A simple method of solution for a class of bioreaction-diffusion problems

Summary A simple method of solution is highlighted for solving a class of bioreaction-diffusion problems. By virtue of the proposed transformation the original boundary value problem is rendered into an equivalent initial value problem. Results are comparable to conventional methods, and have lower computational time requirements.NCL Communication. No. 5179     

生态学中一类n维反应扩散方程组解的性质

本文讨论一类不满足所谓的拟单调条件的反应扩散方程组的初边值问题．应用谱论和单调性方法证明了问题解的存在唯一性和平衡解的渐近稳定性．并进一步讨论了生态学中n种群单食物链模型的第二初值问题,得到了问题的非负平衡解的存在性和渐近性以及相应的吸引区域．     

A parameter identification problem arising from a model of canalicular bile formation

We develop a simple mathematical model for bile formation and analyze some features of the model that suggest the design for future physiological experiments. The mathematical model results in a boundary value problem for a system of functional differential equations depending on several physical parameters. From the observability of the boundary values we can identify, both qualitatively and quantitatively, some of these physical parameters. This identification then suggests physical experiments from which one could infer some of the bile transport phenomena that are not, at present, directly observable. The mathematical parameter identification problem is solved by converting the boundary value problem to a transition time problem for a quadratic system of ordinary differential equations on the plane where we are able to employ some special properties of quadratic systems in order to obtain a solution.The author was supported by the Air Force Office of Scientific Research and the National Science Foundation under the grants AF-AFOSR-89-0078 and DMS-9022621The author was supported by National Institutes of Health under grant number R37 DK-27623     

The distribution of colony-forming cells in the kidney

Abstract. A method is described for producing outgrowths of small nephron segments (average 24 cells) in culture. The method was used to estimate an overall colony-forming efficiency of 4.6% for cells constituting the segments. Efficiency was found to be lower for thick segments (1%) than for thin segments (6%) from Henle's loop. The latter higher level indicates that precursor cells are concentrated near the middle of the nephron. For comparison, a two-dose irradiation technique was used to calculate a mean number of 5 ± 2 (SE) clonogens per segment producing outgrowths. This tended to be higher than the value of about 1 calculated from the 65% of segments producing outgrowths, as expected if the remaining segments contained no clonogens.     

Skin effect in a gaseous plasma with a collision frequency proportional to the electron velocity

An analytic solution to the problem of skin effect in plasma is found for the first time by using a kinetic equation in which the collision frequency is proportional to the absolute value of the electron velocity. Mirror reflection of electrons from the plasma boundary is used as a boundary condition. The calculated expression for the impedance is compared with the classical one.     

人口问题中一广义扩散模型初边值问题的动力性态

本文研究人口问题中的一广义扩散模型考虑它的初边值问题，证明了问题整体吸引子的存在性。     

Lectin histochemistry of rabbit nephron

In order to investigate the usefulness of lectin histochemistry to detail nephronal segmentation we used 12 different biotinylated lectins (Con-A, DBA, GS-I, LCA, PNA, PWN, RCA-I, RCA-II, SWGA, SBA, UEA-I, and WGA) and Avidin-Biotin-Peroxidase (ABC) system on formalin-fixed and paraffin-embedded rabbit kidney sections. Each lectin, except UEA-I which did not stain any nephron structure, shows a different staining pattern along the nephron. Con-A, LCA, and RCA-I display a diffuse staining, while BS-I, RCA-II, SWGA, PWN, DBA, SBA and PNA are selective markers for specific nephron tracts. Furthermore, it is possible, according to the WGA binding pattern, to differentiate the convoluted part of the proximal tubule into two parts, named Segment A and Segment B. Lectin histochemistry on formalin-fixed and paraffin-embedded rabbit kidney sections displays a specific binding pattern along the rabbit nephron and shows interesting morphofunctional correlations.     

Characterization of the efficiency of a cell separation process by the extent of elimination of a contaminating cell type

A stepwise approach to the selection of an appropriate technique for a cell separation problem is presented in which the preparative purification of cells is linked to their analytical separation. We have introduced the extent of elimination of a contaminating cell type from the cell type which one chooses to purify, as a separation parameter that characterizes the efficiency of a separation process independently of the relative cell composition of the starting material. In order to compare different separation techniques, a preparative fraction boundary needs to be chosen between the cell types. We defined this boundary in terms of the physical property on which the separation is based such that yield and purity of the isolated cell suspension are optimized simultaneously. With this analytical approach, it was found that a similar elutriation technique separated human and equine mononuclear cells equally well and that the separability of human monocytes and lymphocytes improved when the cells were separated by increasing the limiting sedimentation coefficient value of the elutriation chamber in small increments.     

