Numerical simulation of motility patterns of the small bowel. II. Comparative pharmacological validation of a mathematical model.

A model of a locus of the small bowel, described earlier by the authors (Miftakhov et al., 1999) was validated in a comparison of the results of numerical simulations of pharmacological compounds to their effects in biological studies. The actions of the following four classes of drugs were simulated, those: (i) acting on the sarcoplasmic reticulum, (ii) altering the permeability of L- and T-type Ca(2+)channels on the smooth muscle membrane, (iii) motilides, and (iv) benzodiazepines. The strong qualitative resemblance between the theoretical and experimental results supports the robustness of the model.     

Numerical simulation of excitation-contraction coupling in a locus of the small bowel

A mathematical model for the excitation-contraction coupling within a functional unit (locus) of the small bowel is proposed. The model assumes that: the functional unit is an electromyogenic syncytium; its electrical activity is defined by kinetics of L- and T-type Ca²⁺-channels, mixed Ca²⁺-dependent K⁺-channels, potential-sensitive K⁺-channels and Cl^–-channels; the basic neural circuit, represented by the cholinergic and adrenergic neurones, provides a regulatory input to the functional unit via receptor-linked L-type Ca²⁺-channels; the smooth muscle syncytium of the locus is a null-dimensional contractile system. With the proposed model the dynamics of active force generation is determined entirely by the concentration of cytosolic calcium. The model describes electrical processes of the propagation of excitation along the neural circuit, chemical mechanisms of nerve-pulse transmission at the synaptic zones and the dynamics of active force generation. Numerical simulations have shown that it is capable of displaying different electrical patterns and mechanical responses of the locus. The simulated effects of: tetrodotoxin, -bungarotoxin, salts of divalent cations, inhibitors of catechol-O-methyltransferase and neuronal uptake mechanisms, and changes in the concentration of external Ca²⁺ on the dynamics of force generation have been analysed. The results are in good qualitative and quantitative agreement with results of experiments conducted on the visceral smooth muscle of the small bowel.     

A cell cycle model for somitogenesis: mathematical formulation and numerical simulation

After many years of research, the mechanisms that generate a periodic pattern of repeated elements (somites) along the length of the embryonic body axis is still one of the major unresolved problems in developmental biology. Here we present a mathematical formulation of the cell cycle model for somitogenesis proposed in Development105 (1989), 119-130. Somite precursor cells in the node are asynchronous, and therefore, as a population, generate continuously pre-somite cells which enter the segmental plate. The model makes the hypothesis that there exists a time window within the cell cycle, making up one-seventh of the cycle, which gates the pre-somite cells so that they make somites discretely, seven per cycle. We show that the model can indeed account for the spatiotemporal patterning of somite formation during normal development as well as the periodic abnormalities produced by heat shock treatment. We also relate the model to recent molecular data on the process of somite formation.     

Relaxin depresses small bowel motility through a nitric oxide-mediated mechanism. Studies in mice

Gastrointestinal motility is reduced and the incidence of functional gastrointestinal disorders is increased in pregnancy, possibly due to hormonal influences. This study aims to clarify whether the hormone relaxin, which attains high circulating levels during pregnancy and has a nitric oxide-mediated relaxant action on vascular and uterine smooth muscle, also reduces bowel motility and, if it does, whether nitric oxide is involved. Female mice in proestrous or estrous were treated for 18 h with relaxin (1 microg s.c.) or vehicle (controls). Isolated ileal preparations from both groups were used to record contractile activity, either basal or after acute administration of relaxin (5 x 10(-8) M). Drugs inhibiting nitric oxide biosynthesis or neurotransmission were used in combination with relaxin. Expression of nitric oxide synthase isoforms by the ileum was assessed by immunocytochemistry and Western blot analysis. Relaxin caused a clear-cut decay of muscle tension and a reduction in amplitude of spontaneous contractions upon either chronic administration to mice or acute addition to isolated ileal preparations. These effects were significantly blunted by N(G)-nitro-L-arginine, but not by the neural blockers we used. Moreover, relaxin increased the expression of nitric oxide synthases II and III, but not synthase I. Relaxin markedly inhibits ileal motility in mice by exerting a direct action on smooth muscle through the activation of intrinsic nitric oxide biosynthesis.     

Non-invasive algorithm for bowel motility estimation using a back-propagation neural network model of bowel sounds

Background

Although cardiac auscultation remains important to detect abnormal sounds and murmurs indicative of cardiac pathology, the application of electronic methods remains seldom used in everyday clinical practice. In this report we provide preliminary data showing how the phonocardiogram can be analyzed using color spectrographic techniques and discuss how such information may be of future value for noninvasive cardiac monitoring.

Methods

We digitally recorded the phonocardiogram using a high-speed USB interface and the program Gold Wave http://www.goldwave.com in 55 infants and adults with cardiac structural disease as well as from normal individuals and individuals with innocent murmurs. Color spectrographic analysis of the signal was performed using Spectrogram (Version 16) as a well as custom MATLAB code.

