BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Developing PDE-compartment hybrid frameworks for modelling cell mi
 gration - Kit Yate\, University of Bath
DTSTART:20161031T140000Z
DTEND:20161031T150000Z
UID:TALK68770@talks.cam.ac.uk
CONTACT:44515
DESCRIPTION:Spatial reaction-diffusion models have been employed to descri
 be many emergent phenomena in biological systems. The modelling technique 
 most commonly adopted in the literature implements systems of partial diff
 erential equations (PDEs)\, which assumes there are sufficient densities o
 f particles that a continuum approximation is valid. However\, due to rece
 nt advances in computational power\, the simulation\, and therefore postul
 ation\, of computationally intensive individual-based models has become a 
 popular way to investigate the effects of noise in reaction-diffusion syst
 ems in which regions of low copy numbers exist.\n\nThe specific stochastic
  models with which we shall be concerned in this talk are referred to as `
 compartment based' or `on-lattice'. These models are characterised by a di
 scretisation of the computational domain into a grid/lattice of `compartme
 nts'. Within each compartment particles are assumed to be well-mixed and a
 re  permitted to react with other particles within their compartment or to
  transfer between neighbouring compartments.\n\nIndividual-based stochasti
 c models provide microscopic/mesoscopic accuracy but at the cost of signif
 icant computational resources. Models which have regions of both low and h
 igh concentrations often necessitate coupled macroscale and microscale mod
 elling paradigms. This is because microscale models are not feasible to si
 mulate at large concentrations and macroscale models are often inappropria
 te at small concentrations.\n\nIn this work we develop hybrid algorithms i
 n which a PDE in one region of the domain is coupled to a compartment-base
 d model in the other. Rather than attempting to balance average fluxes\, o
 ur algorithms  answer a more fundamental question: `how are individual par
 ticles transported between the vastly different model descriptions?' First
 \, we present an algorithm derived by carefully re-defining the continuous
  PDE concentration as a probability distribution. Whilst this first algori
 thm shows very strong convergence to analytic solutions of test problems\,
  it can be cumbersome to simulate. Our second algorithm is a simplified an
 d more efficient implementation of the first\, it is derived in the contin
 uum limit over the PDE region alone. We test our hybrid methods for functi
 onality and accuracy in a variety of different scenarios by comparing the 
  averaged simulations to analytic solutions of PDEs for mean concentration
 s.
LOCATION:Auditorium\, Microsoft Research Ltd\, 21 Station Road\, Cambridge
 \, CB1 2FB
END:VEVENT
END:VCALENDAR