Biomedical subjects

M A Chaplain

Publications and source records attributed to M A Chaplain.

24 records · Page 2Linked to original sources

PubMed1993

A model mechanism for the chemotactic response of endothelial cells to tumour angiogenesis factor.

In order to accomplish the transition from avascular to vascular growth, solid tumours secrete a diffusible substance known as tumour angiogenesis factor (TAF) into the surrounding tissue. Endothelial cells which form the lining of neighbouring blood vessels respond to this chemotactic stimulus in a well-ordered sequence of events consisting, at minimum, of a degradation of their basement membrane, migration, and proliferation. A model mechanism is presented which includes the diffusion of the TAF into the surrounding host tissue and the response of the endothelial cells to the chemotactic stimulus. The model accounts for the main observed events associated with the endothelial cells during the process of angiogenesis (i.e. cell migration and proliferation); the numerical results compare very well with experimental observations. The situation where the tumour (i.e. the source of TAF) is removed and the vessels recede is also considered.

Angiogenesis Inducing Agents↗

PubMed1992

A mathematical model for the growth and classification of a solid tumor: a new approach via nonlinear elasticity theory using strain-energy functions.

Medically, tumors are classified into two important classes--benign and malignant. Generally speaking, the two classes display different behaviour with regard to their rate and manner of growth and subsequent possible spread. In this paper, we formulate a new approach to tumor growth using results and techniques from nonlinear elasticity theory. A mathematical model is given for the growth of a solid tumor using membrane and thick-shell theory. A central feature of the model is the characterization of the material composition of the tumor through the use of a strain energy function, thus permitting a mathematical description of the degree of differentiation of the tumor explicitly in the model. Conditions are given in terms of the strain energy function for the processes of invasion and metastasis occurring in a tumor, being interpreted as the bifurcation modes of the spherical shell, which the tumor is essentially modeled as. Our results are compared with actual medical experimental results and with the general behavior shown by benign and malignant tumors. Finally, we use these results in conjunction with aspects of surface morphogenesis of tumors (in particular, the Gaussian and mean curvatures of the surface of a solid tumor) in an attempt to produce a mathematical formulation and description of the important medical processes of staging and grading cancers. We hope that this approach may form the basis of a practical application.

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PubMed1991

A mathematical model for the diffusion of tumour angiogenesis factor into the surrounding host tissue.

Unless they are furnished with an adequate blood supply and a means of disposing of their waste products by a mechanism other than diffusion, solid tumours cannot grow beyond a few millimetres in diameter. It is now a well-established fact that, in order to accomplish this neovascularization, solid tumours secrete a diffusable chemical compound known as tumour angiogenesis factor (TAF) into the surrounding tissue. This stimulates nearby blood vessels to migrate towards and finally penetrate the tumour. Once provided with the new supply of nutrient, rapid growth takes place. In this paper, a mathematical model is presented for the diffusion of TAF into the surrounding tissue. The complete process of angiogenesis is made up of a sequence of several distinct events and the model is an attempt to take into account as many of these as possible. In the diffusion equation for the TAF, a decay term is included which models the loss of the chemical into the surrounding tissue itself. A threshold distance for the TAF is incorporated in an attempt to reflect the results from experiments on corneal implants in test animals. By formulating the problems in terms of a free boundary problem, the extent of the diffusion of TAF into the surrounding tissue can be monitored. Finally, by introducing a sink term representing the action of proliferating endothelial cells, the boundary of the TAF is seen to recede, and hence the position and movement of the capillaries can be indirectly followed. The changing concentration gradient observed as the boundary recedes may offer a possible explanation for the initiation of anastomosis. Several functions are considered as possible sink terms and numerical results are presented. The situation where the tumour (i.e. the source of TAF) is removed is also considered.

Angiogenesis Inducing Agents↗

PubMed1990

An application of membrane theory to tip morphogenesis in Acetabularia.

