A digital model for the venous junctions

The venous network in the lower limbs is composed of a considerable number of confluent junctions. Each of these singularities introduces some blood flow disturbances. Each physiological junction is unique, in terms of its geometry as well as the blood flow rate. In order to account for this great variability, we developed a numerical model based on the use of the N3S code (a software package for solving Navier-Stokes equations). To test the validity of the model, one of the numerical simulations is compared with the data obtained in the corresponding experimental configuration. The velocity measurements were carried out with an ultrasonic pulsed Doppler velocimeter. We also measured pressure differences using differential sensors. The numerical computations were then used to obtain the values of the flow variables at any point, with various geometrical and flow configurations. As far as the velocity field is concerned, a very marked three-dimensional pattern with swirls was observed. The pressure evolution was also strongly disturbed, with a non-linear decrease. All these data indicate that confluence effects cannot be neglected when evaluating pressure decreases. With a tool of this kind, it is possible to accurately predict the disturbances associated with any geometrical configuration or any flow rate.     

Numerical modeling of arterial pulse wave propagation to characterize aortic hemodynamic: Validation using magnetic resonance data

ObjectivesArterial stiffness, which is caused by aging and other cardiovascular risk factors and primarily affects the aorta, is associated with cardiac and cerebral morbidity and mortality. The objective of our study was to non-invasively estimate local biomechanical and hemodynamic biomarkers related to proximal aortic stiffness, by combining cardiovascular magnetic resonance (CMR) data and numerical simulations.Materials and methodsTo achieve this aim, we used a numerical 1D fluid-structure model to simulate blood flow in the descending aorta, and we combined this model with clinical data (areas and velocities in three levels of the descending aorta, carotid pressures) acquired in two healthy subjects using CMR and applanation tonometry.ResultsFirst, we studied the sensibility of our model on an idealized aorta and showed that our model was able to characterize age-related arterial alterations, when compared to established physiological knowledge. Furthermore, while comparisons of simulations against clinical data revealed low errors (< 20%) in terms of aortic areas and velocities for the two subjects, more important errors were found for pulse pressures (up to 20%). Importantly, errors in terms of velocity and area were lower than their variations occurring with aging.ConclusionsThus, our fast method could enable the non-invasive estimation of aortic functional parameters and a more realistic version of our numerical model could also provide a reliable estimation of central pressure.     

Effects of antihypertensive agents on blood velocity: implications for atherogenesis.

Heart rate and blood velocity are major determinants of flow disturbances at arterial bifurcations. Since endothelial damage due to flow disturbances is thought to be significant in the pathogenesis of atherosclerosis, the effects of drugs on these parameters have to be considered in the selection of medications to prevent atherosclerosis. To determine the effects of antihypertensive drugs on heart rate and blood velocity 15 patients with hypertension were treated with placebo, hydrochlorothiazide, nadolol, propranolol and hydralazine in sequence. The doses given produced significant changes in heart rate and blood pressure, and Doppler ultrasonographic recording of aortic blood velocity showed that there were significant changes in peak blood velocity. Nadolol and propranolol produced significantly lower values of heart rate x blood velocity than placebo, hydralazine and hydrochlorothiazide.     

Estimation of Respiratory Nasal Pressure and Flow Rate Signals Using Different Respiratory Sound Features

BackgroundRespiratory sounds are associated with the flow rate, nasal flow pressure, and physical characteristics of airways. In this study, we aimed to develop the flow rate and nasal flow pressure estimation models for the clinical application, and find out the optimal feature set for estimation to achieve the optimal model performance.MethodsRespiratory sounds and flow rate were acquired from nine healthy volunteers. Respiratory sounds and nasal flow pressure were acquired from twenty-three healthy volunteers. Four types of respiratory sound features were extracted for flow rate and nasal flow pressure estimation using different estimation models. Effects of estimations using these features were evaluated using Bland-Altman analysis, estimation error, and respiratory sound feature calculation time. Besides, expiratory and inspiratory phases divided estimation errors were compared with united estimation errors.ResultsThe personalized logarithm model was selected as the optimal flow rate estimation model. Respiratory nasal flow pressure estimation based on this model was also performed. For the four different respiratory sound features, there is no statistically significant difference in flow rate and pressure estimation errors. LogEnvelope was, therefore, chosen as the optimal feature because of the lowest computational cost. In addition, for any type of respiratory sound feature, no statistically significant difference was observed between divided and united estimation errors (flow rate and pressure).ConclusionRespiratory flow rate and nasal flow pressure can be estimated accurately using respiratory sound features. Expiratory and inspiratory phases united estimation using respiratory sounds is a more reasonable estimation method than divided estimation. LogEnvelope can be used for this united respiratory flow rate and nasal flow pressure estimation with minimum computational cost and acceptable estimation error.     

A two-dimensional numerical analysis of unsteady flow in the carotid artery bifurcation. A comparison with three-dimensional in-vitro measurements and the influence of minor stenoses

In the present study a two-dimensional finite element model for incompressible Newtonian flow is applicated to the modelling of carotid artery flow. In earlier studies, the numerical model was validated experimentally for several flow configurations. In general the pulsatile flow is characterized by reversed flow regions at the non-divider side walls of both the internal and external carotid arteries. The unsteadiness of the flow is associated with rather complex spatial and temporal velocity distributions and leads to temporal variations of the location and length of the reversed flow regions. As a consequence, pronounced spatial and temporal variations in the wall shear stresses are found. At the non-divider side walls, wall shear stresses are relatively low and exhibits an oscillatory behaviour in space and time. At the divider side walls, wall shear stresses are relatively high and approximately follow the flow rate distribution in time. The aim of this study is not only to present two-dimensional calculations but also to compare the calculated two-dimensional velocity profiles with those from three-dimensional experiments. It is observed that in the common carotid artery and in the proximal parts of the internal and external carotid arteries, the two-dimensional numerical model provides valuable information with respect to the three-dimensional configuration. In the more distal parts of especially the internal carotid artery, deviations are found between the two-dimensional numerical and three-dimensional experimental model. These deviations can mainly be attributed to the neglect of the secondary velocity distribution in the two-dimensional model. In the two-dimensional numerical model the influence of a minor stenosis in the internal carotid artery is hardly distinguishable from a minor geometrical variation without stenosis. Full three-dimensional analyses of the influence of minor stenoses are needed to prove numerically whether in-vivo measurements of the axial velocity distribution are useful in the detection of minor stenoses.     

富氢盐水对高压电烧伤大鼠微循环内红细胞流速及组织病理损伤的影响

目的:探讨富氢盐水对高压电烧伤大鼠微循环内红细胞流速及组织病理损伤的影响。方法:80只大鼠随机分为四组,分别为烧伤组、治疗组、对照组和阳性对照组,治疗组烧伤后给予富氢盐水治疗,阳性对照组给予罂粟碱溶液治疗。每组分成三个亚组用于血气分析,肺组织形态学观察和红细胞流动速度检测。结果:治疗组和阳性对照组大鼠肺组织湿干重比均显著低于烧伤组(P0.05),治疗组和阳性对照组大鼠肺组织湿干重比差异不显著(t=0.585,P0.05)。治疗组和阳性对照组大鼠生存时间均显著高于烧伤组(P0.05),治疗组和阳性对照组大鼠生存时间差异不显著(t=0.448,P0.05)。治疗组和阳性对照组氧分压均显著高于烧伤组(P0.05);治疗组和阳性对照组氧分压差异不显著(t=0.424,P0.05)。治疗组和阳性对照组二氧化碳分压均显著低于烧伤组(P0.05);治疗组和阳性对照组二氧化碳分压差异不显著(t=1.285,P0.05)。治疗组和阳性对照组大鼠红细胞流动速度分压均显著高于烧伤组(P0.05);治疗组和阳性对照组之间大鼠红细胞流动速度差异不显著(P0.05)。结论:富氢盐水能够促进烧伤大鼠微循环内红细胞的流动,改善微循环,恢复受损肺组织,在高压电烧伤患者的治疗方面具有较好的应用前景。     

On the choice of outlet boundary conditions for patient-specific analysis of aortic flow using computational fluid dynamics

Boundary conditions (BCs) are an essential part in computational fluid dynamics (CFD) simulations of blood flow in large arteries. Although several studies have investigated the influence of BCs on predicted flow patterns and hemodynamic wall parameters in various arterial models, there is a lack of comprehensive assessment of outlet BCs for patient-specific analysis of aortic flow. In this study, five different sets of outlet BCs were tested and compared using a subject-specific model of a normal aorta. Phase-contrast magnetic resonance imaging (PC-MRI) was performed on the same subject and velocity profiles extracted from the in vivo measurements were used as the inlet boundary condition. Computational results obtained with different outlet BCs were assessed in terms of their agreement with the PC-MRI velocity data and key hemodynamic parameters, such as pressure and flow waveforms and wall shear stress related indices. Our results showed that the best overall performance was achieved by using a well-tuned three-element Windkessel model at all model outlets, which not only gave a good agreement with in vivo flow data, but also produced physiological pressure waveforms and values. On the other hand, opening outlet BCs with zero pressure at multiple outlets failed to reproduce any physiologically relevant flow and pressure features.     

Three-Dimensional Computational Modeling of an Extra-Descending Aortic Assist Device Using Fluid-Structure Interaction

BackgroundThe incidence of heart failure is anticipated to rise by 2030, resulting in more than 8 million adults with this condition in US. Despite the advancement in pharmacological and surgical treatments, some patients progress to severe forms of cardiac dysfunction requiring cardiac transplantation as a last-resort treatment. Cardiac assist devices play an essential role in the recovery of normal cardiac performance through reversible remodeling or in assisting the weak organ to prolong survival rate. However, these devices need to be monitored carefully, as prolonged use may lead to physiological maladaptation and further cardiac complications. The optimization of such devices has done through the development and use of numerical simulations that allow the analysis of in-vivo hemodynamic patterns of blood flow. This study aims to investigate the performance of a model of extra-aortic assist device surrounding the descending aorta through three-dimensional patient-specific modeling.MethodsA three-dimensional model of the aorta was constructed from patient-specific cardiac CT images of a 60-year-old male diagnosed with left ventricular failure at the Tehran Heart Center (THC). Numerical simulation was conducted for two complete cardiac cycles using fluid-structure interaction (FSI) analysis under the assumption that the balloon and the aortic vessel behave as linear elastic materials, and that blood is a Newtonian and incompressible fluid.ResultsThe numerical simulation demonstrated a high correlation between the FSI analysis and clinical data of the patient-specific anatomical and physiological conditions. Blood velocity, pressure, deformation, and strain contours were simulated and analyzed through three-dimensional modeling. Compared to the unassisted aorta, the device provided an increase in blood flow displacement of an additional 15 ml of blood in the descending aorta, brachiocephalic, carotid, and subclavian arteries. The maximum von Mises stress distribution across the aortic vessel was higher than the stress imposed on the system in the unassisted heart, with values of 3.3 MPa and 0.28 MPa, respectively. Numerical investigation of structural responses revealed that no remarkable force was exerted on the aortic valve by the device at the descending aorta.ConclusionWe present the numerical investigation of a counterpulsation device around the descending aorta that has not previously been tested on human or animal models. While this extra-aortic balloon pump (EABP) did not show a significant improvement in coronary perfusion, there is room for improvement in further studies to optimize the geometry of the balloon. Additional investigations are required to determine the efficacy of this device and its safety before in-vivo experimental studies are pursued. This simulation has clinical relevance when choosing an appropriate cardiac assist device to address patient-specific physiological and pathological conditions.     

The use of smoothed particles approach in realistic mathematical model of intracardiac blood flow: Simulation of a self-organizing tornado-like flow

We performed computer simulation and visualization of blood flow in the left ventricle by the method of smooth particle hydrodynamics (SPH). This visualization qualitatively describes the evolution of twisted stream and graphically demonstrates the direction of velocity field at each moment of time. The geometrical features of the left ventricle are approximated by three-dimensional segmentation of experimental clinical images obtained from multispiral computer tomography (MSCT). The model adequately describes the possible configuration of swirling flow in the left ventricle and is a part of a comprehensive study of swirling flows in different compartments of heart, which comply with a family of the exact solutions of hydrodynamic Navier–Stokes equations for the class of quasipotential¹ swirling flows. Computer visualization shows how simulated by SPH method jet of a model liquid, which is placed in limited space, remains continuity and keeps its clockwise vorticity along the direction of the flow propagation during the whole cycle. Then it turns on approximately 120° by the time of ejection into the aorta. Such structure of the flow provides more effective pumping of blood as a model liquid through the ventricle as compared to a lamellar flow mode.     

A multiscale approach for modelling wave propagation in an arterial segment

A mathematical model of blood flow through an arterial vessel is presented and the wave propagation in it is studied numerically. Based on the assumption of long wavelength and small amplitude of the pressure waves, a quasi-one-dimensional (1D) differential model is adopted. It describes the non-linear fluid-wall interaction and includes wall deformation in both radial and axial directions. The 1D model is coupled with a six compartment lumped parameter model, which accounts for the global circulatory features and provides boundary conditions. The differential equations are first linearized to investigate the nature of the propagation phenomena. The full non-linear equations are then approximated with a numerical finite difference method on a staggered grid. Some numerical simulations show the characteristics of the wave propagation. The dependence of the flow, of the wall deformation and of the wave velocity on the elasticity parameter has been highlighted. The importance of the axial deformation is evidenced by its variation in correspondence of the pressure peaks. The wave disturbances consequent to a local stiffening of the vessel and to a compliance jump due to prosthetic implantations are finally studied.     

A One-dimensional Finite Element Method for Simulation-based Medical Planning for Cardiovascular Disease

We have previously described a new approach to planning treatments for cardiovascular disease, Simulation-Based Medical Planning, whereby a physician utilizes computational tools to construct and evaluate a combined anatomic/physiologic model to predict the outcome of alternative treatment plans for an individual patient. Current systems for Simulation-Based Medical Planning utilize finite element methods to solve the time-dependent, three-dimensional equations governing blood flow and provide detailed data on blood flow distribution, pressure gradients and locations of flow recirculation, low wall shear stress and high particle residence. However, these methods are computationally expensive and often require hours of time on parallel computers. This level of computation is necessary for obtaining detailed information about blood flow, but likely is unnecessary for obtaining information about mean flow rates and pressure losses. We describe, herein, a space-time finite element method for solving the one-dimensional equations of blood flow. This method is applied to compute flow rate and pressure in a single segment model, a bifurcation, an idealized model of the abdominal aorta, in three alternate treatment plans for a case of aorto-iliac occlusive disease and in a vascular bypass graft. All of these solutions were obtained in less than 5 min of computation time on a personal computer.     

An introduction to biofluid mechanics--basic models and applications

Cardiovascular disease is the primary cause of morbidity and mortality in the western world. Complex hemodynamics play a critical role in the development of atherosclerosis and the processes of aging, as well as many other disease processes. Biofluid mechanics play a major role in the cardiovascular system and it is important to understand the forces and movement of blood cells and whole blood as well as the interaction between blood cells and the vessel wall. Fundamental fluid mechanical, which are important for the understanding of the blood flow in the cardiovascular circulatory system of the human body aspects are presented. Measurement techniques for model studies such as LDA, ultrasound, and MRI studies will be discussed. Viscosity and flow behavior changes specifically the creation of vortices and flow disturbances can be used to show how medication can influence flow behavior. Experiments have shown that hemodynamics may have a strong influence on the creation of aneurysms and varicose veins. Other factors such as vessel wall structure are also important. In preliminary studies, it has been demonstrated that geometry and elasticity of vessel walls help determine flow behavior. High velocity fluctuations indicate flow disturbances that should be avoided. Health care practitioners must understand fluid dynamic factors such as flow rate ratio, pressure and velocity gradients, and flow behavior, velocity distribution, shear stress on the wall and on blood cells. These mechanical factors are largely responsible for the deposit of blood cells and lipids, a leading cause of atherosclerosis. The interaction between blood cells and of the cells with the vessel, leads to the formation of plaques and agglomerations. These deposits are found predominantly at arterial bends and bifurcations where blood flow is disturbed, where a secondary flow is created, and where flow separation regions are found. Experiments on hemodynamic effects in elastic silicon rubber models of the cardiovascular system with flow wire, stents, or patches for vessel surgery will be discussed. These studies can be important in improving diagnostics and therapeutic applications.     

Validation of a fluid–structure interaction numerical model for predicting flow transients in arteries

Fluid–structure interaction (FSI) numerical models are now widely used in predicting blood flow transients. This is because of the importance of the interaction between the flowing blood and the deforming arterial wall to blood flow behaviour. Unfortunately, most of these FSI models lack rigorous validation and, thus, cannot guarantee the accuracy of their predictions. This paper presents the comprehensive validation of a two-way coupled FSI numerical model, developed to predict flow transients in compliant conduits such as arteries. The model is validated using analytical solutions and experiments conducted on polyurethane mock artery. Flow parameters such as pressure and axial stress (and precursor) wave speeds, wall deformations and oscillating frequency, fluid velocity and Poisson coupling effects, were used as the basis of this validation. Results show very good comparison between numerical predictions, analytical solutions and experimental data. The agreement between the three approaches is generally over 95%. The model also shows accurate prediction of Poisson coupling effects in unsteady flows through flexible pipes, which up to this stage have only being predicted analytically. Therefore, this numerical model can accurately predict flow transients in compliant vessels such as arteries.     

Numerical simulation of blood flow in the left ventricle and aortic sinus using magnetic resonance imaging and computational fluid dynamics

Understanding cardiac blood flow patterns has many applications in analysing haemodynamics and for the clinical assessment of heart function. In this study, numerical simulations of blood flow in a patient-specific anatomical model of the left ventricle (LV) and the aortic sinus are presented. The realistic 3D geometry of both LV and aortic sinus is extracted from the processing of magnetic resonance imaging (MRI). Furthermore, motion of inner walls of LV and aortic sinus is obtained from cine-MR image analysis and is used as a constraint to a numerical computational fluid dynamics (CFD) model based on the moving boundary approach. Arbitrary Lagrangian–Eulerian finite element method formulation is used for the numerical solution of the transient dynamic equations of the fluid domain. Simulation results include detailed flow characteristics such as velocity, pressure and wall shear stress for the whole domain. The aortic outflow is compared with data obtained by phase-contrast MRI. Good agreement was found between simulation results and these measurements.     

Turbulence in the canine ascending aorta and the blood pressure.

Turbulent velocity fluctuations were measured and analyzed in the canine ascending aorta using a hot-film anemometer. Blood flow rate and temperature were stabilized using a special bypass technique. Blood pressure was elevated by Methoxamine infusion. Turbulence components were extracted from measured data using an ensemble averaging technique. Turbulence intensity correlated best with blood flow rate although the variance was relatively large, especially when the blood flow velocity was high. When pooled data were grouped into subclasses using peak aortic flow velocity as the criteria, turbulence intensity correlated well with aortic systolic blood pressure in each of the subclasses. Spectral bandwidth correlated with aortic pressure in the same manner. In summary, turbulence in the aorta developed when blood pressure was high. Both an increase of turbulence intensity and an widening of turbulence spectra may be ascribed to a stiffening of the aortic wall due to an elevation of blood pressure.     

Linear and nonlinear analyses of pulsatile blood flow in a cylindrical tube

A non-Newtonian shear-thinning constitutive relation is proposed to study pulsatile flow of whole blood in a cylindrical tube. The constitutive relation, which satisfies the principle of material frame indifference, is derived from viscometric data obtained from whole blood over a range of hematocrits. Assuming axisymmetric flow in a rigid cylindrical tube of constant diameter, a second-order, nonlinear partial differential equation governing the axial velocity component is obtained. Imposing a periodic pressure gradient, the governing equation was solved numerically using finite difference methods over a range of Stokes values and hematocrits. For a forcing frequency of 1 Hz, results are presented over tube diameters ranging between 0.1 and 2 cm and over hematocrits ranging between 10 and 80%. For a given hematocrit, velocity profiles predicted for the non-Newtonian model under sinusoidal forcing reveal attenuated volume flow rate and enhanced vorticity transport over the tube cross-section relative to a Newtonian fluid having a viscosity corresponding to the high shear-rate limit. For moderate to high Stokes numbers, consistent with flow in large arteries, our results revealed a viscosity distribution that was nearly time invariant. An analytic solution was obtained for a fluid having arbitrarily prescribed radially varying, temporally invariant viscosity and density distributions under arbitrary periodic pressure forcing. Close agreement was observed between our numerical and analytical results when the imposed viscosity distribution was chosen to approximate the time-averaged viscosity distribution predicted by the shear-thinning non-Newtonian model. For St > or approximately= 100, the disparity between our results and those of a Newtonian fluid of constant viscosity grows with a decreasing ratio of the DC to AC components of the pressure-gradient amplitude below 50%. In particular, for any purely oscillatory pressure-gradient (vanishing DC component), the Womersley solution is a particularly poor predictor of the amplitude and phase of wall shear rate for over half of the flow cycle. Under such circumstances, the analytical models presented here provide a simple and accurate means of estimating instantaneous wall shear rate, knowing only the pressure gradient and hematocrit.     

Predicting permeability of regular tissue engineering scaffolds: scaling analysis of pore architecture,scaffold length,and fluid flow rate effects

The main aim of this research is to numerically obtain the permeability coefficient in the cylindrical scaffolds. For this purpose, a mathematical analysis was performed to derive an equation for desired porosity in terms of morphological parameters. Then, the considered cylindrical geometries were modeled and the permeability coefficient was calculated according to the velocity and pressure drop values based on the Darcy’s law. In order to validate the accuracy of the present numerical solution, the obtained permeability coefficient was compared with the published experimental data. It was observed that this model can predict permeability with the utmost accuracy. Then, the effect of geometrical parameters including porosity, scaffold pore structure, unit cell size, and length of the scaffolds as well as entrance mass flow rate on the permeability of porous structures was studied. Furthermore, a parametric study with scaling laws analysis of sample length and mass flow rate effects on the permeability showed good fit to the obtained data. It can be concluded that the sensitivity of permeability is more noticeable at higher porosities. The present approach can be used to characterize and optimize the scaffold microstructure due to the necessity of cell growth and transferring considerations.     

A model of pulsatile flow in a uniform deformable vessel.

Simulations of blood flow in natural and artificial conduits usually require large computers for numerical solution of the Navier-Stokes equations. Often, physical insight into the fluid dynamics is lost when the solution is purely numerical. An alternative to solving the most general form of the Navier-Stokes equations is described here, wherein a functional form of the solution is assumed in order to simplify the required computations. The assumed forms for the axial pressure gradient and velocity profile are chosen such that conservation of mass is satisfied for fully established pulsatile flow in a straight, deformable vessel. The resulting equations are cast in finite-difference form and solved explicitly. Results for the limiting cases of rigid wall and zero applied pressure are found to be in good agreement with analytical solutions. Comparison with the experimental results of Klanchar et al. [Circ. Res. 66, 1624-1635 (1990]) also shows good agreement. Application of the model to realistic physiological parameter values provides insight as to the influence of the pulsatile nature of the flow field on wall shear development in the presence of a moving wall boundary. Specifically, the model illustrates the dependence of flow rate and shear rate on the amplitude of the vessel wall motion and the phase difference between the applied pressure difference and the oscillations of the vessel radius. The present model can serve as a useful tool for experimentalists interested in quantifying the magnitude and character of velocity profiles and shearing forces in natural and artificial biologic conduits.     

Validation of CFD predictions of flow in a 3D alveolated bend with experimental data

Verifying numerical predictions with experimental data is an important aspect of any modeling studies. In the case of the lung, the absence of direct in vivo flow measurements makes such verification almost impossible. We performed computational fluid dynamics (CFD) simulations in a 3D scaled-up model of an alveolated bend with rigid walls that incorporated essential geometrical characteristics of human alveolar structures and compared numerical predictions with experimental flow measurements made in the same model by particle image velocimetry (PIV). Flow in both models was representative of acinar flow during normal breathing (0.82ml/s). The experimental model was built in silicone and silicone oil was used as the carrier fluid. Flow measurements were obtained by an ensemble averaging procedure. CFD simulation was performed with STAR-CCM+ (CD-Adapco) using a polyhedral unstructured mesh. Velocity profiles in the central duct were parabolic and no bulk convection existed between the central duct and the alveoli. Velocities inside the alveoli were approximately 2 orders of magnitude smaller than the mean velocity in the central duct. CFD data agreed well with those obtained by PIV. In the central duct, data agreed within 1%. The maximum simulated velocity along the centerline of the model was 0.5% larger than measured experimentally. In the alveolar cavities, data agreed within 15% on average. This suggests that CFD techniques can satisfactorily predict acinar-type flow. Such a validation ensure a great degree of confidence in the accuracy of predictions made in more complex models of the alveolar region of the lung using similar CFD techniques.     

Mathematical model of the filtration in the vascular network of the ophidian glomerulus.

The present work is a mathematical model of the fluid filtration in the glomerular network occurring in snakes. The model is based on the differential form of Starling's hypothesis and takes into account the angioarchitecture of the network and the behaviour on the microrheology of blood with nucleated red cells. The model predicts the hemodynamics and the transvascular fluxes in each vascular segment within the network. The model is applied to a vascular network of the glomerulus of the garter snake. A value of 0.593 microns/(s.mmHg) was determined for the hydraulic conductivity of the glomerular capillaries using the geometrical data of the network together with experimental data for the pressures and the blood flow rate reported in the literature. The analysis shows that the local filtration rates cover a wide range. In some of the vascular segments, the filtration leads to such a high increase in colloid-osmotic pressure that the level of the transvascular hydrostatic pressure difference is reached. Mathematical simulations of the variation of the glomerular blood flow rate due to vasoactivity of preglomerular arterioles show the effect on the filtration rate and the hemorheologic parameters.