Medical institutions face the challenge of promoting excellence in a variety of competing focus areas, such as grants, publications, income, research, faculty, variety, patient care and teaching. A transposed Markov chain is used analyse the interactions between the various focus areas and their transition towards steady-state. In contradistinction with a regular Markov chain, in the transposed chain used for the present analysis, the sum of inputs (rather than outputs) of each individual state is 100&#x25;, whereas the outputs are left to assume any possible value. The mathematics of calculating the steady state conditions of a transposed Markov matrix are similar to those of a regular Markov matrix. The analysis shows that a focus area more dependent on other areas is also more likely to lose its investment, whereas largely self-reliant areas will generate the largest return. Full strength of all academic focus areas can be achieved only by investments in all areas. In academic systems with one or several exclusively self-reliant focus areas, only investment in these particular areas will invigorate the system, as all other investments are bound to dissipate over time. The newly developed decision tool of a transposed Markov matrix could be helpful in stochastic modelling of medical phenomena.

Amnon Sonnenberg

Transposed Markov Matrix as a New Decision Tool of How to Choose among Competing Investment Options in Academic Medicine

Mark Chaplain

Special Issue on &#8220;Mathematical Modelling and Simulation of Aspects of Cancer Growth&#8221;

The series of ordered mutations that cause a specific cell to become cancerous is modeled so that the fraction of a risk population (e.g. White men) that has developed a specific cancer (e.g. melanoma) at any age can be calculated. The saturated model constructed and solved here is isomorphic to the physical model describing an ordered chain of radioactive nuclei decays with the exception that it allows for the possibility that a fraction of a risk population may be immune to developing a specific cancer.The simplest model developed here depends on only three independent parameters: the number of ordered mutations necessary for a cell to become cancerous, the fraction of the risk population that is immune to developing a specific cancer and the average time between mutations (a time defined as the mutation lifetime). The values of these independent parameters are determined by fitting the model's cancer incidence function to the cancer incidence data.This model was applied to five widely different cancers: melanoma, pancreatic cancer, female breast cancer, non-Hodgkin lymphoma and prostate cancer. The modeling predicts that all White males in the USA are vulnerable to developing melanoma, five-ordered mutations are required to develop it and the mutation lifetime is 48.3 years. By contrast, the modeling predicts that 80.7&#x25; of White females in the USA are immune to developing melanoma, three-ordered mutations are required to develop it and the mutation lifetime is 78.9 years. Remarkably, it was also found that about 70&#x25; of females are immune to developing breast cancer and about 70&#x25; of males are immune to developing prostate cancer, predictions that fit in with the experimental evidence of cancer immunosurveillance and immunoediting.Clearly, different risk populations can develop the same cancer through different pathways. Delineating the mechanism underlying the prevalence of immunity to specific cancers in specific risk populations should become a research priority. Finding ways of blocking or repairing cellular mutations and/or destroying mutated, potentially cancerous cells would prevent cancers from developing altogether and eliminate a major cause of mortality.

Ivan Kramer

Evidence that Natural Immunity to Breast Cancer and Prostate Cancer Exists in the Majority of Their Risk Populations Is Predicted by a Novel, Inherently Saturated, Ordered Mutation Model

Mechanical and chemical models of vasculogenesis are critically reviewed with an emphasis on their ability to predict experimentally measured quantities. Final remarks suggest a possibility to merge the capabilities of different models into a unified approach.

D. Ambrosi

F. Bussolino

L. Preziosi

A Review of Vasculogenesis Models

The development of scarring following accidental injury or surgery is an important clinical problem, often resulting in adverse effects on frowth and function, as well as an undersirable cosmetic appearance. Adult wound healing and scar formation are characterised by acute inflammation, wound contraction and disordered collagen deposition. Similar processes may also be involved in the progression of fibrotic disease states such as pulmonary fibrosis and hepatic cirrhosis. A major clinical objective is therefore, the reduction, and ideally the prevention, of scarring. The embryo and early fetus respond to injury in a way that is fundamentally different from the adult. In general, the early fetus heals rapidly, without scar formation. Extracellular matrix deposition in the fetal wound is rapid and organised in its structure, much more similar in appearance to unwounded skin, whilst, in the adult, matrix deposition is disordered. The inflammatory response, charasterisitic of the early phase of adult wound healing, is absent, or highly limited, in the fetus and the levels of cytokines are generally greatly reduced. Research into fundamental cellular and molecular differences between adult and fetal wound healing have revealed a number o targets in the adult wound which can be manipulated to more closely resemble the fetal wound environment and hence result in the reduction of adult scarring.

R. L. McCallion

M. W. J. Ferguson

Scar-Free Embryonic Wound Healing and the Prevention of Scarring Following Wound Healing in the Adult

Antigen recognition by the adaptive cellular immune system is based on a diverse repertoire of antigen receptors. Since this repertoire is formed by genetic recombination, a number of receptors are autoreactive by chance, giving rise to the threat of autoimmune disease. Potentially autoreactive T lymphocytes (T cells) are rendered ineffective by various tolerance mechanisms. One of these mechanisms is negative selection, the deletion from the repertoire of immature autoreactive T cells in the thymus. The present paper shows how to assess the contribution made by negative selection relative to other tolerisation mechanisms by deducing the impact of negative selection on the T cell repertoire from the statistics of autoantigen presentation in the thymus.

Hugo A. van den Berg

Carmen Molina-Par&#237;s

Thymic Presentation of Autoantigens and the Efficiency of Negative Selection

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Computational and Mathematical Methods in Medicine publishes research and review articles focused on the application of mathematics to problems arising from the biomedical sciences.

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Computational and Mathematical Methods in Medicine