Our aim was to elaborate a method to optimise treatment intervals for the individual low-density lipoprotein (LDL)-apheresis treated patients. After each treatment, plasma LDL concentrations show a time-related increase with a decreasing speed until a maximum level.We searched to interpret the post-LDL-apheresis experimental data trend as the physical process that produces the observed curve, so that the fitting presupposed theoretical function is a direct consequence of the physic process, because to establish the better time. Applying the proposed fitting method to a succession of 15 samples obtained from the mean of six plasmapheresis executed on five different subjects, small estimate standard error (5&#x2009;mg/dl) and relative error (1.7&#37;) with a dispersion evidently related to the experimental error were observed. Obviously, applying the same method to a single case, the dispersion is more marked (relative error &#60;5&#37;), with a SE of 10-13&#x2009;mg/dl, even though the aspect of a casual phenomenon is conserved. Our physical interpretation appears to be a practical model to predict the LDL-rebound kinetic of the single patient.

Franco Corsini

Arrigo F. G. Cicero

Antonia Giannuzzi

Antonio Gaddi

Application of a New Processing Method to Post-LDL-apheresis Data

The comparison of different methods of keratoprosthesis (KP) regarding their long-term success, as far as visual acuity is concerned, is difficult: this is the case both as a standardized reporting method agreed upon by all research groups has not been reported and far less accepted, and as the quality of life for the
patient not only depends on the level of visual acuity, but also quite significantly on the “survival time” of the implant. Therefore, an analysis of a single series of patients with Osteo–Odonto–Keratoprosthesis (OOKP) was performed. Statistical analysis methods used by others in similar groups of surgical procedures have included descriptive statistics, survival analysis and ANOVA. These methods comprised comparisons of empirical densities or distribution functions and empirical survival curves. It is the objective of this paper to provide an inductive statistical method to avoid the problems with descriptive techniques and survival analysis. This statistical model meets four important standards: (1) the efficiency of a surgical technique can be assessed within an arbitrary time interval by a new index (VAT-index), (2) possible autocorrelations of the data are taken into consideration and (3) the efficiency is not only stated by a point estimator, but also 95% point-wise confidence limits are computed based on the Monte Carlo method, and finally, (4) the efficiency of a specific method is illustrated by line and range plots for quick illustration and can also be used for the comparison of different other surgical techniques such as refractive techniques, glaucoma and retinal surgery.

W. Hitzl

G. Grabner

Application of the Monte Carlo Method for the Assessment of Long-term Success in Keratoprosthesis Surgery

The aim of this work is twofold. First we focus on the complex phenomenon of electrogram fractionation, due to the presence of discontinuities in the conduction properties of the cardiac tissue in a bidomain model. Numerical simulations of paced activation may help to understand the role of the membrane ionic currents and of the changes in cellular coupling in the formation of conduction blocks and fractionation of the electrogram waveform. In particular, we show that fractionation is independent of INA alterations and that it can be described by the bidomain model of cardiac tissue. Moreover, some deflections in fractionated electrograms may give nonlocal information about the shape of damaged areas, also revealing the presence of inhomogeneities in the intracellular conductivity of the medium at a distance.The second point of interest is the analysis of the effects of space&#8211;time discretization on numerical results, especially during slow conduction in damaged cardiac tissue. Indeed, large discretization steps can induce numerical artifacts such as slowing down of conduction velocity, alteration in extracellular and transmembrane potential waveforms or conduction blocks, which are not predicted by the continuous bidomain model. Several possible numerical and physiological explanations of these effects are given. Essentially, the discrete system obtained at the end of the approximation process may be interpreted as a discrete model of the cardiac tissue made up of isopotential cells where the effective intracellular conductivity tensor depends on the space discretization steps; the increase of these steps results in an increase of the effective intracellular resistance and can induce conduction blocks if a certain critical value is exceeded.

Simona Sanfelici

Numerical Simulations of Fractionated Electrograms and Pathological Cardiac Action Potential

We propose an artificial lymph node to improve immune function in fighting viral diseases. The device is based on hemodialysis using a cartridge containing a solid phase affinity resin. Virus capture is mediated by a collection of broad specificity antibodies covalently coupled to agarose. Viral proteins, which can directly damage uninfected cells, are also efficiently removed. Immobilized antisense DNA provides a mechanism to remove infectious viral nucleic acids. Theoretical calculations suggest that the device could effectively remove virus, toxic viral proteins and infectious viral nucleic acids from the blood thereby limiting disease by preventing reinfection of new cells. In the absence of newly infected cells, previously infected cells are cleared by the immune system. For a typical immobilized antibody, calculations predict a pseudo-first order rate of capture (t1/2 &#8764; 10&#x2009;min) with viral load reduction &#8764; 660-fold at equilibrium. Theoretical calculations of a diffusion limited process predict t1/2 &#8764; 2.8&#x2009;h. Measured transport rates for latex particles in a prototype device are significantly faster than the theoretical diffusion limit suggesting that transport is primarily convective and sufficient to allow rapid virus clearance. Since the device is highly selective it can be used in conjunction with drug therapy and other treatments.

