Mathematical modelling of cancer cell invasion of tissue

Ramis-Conde, Ignacio; Chaplain, M. A. J.; Anderson, Alexander R.A.

doi:10.1016/j.mcm.2007.02.034

Cited by 116 publications

(103 citation statements)

References 23 publications

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“…This time the tumor takes more time to reach the same size as observed when no ECM was included in the model. It is also important to mention that this kind of behavior has been seen from previous studies (Conde et al, 2008;Kazmi et al, 2012b) which confirm the ECM inclusion in our extended model signifies that ECM itself has an impact on the tumor growth. The tumor growth rate without integrating ECM also quite similar to the rate mentioned in Al-Mamun et al, (2013b).…”

Section: Maspin As An Ecm Constraintsupporting

confidence: 88%

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

Al-Mamun

Farid

Ravenhil

et al. 2016

Journal of Theoretical Biology

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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.

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Section: Maspin As An Ecm Constraintsupporting

confidence: 88%

“…At every time step model calculates the pooling force for each and every cell. The potential function and cell movement direction were calculated using equations (9) and (10) respectively (Conde et al, 2008).…”

Section: Cell-cell Adhesion and Cell Movementmentioning

confidence: 99%

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

Al-Mamun

Farid

Ravenhil

et al. 2016

Journal of Theoretical Biology

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“…A clinically oriented example of the latter is the combination of pharmacokinetics differential equations with discrete state/event simulations in order to simulate the response of large imageable tumors to chemotherapeutic treatment (Stamatakos et al, 2006b). A further example refers to the modeling of cancer cell invasion to tissue (Ramis-Conde et al, 2008). As more and more biological mechanisms are being quantitatively understood most new models tend to fall in this category i.e.…”

Section: Introductionmentioning

confidence: 99%

An advanced discrete state–discrete event multiscale simulation model of the response of a solid tumor to chemotherapy: Mimicking a clinical study

Stamatakos

Kolokotroni

Dionysiou

et al. 2010

Journal of Theoretical Biology

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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“…ABMs are supplied with rules that define the interactions between agents and their environment. The vast majority of the tumor models that utilize ABMs are hybrid models, in which changes in the microenvironment are modeled by systems of differential equations of the type occurring in various tissue models, described in the next section [41,62,83,84,96,107].…”

Section: Agent Based Modelsmentioning

confidence: 99%

“…Ramis-Conde et al [107] studied the effects of the production of chemoattractant by tumor cells and degradation of the extracellular matrix (ECM) on cells motility. Tumor cells are modeled as discrete individual entities which interact with other agents.…”

Section: Agent Based Modelsmentioning

confidence: 99%

Toward Predictive Multiscale Modeling of Vascular Tumor Growth

Oden

Lima

Almeida

et al. 2015

Arch Computat Methods Eng

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New directions in medical and biomedical sciences have gradually emerged over recent years that will change the way diseases are diagnosed and treated and are leading to the redirection of medicine toward patientspecific treatments. We refer to these new approaches for studying biomedical systems as predictive medicine, a new version of medical science that involves the use of advanced computer models of biomedical phenomena, high-performance computing, new experimental methods for model data calibration, modern imaging technologies, cutting-edge numerical algorithms for treating large stochastic systems, modern methods for model selection, calibration, validation, verification, and uncertainty quantification, and new approaches for drug design and delivery, all based on predictive models. The methodologies are designed to study events at multiple scales, from genetic data, to sub-cellular signaling mechanisms, to cell interactions, to tissue physics and chemistry, to organs in living human subjects. The present document surveys work on the development and implementation of predictive models of vascular tumor growth, covering aspects of what might be called modeling-and-experimentally based computational oncology. The work described is that of a multi-institutional team, centered at ICES with strong participation by members at M. D. Anderson Cancer Center and University of Texas at San Antonio. This exposition covers topics on signaling models, cell and cell-interaction models, tissue models based on multi-species mixture theories, models of angiogenesis, and beginning work of drug effects. A number of new parallel computer codes for implementing finite-element methods, multi-level Markov Chain Monte Carlo sampling methods, data classification methods, stochastic PDE solvers, statistical inverse algorithms for model calibration and validation, models of events at different spatial and temporal scales is presented. Importantly, new methods for model selection in the presence of uncertainties fundamental to predictive medical science, are described which are based on the notion of Bayesian model plausibilities. Also, as part of this general approach, new codes for determining the sensitivity of model outputs to variations in model parameters are described that provide a basis for assessing the importance of model parameters and controlling and reducing the number of relevant model parameters. Model specific data is to be accessible through careful and model-specific platforms in the Tumor Engineering Laboratory. We describe parallel computer platforms on which large-scale calculations are run as well as specific time-marching algorithms needed to treat stiff systems encountered in some phase-field mixture models. We also cover new non-invasive imaging and data classification methods that provide in vivo data for model validation. The study concludes with a brief discussion of future work and open challenges.

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Mathematical modelling of cancer cell invasion of tissue

Cited by 116 publications

References 23 publications

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

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

An advanced discrete state–discrete event multiscale simulation model of the response of a solid tumor to chemotherapy: Mimicking a clinical study

Toward Predictive Multiscale Modeling of Vascular Tumor Growth

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