Mathematical modeling of the dynamics of the intestinal epithelium in non-irradiated and irradiated mammals]

A mathematical model has been developed to describe the dynamics of the crypt-villus system of the small intestine epithelium in nonirradiated and chronically irradiated mammals. The model involves the chalone mechanism of regulation of crypt cell reproduction and represents a system of nonlinear differentiation equations. The model presents the dynamics of the small intestine epithelium in nonirradiated animals, including stable fluctuations of the concentrations of crypt and villus cells (the limited cycle), and simulates quantitatively the impairment of the intestinal epithelium in small laboratory animals subjected to long-term irradiation.     

Patterns of postradiation recovery of the spermatogenic epithelium in rodents and man

On the basis of the data reported in the literature a model is proposed describing the kinetics of the post-irradiation recovery of the main spermatogenous epithelium populations. In studying the spermatogenous epithelium structure of rodents and comparing the experimental and theoretical curves the parameters necessary for the kinetics estimations have been quantitated and their specific variations analysed. From these the parameters have been obtained and the kinetic curves shaped with a reference to human spermatogenous epithelium.     

Principles of the organization of intestinal epithelium and its recovery from damage revealed by modeling

Using the developed method of modelling the curves of the fraction of labelled indexes (FLI) in the small intestine epithelium, a relationship was found between the FLI shape and duration of the S phase and the whole generation cycle for various generations of proliferating crypt cells. On the basis of the comparison between the theoretical and experimental FLI the normal values of the generation cycles along the crypt were specified for various intestinal parts. FLI were shaped along the crypt at various time intervals after irradiation. As a result, the data were obtained on the correlation between the duration of generation cycles and their phases during the postirradiation period and for various cell generations.     

Mathematical modeling and analysis of meningococcal meningitis transmission dynamics

Meningococcal meningitis(MCM)is one of the serious public health threats in the tropical and sub-tropical regions.In this paper,we propose an epidemic model to study the transmission dynamics of MCM with high-and low-risk susceptible populations.The model considers two different groups of susceptible individuals depending on the availability of medical resources(MR,including hospitals,health workers,etc.),which varies the infection risk.We find that the model exhibits the phenomenon of backward bifurcation(BB),which increases the difficulty of MCM control since the dynamics are not merely relying on the basic reproduction number,TZo.This study explores the effects of MR on the MCM epidemics by mathematical analysis and shows the existence of BB on MCM disease.Our findings suggest that providing adequate MR in a community is crucial in mitigating MCM incidences and deaths,especially,in the MCM endemic regions.     

Cell dynamics in fetal intestinal epithelium: implications for intestinal growth and morphogenesis

The cellular mechanisms that drive growth and remodeling of the early intestinal epithelium are poorly understood. Current dogma suggests that the murine fetal intestinal epithelium is stratified, that villi are formed by an epithelial remodeling process involving the de novo formation of apical surface at secondary lumina, and that radial intercalation of the stratified cells constitutes a major intestinal lengthening mechanism. Here, we investigate cell polarity, cell cycle dynamics and cell shape in the fetal murine intestine between E12.5 and E14.5. We show that, contrary to previous assumptions, this epithelium is pseudostratified. Furthermore, epithelial nuclei exhibit interkinetic nuclear migration, a process wherein nuclei move in concert with the cell cycle, from the basal side (where DNA is synthesized) to the apical surface (where mitosis takes place); such nuclear movements were previously misinterpreted as the radial intercalation of cells. We further demonstrate that growth of epithelial girth between E12.5 and E14.5 is driven by microtubule- and actinomyosin-dependent apicobasal elongation, rather than by progressive epithelial stratification as was previously thought. Finally, we show that the actin-binding protein Shroom3 is crucial for the maintenance of the single-layered pseudostratified epithelium. In mice lacking Shroom3, the epithelium is disorganized and temporarily stratified during villus emergence. These results favor an alternative model of intestinal morphogenesis in which the epithelium remains single layered and apicobasally polarized throughout early intestinal development.     

Mathematical modeling of viral infection dynamics in spherical organs

A general mathematical model of viral infections inside a spherical organ is presented. Transported quantities are used to represent external cells or viral particles that penetrate the organ surface to either promote or combat the infection. A diffusion mechanism is considered for the migration of transported quantities to the organ inner tissue. Cases that include the effect of penetration, diffusion and proliferation of immune system cells, the generation of latently infected cells and the delivery of antiviral treatment are analyzed. Different antiviral mechanisms are modeled in the context of spatial variation. Equilibrium conditions are also calculated to determine the radial profile after the infection progresses and antiviral therapy is delivered for a long period of time. The dynamic and equilibrium solutions obtained in this paper provide insight into the temporal and spatial evolution of viral infections.     

Effect of myelopeptides on the postradiation recovery of the thymus

The influence of myelopeptides on the postirradiation recovery of thymus was studied by estimating the thymus cellularity, proliferation of thymocytes in vivo, and composition of thymocyte subpopulations characterized by the expression of Thy-1,2 and Sc-1 antigens and receptors for peanut agglutinin. A single intraperitoneal administration of myelopeptide (the optimal dose of 10(-5) mg/mouse) 24 h following 6.5 Gy irradiation gives rise to proliferative and differentiation processes favoring the recovery of thymus.     

Mathematical and computation modeling of self-organizing sarcomere with chaotic dynamics of the order parameter

The results of constructing a nonlinear model of sarcomere contraction are summarized. A strange attractor has been obtained, which is related to the randomness of the dynamics of the order parameter during sarcomere deformation. A hypothesis is proposed that upon fixation of the actin filaments in the sarcomere the myosin system undergoes nonlinear oscillations with dissipation, which leads to elevation of solution temperature. The increase in temperature has been determined for pulsations of the inertial range. Normalized power spectra of the pulsations of the order parameter have been constructed for the model by Fourier transform. The thermodynamics of sarcomere contraction is considered.     

Mathematical modeling of mortality dynamics of mammalian populations exposed to radiation

A mathematical model is developed which describes the dynamics of radiation-induced mortality of a non-homogeneous (in radiosensitivity) mammalian population. It relates statistical biometric functions with statistical and dynamic characteristics of a critical system in organism of specimens composing this population. The model involves two types of distributions, the normal and the log-normal, of population specimens with respect to the radiosensitivity of the critical system cells. This approach suggests a new pathway in developing the methods of radiation risk assessment.     

Uptake dynamics of scrapie agent in the intestinal villous epithelium of suckling and weanling Syrian hamsters

In mice, the number of intestinal villous columnar epithelium cells that incorporate abnormal prion protein (PrP(Sc) ) decreases significantly after weaning. In this study, the dynamics of PrP(Sc) uptake during the growth of hamsters were investigated by inoculating scrapie 263K agent orally into suckling and weanling Syrian hamsters and estimating the number of PrP(Sc) -positive villous epithelium cells immunohistochemically. The number of PrP(Sc) -positive cells declined significantly as the hamsters aged. The present results suggest that a tendency toward decline of PrP(Sc) -positive cells with increasing age might be a common phenomenon among the superfamily Muridae.