Focusing our attention on the cell wall and the plasmalemma (i.e. the cell membrane), we seek to show that the initiation of the regenerative, growing tip in the unicellular marine alga Acetabularia mediterranea, can be predicted using the techniques of thin-shell and elasticity theory. We build upon and extend the work of Goodwin & Trainor (1985, J. theor. Biol. 117, 79-106), Trainor & Goodwin (1986, Physica D. 21D, 137-145) and Brière & Goodwin (1988, J. theor. Biol. 131, 461-475) where the attention was focused on the calcium-regulated strain and stress fields of the cortical cytoplasm. Finally, we attempt to model the subsequent tip growth using a moving-boundary formulation, with cytosolic free calcium concentration and turgor pressure being the two variables responsible for the growth.

Acetabularia↗

PubMed1990

A mathematical model for the production and secretion of tumour angiogenesis factor in tumours.

Solid tumour growth was hypothesized by Folkman (1976) to take place in two phases: the avascular phase and the vascular phase. In the first (avascular) phase, the tumour obtains its nutrients and disposes of its metabolic wastes by diffusion transport processes alone. Since the mechanism for growth is diffusion-limited, these tumours cannot expand indefinitely, but grow to a dormant state in which they have ceased expanding. The second (vascular) phase involves the eliciting of new blood vessels from the surrounding tissue and there is now firm evidence that tumour cells produce a chemical compound which triggers this process. The compound has been termed tumour angiogenesis factor (TAF) and considerable research has been carried out to try and isolate it and identify its biological structure as well as to elucidate its effects on the endothelial cells which form the lining of the blood vessels. In this second phase, the tumour grows rapidly and can spread to other parts of the body via blood-borne metastases. In this paper, the authors present a theoretical model for the production of the TAF within the tumour while in its diffusion-limited state and prior to its release into the surrounding host tissue. Using experimental results on vascularized tumours in conjunction with the findings of Oosaki et al. (1987), it is assumed that the profile of the TAF concentration within the tumour prior to secretion is qualitatively the same as that of the blood vessels found in neovascularized tumours. The TAF concentration c(x, t) is taken to satisfy the diffusion equation and the TAF production is accounted for either by the inclusion of a production term phi(c) in the diffusion equation itself or via inclusion in the boundary conditions. Taking phi(c) to be of the form 1/(1-c) produces the desired TAF profile and also leads to the possibility of a critical level being reached. It is shown that if the tumour is small enough this critical level can never be attained. However, if the tumour exceeds a certain size, then the critical level is attained and the TAF is subsequently secreted into the external tissue. This is described mathematically by the phenomenon of quenching, that is, the solution c(x, t) remains finite while some derivative becomes unbounded in finite time.

Angiogenesis Inducing Agents↗

PubMedDate not supplied

Mathematical modelling of angiogenesis.

Angiogenesis, the formation of blood vessels from a pre-existing vasculature, is a process whereby capillary sprouts are formed in response to externally supplied chemical stimuli. The sprouts then grow and develop, driven initially by endothelial cell migration, and organize themselves into a branched, connected network. Subsequent cell proliferation near the sprout-tips permits further extension of the capillaries and ultimately completes the process. Angiogenesis occurs during embryogenesis, wound healing, arthritis and during the growth of solid tumours. In this article we first of all present a review of a variety of mathematical models which have been used to describe the formation of capillary networks and then focus on a specific recent model which uses novel mathematical modelling techniques to generate both two- and three-dimensional vascular structures. The modelling focusses on key events of angiogenesis such as the migratory response of endothelial cells to exogenous cytokines (tumour angiogenic factors, TAF) secreted by a solid tumour; endothelial cell proliferation; endothelial cell interactions with extracellular matrix macromolecules such as fibronectin; capillary sprout branching and anastomosis. Numerical simulations of the model, using parameter values based on experimental data, are presented and the theoretical structures generated by the model are compared with the morphology of actual capillary networks observed in in vivo experiments. A final conclusions section discusses the use of the mathematical model as a possible angiogenesis assay.

Animals↗