869 research outputs found
Computational Methods and Results for Structured Multiscale Models of Tumor Invasion
We present multiscale models of cancer tumor invasion with components at the
molecular, cellular, and tissue levels. We provide biological justifications
for the model components, present computational results from the model, and
discuss the scientific-computing methodology used to solve the model equations.
The models and methodology presented in this paper form the basis for
developing and treating increasingly complex, mechanistic models of tumor
invasion that will be more predictive and less phenomenological. Because many
of the features of the cancer models, such as taxis, aging and growth, are seen
in other biological systems, the models and methods discussed here also provide
a template for handling a broader range of biological problems
Computer simulation of glioma growth and morphology
Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and therapy. Although molecular biology, histopathology, and radiological imaging are employed in this endeavor, studies are severely challenged by the multitude of different physical scales involved in tumor growth, i.e., from molecular nanoscale to cell microscale and finally to tissue centimeter scale. Consequently, it is often difficult to determine the underlying dynamics across dimensions. New techniques are needed to tackle these issues. Here, we address this multi-scalar problem by employing a novel predictive three-dimensional mathematical and computational model based on first-principle equations (conservation laws of physics) that describe mathematically the diffusion of cell substrates and other processes determining tumor mass growth and invasion. The model uses conserved variables to represent known determinants of glioma behavior, e.g., cell density and oxygen concentration, as well as biological functional relationships and parameters linking phenomena at different scales whose specific forms and values are hypothesized and calculated based on in vitro and in vivo experiments and from histopathology of tissue specimens from human gliomas. This model enables correlation of glioma morphology to tumor growth by quantifying interdependence of tumor mass on the microenvironment (e.g., hypoxia, tissue disruption) and on the cellular phenotypes (e.g., mitosis and apoptosis rates, cell adhesion strength). Once functional relationships between variables and associated parameter values have been informed, e.g., from histopathology or intra-operative analysis, this model can be used for disease diagnosis/prognosis, hypothesis testing, and to guide surgery and therapy. In particular, this tool identifies and quantifies the effects of vascularization and other cell-scale glioma morphological characteristics as predictors of tumor-scale growth and invasion
On the foundations of cancer modelling: selected topics, speculations, & perspectives
This paper presents a critical review of selected topics related to the modelling of cancer onset, evolution and growth, with the aim of illustrating, to a wide applied mathematical readership, some of the novel mathematical problems in the field. This review attempts to capture, from the appropriate literature, the main issues involved in the modelling of phenomena related to cancer dynamics at all scales which characterise this highly complex system: from the molecular scale up to that of tissue. The last part of the paper discusses the challenge of developing a mathematical biological theory of tumour onset and evolution
A multiple scale model for tumor growth
We present a physiologically structured lattice model for vascular tumor growth which accounts for blood flow and structural adaptation of the vasculature, transport of oxygen, interaction between cancerous and normal tissue, cell division, apoptosis, vascular endothelial growth factor release, and the coupling between these processes. Simulations of the model are used to investigate the effects of nutrient heterogeneity, growth and invasion of cancerous tissue, and emergent growth laws
A Multiscale Model of Biofilm as a Senescence-Structured Fluid
We derive a physiologically structured multiscale model for biofilm
development. The model has components on two spatial scales, which induce
different time scales into the problem. The macroscopic behavior of the system
is modeled using growth-induced flow in a domain with a moving boundary.
Cell-level processes are incorporated into the model using a so-called
physiologically structured variable to represent cell senescence, which in turn
affects cell division and mortality. We present computational results for our
models which shed light on modeling the combined role senescence and the
biofilm state play in the defense strategy of bacteria
Modeling and Simulation of the Effects of Cyclic Loading on Articular Cartilage Lesion Formation
We present a model of articular cartilage lesion formation to simulate the
effects of cyclic loading. This model extends and modifies the
reaction-diffusion-delay model by Graham et al. 2012 for the spread of a lesion
formed though a single traumatic event. Our model represents "implicitly" the
effects of loading, meaning through a cyclic sink term in the equations for
live cells.
Our model forms the basis for in silico studies of cartilage damage relevant
to questions in osteoarthritis, for example, that may not be easily answered
through in vivo or in vitro studies.
Computational results are presented that indicate the impact of differing
levels of EPO on articular cartilage lesion abatement
Linking Cellular and Mechanical Processes in Articular Cartilage Lesion Formation: A Mathematical Model
A severe application of stress on articular cartilage can initiate a cascade
of biochemical reactions that can lead to the development of osteoarthritis. We
constructed a multiscale mathematical model of the process with three
components: cellular, chemical, and mechanical. The cellular component
describes the different chondrocyte states according to the chemicals these
cells release. The chemical component models the change in concentrations of
those chemicals. The mechanical component contains a simulation of pressure
application onto a cartilage explant and the resulting strains that initiate
the biochemical processes. The model creates a framework for incorporating
explicit mechanics, simulated by finite element analysis, into a theoretical
biology framework
Global existence for a degenerate haptotaxis model of tumor invasion under the go-or-grow dichotomy hypothesis
We propose and study a strongly coupled PDE-ODE-ODE system modeling cancer
cell invasion through a tissue network under the go-or-grow hypothesis
asserting that cancer cells can either move or proliferate. Hence our setting
features two interacting cell populations with their mutual transitions and
involves tissue-dependent degenerate diffusion and haptotaxis for the moving
subpopulation. The proliferating cells and the tissue evolution are
characterized by way of ODEs for the respective densities. We prove the global
existence of weak solutions and illustrate the model behaviour by numerical
simulations in a two-dimensional setting.Comment: arXiv admin note: text overlap with arXiv:1512.0428
Colorectal Cancer Through Simulation and Experiment
Colorectal cancer has continued to generate a huge amount of research interest over several decades, forming a canonical example of tumourigenesis since its use in Fearon and Vogelstein’s linear model of genetic mutation. Over time, the field has witnessed a transition from solely experimental work to the inclusion of mathematical biology and computer-based modelling. The fusion of these disciplines has the potential to provide valuable insights into oncologic processes, but also presents the challenge of uniting many diverse perspectives. Furthermore, the cancer cell phenotype defined by the ‘Hallmarks of Cancer’ has been extended in recent times and provides an excellent basis for future research. We present a timely summary of the literature relating to colorectal cancer, addressing the traditional experimental findings, summarising the key mathematical and computational approaches, and emphasising the role of the Hallmarks in current and future developments. We conclude with a discussion of interdisciplinary work, outlining areas of experimental interest which would benefit from the insight that mathematical and computational modelling can provide
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