The impedance of curved artery models

The impedance (pressure drop/flow rate) of four curved artery models has been determined experimentally for steady and periodic flows simulating conditions in the aortic arch. Steady flow results indicate that very short entry lengths are required for flow development in curved artery models, and impedance is elevated above straight tube values by a factor of 3-4 for mean flow conditions in the aortic arch. Results for periodic flow with a nonzero mean show a significant elevation of mean flow impedance relative to values for steady flow at the mean flow rate--a factor of 2-3 for aortic arch flow conditions. The impedance of the first harmonic of periodic flows follows straight tube theory at high values of the unsteadiness parameter in agreement with available theory for curved tubes. The implications of the impedance measurements for wall shear stress in the aortic arch are discussed.     

Effects of diagnostic guidewire catheter presence on translesional hemodynamic measurements across significant coronary artery stenoses

This study gains insight on the nature of flow blockage effects of small guidewire catheter sensors in measuring mean trans-stenotic pressure gradients Deltap across significant coronary artery stenoses. Detailed pulsatile hemodynamic computations were made in conjunction with previously reported clinical data in a group of patients with clinically significant coronary lesions before angioplasty. Results of this study ascertain changes in hemodynamic conditions due to the insertion of a guidewire catheter (di=0.46 mm) across the lesions used to directly determine the mean pressure gradient (Deltap) and fall in distal mean coronary pressure (pr). For the 32 patient group of Wilson et al. [1988] (minimal lesion diameter dm=0.95 mm; 90% mean area stenosis; proximal measured coronary flow reserve (CFR) of 2.3 in the abnormal range) the diameter ratio of guidewire catheter to minimal lesion was 0.48, causing a tighter "artifactual" mean area stenosis of 92.1%. The results of the computations indicated a significant shift in the Deltap-Q relation due to guidewire induced increases in flow resistances (R=Deltap/Q) of 110% for hyperemic flow, a 35% blockage in hyperemic flow (Qh) and a phase shift of the coronary flow waveform to systolic predominance. These alterations in flow resulted in a fall in distal mean coronary pressure (at lower mean flow rates) below the patho-physiological range of prh approximately 55 mmHg, which is known to cause ischemia in the subendocardium (Brown et al. [1984]) and coincides with symptomatic angina. Transient wall shear stress levels in the narrow throat region (with flow blockage) were of the order of levels during hyperemic conditions for patho-physiological flow. In the separated flow region along the distal vessel wall, vortical flow cells formed periodically during the systolic phase when instantaneous Reynolds numbers Ree(t) exceeded about 110. For patho-physiological flow without the presence of the guidewire these vortical flow cells were much stronger than in the more viscous flow regime with the guidewire present. The non-dimensional pressure data given in tabular form may be useful in interpretation of guidewire measurements done clinically for lesions of similar geometry and severity.     

The distribution of blood flow to the reproductive organs of rats near term.

The rate of ovarian and utero-placental blood flow through vessels of less than 25 mum diameter was examined with radioactive microspheres in 5 non-pregnant rats and 19 rats at Day 22 of pregnancy. Total blood flow to the reproductive organs was 0-559 ml/min in the non-pregnant animals and 13-2 ml/min in those near term, a 23-fold difference. The mean ovarian blood flow was high and increased from 0-202 ml/min to 0-845 ml/min. Myometrial and endometrial blood flow increased from 0-156 to 2-24 ml/min. The mean maternal placental blood flow at Day 22 of pregnancy was 0-76 ml/min or 121 ml.,min-1 .100 g-1. Litter size was negatively correlated with mean fetal weight but showed little relationship to mean placental weight or to mean maternal placental blood flow.     