Ultrastructure of the crayfish antennal gland revealed by scanning and transmission electron microscopy combined with ultrasonic microdissection

The antennal gland of the crayfish Pacifasticus leniusculus was studied using standard techniques for scanning electron microscopy as well as newer procedures for ultrasonic microdissection. To clarify relationships in the nephron tubule, transmission electron microscopy was employed. The coelomosac contains elongated cells (podocytes) displaying microvilli and extensive apical blebbing. A smooth basal lamina lines the blood space that furnishes hemolymph to the coelomosac. The labyrinth consists of tall columnar cells displaying apical microvilli, numerous blebs that seem to represent an expansion of apical plasma membrane, and lateral interdigitations. The nephron tubule consists of two distinctly different areas: a proximal region of flattened cells with extensive intercellular fusions, and a distal segment of separate, dome-shaped cells. Despite many similarities between the crayfish kidney and the vertebrate nephron, there are striking differences. The amount of surface blebbing that occurs in the coelomosac and labyrinth far exceeds that of the vertebrate nephron and may reflect its importance in the function of the crayfish kidney. The cells of the coelomosac are taller than are the vertebrate podocytes and possess less obvious arms and pedicels. In addition, the proximal segment of the nephron tubule is notable for its intercellular fusions, which are not present in the vertebrate nephron. Although the function of the intercellular fusions is unknown, they may play a role in cellular communication or the redistribution of fluids or electrolytes between cells.     

Modeling of Kidney Hemodynamics: Probability-Based Topology of an Arterial Network

Through regulation of the extracellular fluid volume, the kidneys provide important long-term regulation of blood pressure. At the level of the individual functional unit (the nephron), pressure and flow control involves two different mechanisms that both produce oscillations. The nephrons are arranged in a complex branching structure that delivers blood to each nephron and, at the same time, provides a basis for an interaction between adjacent nephrons. The functional consequences of this interaction are not understood, and at present it is not possible to address this question experimentally. We provide experimental data and a new modeling approach to clarify this problem. To resolve details of microvascular structure, we collected 3D data from more than 150 afferent arterioles in an optically cleared rat kidney. Using these results together with published micro-computed tomography (μCT) data we develop an algorithm for generating the renal arterial network. We then introduce a mathematical model describing blood flow dynamics and nephron to nephron interaction in the network. The model includes an implementation of electrical signal propagation along a vascular wall. Simulation results show that the renal arterial architecture plays an important role in maintaining adequate pressure levels and the self-sustained dynamics of nephrons.     

Nephrotoxic action of platinum, chromium and cadmium compounds on marine bony fishes

Intra-abdominal injections of platinum, chromium and cadmium salts to Myoxocephalus scorpius produce nephrotoxic effect which includes the disturbances in magnesium secretion. Basic ultrastructural changes in the nephron cells of the fish after the injection of nephrotoxic substances are similar to those in mammals. Cis-platinum induces significant damage in the terminal part of the proximal tubules. One day after the injection of chromium compounds, total damage of the proximal tubule is observed, whereas cadmium salt affects cells within the whole nephron. After 5 days of administration of cadmium and chromium salts, partial recovery was found with respect to both functional and ultrastructural properties of nephron cells. Administration of nephrotoxic substances which selectively injure different parts of the nephron enabled to perform more exact differentiation of the nephron elements in marine teleosts.     

A mathematical model for the transport of PAH analogues in the kidney

A single nephron model for the transport of p-aminohippurate (PAH) and its analogues through the kidney is investigated. One of the new features of the model is that it incorporates the epithelial cells surrounding the proximal tubules. These cells are the main anatomical sites of transport of PAH. The kinetics of PAH transport is described by a set of linear conservation equations. A stable numerical scheme which is backward Euler's in both space and time coordinates is used to analyze the mathematical problem. Our results are compatible with those of previously published models. An advantage of the present model is that we could study renal isotope images in terms of transport coefficients, flow rates, etc., of the isotope in the kidney and thus could evaluate the renal function in a more meaningful manner.     

