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Biomedical subjects

P K Maini

Publications and source records attributed to P K Maini.

At least 55 records · Page 3Linked to original sources
PubMed1996

A mathematical model for collagen fibre formation during foetal and adult dermal wound healing.

Adult dermal wounds, in contrast to foetal wounds, heal with the formation of scar tissue. A crucial factor in determining the nature of the healed tissue is the ratio of collagen 1 to collagen 3, which regulates the diameter of collagen fibres. We develop a mathematical model which focuses on the stimulus for collagen synthesis due to the secretion of the different isoforms of the regulatory chemical transforming growth factor beta. Numerical simulations of the model lead to a value of this ratio consistent with that of healthy tissue for the foetus but corresponding to scarring in adult wound healing. We investigate the effect of topical application of TGF beta isoforms during healing and determine the key parameters which control the difference between adult and foetal repair.

Animals↗
PubMed1996

A mathematical model for fibro-proliferative wound healing disorders.

The normal process of dermal wound healing fails in some cases, due to fibro-proliferative disorders such as keloid and hypertrophic scars. These types of abnormal healing may be regarded as pathologically excessive responses to wounding in terms of fibroblastic cell profiles and their inflammatory growth-factor mediators. Biologically, these conditions are poorly understood and current medical treatments are thus unreliable. In this paper, the authors apply an existing deterministic mathematical model for fibroplasia and wound contraction in adult mammalian dermis (Olsen et al., J. theor. Biol. 177, 113-128, 1995) to investigate key clinical problems concerning these healing disorders. A caricature model is proposed which retains the fundamental cellular and chemical components of the full model, in order to analyse the spatiotemporal dynamics of the initiation, progression, cessation and regression of fibro-contractive diseases in relation to normal healing. This model accounts for fibroblastic cell migration, proliferation and death and growth-factor diffusion, production by cells and tissue removal/decay. Explicit results are obtained in terms of the model processes and parameters. The rate of cellular production of the chemical is shown to be critical to the development of a stable pathological state. Further, cessation and/or regression of the disease depend on appropriate spatiotemporally varying forms for this production rate, which can be understood in terms of the bistability of the normal dermal and pathological steady states-a central property of the model, which is evident from stability and bifurcation analyses. The work predicts novel, biologically realistic and testable pathogenic and control mechanisms, the understanding of which will lead toward more effective strategies for clinical therapy of fibro-proliferative disorders.

Adult↗
PubMed1996

Simple versus sophisticated models of breath alcohol exhalation profiles.

For medicolegal purposes, breath alcohol content is typically determined from an end-expiratory sample. Measurements obtained by this method necessarily underestimate the alveolar breath alcohol content, and therefore underestimate the blood alcohol content. We suggest and analyse an improved paradigm which uses the entire time-series of breath alcohol measurements during exhalation, not simply the last recorded value. We present two mathematical models for the exhaling lung, and discuss the implications of each for more accurate and therefore more reliable breath alcohol measurement.

Adult↗
PubMed1995

A mechanochemical model for adult dermal wound contraction and the permanence of the contracted tissue displacement profile.

The healing of adult mammalian skin wounds involves a complex sequence of spatially and temporally coordinated processes. Wound contraction, by reducing the size of the injury, is an intrinsic component of full-thickness excisional dermal wound healing. The underlying biomechanics of wound contraction, however, are not fully understood, and little is known about the pathogenesis of severe medical conditions known as fibrocontractive diseases. The aim of this work is to investigate a deterministic mathematical model in order to obtain insight into the mechanistic relationships between wound contraction and associated normal and pathological healing processes. The model describes the essential roles of fibroblast and myofibroblast cells, a chemical growth factor and the extracellular matrix which includes type I collagen. The model results are qualitatively consistent with the biology of fibroplasia and wound contraction. It is shown that a contracted state evolves during a (long) transient phase of healing known as "proliferation", while collagen kinetics are fundamental to the considerably longer "remodelling" phase. Some quantitative results, notably on the evolution of wound contraction, compare favourably with experimental data. Application of the model to adult human dermal wound healing in vivo, with a greater understanding of the underlying biological mechanisms involved, may suggest strategies for controlling contraction and fibrocontractive diseases.

Adult↗
PubMed1995

Dictyostelium discoideum: cellular self-organization in an excitable biological medium.