Oronasal partitioning of ventilation during exercise in humans

The partitioning of oronasal breathing was studied in five normal subjects during progressive exercise. Subjects performed three to five identical runs, each consisting of four 1-min work periods at increments of 50 W. Nasal and oral airflow were measured simultaneously using a partitioned face mask both during and for 4 min after exercise. Total mean flows were the sum of nasal and oral flows. At a total mean inspiratory flow of 2 l/s, the nasal fraction of total flow was 0.36 +/- 0.04 (SE) and decreased by 6 +/- 3% between total flows of 1.5 and 2.5 l/s. Throughout exercise, the nasal fraction of total mean inspiratory flow did not differ from that of total expiratory flow and was similar to that of total mean inspiratory flow during the postexercise period at a corresponding total mean flow (both P greater than 0.02). The results show that oronasal flow partitioning is not directly due to the exercise itself but is related to the level of ventilation and is uninfluenced by the direction of upper airway flow (i.e., inspiratory vs. expiratory). These findings suggest tightly controlled modulation of the relative resistances of the oral and/or nasal pathways.     

Retrograde flow of spermatozoa into the urinary bladder of boars during collection of semen by electroejaculation

Boars that had a catheter implanted in the urinary bladder (n = 11) were used to determine the magnitude of retrograde flow of spermatozoa into the urinary bladder during electroejaculation. The overall mean (+/- SD) number of spermatozoa in the electroejaculate of boars was 22 +/- 20 x 10(9), with a mean range for individual boars of 3 +/- 3 to 48 +/- 13 x 10(9). The overall mean adjusted total number of spermatozoa in the post-electroejaculation urine was 1.038 +/- 2.656 x 10(9), and the mean percentage of retrograde flow of spermatozoa into the urinary bladder among boars ranged from 0% to 32.69%, with an overall mean percentage of retrograde flow of 7.51 +/- 17.82%. These findings indicate that in boars electroejaculation is associated with retrograde flow of spermatozoa into the bladder.     

Pulsatile flow of Casson's fluid through stenosed arteries with applications to blood flow

The effects of non-Newtonian nature of blood and pulsatility on flow through a stenosed tube have been investigated. A perturbation method is used to analyse the flow. It is of interest to note that the thickness of the viscous flow region is non-uniform (changing with axial distance). An analytic relation between viscous flow region thickness and red cell concentration has been obtained. It is important to mention that some researchers have obtained an approximate solution for the flow rate-pressure gradient equation (assuming the ratio between the yield stress and the wall shear to be very small in comparison to unity); in the present analysis, we have obtained an exact solution for this non-linear equation without making that assumption. The approximate and exact solutions compare well with one of the exact solutions. Another important result is that the mean and steady flow rates decrease as the yield stress theta increases. For the low values of the yield stress, the mean flow rate is higher than the steady flow rate, but for high values of the yield stress, the mean flow rate behaviour is of opposite nature. The critical value of the yield stress at which the flow rate behaviour changes from one type to another has been determined. Further, it seems that there exists a value of the yield stress at which flow stops for both the flows (steady and pulsatile). It is observed that the flow stop yield value for pulsatile flow is lower than the steady flow. The most notable result of pulsatility is the phase lag between the pressure gradient and flow rate, which is further influenced by the yield stress and stenosis. Another important result of pulsatility is the mean resistance to flow is greater than its steady flow value, whereas the mean value of the wall shear for pulsatile flow is equal to steady wall shear. Many standard results regarding Casson and Newtonian fluids flow, uniform tube flow and steady flow can be obtained as the special cases of the present analysis. Finally, some applications of this theoretical analysis have been cited.     

Flow separation, an important mechanism in the formation of mean pulmonary pressure during high-frequency oscillation

Mean pressures within the lungs and lung volume, respectively, are clinically important parameters. During ventilation by way of high-frequency oscillation (HFO), these parameters have been shown to be strongly frequency dependent. To identify mechanisms leading to mean pressure formation during HFO, findings of the theory of stationary flow were extended to oscillatory flow by a quasi-stationary approach. To confirm the theoretical findings, in-vitro experiments on HFO-models were performed. Flow separation was found to be an important mechanism in the formation of mean pressure. Flow separation causes a significant flow resistance, which may be distinctly different for in- and outflow. During oscillatory flow, a mean pressure difference thus results. This mechanism is of particular importance in bifurcations, which are present in the HFO-circuit as well as in the airways. With the direction-dependent flow separation, a general mechanism was found, which accounts for differing mean pressure values within the lungs with different HFO-circuits. This mechanism also contributes to interregionally different mean pressure values within the lungs.     

