How small is the functional variability of liver sinusoids?

Published experimental results on steady elimination of galactose by isolated rat livers perfused at different flow rates, predicted earlier from a model of hepatic elimination with functionally identical sinusoids, are assessed in terms of a more general model. An upper limit on the functional variability (heterogeneity) of liver sinusoids is deduced from the experimental results, and conditions for the detection of the actual variability by the same type of experiment are discussed quantitatively.     

On the relation between extended forms of the sinusoidal perfusion and of the convection-dispersion models of hepatic elimination

Two models of hepatic elimination, the distributed sinusoidal perfusion model, and the convection-dispersion model, are extended and then compared for first order kinetics in the steady-state. The sinusoidal perfusion model is extended by the inclusion of intrahepatic sites of mixing between sinusoids. The degree of such mixing is estimated for taurocholate elimination by isolated perfused rat livers by a comparison of anatomical and kinetic estimates of uptake heterogeneity, using previously published data. The dispersion model is generalized by the inclusion of distributions of enzyme activity along the flow. Direct comparison of the two models in the limit in which the degree of dispersion is small, allows the flow-dependence of the dispersion coefficient to be determined, thereby greatly extending the explanatory power of the convection-dispersion model. Finally, the effect of intrahepatic mixing sites on uptake by Michaelis-Menten kinetics is quantified in terms of the distributed sinusoidal perfusion model, with results which may be applicable to capillary beds in general.     

SD大鼠血管内皮细胞的凝集素组织化学研究

为进一步了解大鼠血管内皮细胞表面糖基的分布, 本文应用５ 种生物素化凝集素（ＧＳ－Ｉ、ＲＣＡ－Ｉ、ＷＧＡ、ＣｏｎＡ和ＵＥＡ－Ｉ） 对大鼠心脏、胸主动脉、肝脏和子宫的血管内皮细胞采用ＡＢＣ法标记。结果表明,光镜下, ＧＳ－Ｉ对心脏、胸主动脉、子宫的血管内皮染色阳性; ＲＣＡ－Ｉ对所检组织内血管内皮细胞染色阳性,其中对心脏和肝的血管内皮与血管外组织细胞的染色强度有显著不同; ＣｏｎＡ对肝血窦内皮与对肝细胞的染色强度有明显不同; ＵＥＡ－Ｉ对各脏器血管内皮细胞未见阳性标记。电镜下ＧＳ－Ｉ阳性反应产物位于心肌毛细血管内皮细胞表面。提示, 血管内皮细胞表面存在的某些糖复合物含有Ｄ－半乳糖、Ｎ－乙酰氨基半乳糖、Ｎ－乙酰氨基葡萄糖、Ｄ－甘露糖。ＧＳ－Ｉ可视为心脏、胸主动脉、子宫的血管内皮细胞的特异性标记物。ＲＣＡ－Ｉ既可作为心脏的血管内皮, 亦可作为肝血窦内皮的特异性标记物, ＣｏｎＡ可作为肝血窦内皮的特异性标记物。     

Effects of hepatic blood flow on hepatic ethanol kinetics measured in cats and predicted from the parallel tube model

In cats anesthetized with pentobarbital, a long-circuit technique was used to measure hepatic blood flow while portal flow was varied from 0 to 300% of normal in random steps. Arterial, portal, and hepatic venous blood samples were analyzed for ethanol concentrations during continuous infusion of ethanol (20 mumol/(min.kg body weight) into the reservoir. Measured values for logarithmic mean sinusoidal ethanol concentration, hepatic venous ethanol concentration, hepatic ethanol uptake, and ethanol extraction were compared with the values predicted by the parallel tube model for hepatic uptake of substrates using Vmax and Km determined in each cat at the start of the experiment. Measured and predicted values were very similar at all blood flows above 65% control, but statistical regression analysis indicated a small but highly significant deviation of the measured values from the predicted values. At low flows, measured values of logarithmic mean sinusoidal and hepatic venous concentrations markedly exceeded the predicted values in most cats. The results indicate that the parallel tube model, which assumes all sinusoids are identical and equally perfused, provides a useful approximation for the effects of hepatic blood flow on hepatic ethanol kinetics except at low flows. However, there appears to be a significant degree of sinusoidal heterogeneity that results in a better fit to the distributed model. Our previously reported data for hepatic galactose uptake followed a similar pattern when reanalyzed in this more rigorous way.     