Richard H. Tullis

David O. Scamurra

Julian L. Ambrus

Affinity Hemodialysis for Antiviral Therapy with Specific Application to HIV

The requirements for the eradication of HIV in infected individuals are unknown. Intermittent administration of the immune activator interleukin-2 (IL-2) in combination with highly-active antiretroviral therapy (HAART) has been suggested as an effective strategy to realize long-term control of HIV replication in vivo. However, potential latent virus reservoirs are considered to be a major impediment in achieving this goal. In this paper, a new mathematical model is designed and used to monitor the interactions between HIV, CD4+ T-cells, CD8+ T-cells, productively infected and latently infected CD4+ T-cells, and to evaluate therapeutic strategies during the first 3 years of HIV infection. The model shows that current anti-HIV therapies, including intermittent IL-2 and HAART, are insufficient in achieving eradication of HIV. However, it suggests that the HIV eradication may indeed be theoretically feasible if such therapy is administered continuously (without interruption) under some specified conditions. These conditions may realistically be achieved using an agent (such as a putative anti-HIV vaccine) that brings about a concomitant increase in the proliferation of HIVspecific CD4+ T- and CD8+ T-cells and the differentiation of CD8+ T-cells into anti-HIV cytotoxic T lymphocytes (CTLs).

A. B. Gumel

Xue-Wu Zhang

P. N. Shivakumar

M. L. Garba

B. M. Sahai

A New Mathematical Model for Assessing Therapeutic Strategies for HIV Infection

Tumour angiogenesis is the process whereby a capillary network is formed from a pre-existing vasculature in response to tumour secreted growth factors (TAF). The capillary network is largely composed of migrating endothelial cells which organise themselves into dendritic structures. In this paper we model angiogenesis via the theory of reinforced random walks, whereby the chemotactic response of the endothelial cells to TAF and their haptotactic response to the matrix macromolecule fibronectin is accomplished through transition probability rate functions. Tumour secreted growth and inhibitory factors are modelled on the basis of Michaelis–Menten kinetics. Particular attention is focussed on the action of anti-angiogenic agents (i.e. angiostatins). That is as a mechanism whereby angiostatin acts as a protease inhibitor. Numerical simulations yield results, which are in good agreement with the experimental observations obtained by Folkman and his co-workers in their classical rabbit eye cornea experiments. The model offers a theoretical understanding of how some angiostatins work to inhibit tumour growth.

Howard A. Levine

Serdal Pamuk

Brian D. Sleeman

Marit Nilsen-Hamilton

Mathematical Modelling of Tumour Angiogenesis and the Action of Angiostatin as a Protease Inhibitor

Allergic hypersensitivity of type I for hymenoptera venoms is the most frequent reason for acute IgE-mediated anaphylactic reactions. The subcutaneous injection of increasing doses of purified allergen followed by long-term administration of an adequate maintenance dose over a period of 3–5 years called venom immunotherapy (VIT) has been proven to be a very effective treatment achieving protection in about 96% of allergic patients. Even though the principle of hyposensitisation has been introduced already 90 years ago, the underlying immunoregulatory mechanisms of VIT remain poorly understood. Recent studies suggest a shift in cytokine production from a Th2 to a Th1 cytokine profile during therapy. In this paper, a mathematical model for T-cell regulation and a model for mast cell/basophil desensitisation are presented and analysed to explain the mechanism of conventional rush and ultra-rush VIT.

Jan Richter

Gerhard Metzner

Ulrich Behn

Mathematical Modelling of Venom Immunotherapy

We formulate a model to describe the dynamics of hepatitis C virus (HCV) considering four populations: uninfected liver cells, infected liver cells, HCV and T cells. Analysis of the model reveals the existence of two equilibrium states, the uninfected state in which no virus is present and an endemically infected state, in which virus and infected cells are present. There exists a threshold condition that determines the existence and stability of the endemic equilibrium. We discuss the efficacy of the therapy methods for hepatitis C in terms of the threshold parameter. Success of the therapy could possibly be predicted from the early viral dynamics in the patients.

R. Avendano

L. Esteva

J. A. Flores

J. L. Fuentes Allen

G. Gómez

Je. López-Estrada

A Mathematical Model for the Dynamics of Hepatitis C

Mark Chaplain

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

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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 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