Validation of a spatial-time concentration gradients estimation by the superposition of sphere sources diffusion fields using the finite element method

Abstract

Abstract A convectional reaction-diffusion is the main process causing a stable distribution of nutrients in biological objects. Indeed, the boundary problems for PDE are always used to describe this phenomenon. The spatial structure of biological objects is usually complex and non-uniform. Therefore, the creation of a digital phantom where gradients will be estimated becomes an especial procedure taking both a computational time and the resources. Recently, a simplified method of time dependent concentration gradient evaluation has been introduced. It represents the final spatial-time distribution as a superposition of the sphere sources diffusion fields. Using such an approximation, one can avoid preliminary reconstruction of digital mech-objects simulating a biological structure. In the present study the introduced approach is validated using the finite element method (FEM). It was shown that the exactness of coincidence is determined by the reciprocal distance of the sources and the scale of the considered area. The symmetry of a mutual boundary position plays an essential part in a validation conformity. A sphere sources formed field differs from the finite element method estimation on 7% under the most appropriate conditions. Other possible applications of the introduced approach to concentration gradient modelling in biological objects are discussed.