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Biomedical subjects

P K Maini

Publications and source records attributed to P K Maini.

62 records · Page 4Linked to original sources
PubMed1989

On the spatial spread of the grey squirrel in Britain.

We present a diffusion-competition model to describe the interaction between the externally introduced grey squirrel and the indigenous red squirrel in Britain. We estimate the model parameters from field data. Solution of the model predicts waves of grey squirrel invasion with speed of invasion typical of that observed in the field. Numerical solution of the model on a two-dimensional domain gives population distributions qualitatively similar to those observed. We suggest that competition alone could account for the observed displacement of the red squirrel by the grey in large regions of Britain. The solutions are qualitatively similar to those for a single species spreading in the absence of competition. The quantitative difference is because competition slows down the speed of advance of the invading species.

Animals↗
PubMed1989

Spatial and spatio-temporal patterns in a cell-haptotaxis model.

We investigate a cell-haptotaxis model for the generation of spatial and spatio-temporal patterns in one dimension. We analyse the steady state problem for specific boundary conditions and show the existence of spatially hetero-geneous steady states. A linear analysis shows that stability is lost through a Hopf bifurcation. We carry out a nonlinear multi-time scale perturbation procedure to study the evolution of the resulting spatio-temporal patterns. We also analyse the model in a parameter domain wherein it exhibits a singular dispersion relation.

Animals↗
PubMed1988

Enzyme kinetics for a two-step enzymic reaction with comparable initial enzyme-substrate ratios.

We extend the validity of the quasi-steady state assumption for a model double intermediate enzyme-substrate reaction to include the case where the ratio of initial enzyme to substrate concentration is not necessarily small. Simple analytical solutions are obtained when the reaction rates and the initial substrate concentration satisfy a certain condition. These analytical solutions compare favourably with numerical solutions of the full system of differential equations describing the reaction. Experimental methods are suggested which might permit the application of the quasi-steady state assumption to reactions where it may not have been obviously applicable before.

Enzymes↗
PubMed1986

Nonlinear pattern selection in a mechanical model for morphogenesis.

We present a numerical study of the nonlinear mechanical model for morphogenesis proposed by Oster et al. (1983) with the aim of establishing the pattern forming capability of the model. We present a technique for mode selection based on linear analysis and show that, in many cases, it is a reliable predictor for nonlinear mode selection. In order to determine the set of model parameters that can generate a particular pattern we develop a technique based on nonlinear least square fitting to a dispersion relation. As an application we present a scenario for sequential pattern formation of dermal aggregations in chick embryos which leads to the hexagonal array of cell aggregations observed in feather germ formation in vivo.

Animals↗
PubMed1985

A model for chondrogenic condensations in the developing limb: the role of extracellular matrix and cell tractions.

The hyaluronate component of the extracellular matrix is a powerfully hydrophilic polymer, capable of osmotically swelling and deswelling by a volume factor of 5 or more. At the time of cartilage condensation in the limb bud the chondrocytes start to produce hyaluronidase, an enzyme which degrades hyaluronate. The consequent deswelling brings the chondrocytes closer together - close enough for intercellular cell tractions to become effective and intercellular junctions to form. By analysing the physicochemical situation we show how these processes, principally the coupling of the osmotic deswelling with cellular traction forces, can produce cartilage condensation patterns resembling those in the early limb bud. In distinction from our earlier model for chondrogenic condensations this mechanism does not depend on cell motions other than convective transport by contraction.

Animals↗
PubMedDate not supplied

Towards whole-organ modelling of tumour growth.

Multiscale approaches to modelling biological phenomena are growing rapidly. We present here some recent results on the formulation of a theoretical framework which can be developed into a fully integrative model for cancer growth. The model takes account of vascular adaptation and cell-cycle dynamics. We explore the effects of spatial inhomogeneity induced by the blood flow through the vascular network and of the possible effects of p27 on the cell cycle. We show how the model may be used to investigate the efficiency of drug-delivery protocols.

Adaptation, Physiological↗
PubMedDate not supplied

Modeling the effects of transforming growth factor-beta on extracellular matrix alignment in dermal wound repair.

We present a novel mathematical model for collagen deposition and alignment during dermal wound healing, focusing on the regulatory effects of transforming growth factor-beta (TGFbeta.) Our work extends a previously developed model which considers the interactions between fibroblasts and an extracellular matrix composed of collagen and a fibrin based blood clot, by allowing fibroblasts to orient the collagen matrix, and produce and degrade the extracellular matrix, while the matrix directs the fibroblasts and control their speed. Here we extend the model by allowing a time varying concentration of TGFbeta to alter the properties of the fibroblasts. Thus we are able to simulate experiments which alter the TGFbeta profile. Within this model framework we find that most of the known effects of TGFbeta, i.e., changes in cell motility, cell proliferation and collagen production, are of minor importance to matrix alignment and cannot explain the anti-scarring properties of TGFbeta. However, we find that by changing fibroblast reorientation rates, consistent with experimental evidence, the alignment of the regenerated tissue can be significantly altered. These data provide an explanation for the experimentally observed influence of TGFbeta on scarring.

Cell Movement↗