Biomedical subjects

G J Pettet

Publications and source records attributed to G J Pettet.

9 recordsLinked to original sources

PubMed2006

Modelling external bone adaptation using evolutionary structural optimisation.

External remodelling is significant in the bone healing process, and it is essential to predict the bone external shape in the design of artificial bone grafts. This paper demonstrates the effectiveness of the evolutionary structural optimisation (ESO) method for the simulation of bone morphology. A two-dimensional ESO strategy is developed which is capable of finding the modified bone topology beginning with any geometry under any loading conditions. The morphology of bone structure is described by the quantitative bone adaptation theory, which is integrated with the finite element method. The evolutionary topology optimisation process is introduced to find the bone shape. A rectangle, which occupies a larger space than the external shape of the bone structure, is specified as a design domain; the evolutionary process iteratively eliminates and redistributes material throughout the domain to obtain an optimum arrangement of bone materials. The technique has been tested on a wide range of examples. In this paper, the formation of trabecular bone architecture around an implant is studied; as another example, the growth of the coronal section of a vertebral body is predicted. The examples support the assertion that the external shape of bone structure can be successfully predicted by the proposed ESO procedure.

Adaptation, Physiological↗

PubMed2006

A mathematical model of integrin-mediated haptotactic cell migration.

Haptotactic cell migration, a directed response to gradients of cell-extracellular matrix adhesion, is an important process in a number of biological phenomena such as wound healing and tumour cell invasion. Previously, mathematical models of haptotaxis have been developed on the premise that cells migrate in response to gradients in the density of the extracellular matrix. In this paper, we develop a novel mathematical model of haptotaxis which includes the adhesion receptors known as integrins and a description of their functional activation, local recruitment and protrusion as part of lamellipodia. Through the inclusion of integrins, the modelled cell matter is able to respond to a true gradient of cell-matrix adhesion, represented by functionally active integrins. We also show that previous matrix-mediated models are in fact a subset of the novel integrin-mediated models, characterised by specific choices of diffusion and haptotaxis coefficients in their model equations. Numerical solutions suggest the existence of travelling waves of cell migration that are confirmed via a phase plane analysis of a simplified model.

Algorithms↗

PubMed2003

Mathematical models of cell colonization of uniformly growing domains.

During the development of vertebrate embryos, cell migrations occur on an underlying tissue domain in response to some factor, such as nutrient. Over the time scale of days in which this cell migration occurs, the underlying tissue is itself growing. Consequently cell migration and colonization is strongly affected by the tissue domain growth. Numerical solutions for a mathematical model of chemotactic migration with no domain growth can lead to travelling waves of cells with constant velocity; the addition of domain growth can lead to travelling waves with nonconstant velocity. These observations suggest a mathematical approximation to the full system equations, allowing the method of characteristics to be applied to a simplified chemotactic migration model. The evolution of the leading front of the migrating cell wave is analysed. Linear, exponential and logistic uniform domain growths are considered. Successful colonization of a growing domain depends on the competition between cell migration velocity and the velocity and form of the domain growth, as well as the initial penetration distance of the cells. In some instances the cells will never successfully colonize the growing domain. These models provide an insight into cell migration during embryonic growth, and its dependence upon the form and timing of the domain growth.

Animals↗

PubMed2001

The migration of cells in multicell tumor spheroids.

A mathematical model is proposed to explain the observed internalization of microspheres and 3H-thymidine labelled cells in steady-state multicellular spheroids. The model uses the conventional ideas of nutrient diffusion and consumption by the cells. In addition, a very simple model of the progress of the cells through the cell cycle is considered. Cells are divided into two classes, those proliferating (being in G1, S, G2 or M phases) and those that are quiescent (being in G0). Furthermore, the two categories are presumed to have different chemotactic responses to the nutrient gradient. The model accounts for the spatial and temporal variations in the cell categories together with mitosis, conversion between categories and cell death. Numerical solutions demonstrate that the model predicts the behavior similar to existing models but has some novel effects. It allows for spheroids to approach a steady-state size in a non-monotonic manner, it predicts self-sorting of the cell classes to produce a thin layer of rapidly proliferating cells near the outer surface and significant numbers of cells within the spheroid stalled in a proliferating state. The model predicts that overall tumor growth is not only determined by proliferation rates but also by the ability of cells to convert readily between the classes. Moreover, the steady-state structure of the spheroid indicates that if the outer layers are removed then the tumor grows quickly by recruiting cells stalled in a proliferating state. Questions are raised about the chemotactic response of cells in differing phases and to the dependency of cell cycle rates to nutrient levels.

Cell Cycle↗

PubMed2000

Lotka-Volterra equations with chemotaxis: walls, barriers and travelling waves.