The dynamics which govern the establishment of pattern and form in multicellular organisms remain a key problem of developmental biology. We study this question in the case of morphogenesis during aggregation of the slime mould Dictyostelium discoideum. Here detailed experimental information allows the formulation of a mechanistic model in which the central element is the coupling of the previously much-studied intracellular cyclic AMP signalling with the chemotactic cell response in cyclic AMP gradients. Numerical simulations of the model show quantitatively how signal relay, chemotactic movement and adaptation orchestrate the collective modes of cell signalling and migration in the aggregating cell layer. The interaction of chemotaxis with the cyclic AMP excitation waves causes the initially homogeneous cell layer to become unstable towards the formation of a branching cell stream pattern with close cell-cell contacts as observed in situ. The evolving cell morphology in turn leads to a pattern of non-homogeneous excitability of the medium and thus feeds back into the cAMP dynamics. This feedback can explain the decrease in signalling period and propagation speed with time, as well as observations on the structure of the spiral wave core in this self-organized excitable medium.

Animals↗
PubMed1995

Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis.

We present an in-depth study of spatio-temporal patterns in a simplified version of a mechanical model for pattern formation in mesenchymal morphogenesis. We briefly motivate the derivation of the model and show how to choose realistic boundary conditions to make the system well-posed. We firstly consider one-dimensional patterns and carry out a nonlinear perturbation analysis for the case where the uniform steady state is linearly unstable to a single mode. In two-dimensions, we show that if the displacement field in the model is represented as a sum of orthogonal parts, then the model can be decomposed into two sub-models, only one of which is capable of generating pattern. We thus focus on this particular sub-model. We present a nonlinear analysis of spatio-temporal patterns exhibited by the sub-model on a square domain and discuss mode interaction. Our analysis show that when a two-dimensional mode number admits two or more degenerate mode pairs, the solution of the full nonlinear system of partial differential equations is a mixed mode solution in which all the degenerate mode pairs are represented in a frequency locked oscillation.

Animals↗
PubMed1995

Rhythmic firing patterns in suprachiasmatic nucleus (SCN): the rôle of circuit interactions.

The suprachiasmatic nucleus (SCN) is believed to contain the main generator of circadian rhythmicity in mammals. In order to obtain further functional details of this, electrophysiological extracellular measurements in vitro were made. By means of an interspike interval distribution analysis, it is shown that there is a novel kind of neuronal firing pattern: the harmonic pattern. From these observations, we have developed a theoretical model based on possible filtering processes occurring during synaptic transmission. The model suffices to infer that regular ultradian oscillators could be an emergent property of circuit interactions of cells in the suprachiasmatic nucleus.

Action Potentials↗
PubMed1994

Travelling waves in a tissue interaction model for skin pattern formation.

Tissue interaction plays a major role in many morphogenetic processes, particularly those associated with skin organ primordia. We examine travelling wave solutions in a tissue interaction model for skin pattern formation which is firmly based on the known biology. From a phase space analysis we conjecture the existence of travelling waves with specific wave speeds. Subsequently, analytical approximations to the wave profiles are derived using perturbation methods. We then show numerically that such travelling wave solutions do exist and that they are in good agreement with out analytical results. Finally, the biological implications of our analysis are discussed.

Animals↗
PubMed1994

Nonlinear diffusion of a growth inhibitory factor in multicell spheroids.

A mathematical model is presented for the production of a growth inhibitory factor (GIF) within a multicell spheroid. The model is based on the assumption that the GIF diffuses within the spheroid in a nonlinear spatially dependent manner. This is in contrast with previous models, in which the nonlinearity was assumed in the production term. The results of the new model are compared with those of previous models and with experimental data.

Animals↗
PubMed1994

Mathematical modeling of corneal epithelial wound healing.

We propose a reaction-diffusion model of the mechanisms involved in the healing of corneal surface wounds. The model focuses on the stimulus for increased mitotic and migratory activity, specifically the role of epidermal growth factor. Analysis of the model equations elucidates the interaction and roles of the model parameters in determining the speed of healing and the shape of the traveling wave solutions which correspond to the migration of cells into the wound during the initial phase of healing. We determine an analytic approximation for the speed of traveling wave solutions of the model in terms of the parameters and verify the results numerically. By comparing the predicted speed with experimentally measured healing rates, we conclude that serum-derived factors can alone account for the overall features of the healing process, but that the supply of growth factors by the tear film in the absence of serum-derived factors is not sufficient to give the observed healing rate. Numerical solutions of the model equations also confirm the importance of both migration and mitosis for effective would healing. By modifying the model we obtain an analytic prediction for the healing rate of corneal surface wounds when epidermal growth factor is applied topically to the wound.

Animals↗
PubMed1993

Suicide substrate reaction--diffusion equations: varying the source.

