A new mathematical model of proliferation control during immune response

A considerable proliferation of participating cells is a characteristic feature of the immune response. This proliferation may be controlled by Interleukin 2. Assumptions on the course of the immune response under such a control are formulated, and a new mathematical model of the immune response involving regulation of the proliferation of appropriate cells is constructed.     

Problems associated with potential massive use of antimicrobial agents as prophylaxis or therapy of a bioterrorist attack

In addition to the direct sanitary damage of a terrorist attack caused by biological weapons, the consequences of the massive stockpiling and consumption of antimicrobial agents in order to treat or prevent the disease under a potential epidemic due to pathogenic bacteria must also be considered. Bacillus anthracis , Francisella tularensis and Yersinia pestis are the bacteria most likely to be used as terrorist weapons. Tetracyclines, quinolones and aminoglycoside are the antibiotics of choice against these microorganisms. The recent terrorist attack with anthrax spores in the USA caused a substantial increase in the sales of ciprofloxacin, as thousands of citizens received antibiotic prophylaxis for either confirmed or suspected exposure to anthrax, and many others stockpiled antibiotic supplies at their homes under a panic scenario. The massive consumption of antimicrobial drugs may lead to the selection of antibiotic resistant strains, and to the appearance of undesirable side effects, such as anaphylaxis or teratogenesis.
National health authorities must develop realistic protocols in order to detect, treat and prevent mass casualties caused by biological weapons. An antibiotic stockpile has to be planned and implemented, and home stockpiling of antibiotics must be strongly discouraged.     

Morphology of deltoid origin and end tendons – a generic model

This study provides a model of the complex deltoid origin and end tendons, as a basis for further anatomical, biomechanical and clinical research. Although the deltoid is used in transpositions with upper limb paralysis, its detailed morphology and segmentation has not been object of much study. Morphologically, the deltoid faces two distinct challenges. It closely envelops a ball joint, and it reduces its width over a short distance from a very wide origin along clavicle, acromion and spina scapula, to an insertion as narrow as the humerus. These challenges necessitate specific morphological tendon adaptations. A qualitative model for these tendons is developed by the stepwise transformation of a unipennate muscle model into a functional deltoid muscle. Each step is the solution to one of the mentioned morphological challenges. The final model is of an end tendon consisting of a continuous succession of bipennate end tendon blades centrally interspaced by unipennate tendon parts. The origin tendon consists of lamellae that interdigitate with the end tendon blades, creating a natural segmentation. The model is illustrated by qualitative dissection results. In addition, in view of a proliferation of terms found in the literature to describe deltoid tendons, tendon concepts are reviewed and the systematic use of the unique and simple terminology of ‘origin and end tendons’ is proposed.     

A mathematical model for a thermal clearance probe

We introduce a new mathematical model for a thermal clearance probe for the measurement of skin blood flow. It is concluded that the technique is more sensitive to differences in the thermal conductivity of the skin than to differences in blood flow. The depth of measurement is also considered.     

A mathematical model of insulin secretion

Diabetes mellitus is a chronic state of excessive blood glucoselevels (hyperglycaemia), which may result from many environmentaland genetic factors, often acting jointly. The major regulatorof glucose concentration in the blood is insulin. It is knownthat about 50% of the insulin is taken up by the liver on passingthrough it after secretion from the pancreas. The precise valueof this fractional uptake is not known, so the prehepatic insulinsecretion rates cannot be readily estimated from the plasmainsulin concentration levels. By utilizing the equimolar secretionof insulin and connecting peptide (C-peptide) from the pancreas,a noninvasive method has been formulated. This was based ona compartmental model which involved the pancreas, liver, andplasma. The resulting differential equation yielded a gammavariate solution which could be readily linearized. The modelwas then tested on 56 normal (51 nonobese and 5 obese) subjects,and three groups of subjects with diabetes who could be labelledas mild, moderate, and severe (based on the fasting plasma glucoseconcentration) with 83, 88, and 64 subjects respectively. Wehave focused on the human patient environment of the clinicianto produce a distinct model which gave a consistent patternwithin all four groups with good fits between observed and theoreticalvalues of the plasma insulin levels. The consequent rates forinsulin secretion were consistent across the groups and wereclinically meaningful.     

