James Osborne : Oxford University Computing Laboratory

My expertise is in numerical and computational methods for mathematical models of biological phenomena. I have experience in the formation and simulation of continuum, discrete and hybrid modes using techniques from both applied mathematics and numerical analysis.

My current Interests are in the development of robust mathematical and numerical methods for multiscale modeling in systems biology. Key areas of interest are

The propagation of error in multiscale systems and the development of methods that minimise this error.
At what scales do we need to model and at what level of detail.
To what extent do we need to couple the mathematical models of differing scales.
What the role of noise (both intrinsic and extrinsic) is in biological systems and ways to model this.

Another of my research interests is the area of numerical and computational methods for multiphase models of tissue growth. Involving the application of the finite element method to coupled and constrained partial differential equations. For my doctoral thesis I developed a numerical and computational framework based upon the galerkin finite element method that allows the numerical solution of coupled systems of parabolic, elliptic and hyperbolic PDEs resulting from multiphase models of tissue growth. the modelling approach is to consider the tissue to be composed of separate constitutive phases, which are each governed by suitable continuum physical laws. This enables investigation of the effect of interactions between constitutive phases on the growth of the tissue. The framework has been used to investigate tissue growth in a perfusion bioreactor and also the development of a solid tumour, under non-uniform environmental conditions.

James Osborne

interests

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