The suicide substrate reaction is a model for certain enzyme-inhibiting drugs. This reaction system is examined assuming that the substrate diffuses freely while the enzyme remains fixed. Two sets of initial and boundary conditions are examined: one modelling an instantaneous point source, akin to an injection of substrate, the other, a continuous point source, akin to a continuing influx, or intravenous drip, of substrate. The quasi-steady-state assumption is applied to obtain analytical solutions for a limited parameter space. Finally, further applications of numerical and analytical experimentation on pharmaceutical mechanisms are described.

Enzyme Inhibitors↗
PubMed1993

Mathematical modelling of ethanol metabolism in normal subjects and chronic alcohol misusers.

The time course of ethanol disappearance from the blood has been examined in normal males and females and in alcohol misusers. Blood alcohol estimations were made over a period of 3 hr, following an oral dose of ethanol (0.8 g/kg body weight) administered in the form of whisky. Attempts were made to fit the data to zero order, first order and mixed zero + first order kinetics. In the majority (75%) of normal females the blood ethanol concentrations was still increasing at 30 min. This was only seen in 50% of normal males and in 50% of non-dependent alcohol misusers, but not in dependent alcohol misusers. In all of the normal females the disappearance of ethanol could be adequately described by zero order kinetics. However, in the normal male group only 20% could be described by zero order kinetics, 10% fitted first order kinetics and the remainder required a mixed model of zero + first order. The rate constant for the zero order component of the control male group was identical to zero order rate constant obtained for the female control group. In the female alcohol misuser group, 40% of the curves could not be described by zero order kinetics and fitted best to a mixed model. The zero order component of the entire group was significantly increased (by 35%) compared to that obtained for the female control group. In the male dependent and non-dependent alcohol misuser groups, all blood alcohol concentration curves fitted best to mixed zero and first order kinetics.(ABSTRACT TRUNCATED AT 250 WORDS)

Adult↗
PubMed1992

Sequential pattern formation in a model for skin morphogenesis.

During morphogenesis regular patterns often develop behind a frontier of pattern formation which travels across the prospective tissue. Here the authors consider the propagating patterns exhibited in a two-dimensional domain by a tissue interaction mechanochemical model for skin pattern formation. It is shown that the model can exhibit travelling waves of complex spatial pattern formation. Two alternative mechanisms that can produce such sequential patterning are presented. In particular, it is demonstrated that the specification of a simple quasi-one-dimensional pattern is all that is required to determine a complex two-dimensional pattern. Finally, the model solutions are related to actual pattern propagation during chick feather primordia initiation.

Animals↗
PubMed1991

Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern generation.

We consider a simple cell-chemotaxis model for spatial pattern formation on two-dimensional domains proposed by Oster and Murray (1989, J. exp. Zool. 251, 186-202). We determine finite-amplitude, steady-state, spatially heterogeneous solutions and study the effect of domain growth on the resulting patterns. We also investigate in-depth bifurcating solutions as the chemotactic parameter varies. This numerical study shows that this deceptively simple-chemotaxis model can produce a surprisingly rich spectrum of complex spatial patterns.

Animals↗
PubMed1991

Analysis of a risk-based model for the growth of AIDS infection.

Several models for the spread of AIDS within a homosexual community have been proposed that incorporate biased mixing of different risk groups. A simple model is presented that captures many of the features of these more complex models. Analytical expressions are derived for the time to the state of maximum infection (SMI) in a particular risk group, the proportion infected at SMI, and the number of infected individuals as the group approaches SMI. These results agree qualitatively with numerical simulations of the model.

Acquired Immunodeficiency Syndrome↗
PubMed1990

On the kinetics of suicide substrates.

We consider a realistic suicide substrate reaction which can be represented by four rate equations for the concentrations of the various molecules as functions of time. We present a general procedure to obtain accurate, approximate solutions analytically in terms of the rate equation parameters. This systematic technique provides more accurate approximations to the exact (numerical) solutions than other approximate methods which have been proposed based on a pseudo-steady state hypothesis.

Enzyme Inhibitors↗
PubMed1990

Superposition of modes in a caricature of a model for morphogenesis.

In a model proposed for cell pattern formation by Nagorcka et al. (J. Theor. Biol. 1987) linear analysis revealed the possibility of an initially spatially uniform cell density going unstable to perturbations of two distinct spatial modes. Here we examine a simple one-dimensional caricature of their model which exhibits similar linear behaviour and present a nonlinear analysis which shows the possibility of superposition of modes subject to appropriate parameter values and initial conditions.

Animals↗