A mathematical model of left-ventricular function

A model of the left ventricle is developed which characterises ventricular elastance as a function of end-diastolic volume and time. The heart model is terminated in a modifiedWindkessel load, and accurately simulates the mechanical response of the heart to various various pre- and after-load conditions.     

A mathematical model of post-canalization thrombolysis

During the initial phase of lysis of an occlusive thrombus using lytic agents such as tissue plasminogen activator, blood flow through the centre of the clot is established (the process of recanalization). Following canalization, the clot remains on the vessel wall and further lysis is required. This paper develops a multi-species mathematical model to describe the bulk chemical reactions in the bloodstream and the convective and diffusive transport of chemical species to and from the clot surface in conditions following canalization. For the steady state case, the model indicates that the process of clot lysis following initial recanalization is dominated by surface chemical reactions and the bulk reactions play little role in the lytic process. Lytic rate is dependent on the clot geometry and flow conditions. The rate of clot dissolution is greatest at the upstream end of the clot and decreases steadily downstream due to lytic agent being removed from the flowing blood as it binds to the clot surface. This model may be further developed and used to simulate and compare different lytic regimes.     

Spitz melanocytic tumours – a review

Spitz tumours comprise a spectrum of melanocytic proliferations that share a set of distinct cytological features and molecular pathways. They include benign naevi, intermediate or indeterminate tumours and rare melanomas. Spitz tumours are notorious for the difficulty of distinguishing benign neoplasms with atypical features from melanomas and the related diagnostic uncertainty. Advances in the knowledge of the molecular pathways and genomic aberrations associated with these neoplasms have permitted opportunities for a reduction in the number of uncertain diagnoses and a more objective distinction between Spitz tumours from Spitz-like neoplasms. The presence of a Spitz molecular pathway, such as Harvey rat sarcoma viral oncogene homologue (HRAS) aberrations or kinase fusions, distinguishes a bona fide Spitz neoplasm from Spitz-like naevi or melanomas with conventional driver mutations. Spitz neoplasms with benign histopathological features and, if such testing is performed, benign cytogenetic and molecular findings, are termed Spitz naevi. Spitz neoplasms with frankly malignant histopathological findings or ambiguous microscopic findings associated with genetic or genomic aberrations most in keeping with melanoma are designated as Spitz melanoma. Tumours with microscopic features and genetic/genomic aberrations in between naevi and melanomas are classified as Spitz melanocytoma.     

A mathematical model for simulation of early decelerations in the cardiotocogram during labor

Fetal welfare during labor and delivery is commonly monitored through the cardiotocogram (CTG), the combined registration of uterus contractions and fetal heart rate (FHR). The CTG gives an indication of the main determinant of the acute fetal condition, namely its oxygen state. However, interpretation is complicated by the complex relationship between the two. Mathematical models can be used to assist with the interpretation of the CTG, since they enable quantitative modeling of the cascade of events through which uterine contractions affect fetal oxygenation and FHR. We developed a mathematical model to simulate 'early decelerations', i.e. variations in FHR originating from caput compression during uterine contractions, as mediated by cerebral flow reduction, cerebral hypoxia and a vagal nerve response to hypoxia. Simulation results show a realistic response, both for fetal and maternal hemodynamics at term, as for FHR variation during early decelerations. The model is intended to be used as a training tool for gynaecologists. Therefore 6 clinical experts were asked to rate 5 real and 5 model-generated CTG tracings on overall realism and realism of selected aspects. Results show no significant differences between real and computer-generated CTG tracings.     

A mathematical model of flow in a liquid-filled visco-elastic tube

In biofluid mechanics the fluid-solid interaction is important. To this aim the propagation of waves in a distensible tube filled with a viscous fluid was studied numerically. Based on the assumption of long wavelength and small amplitude of pressure waves, a quasi-1D differential model was adopted. The model accounted for vessel wall visco-elasticity and included the wall deformations in both radial and axial directions. The non-linear problem was solved in non-dimensional form by a finite difference method on a staggered grid. The boundary conditions were for two relevant cases: natural oscillations in a deformable tube fixed at the ends and persistent oscillations due to a periodical forcing pressure. The natural frequency St^* was found to vary as the square root of the elasticity coefficient K, with 0≤K≤6000, and was not affected by the viscosity. These results highlight a strong influence of both wall visco-elasticity and blood viscosity. The natural oscillations are damped in a few time units and the damping time was found to be inversely proportional to the wall viscosity coefficient and the fluid viscosity provided an even larger damping factor.     

