors p53 and p21 may partially explain exceptional drug resistance of the CR4 cells. CONCLUSIONS: The highly tumorigenic and clonogenic CIC-enriched CR4 cell line may provide an important new tool to support the discovery of novel diagnostic and/or prognostic biomarkers as well as the development of more effective therapeutic strategies

Quiescience as a mechanism for cyclical hypoxia and acidosis

Tumour tissue characteristically experiences fluctuations in substrate supply. This unstable microenvironment drives constitutive metabolic changes within cellular populations and, ultimately, leads to a more aggressive phenotype. Previously, variations in substrate levels were assumed to occur through oscillations in the hæmodynamics of nearby and distant blood vessels. In this paper we examine an alternative hypothesis, that cycles of metabolite concentrations are also driven by cycles of cellular quiescence and proliferation. Using a mathematical modelling approach, we show that the interdependence between cell cycle and the microenvironment will induce typical cycles with the period of order hours in tumour acidity and oxygenation. As a corollary, this means that the standard assumption of metabolites entering diffusive equilibrium around the tumour is not valid; instead temporal dynamics must be considered

Dynamic Computational Model Suggests That Cellular Citizenship Is Fundamental for Selective Tumor Apoptosis

Computational models in the field of cancer research have focused primarily on estimates of biological events based on laboratory generated data. We introduce a novel in-silico technology that takes us to the next level of prediction models and facilitates innovative solutions through the mathematical system. The model's building blocks are cells defined phenotypically as normal or tumor, with biological processes translated into equations describing the life protocols of the cells in a quantitative and stochastic manner. The essentials of communication in a society composed of normal and tumor cells are explored to reveal “protocols” for selective tumor eradication. Results consistently identify “citizenship properties” among cells that are essential for the induction of healing processes in a healthy system invaded by cancer. These properties act via inter-cellular communication protocols that can be optimized to induce tumor eradication along with system recovery. Within the computational systems, the protocols universally succeed in removing a wide variety of tumors defined by proliferation rates, initial volumes, and apoptosis resistant phenotypes; they show high adaptability for biological details and allow incorporation of population heterogeneity. These protocols work as long as at least 32% of cells obey extra-cellular commands and at least 28% of cancer cells report their deaths. This low percentage implies that the protocols are resilient to the suboptimal situations often seen in biological systems. We conclude that our in-silico model is a powerful tool to investigate, to propose, and to exercise logical anti-cancer solutions. Functional results should be confirmed in a biological system and molecular findings should be loaded into the computational model for the next level of directed experiments

Mathematical modelling of extracellular matrix dynamics using discrete cells: Fiber orientation and tissue regeneration

Matrix orientation plays a crucial role in determining the severity of scar tissue after dermal wounding. We present a model framework which allows us to examine the interaction of many of the factors involved in orientation and alignment. Within this framework, cells are considered as discrete objects, while the matrix is modelled as a continuum. Using numerical simulations, we investigate the effect on alignment of changing cell properties and of varying cell interactions with collagen and fibrin

A Three Species Model to Simulate Application of Hyperbaric Oxygen Therapy to Chronic Wounds

Chronic wounds are a significant socioeconomic problem for governments worldwide. Approximately 15% of people who suffer from diabetes will experience a lower-limb ulcer at some stage of their lives, and 24% of these wounds will ultimately result in amputation of the lower limb. Hyperbaric Oxygen Therapy (HBOT) has been shown to aid the healing of chronic wounds; however, the causal reasons for the improved healing remain unclear and hence current HBOT protocols remain empirical. Here we develop a three-species mathematical model of wound healing that is used to simulate the application of hyperbaric oxygen therapy in the treatment of wounds. Based on our modelling, we predict that intermittent HBOT will assist chronic wound healing while normobaric oxygen is ineffective in treating such wounds. Furthermore, treatment should continue until healing is complete, and HBOT will not stimulate healing under all circumstances, leading us to conclude that finding the right protocol for an individual patient is crucial if HBOT is to be effective. We provide constraints that depend on the model parameters for the range of HBOT protocols that will stimulate healing. More specifically, we predict that patients with a poor arterial supply of oxygen, high consumption of oxygen by the wound tissue, chronically hypoxic wounds, and/or a dysfunctional endothelial cell response to oxygen are at risk of nonresponsiveness to HBOT. The work of this paper can, in some way, highlight which patients are most likely to respond well to HBOT (for example, those with a good arterial supply), and thus has the potential to assist in improving both the success rate and hence the cost-effectiveness of this therapy

