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CATEGORIES:Microsoft Research Cambridge\, public talks
SUMMARY:Developing PDE-compartment hybrid frameworks for m
odelling cell migration - Kit Yate\, University of
Bath
DTSTART;TZID=Europe/London:20161031T140000
DTEND;TZID=Europe/London:20161031T150000
UID:TALK68770AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/68770
DESCRIPTION:Spatial reaction-diffusion models have been employ
ed to describe many emergent phenomena in biologic
al systems. The modelling technique most commonly
adopted in the literature implements systems of pa
rtial differential equations (PDEs)\, which assume
s there are sufficient densities of particles that
a continuum approximation is valid. However\, due
to recent advances in computational power\, the s
imulation\, and therefore postulation\, of computa
tionally intensive individual-based models has bec
ome a popular way to investigate the effects of no
ise in reaction-diffusion systems in which regions
of low copy numbers exist.\n\nThe specific stocha
stic models with which we shall be concerned in th
is talk are referred to as `compartment based' or
`on-lattice'. These models are characterised by a
discretisation of the computational domain into a
grid/lattice of `compartments'. Within each compar
tment particles are assumed to be well-mixed and a
re permitted to react with other particles within
their compartment or to transfer between neighbou
ring compartments.\n\nIndividual-based stochastic
models provide microscopic/mesoscopic accuracy but
at the cost of significant computational resource
s. Models which have regions of both low and high
concentrations often necessitate coupled macroscal
e and microscale modelling paradigms. This is beca
use microscale models are not feasible to simulate
at large concentrations and macroscale models are
often inappropriate at small concentrations.\n\nI
n this work we develop hybrid algorithms in which
a PDE in one region of the domain is coupled to a
compartment-based model in the other. Rather than
attempting to balance average fluxes\, our algorit
hms answer a more fundamental question: `how are
individual particles transported between the vastl
y different model descriptions?' First\, we presen
t an algorithm derived by carefully re-defining th
e continuous PDE concentration as a probability di
stribution. Whilst this first algorithm shows very
strong convergence to analytic solutions of test
problems\, it can be cumbersome to simulate. Our s
econd algorithm is a simplified and more efficient
implementation of the first\, it is derived in th
e continuum limit over the PDE region alone. We te
st our hybrid methods for functionality and accura
cy in a variety of different scenarios by comparin
g the averaged simulations to analytic solutions
of PDEs for mean concentrations.
LOCATION:Auditorium\, Microsoft Research Ltd\, 21 Station R
oad\, Cambridge\, CB1 2FB
CONTACT:
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