Enhanced central and conduit pulmonary arterial reservoir function offsets reduced ductal systolic outflow during constriction of the fetal ductus arteriosus

Constriction of the fetal ductus arteriosus (DA) has disparate effects on mean and phasic hemodynamics, as mean DA blood flow is preserved until constriction is severe, but DA systolic and diastolic blood velocities change with only mild constriction. To determine the basis of this disparity and its physiological significance, seven anesthetized late-gestation fetal sheep were instrumented with pulmonary trunk (PT), DA, and left pulmonary artery (PA) micromanometer catheters and transit-time flow probes. Blood flow profile and wave intensity analyses were performed at baseline and during mild, moderate, and severe DA constriction (defined as pulmonary-aortic mean pressure differences of 4, 8, and 14 mmHg, respectively), produced with an adjustable snare. With DA constriction, mean DA flow was initially maintained but decreased with severe constriction (P < 0.05) in conjunction with a reduction (P < 0.05) in PT flow (i.e., right ventricular output). By contrast, DA systolic flow fell progressively during DA constriction (P < 0.001), due to decreased transmission of both early and midsystolic proximal flow-enhancing forward-running compression waves into the DA. However, DA constriction was also accompanied by greater systolic storage of blood in the PT and main PA (P < 0.025), and increased retrograde diastolic flow from compliant major branch PA (P < 0.001). Transductal discharge of these central and conduit PA blood reservoirs in diastole offset systolic DA flow reductions. These data suggest that, during DA constriction in the fetus, enhanced central and conduit PA reservoir function constitutes an important compensatory mechanism that contributes to preservation of mean DA flow via a systolic-to-diastolic redistribution of phasic DA flow.     

Determinants of gas flow through a bronchopleural fistula

To assess the determinants of bronchopleural fistula (BPF) flow, we used a surgically created BPF to study 15 anesthetized intubated mechanically ventilated New Zealand White rabbits. Mean airway pressure and intrathoracic pressure were evaluated independently. Mean airway pressure was varied (8, 10, or 12 cmH2O) by independent manipulations of either peak inspiratory pressure, positive end-expiratory pressure, or inspiratory time. Intrathoracic pressure was varied from 0 to -40 cmH2O. BPF flow varied directly with mean airway pressure (P less than 0.001). However, at constant mean airway pressure, BPF flow was not influenced independently by changes in peak inspiratory pressure, positive end-expiratory pressure, or inspiratory time. Resistance of the BPF increased as intrathoracic pressure became more negative. Despite increased resistance, BPF flow also increased. BPF resistance was constant over the range of mean airway (P less than 0.01) pressures investigated. Our data document the influence of mean airway pressure and intrathoracic pressure on BPF flow and suggest that manipulations which reduce transpulmonary pressure will decrease BPF flow.     

Physiological flow analysis in significant human coronary artery stenoses

To evaluate the local hemodynamics in flow limiting coronary lesions, computational hemodynamics was applied to a group of patients previously reported by Wilson et al. (1988) with representative pre-angioplasty stenosis geometry (minimal lesion size d(m)=0.95 mm; 68% mean diameter stenosis) and with measured values of coronary flow reserve (CFR) in the abnormal range (2.3+/-0.1). The computations were at mean flow rates (Q) of 50, 75 and 100 ml/min (the limit of our converged calculations). Computed mean pressure drops Deltap were approximately 9 mmHg for basal flow (50 ml/min), approximately 27 mmHg for elevated flow (100 ml/min) and increased to an extrapolated value of approximately 34 mmHg for hyperemic flow (115 ml/min), which led to a distal mean coronary pressure p(rh) of approximately 55 mmHg, a level known to cause ischemia in the subendocardium (Brown et al., 1984), and consistent with the occurrence of angina in the patients. Relatively high levels of wall shear stress were computed in the narrow throat region and ranged from about 600 to 1500 dyn/cm(2), with periodic (phase shifted) peak systolic values of about 3500 dyn/cm(2). In the distal vessel, the interaction between the separated shear layer wave, convected downstream by the core flow, and the wall shear layer flow, led to the formation of vortical flow cells along the distal vessel wall during the systolic phase where Reynolds numbers Re(e)(t) were higher. During the phasic vortical mode observed at both basal and elevated mean flow rates, wide variations in distal wall shear stress occurred, distal transmural pressures were depressed below throat levels, and pressure recovery was larger farther along the distal vessel. Along the constriction (convergent) and throat segments of the lesion the pulsatile flow field was principally quasi-steady before flow separation occurred. The flow regimes were complex in the narrow mean flow Reynolds number range Re(e)=100-230 and a frequency parameter of alphae=2.25. The shear layer flow disturbances diminished in strength due to viscous damping along the distal vessel at these relatively low values of Re(e), typical of flow through diseased epicardial coronary vessels. The distal hyperemic flow field was likely to be in an early stage of turbulent flow development during the peak systolic phase.     