Results

Our preliminary data is presented as a series of seven cases.

Conclusions

We expect the application of spectrographic techniques to phonocardiography to grow substantially as ongoing research demonstrates its utility in various clinical settings. Our evaluation of a simple, low-cost phonocardiographic recording and analysis system to assist in determining the characteristic features of heart murmurs shows promise in helping distinguish innocent systolic murmurs from pathological murmurs in children and is expected to useful in other clinical settings as well.     

A mathematical model and a computerized simulation of PCR using complex templates.

A mathematical model and a computer simulation were used to study PCR specificity. The model describes the occurrences of non-targeted PCR products formed through random primer-template interactions. The PCR simulation scans DNA sequence databases with primers pairs. According to the model prediction, PCR with complex templates should rarely yield non-targeted products under typical reaction conditions. This is surprising as such products are often amplified in real PCR under conditions optimized for stringency. The causes for this 'PCR paradox' were investigated by comparing the model predictions with simulation results. We found that deviations from randomness in sequences from real genomes could not explain the frequent occurrence of non-targeted products in real PCR. The most likely explanation to the 'PCR paradox' is a relatively high tolerance of PCR to mismatches. The model also predicts that mismatch tolerance has the strongest effect on the number of non-targeted products, followed by primer length, template size and product size limit. The model and the simulation can be utilized for PCR studies, primer design and probing DNA uniqueness and randomness.     

Numerical simulation of steady flow in a model of the aortic bifurcation.

The governing equations of steady flow of an incompressible viscous fluid through a 3-D model of the aortic bifurcation are solved with the finite element method. The effect of Reynolds number on the flow was studied for a range including the physiological values (200 < or = Re < or = 1600). The symmetrical bifurcation, with a branch angle of 70 degrees and an area ratio of 0.8, includes a tapered transition zone. Secondary flows induced by the tube curvature are observed in the daughter tubes. Transverse currents in the transition zone are generated by the combined effect of diverging and converging walls. Flow separation depends on both the Reynolds number and the inlet wall shear.     

A mathematical simulation model of the AIDS pandemic]

In this work the mathematical model of the spread of AIDS pandemic over 5 regions of the world are presented. With the values of all parameters corresponding to the initial dynamics of the process the prognosis obtained with the use of this model is highly unfavorable. The program of mathematical modeling, developed in this investigation, may help in the evaluation of the effectiveness of different measures aimed at the liquidation of the epidemic process and in their correction, as well as in the choice of the optimum strategy of AIDS control.     

A novel formulation for blood trauma prediction by a modified power-law mathematical model

With the increasing use of artificial organs, blood damage has been raising ever more clinical concern. Blood trauma is in fact a major complication resulting from the implantation of medical devices and the use of life support apparatuses. Red blood cells damage predictive models furnish critical information on both the design and the evaluation of artificial organs, because their correct usage and implementation are thought to provide clear and rational guidance for the improvement of safety and efficacy. The currently adopted power-law shear-induced haemolysis prediction model lacks sensitivity with respect to the cumulative effect of previously applied stress magnitudes. An alternative model is proposed where a mechanical quantity was defined, able to describe the blood damage sustained by red cells under unsteady stress conditions, taking into account the load history. The proposed formulation predicted the same trend as the available experimental data. The obtained results have to be considered a preliminary validation of the basic hypothesis of this modified red blood cell damage prediction model. To date, the necessity to design further experiments to validate the proposed damage function clashes with the limitations inherent to current systems to get the time-varying shear stress completely under control.     

The simulation of aerial movement--II. A mathematical inertia model of the human body

A mathematical inertia model which permits the determination of personalized segmental inertia parameter values from anthropometric measurements is described. The human body is modelled using 40 geometric solids which are specified by 95 anthropometric measurements. A 'stadium' solid is introduced for modelling the torso segments using perimeter and width measurements. This procedure is more accurate than the use of elliptical discs of given width and depth and permits a smaller number of such solids to be used. Inertia parameter values may be obtained for body models of up to 20 segments. Errors in total body mass estimates from this and other models are discussed with reference to the unknown lung volumes.     

Numerical simulation of steady flow in a two-dimensional total artificial heart model.

In this paper, a numerical simulation of steady laminar and turbulent flow in a two-dimensional model for the total artificial heart is presented. A trileaflet polyurethane valve was simulated at the outflow orifice while the inflow orifice had a trileaflet or a flap valve. The finite analytic numerical method was employed to obtain solutions to the governing equations in the Cartesian coordinates. The closure for turbulence model was achieved by employing the k-epsilon-E model. The SIMPLER algorithm was used to solve the problem in primitive variables. The numerical solutions of the simulated model show that regions of relative stasis and trapped vortices were smaller within the ventricular chamber with the flap valve at the inflow orifice than that with the trileaflet valve. The predicted Reynolds stresses distal to the inflow valve within the ventricular chamber were also found to be smaller with the flap valve than with the trileaflet valve. These results also suggest a correlation between high turbulent stresses and the presence of thrombus in the vicinity of the valves in the total artificial hearts. The computed velocity vectors and turbulent stresses were comparable with previously reported in vitro measurements in artificial heart chambers. Analysis of the numerical solutions suggests that geometries similar to the flap valve (or a tilting disk valve) results in a better flow dynamics within the total artificial heart chamber compared to a trileaflet valve.     

