Relating PDEs in Cylindrical Coordinates and CTMCs with Levels of Concentration

Authors:
Andrea Degasperi;Muffy Calder
Affiliations:
Department of Computing Science, University of Glasgow, Glasgow, U.K.;Department of Computing Science, University of Glasgow, Glasgow, U.K.
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2010

Citing 10
Cited 0

A compositional approach to performance modelling

A compositional approach to performance modelling
BioNetGen: software for rule-based modeling of signal transduction based on the interactions of molecular domains

Bioinformatics
BIOCHAM: an environment for modeling biological systems and formalizing experimental knowledge

Bioinformatics
A Language for Biochemical Systems

CMSB '08 Proceedings of the 6th International Conference on Computational Methods in Systems Biology
Modelling Biological Compartments in Bio-PEPA

Electronic Notes in Theoretical Computer Science (ENTCS)
Some Investigations Concerning the CTMC and the ODE Model Derived From Bio-PEPA

Electronic Notes in Theoretical Computer Science (ENTCS)
Bio-PEPA: A framework for the modelling and analysis of biological systems

Theoretical Computer Science
Beta binders for biological interactions

CMSB'04 Proceedings of the 20 international conference on Computational Methods in Systems Biology
Modelling the influence of RKIP on the ERK signalling pathway using the stochastic process algebra PEPA

Transactions on Computational Systems Biology VII
Rule-based modelling of cellular signalling

CONCUR'07 Proceedings of the 18th international conference on Concurrency Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present the derivation of a CTMC with levels model of diffusion in cylindrical coordinates from the partial differential equation for Fick's law. The resulting model abstracts both molar concentration, by discrete levels, and spatial location, by discrete compartments. We apply the results to the diffusion of nitric oxide in human vessels and illustrate with simulations in the PRISM tool.