二阶脉冲微分方程边值问题解的存在性

利用Leray-Schauder不动点理论研究了一类二阶脉冲微分方程三点边值问题,将以往所研究的方程的边界条件和脉冲项做了推广,得到了其解的存在性的新结果,最后通过实例说明了结论的应用.     

Neonatal rabbit kidney cortex in culture as tool for the study of collecting duct formation and nephron differentiation

By stripping off the capsula fibrosa of neonatal rabbit kidneys a consistently thin tissue layer consisting of collecting duct anlagen, S-shaped bodies and nephrogenic blastema is obtained. This thin layer seems to be an excellent object for investigation of epithelium formation and nephron differentiation. Three different tissue culture protocols are described: 1. A polarly differentiated collecting duct epithelium with 'tight' characteristics consisting only of principal cells, grown on specific renal support 2. A morphologically dedifferentiated collecting duct principal cell monolayer grown on the unspecific bottom of a plastic culture dish 3. An embryonic tissue layer with numerous S-shaped bodies which might be a suitable model for investigation of the development of maturing nephron structures in serum-free culture medium.     

生物数学中的反应扩散系统奇摄动问题

研究了一类具有非线性捕食-被捕食反应扩散系统奇摄动问题,利用微分不等式理论,讨论了问题解的渐近性态。     

具势能衰减的非线性拟抛物方程整体解的不存在性

利用Laplace算子的特征函数法研究了一类具势能衰减的非线性拟抛物方程的初边值问题整体解的不存在性与有限时间爆破．     

A direct substitution, equation error technique for solving the thermographic tomography problem

A new technique for solving the combined state and parameter estimation problem in thermographic tomography is presented. The technique involves the direct substitution of known skin temperatures into the finite difference form of the bio-heat transfer equation as formulated for solving an initial value problem with a convection boundary condition at the skin surface. These equations are then used to solve the inverse bio-heat transfer problem for the unknown subcutaneous tissue temperatures and physiological parameters. For a small number of nodal points, closed form algebraic solutions are obtained. For larger sets of equations, a hybrid technique is used in which the problem is initially posed as an unconstrained optimization problem in which the model equation error is minimized using the conjugate gradient descent technique to get close to a solution. Then a generalized Newton-Raphson technique was used to solve the equations. A numerical simulation of a one-dimensional problem is investigated both with and without noise superimposed on the input (transient) skin temperature data. The results show that the technique gives very accurate results if the skin temperature data contains little noise. It is also shown that if the physical properties of the tissue and the metabolism are known, that a given set of proper transient skin temperature inputs yields a unique solution for the unknown internal temperatures and blood perfusion rates. However, the similar problem with known blood perfusion rates and unknown metabolisms does not yield a unique solution for the internal temperatures and metabolisms.     

Fluid-dynamical study of protoplasmic streaming in a plant cell

A mathematical model of protoplasmic streaming in a plant cell such as Nitella and Chara is studied. General rheological equations for the non-Newtonian fluid is derived theoretically, and the boundary value problem for the model is solved. The pattern of motion of cytoplasm in a living cell is obtained, and the rheological property of protoplasm is evaluated in vivo.     

Numerical simulation of peristaltic flow of a biorheological fluid with shear-dependent viscosity in a curved channel

Peristaltic motion of a non-Newtonian Carreau fluid is analyzed in a curved channel under the long wavelength and low Reynolds number assumptions, as a simulation of digestive transport. The flow regime is shown to be governed by a dimensionless fourth-order, nonlinear, ordinary differential equation subject to no-slip wall boundary conditions. A well-tested finite difference method based on an iterative scheme is employed for the solution of the boundary value problem. The important phenomena of pumping and trapping associated with the peristaltic motion are investigated for various values of rheological parameters of Carreau fluid and curvature of the channel. An increase in Weissenberg number is found to generate a small eddy in the vicinity of the lower wall of the channel, which is enhanced with further increase in Weissenberg number. For shear-thinning bio-fluids (power-law rheological index, n < 1) greater Weissenberg number displaces the maximum velocity toward the upper wall. For shear-thickening bio-fluids, the velocity amplitude is enhanced markedly with increasing Weissenberg number.