Residence time distribution of diazepam in the isolated perfused rat liver. Analysis with the axial dispersion model.

The application of the axial dispersion model to diazepam hepatic elimination was evaluated using data obtained for impulse-response experiments with diazepam in the single-pass isolated perfused rat liver preparation. The transient form of the two-compartment dispersion model was applied to the output concentration versus time profile of diazepam after bolus input of a radiolabelled tracer into the hepatic portal vein (n = 4), providing DN and CLint estimates of 0.251 +/- 0.093 and 135 +/- 59 ml min-1, respectively. In contrast, the one-compartment form of the axial dispersion model, which assumes instantaneous transversal distribution of substance to the accessible spaces within the liver, could not adequately describe the residence time distribution (RTD) of diazepam. Furthermore, the magnitude of DN, a stochastic parameter which characterizes the axial spreading of solutes during transit through the liver, is similar to that determined for non-eliminated substances such as erythrocytes, albumin, sucrose and water. These findings suggest that the dispersion of diazepam in the perfused rat liver is determined primarily by the architecture of the hepatic microvasculature.     

A lumped parameter mathematical model of the splanchnic circulation.

A lumped parameter mathematical model to describe the propulsion of blood in the splanchnic circulation was developed by integrating the principles of mechanics and physiology. A set of governing equations by derived by specifically considering the contractility of the portal vein, hepatic vein, liver sinusoids, and of the draining lymphatics. These equations were then simulated on a computer. The present simulation results substantiate previous experimental observations that hepatic venous pressure leads to portal hypertension and increased liver interstitial fluid volume.     

Slow nonlinear waves in magnetic flux tubes

A theory of weakly nonlinear slow waves in magnetic flux tubes is developed in the ideal MHD approximation. Fairly simple approximate dispersion relations are derived that are valid for waves of arbitrary wavelength. These dispersion relations make it possible to obtain a number of new model evolutionary equations for body and surface slow waves in magnetic flux tubes. It is established that there are two families of exact analytic solutions to the equations for weakly nonlinear slow waves. It is found that both the body and surface solitary waves can be in the form of either contractions or bulges running along the tube. A model Korteweg-de Vries-Burgers equation is derived and generalized to waves of arbitrary wavelength. It is shown that exact analytic solutions to these equations correspond to shock waves and hydraulic jumps (or bores) with nonoscillating fronts.     

Axial dispersion in respiratory bronchioles and alveolar ducts

The mixing of gases in the pulmonary acinus was characterized by analyzing axial gas dispersion during steady flow in models of respiratory bronchioles and alveolar ducts. An analysis (method of moments) developed for addressing dispersion in porous media was used to derive an integral expression for the axial dispersion coefficient (D*). Evaluation of D* required solving the Navier-Stokes equations for the flow field and a convection-diffusion type equation arising from the analysis. D* was strongly dependent on alveolar volume per central duct volume, the aperture size through which the alveoli communicate with the central duct, and the Péclet number (Pe). At smaller Pe (flow rate) D* was substantially smaller than the molecular diffusion coefficient, whereas at larger Pe (flow rate) D* was much greater than the Taylor-Aris result for flow-enhanced dispersion in straight tubes. Also, flow-enhanced dispersion became appreciable at smaller Pe than indicated by the Taylor-Aris result. These behaviors transcend both the lower and upper limits established previously for gas mixing in the pulmonary acinus.     