In this paper we consider a simple two species model for the growth of new blood vessels. The model is based upon the Lotka-Volterra system of predator and prey interaction, where we identify newly developed capillary tips as the predator species and a chemoattractant which directs their motion as the prey. We extend the Lotka-Volterra system to include a one-dimensional spatial dependence, by allowing the predators to migrate in a manner modelled on the phenomenon of chemotaxis. A feature of this model is its potential to support travelling wave solutions. We emphasize that in order to determine the existence of such travelling waves it is essential that the global relationships of a number of phase plane features other than the equilibria be investigated.

Animals↗

PubMed1999

Difficulties in estimating muscle forces from muscle cross-sectional area. An example using the psoas major muscle.

Most biomechanical models use muscle cross-sectional area (CSA) as an indicator of maximum isometric muscle force. In general, there are multiple estimates of CSA for the same muscle. For example, numerous studies have estimated the CSA of the psoas major muscle using different subject populations and positions. However, few studies have combined the available information to obtain an overall estimate of CSA or investigated the effect different subject characteristics may have on CSA. In the present update, nine studies that reported psoas major CSA or physiologic CSA were compared with respect to subject characteristics, methodology, and results. Corrections to cadaveric data were made to adjust physiologic CSA to CSA. Comparison of reported values for living subjects indicated that females have smaller mean CSA than males for the psoas major muscle and that body size does not significantly influence muscle CSA in males. Areas derived from cadaveric data were smaller than similar studies on living subjects, possibly because of subject age, removal of tendinous and fatty components of fascicles, and lack of detailed data for fascicle angles in the supine position. Results indicate that researchers who use muscle CSA in biomechanical models should carefully assess the appropriateness of the data used, particularly in relation to potential sex differences and the influence of postural changes on CSA.

Biomechanical Phenomena↗

PubMed1998

Modelling the action of proteinase and inhibitor in tissue invasion.

Tissue invasion processes have been receiving considerable attention in recent years. The successful invasion and subsequent implantation of a mammalian trophoblast into maternal uterine tissue is under the control of a self-regulating mechanism, as yet not fully determined, which if operating incorrectly can lead to the excessive placental invasion associated with choriocarcinoma or insufficient placental invasion as occurs in the condition of pre-eclampsia. It is hoped that developing an understanding of the mechanisms governing the invasion of trophoblast cells into uterine tissue may lead to an understanding of the control of invasive mechanisms such as those observed in the development of invasive cancers. We have developed here a number of mathematical models in order to gain a better understanding of the role of proteinase and inhibitors in the context of trophoblast invasion. The models, which may be extended to other tissue invasion mechanisms, are based upon a series of proposed experiments involving blastocysts invading reconstituted basement membrane (Matrigel) allowing the quantification of the proteinase-Matrigel and proteinase-inhibitor interactions.

Biocompatible Materials↗

PubMed1996

A model of wound-healing angiogenesis in soft tissue.

Angiogenesis, or blood vessel growth, is a critical step in the wound-healing process, involving the chemotactic response of blood vessel endothelial cells to macrophage-derived factors produced in the wound space. In this article, we formulate a system of partial differential equations that model the evolution of the capillary-tip endothelial cells, macrophage-derived chemoattractants, and the new blood vessels during the tissue repair process. Chemotaxis is incorporated as a dominant feature of the model, driving the wave-like ingrowth of the wound-healing unit. The resulting model admits traveling wave solutions that exhibit many of the features characteristic of wound healing in soft tissue. The steady propagation of the healing unit through the wound space, the development of a dense band of fine, tipped capillaries near the leading edge of the wound-healing unit (the brush-border effect), and an elevated vessel density associated with newly healed wounds, prior to vascular remodeling, are all discernible from numerical simulations of the full model. Numerical simulations mimic not only the normal progression of wound healing but also the potential for some wounds to fail to heal. Through the development and analysis of a simplified model, insight is gained into how the balance between chemotaxis, tip proliferation, and tip death affects the structure and speed of propagation of the healing unit. Further, expressions defining the healed vessel density and the wavespeed in terms of known parameters lead naturally to the identification of a maximum wavespeed for the wound-healing process and to bounds on the healed vessel density. The implications of these results for wound-healing management are also discussed.

Animals↗

PubMed1993

Cell migration in multicell spheroids: swimming against the tide.

Multicell spheroids, small spherical clusters of cancer cells, have become an important in vitro model for studying tumour development given the diffusion limited geometry associated with many solid tumour growths. Spheroids expand until they reach a dormant state where they exhibit a grossly static three-layered structure. However, at a cellular level, the spheroid is demonstrably dynamic with constituent cells migrating from the outer well-nourished region of the spheroid toward the necrotic central core. The mechanism that drives the migrating cells in the spheroid is not well understood. In this paper we demonstrate that recent experiments on internationalization can be adequately described by implicating pressure gradients caused by differential cell proliferation and cell death as the primary mechanism. Although chemotaxis plays a role in cell movement, we argue that it acts against the passive movement caused by pressure differences.

Animals↗