A mathematical model for quantifying training

A systems modelling approach has been used to quantify the dose-response nature of training. Considerable attention has been focused on the modelling process with little work on the determination of the training impulse (TRIMP) scores. Currently, the methods employed to calculate TRIMPs are subject to various limitations including the use of generic ordinal category or exponential weighting factors for higher exercise intensities. These weightings are necessary to prevent excessively high scores from long duration, low intensity bouts of exercise. We propose a new method to calculate TRIMP scores based upon a whole body bioenergetic model. Our method is individual specific, removing many of the previous limitations. Furthermore, this model could enable a greater comparison of continuous and interval training methods. This model takes into account the length of repetition(s), concentration of the interval session and mode of recovery. This approach, while requiring further research, offers a potential improvement in the accuracy of training load calculations.     

Transplantation tolerance – a historical introduction

The concept of immunological tolerance – the state of specific unresponsiveness to allogeneic transplants and all manner of other antigens – began in 1945 with R.D. Owen's finding that cattle dizygotic twins are red blood cell chimeras. Peter Medawar's group in Birmingham likewise discovered, quite independently, that cattle dizygotic twins accept each others’ skin grafts. These findings, together with F.M. Burnet and F. Fenner's speculations in 1949, prompted Medawar, together with R.E. Billingham and L. Brent, now at University College London, to embark on an extensive series of experiments that established immunological tolerance as a fundamental phenomenon, forming a new branch of immunology.     

A mathematical model of the electrocardiographicQT-RR relationship

A mathematical model of the electrocardiographicQT-RR relationship is presented. Numerical estimates produced a curve that fits reasonably well the empirical approximation made with Bazett's formula. The model is general and would agree in principle with previous membrane theories; this fact should encourage experiments in the mammalian heart and in single cells. The ‘activation’ constant A was found to be 3·88×10^?2 1/s. The critical periodT _k =x ₀ estimated from the experimental data was 0·5 s with a corresponding critical frequencyf _k of 120 beats/min. These values are valid for the whole ventricle of the snakeConstrictor constrictor; beyondf _k fibrillation would be expected to occur.     

Extended spectrum cephalosporin resistance among clinical isolates of Enterobacteriaceae in West Norway during 2006–2013; a prospective surveillance study

Routine surveillance of resistance to broad‐spectrum cephalosporins in Enterobacteriaceae and phenotypic identification of underlying mechanisms using a simple strategy was commenced in 2006 at our laboratory, serving West Norway. This report focuses on the results until 2013. The classical plasmid‐mediated extended spectrum beta‐lactamase (ESBL_A) among clinically relevant Escherichia coli isolates showed an increase from 0.6% to 4.3% during the surveillance period, while prevalence for other mechanisms remained stable, below 0.7%. ESBL_A in Klebsiella pneumoniae had similar prevalence in 2006 (0.6%) and 2013 (4.4%), but in between it peaked to 3.9% in 2008 and to 9.3% in 2011. Within the other species, the numbers of clinically relevant isolates and isolates‐producing ESBL_A were much lower. An increasing resistance due to hyperproduction of AmpC enzymes was seen in Enterobacter and Citrobacter, with prevalence increasing from 18% and 12.2% in 2006 to 27.5% and 26.1% in 2013, respectively. Hyperproduction of KOXY enzyme in Klebsiella oxytoca remained below 9.5% and did not show an increasing trend. The overall increase in the proportions of isolates‐producing ESBL_A in E. coli/K. pneumoniae and hyperproduction of AmpC in Enterobacter/Citrobacter necessitates measures to hinder the spread of resistant bacteria and vigilant antibiotic stewardship.