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.     

Effects of airway pressure on bronchial blood flow

We studied the effects of increased airway pressure caused by increasing levels of positive end-expiratory pressure (PEEP) on bronchial arterial pressure-flow relationships. In eight alpha-chloralose-anesthetized mechanically ventilated sheep (23-27 kg), the common bronchial artery, the bronchial branch of the bronchoesophageal artery, was cannulated and perfused with a pump. The control bronchial blood flow (avg 12 +/- 1 ml/min or 0.48 ml X min-1 X kg-1) was set to maintain mean bronchial arterial pressure equal to systemic blood pressure. Pressure-flow curves of the bronchial circulation were measured by making step changes in bronchial blood flow, and changes in these curves were analyzed with measurements of the pressure at zero flow and the slope of the linearized curve. The zero-flow pressure represents the effective downstream pressure, and the slope represents the resistance through the bronchial vasculature. At a constant bronchial arterial pressure of 100 mmHg, an 8 mmHg increase in mean airway pressure caused a 40% reduction in bronchial blood flow. Under constant flow conditions, increases in mean airway pressure with the application of PEEP caused substantial increases in bronchial arterial pressure, averaging 4.6 mmHg for every millimeters of mercury increase in mean airway pressure. However, bronchial arterial pressure at zero flow increased approximately one-for-one with increases in mean airway pressure. Thus the acute sensitivity of the bronchial artery to changes in mean airway pressure results primarily from changes in bronchovascular resistance and not downstream pressure.     

Simple pulsatile flow in an artery with a constriction

A smooth isolated, axisymmetric occlusion in a straight vascular tube is a tractable problem for pulsatile flow calculations via finite-difference approximations to the Navier-Stokes equation. Steady flow depends on the Reynolds number and two geometric parameters which describe the stenosis. The mere addition of a simple harmonic to the mean flow adds two more parameters. One is the reduced frequency, or Strokes number, and the other epsilon, the ratio of unsteady to steady flux. After describing steady stenosis flow examples, the dynamic patterns of pulsatile flow are illustrated indicating the inadequacy of basing hypotheses of atherosclerosis on mean (steady) flow.     

Flow of urine through the ureter: a collapsible, muscular tube undergoing peristalsis

In steady flow through nonuniform collapsible tubes a key concept is the compressive zone, at which flow limitation can occur at both high and low Reynolds numbers. Ureteral peristalsis can be considered as a series of compressive zones, corresponding to waves of active muscular contraction, that move at near-constant speed along the ureter towards the bladder. One-dimensional, lubrication-theory analysis shows that peristalsis can pump urine from kidney into the bladder only at relatively low mean rates of urine flow. Under these circumstances isolated boluses of urine are propelled steadily through the ureter (assumed uniform) by the contraction waves. At higher mean rates of flow the behavior depends on whether the frequency of peristalsis is higher or lower than a critical value. For frequencies above the critical value steady propagation of boluses that are in contact with contraction waves at both ends is possible. As the flow rate rises the urine begins to leak through the contraction waves and steady peristaltic flow breaks down. There is an upper limit to the mean flow rate that can be carried by steady peristalsis, which depends on the mechanical properties of the ureter. At high flow rates the peristaltic contractions do not pump but hinder the flow of urine through the ureter.     

Blood flow measurement from plethysmographic pulse waves without venous occlusion

An air plethysmograph with a sensitive phototransducer was constructed so that plethysmographic volume-change pulsations could be displayed in detail without using venous occlusion. