Computer simulation of arterial flow with applications to arterial and aortic stenoses

A computer model for simulating pressure and flow propagation in the human arterial system is developed. The model is based on the one-dimensional flow equations and includes nonlinearities arising from geometry and material properties. Fifty-five arterial segments, representing the various major arteries, are combined to form the model of the arterial system. Particular attention is paid to the development of peripheral pressure and flow pulses under normal flow conditions and under conditions of arterial and aortic stenoses. Results show that the presence of severe arterial stenoses significantly affects the nature of the distal pressure and flow pulses. Aortic stenoses also have a profound effect on central and peripheral pressure pulse formation. Comparison with the published experimental data suggests that the model is capable of simulating arterial flow under normal flow conditions as well as conditions of stenotic obstructions in a satisfactory manner.     

Coronary venous pressure and flow: effects of vagal stimulation, aortic occlusion, and vasodilators

Coronary venous pressure and coronary sinus flow in the canine heart were compared with intramyocardial, intraventricular, aortic, and coronary artery pressures. Stimulation of the thoracic vagus augmented coronary venous pressure, mean venous flow per systole, and coronary venous systolic resistance, but decreased the mean venous flow. Partial occlusion of the aorta augmented coronary venous pressure and coronary venous flow, while systolic coronary venous resistance remained unchanged. Adenosine increased peripheral and central coronary venous pressure and venous flow; it reduced peripheral coronary artery pressure. Adenosine augmented flow per systole and reduced venous resistance more than the other interventions. Dipyridamole decreased left ventricular, aortic, and central coronary artery systolic pressures and systolic venous resistance. It increased the venous flow, mean flow per systole, and coronary venous pressure, even though intramyocardial pressure remained unchanged. Nitroglycerine elevated coronary venous pressure and flow, as well as venous flow per systole, even though it decreased left ventricular, aortic, and central coronary artery pressures. Nitroglycerine significantly decreased coronary venous resistance. It is concluded that coronary venous resistance may be an important resistive component to consider when the total coronary circulation is studied.     

Wave propagation in a model of the arterial circulation

The propagation of the arterial pulse wave in the large systemic arteries has been calculated using a linearised method of characteristics analysis to follow the waves generated by the heart. The model includes anatomical and physiological data for the 55 largest arteries adjusted so that the bifurcating tree of arteries is well matched for forward travelling waves. The peripheral arteries in the model are terminated by resistance elements which are adjusted to produce a physiologically reasonable distribution of mean blood flow. In the model, the pressure and velocity wave generated by the contraction of the left ventricle propagates to the periphery where it is reflected. These reflected waves are re-reflected by each of the bifurcations that they encounter and a very complex pattern of waves is generated. The results of the calculations exhibit many of the features of the systemic arteries, including the increase of the pulse pressure with distance away from the heart as well as the initial decrease and then the large increase in the magnitude of back flow during late systole going from the ascending aorta to the abdominal aorta to the arteries of the leg. The model is then used to study the effects of the reflection or absorption of waves by the heart and the mechanisms leading to the incisura are investigated. Calculations are carried out with the total occlusion of different arterial segments in order to model experiments in which the effects of the occlusion of different arteries on pressure and flow in the ascending aorta were measured. Finally, the effects of changes in peripheral resistance on pressure and velocity waveforms are also studied. We conclude from these calculations that the complex pattern of wave propagation in the large arteries may be the most important determinant of arterial haemodynamics.     

Hemodynamic changes in immobilization stress

In chronic experiments on 75 Wistar, August and randombred rats hemodynamic changes were examined during 30-hour immobilization stress. The ECG was recorded and arterial blood pressure measured. The basic hemodynamic characteristics were determined with the help of the previously implanted ultrasonic blood flow probes. Analysis of hemodynamic changes in animals resistant, adapted and prone to stress demonstrated that changes in the total peripheral resistance play the leading role in the disturbance of the arterial blood pressure control. It was established that a progressive lowering of arterial blood pressure resulting from the abruptly reduced total peripheral resistance is the main and the most frequent cause of death of animals exposed to immobilization stress. At the same time the cardiac hemodynamic component may play an essential role in the mechanism of death. This component may include either progressive bradycardia or a combination of an ischemic myocardial damage and reduced total peripheral resistance.     

Haemodynamic Effects of Salbutamol in Patients Needing Circulatory Support after Open-heart Surgery

The effects of substituting an infusion of salbutamol for isoprenaline were studied in 12 patients needing circulatory support after valve replacement surgery. The cardiac output rose while the heart rate remained unaltered. There was a reduction in systemic vascular resistance, and though the oxygen uptake tended to rise the increase in cardiac output was proportionately greater so that the arteriovenous oxygen difference fell.It is suggested that the drug is of value for two reasons. It causes a selective reduction in peripheral arteriolar resistance, which avoids peripheral pooling, but permits limited myocardial work to be used to generate flow rather than pressure, and the increase in cardiac output is not accompanied by a corresponding rise in oxygen uptake.     

An analysis of aortic pressure curves taking into account visco-elastic properties of the aorta and variations in peripheral resistance

The aortic pressure curve necessarily reveals the mechanical properties of the aorta and peripheral resistance as well as of the dynamics of blood flow. The present study uses a reasonable model of visco-elastic properties of the aorta, a reasonable form for variations in peripheral resistance and blood flow to predict an aortic pressure tracing. Numerical values of constants measured experimentally were available in the published literature. These were used in the nonlinear differential equations of motion of the system under analysis. The equations yielded to piece-wise solution, giving the aortic circumference and the aortic pressure as functions of time. The form of both curves resembles clinical tracings, but numerical values of circumference were higher and of pressure lower thanin vivo. The discrepancies between predicted and clinical curves may reveal certain inadequacies in published measurements on visco-elastic constants. These measurements have been made on longitudinal rather than circumferential strips often containing dead rather than living muscle. The discrepancies, therefore, indicate specific gaps in our knowledge of aortic behaviorin vitro. The suggested model of the system aided in the design of experiments which could supply data necessary to substantiate or to revise the model.     

Pulsatile flow and mass transport over an array of cylinders: gas transfer in a cardiac-driven artificial lung

The pulsatile flow and gas transport of a Newtonian passive fluid across an array of cylindrical microfibers are numerically investigated. It is related to an implantable, artificial lung where the blood flow is driven by the right heart. The fibers are modeled as either squared or staggered arrays. The pulsatile flow inputs considered in this study are a steady flow with a sinusoidal perturbation and a cardiac flow. The aims of this study are twofold: identifying favorable array geometry/spacing and system conditions that enhance gas transport; and providing pressure drop data that indicate the degree of flow resistance or the demand on the right heart in driving the flow through the fiber bundle. The results show that pulsatile flow improves the gas transfer to the fluid compared to steady flow. The degree of enhancement is found to be significant when the oscillation frequency is large, when the void fraction of the fiber bundle is decreased, and when the Reynolds number is increased; the use of a cardiac flow input can also improve gas transfer. In terms of array geometry, the staggered array gives both a better gas transfer per fiber (for relatively large void fraction) and a smaller pressure drop (for all cases). For most cases shown, an increase in gas transfer is accompanied by a higher pressure drop required to power the flow through the device.     

Foetal circulatory responses to arrest of uterine blood flow in sheep: effects of chemical sympathectomy.

Acute foetal asphyxia, caused by arrest of uterine blood flow, increases both sympathetic activity and peripheral vascular resistance and decreases blood flow to peripheral organs (Jensen et al., J. Dev. Physiol., 9, 543-559). The rapidity and uniformity of this peripheral vasoconstriction suggest that the sympatho-neuronal system may reflexly cause these initial blood flow changes during acute asphyxia. To test this hypothesis, we studied 5 intact and 6 chemically sympathectomized (6-hydroxy-dopamine, 46.1 +/- 6 mg/kg foetal weight) chronically prepared normoxaemic foetal sheep in utero at 0.9 of gestation. Organ blood flows (microsphere method), plasma concentrations of catecholamines, vasopressin, and angiotensin II, acid-base balance and blood gases were measured before, during and after arrest of uterine blood flow for 2 min, i.e., at 0, 1, 2, 3, 4 & 30 min. In intact foetuses there was a progressive increase in arterial blood pressure and a rapid circulatory centralization in favour of the brain stem and heart and at the expense of most of the peripheral organs. The changes in peripheral blood flow during and after asphyxia were well reflected by those in the skin and scalp. In chemically sympathectomized foetuses, arterial blood pressure fell transiently at 1 min of asphyxia and cardiac output was redistributed towards the carcass and intestinal organs at the expense of the heart, spinal medulla, and placenta. We conclude that in foetal sheep at 0.9 of gestation, the short-term adaptation to arrest of uterine blood flow is a rapid and profound peripheral vasoconstriction to effect an increase in arterial blood pressure. This initial response during circulatory centralization, which is necessary to increase or maintain blood flow to the heart, brain stem, and placenta, is blunted by sympathectomy. Thus, the foetal sympatho-neuronal system is important for short-term adaptation to and intact survival of asphyxia.     

Does gravitational pressure of blood hinder flow to the brain of the giraffe?

Vascular pressure consists of the sum of two pressures: (a) pressure developed by the pumping of the ventricles against the resistance of vessels, designated as viscous flow pressure, and (b) pressure caused by gravity, traditionally called hydrostatic, better described as gravitational pressure. In a conduit, both of these pressures must be overcome when a liquid is discharged to a higher level of gravitational potential energy. If a liquid is returned to its original level, gravity neither helps nor hinders flow because of the siphon effect. This circumstance prevails in the circulatory system. Hence, P1-P2 in the Poiseuille equation excludes gravitational pressure between those points. The long neck of the giraffe, therefore, poses no impediment to blood flow in the erect posture. The giraffe has a high aortic pressure. This is not for driving the blood to its head but is for minimizing the gravitational drop of intravascular pressure and collapse of the vessels. The cerebral circulation is protected by the cerebrospinal fluid which undergoes parallel changes in pressure with posture. Other vessels in the head are less protected by connective tissue, surrounding muscles and other structures. The high aortic pressure in the giraffe is probably caused by the high total peripheral resistance of the systemic circuit due to vascular adaptations related to the overall height of the animal.     

Network thermodynamic analysis of vasomotion in a microvascular network.

The modulation of microvascular blood flow by vasomotion in the individual vessels of a simple vascular network was simulated by means of a network thermodynamic model. The flow is driven under a pulsating pressure through two arcades of branching vasoactive arterioles into a passive resistance representing the capillary and venular beds. Each vessel was assumed to have the capability of decreasing rhythmically the local diameter over a short section by a specified fraction of the maximum value and to change the average diameter along its total length in response to alterations in intraluminal pressure. Blood was assumed to exhibit a simple linear viscous flow resistance. Alterations in flow rate and distribution through the network were determined as a function of the magnitude and frequency of vasomotion within the individual arterioles supplying blood to the microvascular bed. Specific cases are shown to illustrate how blood flow can be influenced by the patterns of vasomotion within the network.     

Central nervous effects of CRF and angiotensin II on cardiac output in conscious rats

Studies were performed to determine whether the central nervous system actions of corticotropin-releasing factor (CRF) and angiotensin II (ANG II) on systemic arterial pressure are mediated, in part, through changes in cardiac output (CO). Changes in CO after intracerebroventricular administration of ANG II and CRF were assessed in conscious unrestrained rats bearing pulsed Doppler flow probes on the ascending aorta. Intracerebroventricular injection of CRF (0.15 nmol) increased arterial pressure (15-20 mmHg), heart rate (70-100 beats/min), and CO (25-35%) without significantly affecting total peripheral resistance. Intracerebroventricular injection of ANG II (0.1 nmol) produced similar elevations of arterial pressure (15-20 mmHg). However, the ANG II-induced pressor response was attended by significant decreases in heart rate (20 beats/min) and CO (10-15%) and significant increases in total peripheral resistance (30-40%). The results of these studies demonstrate that CO, as assessed by pulsed Doppler flow probe methodology, may be influenced significantly and differentially by central nervous system administration of CRF and ANG II.     

Nonlinear interactions in renal blood flow regulation

We have developed a model of tubuloglomerular feedback (TGF) and the myogenic mechanism in afferent arterioles to understand how the two mechanisms are coupled. This paper presents the model. The tubular model predicts pressure, flow, and NaCl concentration as functions of time and tubular length in a compliant tubule that reabsorbs NaCl and water; boundary conditions are glomerular filtration rate (GFR), a nonlinear outflow resistance, and initial NaCl concentration. The glomerular model calculates GFR from a change in protein concentration using estimates of capillary hydrostatic pressure, tubular hydrostatic pressure, and plasma flow rate. The arteriolar model predicts fraction of open K channels, intracellular Ca concentration (Ca(i)), potential difference, rate of actin-myosin cross bridge formation, force of contraction, and length of elastic elements, and was solved for two arteriolar segments, identical except for the strength of TGF input, with a third, fixed resistance segment representing prearteriolar vessels. The two arteriolar segments are electrically coupled. The arteriolar, glomerular, and tubular models are linked; TGF modulates arteriolar circumference, which determines vascular resistance and glomerular capillary pressure. The model couples TGF input to voltage-gated Ca channels. It predicts autoregulation of GFR and renal blood flow, matches experimental measures of tubular pressure and macula densa NaCl concentration, and predicts TGF-induced oscillations and a faster smaller vasomotor oscillation. There are nonlinear interactions between TGF and the myogenic mechanism, which include the modulation of the frequency and amplitude of the myogenic oscillation by TGF. The prediction of modulation is confirmed in a companion study (28).     

Improvement of the microcirculation in the acute ischemic rat limb during intravenous infusion of drag-reducing polymers

Drag-reducing polymers (DRPs) are blood-soluble macromolecules that can increase blood flow and reduce vascular resistance. The purpose of the present study is to examine the effects of DRPs on microcirculation in rat hind limb during acute femoral artery occlusion. Two groups of 20 male Wistar rats were subjected to either hemodynamic measurement or contrast enhanced ultrasound (CEU) imaging during peripheral ischemia. Both groups were further subdivided into a DRP-treated group or a saline-treated group. Polyethylene oxide (PEO) was chosen as the test DRP, and rats were injected with either 10 ppm PEO solution or saline through the caudal vein at a constant rate of 5 ml/h for 20 min. Abdominal aortic flow, iliac artery pressure, iliac vein pressure, heart rate, carotid artery pressure and central venous pressure (CVP) were monitored, and vascular resistance was calculated by (iliac artery pressure-iliac vein pressure)/abdominal aortic blood flow. Flow perfusion and capillary volume of skeletal muscle were measured by CEU. During PEO infusion, abdominal aortic blood flow increased (p<0.001) and vascular resistance decreased (p<0.001) compared to rats that received saline during peripheral ischemia. There was no significant change in ischemic skeletal capillary volume (A) with DRP treatment (p>0.05), but red blood cell velocity (β) and capillary blood flow (A×β) increased significantly (p<0.05) during PEO infusion. In addition, A, β and A×β all increased (p<0.05) in the contralateral hind limb muscle. In contrast, PEO had no significant influence on heart rate, mean carotid artery blood pressure or CVP. Intravenous infusion of drag reducing polymers may offer a novel hydrodynamic approach for improving microcirculation during acute peripheral ischemia.     

Site of airway obstruction in pulmonary disease: direct measurement of intrabronchial pressure.

To partition the central and peripheral airway resistance in awake humans, a catheter-tipped micromanometer sensing lateral pressure of the airway was wedged into the right lower lobe of a 3-mm-ID bronchus in 5 normal subjects, 7 patients with chronic bronchitis, 8 patients with emphysema, and 20 patients with bronchial asthma. We simultaneously measured mouth flow, transpulmonary pressure, and intra-airway lateral pressure during quiet tidal breathing. Total pulmonary resistance (RL) was calculated from transpulmonary pressure and mouth flow and central airway resistance (Rc) from intra-airway lateral pressure and mouth flow. Peripheral airway resistance (Rp) was obtained by the subtraction of Rc from RL. The technique permitted identification of the site of airway resistance changes. In normal subjects, RL was 3.2 +/- 0.2 (SE) cmH2O.l-1.s and the ratio of Rp to RL was 0.24 during inspiration. Patients with bronchial asthma without airflow obstruction showed values of Rc and Rp similar to those of normal subjects. Although Rc showed a tendency to increase, only Rp significantly increased in those patients with bronchial asthma with airflow obstruction and patients with chronic bronchitis and emphysema. The ratio of Rp to RL significantly increased in three groups of patients with airflow obstruction (P less than 0.01). These observations suggest that peripheral airways are the predominant site of airflow obstruction, irrespective of the different pathogenesis of chronic airflow obstruction.     

压力室测定根系导水率方法探讨

用压力室连续测定了玉米根系长压和降压过程的导水率,结果表明,降压过程湍 得的根系导水率显著大于用升压过程的,并且前者的相关系数大于后者,这种差异是由于这两个过程中质外体途径细胞壁空间充水量不同造成的,开始升压时,由于细胞壁空间含水量低,质外体途径阻力大,导致非结构阻力;随着压力的升高,细胞壁空间含水量增大,质外体途径导度增大,减小甚至可以消除非结构阻力,降压法可以使根系快速复水,消除传统方法因长时间复水所致根结构的改变。建议用降压法测定根系导水率。     

Analysis by digital simulation of the peripheral and renal resistance in hypovolemic hypotension.

A haemorrhage was simulated and analysis of dynamic behaviour of renal resistance, renal nervous activity and peripheral resistances were processed, with the aim of studying the paradoxical behaviour of renal resistance as opposed to peripheral resistances and the increase of sympathetic activity in hypovolemic shock situations using both non-linear models of the renal blood flow and arterial pressure and body fluids. The following conclusions can be made after comparing the results obtained by simulation with data related to animal experimentation models: the model is useful for its use in the analysis of nervous activity, resistance and renal flow in hypovolemic shock situations in humans and the control structure it puts forward can explain the paradoxical behaviour of renal vascular resistance as opposed to the peripheral resistances and the increase in the renal nervous activity in the aforementioned circumstances.     

Hydrodynamics of arterial branching--the effect of arterial branching on distal blood supply

A study was conducted to investigate the hydrodynamics of branching flow in relation to the blood supply to the basal part of the brain. A series of measurements of the branching loss-coefficients under laminar steady flow were conducted using model branches with various geometries, and the effect of branching on blood supply to distal areas was described using a lumped-parameter model of the vascular structure. It was revealed that in the blood circulation, branching loss is important where a small artery divides off with a large branching angle from a large trunk. It was also indicated that the effect of such branching on the distal blood supply might become more significant when the peripheral resistance is reduced, thereby increasing the blood velocity in the trunk.     

Arterial blood pressure during voluntary diving in the tufted duck,Aythya fuligula

Arterial blood pressure was monitored in voluntarily diving tufted ducks. Mean arterial blood pressure while diving increased during the pre-dive tachycardia, fell to resting levels on submersion, then gradually increased before peaking on surfacing. Estimated total peripheral resistance fell during the pre-dive and post-dive tachycardia, presumably to allow the oxygen stores to be loaded and replenished respectively and/or for carbon dioxide levels to be reduced. Changes in mean arterial blood pressure and total peripheral resistance suggest that peripheral vasoconstriction occurs in some vascular beds during a dive. An increase in arterial blood pressure (and therefore perfusion pressure) may be employed to increase blood flow and oxygen delivery to the active leg muscles.Abbreviations ecg Electrocardiogram, f _H, heart rate - MABP mean arterial blood pressure - P _b blood pressure(s) - TPR total peripheral resistance - V _b cardiac output     

Peristaltic transport of blood: Casson model--II

The problem of peristaltic transport of blood in a uniform and non-uniform tube has been investigated, under zero Reynolds number and long wavelength approximation. Blood is represented by a two-layered fluid model consisting of a central layer of suspension of all erythrocytes, etc., assumed to be a Casson fluid, and a peripheral layer of plasma as a Newtonian fluid. A comparison of results with those without peripheral layer shows that the magnitude of the pressure rise, under a given set of conditions is smaller in the case of model with peripheral layer. It is found that, for a given flow rate, the pressure rise decreases as the viscosity of the peripheral layer decreases, and for a given non zero pressure drop, the flow rate increases as the viscosity of the peripheral layer decreases. However, the flow is independent of the presence of the peripheral layer, for zero pressure rise. Further, the pressure rise in the case of non-uniform geometry is found much smaller than the corresponding value in the uniform geometry.     

Hemodynamic analysis of Hyrtl anastomosis in human placenta

The Hyrtl anastomosis is a common connection between the umbilical arteries near the cord insertion in most human placentas. It has been speculated that it equalizes the blood pressure between the territories supplied by the umbilical arteries. However, its functional role in the regulation and distribution of fetal blood flow to the placenta has not yet been explored. A computational model has been developed for quantitative analysis of hemodynamic characteristic of the Hyrtl anastomosis in cases of discordant blood flow in the umbilical arteries. Simulations were performed for cases of either increased placental resistance at the downstream end or reduced arterial blood flow due to some pathologies upstream of one of the arteries. The results indicate that when placental territories of one artery impose increased resistance to fetal blood flow, the Hyrtl anastomosis redistributes the blood flow into the second artery to reduce the large pressure gradients that are developed in the affected artery. When one of the arteries conducts a smaller blood flow into the placenta and a relatively smaller pressure gradient is developed, the Hyrtl anastomosis rebuilds the pressure gradients in the affected artery and redistributes blood flow from the unaffected artery to the affected one to improve placental perfusion. In conclusion, the Hyrtl anastomosis plays the role of either a safety valve or a pressure stabilizer between the umbilical arteries at the placental insertion.