Population Receptive Field Dynamics in Human Visual Cortex

Seminal work in the early nineties revealed that the visual receptive field of neurons in cat primary visual cortex can change in location and size when artificial scotomas are applied. Recent work now suggests that these single neuron receptive field dynamics also pertain to the neuronal population receptive field (pRF) that can be measured in humans with functional magnetic resonance imaging (fMRI). To examine this further, we estimated the pRF in twelve healthy participants while masking the central portion of the visual field. We found that the pRF changes in location and size for two differently sized artificial scotomas, and that these pRF dynamics are most likely due to a combination of the neuronal receptive field position and size scatter as well as modulatory feedback signals from extrastriate visual areas

Model Cortical Association Fields Account for the Time Course and Dependence on Target Complexity of Human Contour Perception

Can lateral connectivity in the primary visual cortex account for the time dependence and intrinsic task difficulty of human contour detection? To answer this question, we created a synthetic image set that prevents sole reliance on either low-level visual features or high-level context for the detection of target objects. Rendered images consist of smoothly varying, globally aligned contour fragments (amoebas) distributed among groups of randomly rotated fragments (clutter). The time course and accuracy of amoeba detection by humans was measured using a two-alternative forced choice protocol with self-reported confidence and variable image presentation time (20-200 ms), followed by an image mask optimized so as to interrupt visual processing. Measured psychometric functions were well fit by sigmoidal functions with exponential time constants of 30-91 ms, depending on amoeba complexity. Key aspects of the psychophysical experiments were accounted for by a computational network model, in which simulated responses across retinotopic arrays of orientation-selective elements were modulated by cortical association fields, represented as multiplicative kernels computed from the differences in pairwise edge statistics between target and distractor images. Comparing the experimental and the computational results suggests that each iteration of the lateral interactions takes at least ms of cortical processing time. Our results provide evidence that cortical association fields between orientation selective elements in early visual areas can account for important temporal and task-dependent aspects of the psychometric curves characterizing human contour perception, with the remaining discrepancies postulated to arise from the influence of higher cortical areas

Cortical Surround Interactions and Perceptual Salience via Natural Scene Statistics

Spatial context in images induces perceptual phenomena associated with salience and modulates the responses of neurons in primary visual cortex (V1). However, the computational and ecological principles underlying contextual effects are incompletely understood. We introduce a model of natural images that includes grouping and segmentation of neighboring features based on their joint statistics, and we interpret the firing rates of V1 neurons as performing optimal recognition in this model. We show that this leads to a substantial generalization of divisive normalization, a computation that is ubiquitous in many neural areas and systems. A main novelty in our model is that the influence of the context on a target stimulus is determined by their degree of statistical dependence. We optimized the parameters of the model on natural image patches, and then simulated neural and perceptual responses on stimuli used in classical experiments. The model reproduces some rich and complex response patterns observed in V1, such as the contrast dependence, orientation tuning and spatial asymmetry of surround suppression, while also allowing for surround facilitation under conditions of weak stimulation. It also mimics the perceptual salience produced by simple displays, and leads to readily testable predictions. Our results provide a principled account of orientation-based contextual modulation in early vision and its sensitivity to the homogeneity and spatial arrangement of inputs, and lends statistical support to the theory that V1 computes visual salience