Microcirculation in the murine liver: a computational fluid dynamic model based on 3D reconstruction from in vivo microscopy

The liver is organized in hexagonal functional units – termed lobules – characterized by a rather peculiar blood microcirculation, due to the presence of a tangled network of capillaries – termed sinusoids. A better understanding of the hemodynamics that governs liver microcirculation is relevant to clinical and biological studies aimed at improving our management of liver diseases and transplantation.Herein, we built a CFD model of a 3D sinusoidal network, based on in vivo images of a physiological mouse liver obtained with a 2-photon microscope. The CFD model was developed with Fluent 16.0 (ANSYS Inc., Canonsburg, PA), particular care was taken in imposing the correct boundary conditions representing a physiological state. To account for the remaining branches of the sinusoids, a lumped parameter model was used to prescribe the correct pressure at each outlet. The effect of an adhered cell on local hemodynamics is also investigated for different occlusion degrees.The model here proposed accurately reproduces the fluid dynamics in a portion of the sinusoidal network in mouse liver. Mean velocities and mass flow rates are in agreement with literature values from in vivo measurements. Our approach provides details on local phenomena, hardly described by other computational studies, either focused on the macroscopic hepatic vasculature or based on homogeneous porous medium model.     

Three-Dimensional Imaging of Hepatic Sinusoids in Mice Using Synchrotron Radiation Micro-Computed Tomography

Hepatic sinusoid, the smallest vessel in the liver, plays important roles in hepatic microcirculation. Although the structure of the hepatic sinusoids affects diverse functions of the liver, little is known about morphological alterations in the sinusoids under pathological conditions. In this study, we show that the structure of hepatic sinusoids can be identified three-dimensionally in normal and carbon tetrachloride-injured mouse liver, using the absorption mode of synchrotron radiation micro-computed tomography. We observed that the hepatic sinusoidal structure on tomographic slice images was similar to that on histological images of normal and acutely injured mice. Moreover, centrilobular necrosis and structural alterations of the sinusoids in the necrotic region were detectable on tomographic slice and volume-rendered images of the acutely injured mice. Furthermore, quantitative analyses on 3D volume-rendered images of the injured sinusoid revealed decrease in the volume of the sinusoid and connectivity of the sinusoidal network. Our results suggest that the use of synchrotron radiation micro-computed tomography may improve our understanding of the pathogenesis of hepatic diseases by detecting the hepatic sinusoids and their alterations in three-dimensional structures of the damaged liver.     

Biophysical Model of the Spatial Heterogeneity of Myocardial Flow

The blood flow in the myocardium has significant spatial heterogeneity. The objective of this study was to develop a biophysical model based on detailed anatomical data to determine the heterogeneity of regional myocardial flow during diastole. The model predictions were compared with experimental measurements in a diastolic porcine heart in the absence of vessel tone using nonradioactive fluorescent microsphere measurements. The results from the model and experimental measurements showed good agreement. The relative flow dispersion in the arrested, vasodilated heart was found to be 44% and 48% numerically and experimentally, respectively. Furthermore, the flow dispersion was found to have fractal characteristics with fractal dimensions (D) of 1.25 and 1.27 predicted by the model and validated by the experiments, respectively. This validated three-dimensional model of normal diastolic heart will play an important role in elucidating the spatial heterogeneity of coronary blood flow, and serve as a foundation for understanding the interplay between cardiac mechanics and coronary hemodynamics.     

Pressure, flow, and density relationships in airway models during constant-flow ventilation

Adequate CO2 elimination and normal arterial PCO2 levels can be maintained in dogs during apnea by delivering a continuous flow of inspired gas at high flow rate (1-3 l.min-1.kg-1) through tubes placed in the main-stem bronchi. However, during constant-flow ventilation (CFV) the mean alveolar pressure is increased, causing increased lung volume despite low pressures in the trachea. We hypothesized that the increased dynamic alveolar pressures during CFV were due to momentum transfer from the high-velocity jet stream to resident gas in the lung. To test this, we simulated CFV in straight tubes and in a branched airway model to determine whether changes in gas flow rate (V), gas density (rho), and tube diameter (D) altered the pressure difference (delta P) between alveoli and airway opening in a manner consistent with that predicted by conservation of momentum. Momentum analysis predicts that delta P should vary with V2, whereas measurements yielded a dependence of V1.69 in branched tubes and V1.9 in straight tubes. Substitution of heliox (80% He-20% O2) for air significantly reduced lung hyperinflation during CFV. As predicted by momentum transfer, delta P varied with rho 1.0. Momentum analysis also predicts that delta P should vary with D-2.0, whereas measurements indicated a dependence on D-2.02. The influence of V and rho on depth of penetration of the jet down the airway was explored in a straight tube model by varying the flow rate and gas used. The influence of geometry on penetration was measured by changing the ratio of jet-to-airway tube diameters.(ABSTRACT TRUNCATED AT 250 WORDS)     

Vital statistics,absolute abundance and preservation rate of Tyrannosaurus rex

I present a simulation model on vital statistics, absolute abundance (N, total number of individuals that ever lived) and preservation rate (p, minimum number of fossils known divided by N) of Tyrannosaurus rex. It is based on a published age-structured population model that assumes a reptile or bird-like reproduction for T. rex to estimate its age-specific survival rates. My model applies input variables and equations from a recently published model on N and p. This model yielded 2.5 billion T. rex individuals (N) and one fossil per 80 million individuals (p). The average N values calculated by my model were at minimum 27.6% and p values at maximum 361.5% that of a previous model and uncertainties in all output variables were always larger in my model. The equation on output variable ‘population density’ introduced the largest uncertainty to N and p. The output variable ‘generation time’ differed the most between models, but for N and p, the huge size of the input area modelled and geological longevity minimized this difference. Unlike my model, the generation time as well as life expectancies, gross reproduction rates, and reproductive values of individuals calculated from the previous model all strongly contradicted our current understanding of the biology of T. rex and of other theropods. Their values also disagreed with those of large extant reptiles, birds and mammals. All of these shortcomings of the previous model favour the assessment of individual and population characteristics of T. rex and of other extinct species using my model.     

Transit time dispersion in pulmonary and systemic circulation: effects of cardiac output and solute diffusivity

We present an in vivo method for analyzing the distribution kinetics of physiological markers into their respective distribution volumes utilizing information provided by the relative dispersion of transit times. Arterial concentration-time curves of markers of the vascular space [indocyanine green (ICG)], extracellular fluid (inulin), and total body water (antipyrine) measured in awake dogs under control conditions and during phenylephrine or isoproterenol infusion were analyzed by a recirculatory model to estimate the relative dispersions of transit times across the systemic and pulmonary circulation. The transit time dispersion in the systemic circulation was used to calculate the whole body distribution clearance, and an interpretation is given in terms of a lumped organ model of blood-tissue exchange. As predicted by theory, this relative dispersion increased linearly with cardiac output, with a slope that was inversely related to solute diffusivity. The relative dispersion of the flow-limited indicator antipyrine exceeded that of ICG (as a measure of intravascular mixing) only slightly and was consistent with a diffusional equilibration time in the extravascular space of approximately 10 min, except during phenylephrine infusion, which led to an anomalously high relative dispersion. A change in cardiac output did not alter the heterogeneity of capillary transit times of ICG. The results support the view that the relative dispersions of transit times in the systemic and pulmonary circulation estimated from solute disposition data in vivo are useful measures of whole body distribution kinetics of indicators and endogenous substances. This is the first model that explains the effect of flow and capillary permeability on whole body distribution of solutes without assuming well-mixed compartments.     

A model of plasma membrane flow and cytosis regulation in growing pollen tubes

A model of cytosis regulation in growing pollen tubes is developed and simulations presented. The authors address the question on the minimal assumptions needed to describe the pattern of exocytosis and endocytosis reported recently by experimental biologists. Biological implications of the model are also treated. Concepts of flow and conservation of membrane material are used to pose an equation system, which describes the movement of plasma membrane in the tip of growing pollen tubes. After obtaining the central equations, relations describing the rates of endocytosis and exocytosis are proposed. Two cytosis receptors (for exocytosis and endocytosis), which have different recycling rates and activation times, suffice to describe a stable growing tube. Simulations show a very good spatial separation between endocytosis and exocytosis, in which separation is shown to depend strongly on exocytic vesicle delivery. In accordance to measurements, most vesicles in the clear zone are predicted to be endocytic. Membrane flow is essential to maintain cell polarity, and bi-directional flow seems to be a natural consequence of the proposed mechanism. For the first time, a model addressing plasma membrane flow and cytosis regulation were posed. Therefore, it represents a missing piece in an integrative model of pollen tube growth, in which cell wall mechanics, hydrodynamic fluxes and regulation mechanisms are combined.     