Characterization and simulation of cDNA microarray spots using a novel mathematical model

Background  

The quality of cDNA microarray data is crucial for expanding its application to other research areas, such as the study of gene regulatory networks. Despite the fact that a number of algorithms have been suggested to increase the accuracy of microarray gene expression data, it is necessary to obtain reliable microarray images by improving wet-lab experiments. As the first step of a cDNA microarray experiment, spotting cDNA probes is critical to determining the quality of spot images.     

A mathematical model for pH patterns in the rhizospheres of growth zones

In the classical model by Nye (1981), the main process for the change in pH across the rhizosphere is assumed to be diffusion. The classical model focuses on the non-growing part of the root and assumes that the distribution of ion fluxes along the root is spatially uniform. We consider the rhizosphere of the growth zone and take into account the root growth rate and spatially varying flux along the root surface. We present both analytical (dimensional analysis) and experimental (computational) evidence of the importance of taking into account the root growth rate. We describe a conceptual and mathematical model to analyse the pH field around the root tip over time. The model is used with published data to show that, for typical growth rates in sandy soil, the pH field becomes steady (independent of time) after 6 h. Dimensional analysis reveals that a version of the Péclet number, related to the quotient of root elongation rate and proton diffusivity, can be used to predict the extent of the rhizosphere and the time required for it to become steady. For Péclet numbers much greater than 1 (soils), the root influences soil pH for distances on the millimetre scale. In contrast, for Péclet numbers much less than one (agar, aqueous solution), the root influences substrate pH for radial distances on the scale of centimetres. We also present some evidence that agar-contact techniques to measure the soil pH may not be appropriate for measuring the millimetre-scale gradients in soil pH.     

Neutron and X-ray effects on small intestine summarized by using a mathematical model or paradigm.

The responses of intestinal tissues to ionizing radiation can be described by comparing irradiated cell populations qualitatively or quantitatively with corresponding controls. This paper describes quantitative data obtained from resin-embedded sections of neutron-irradiated mouse small intestine at different times after treatment. Information is collected by counting cells or structures present per complete circumference. The data are assessed by using standard statistical tests, which show that early mitotic arrest precedes changes in goblet, absorptive, endocrine and stromal cells and a decrease in crypt numbers. The data can also produce ratios of irradiated: control figures for cells or structural elements. These ratios, along with tissue area measurements, can be used to summarize the structural damage as a composite graph and table, including a total figure, known as the Morphological Index. This is used to quantify the temporal response of the wall as a whole and to compare the effects of different qualities of radiation, here X-ray and cyclotron-produced neutron radiations. It is possible that such analysis can be used predictively along with other reference data to identify the treatment, dose and time required to produce observed tissue damage.     

Some mathematical aspects of the medical diagnostic process. I: a general mathematical model

Making a medical diagnosis consists of correlating knownpatterns of disease with the various classes of clinical data elicited from the history, physical examination, and batteries of tests relative to the diagnostic dynamics symbolized by atree branching into the various possible diagnostic decisions. In this paper a relational mathematical model of the reasoning aspects of the conventional medical diagnostic process is suggested as a way of extracting a general, formal concept of medical diagnosis. Computer implementation of the model is discussed briefly.     

Numerical study of the stability of some autowave solutions in a mathematical model of blood clotting

The stability of some types of solution for a set of equations representing a blood clotting model is examined using numerical methods of solving perturbation problems and the apparatus of adjoint equations. It is concluded that spiral waves are stable in this system, whereas traveling pulses are unstable at parameters corresponding to a chaotic regime in the punctual problem.     

Reproducibility and usability of chronic virus infection model using agent-based simulation; comparing with a mathematical model

We created agent-based models that visually simulate conditions of chronic viral infections using two software. The results from two models were consistent, when they have same parameters during the actual simulation. The simulation results comprise a transient phase and an equilibrium phase, and unlike the mathematical model, virus count transit smoothly to the equilibrium phase without overshooting which correlates with actual biology in vivo of certain viruses. We investigated the effects caused by varying all the parameters included in concept; increasing virus lifespan, uninfected cell lifespan, uninfected cell regeneration rate, virus production count from infected cells, and infection rate had positive effects to the virus count during the equilibrium period, whereas increasing the latent period, the lifespan-shortening ratio for infected cells, and the cell cycle speed had negative effects. Virus count at the start did not influence the equilibrium conditions, but it influenced the infection development rate. The space size had no intrinsic effect on the equilibrium period, but virus count maximized when the virus moving speed was twice the space size. These agent-based simulation models reproducibly provide a visual representation of the disease, and enable a simulation that encompasses parameters those are difficult to account for in a mathematical model.