Adrenergic mechanisms in the hepatic microcirculation in the rat

The in vivo hepatic microvascular bed of the rat was observed microscopically in the transilluminated liver and the diameter of the hepatic sinusoids was measured by serial photomicrography. Intraportal infusion of tyramine induced concentration-dependent constriction of the hepatic sinusoids, but also dilatation of the sinusoids when the dose was small. These effects were attributed to the release of endogenous noradrenaline which activated either alpha- or beta-adrenergic receptors and caused constriction, or dilatation, of the sinusoids respectively. Adrenaline and noradrenaline induced similar changes in the hepatic sinusoids as tyramine, while phenoxybenzamine induced dilatation, and propranolol constriction, of the sinusoids. All the above responses were abolished by pretreatment with reserpine. A possible noradrenaline-mediated basal vasomotor tone in the hepatic sinusoids for autonomic control of the blood flow in the sinusoids was postulated.     

A minimal model of liver glycogen metabolism; feasibility for predicting flux rates

A minimal model of glycogen metabolism can allow the estimation of the flux rates in the glycogen pathway from the time course of the intermediates in the pathway, measured during substrate administration and hormonal stimulation. The comprehensive model of El-Refai & Bergman (Am. J. Physiol. 231, 1608, 1976) consisting of six compartments and 26 non-estimable parameters has successfully accounted for the responses of hepatic glycogenic intermediates in response to a glucose load in hepatocytes (Katz et al., J. biol. Chem. 253, 4530, 1978), in perfused liver (Nordlie et al., J. biol. Chem. 255, 1834, 1980) and during refeeding in vivo (Van DeWerve & Jeanrenaud, Am. J. Physiol. 247, E271, 1984). The comprehensive model is here reduced to a minimal model, consisting of five compartments representing extracellular and intracellular glucose, glucose-phosphate, uridine diphosphate glucose (UDPG), glycogen, and five parameters estimated from the hepatic response to a given stimulus. Estimation of these parameters requires the measurement of the net hepatic glucose balance, the net gluconeogenic flux, and the time course of glycogenic intermediates responding to a hormone or substrate stimulus. The hepatic glycogenolytic response predicted by the comprehensive model in response to an increase in glucagon is closely fitted by the minimal model. When Gaussian distributed random error was added, 0-5% SD in the glucose and glycogen compartments and 0-10% SD in the glucose-phosphate and UDPG compartments, the hepatic response predicted by the minimal model was virtually free of the added error, and the model parameters were found to be within 30% of their true values. When the minimal model was used to interpret the experimental response to an increase in glucose concentration it predicted that: (1) glucokinase can phosphorylate glucose at rates similar to maximal rates of net glycogen synthesis; (2) futile cycling at the glycogen/glucose-1-phosphate level can limit glycogen synthesis; and (3) glucose-6-phosphatase inhibition by glucose has a significant role in net glycogen synthesis.     

Hepatic elimination of flowing substrates: the distributed model

An earlier model of hepatic elimination with functionally identical sinusoids is extended by introducing statistical distributions of enzyme contents per sinusoid and of blood flow per sinusoid, these being either uncorrelated or closely correlated. The steady-state theory of the resulting distributed model is developed, including methods of determining experimentally the coefficients of variation of the distributions. Such determinations are made on an illustrative experimental example. Quantitative predictions of expected effects of changes in blood flow are given, including one for which the undistributed model predicts a null effect. Shapes of the postulated distributions are discussed only in relation to observable effects. Effects of the distributions are compared with maximum possible effects of incomplete equilibration of substrate within each sinusoidal cross-section, and methods for distinguishing these effects from each other are outlined.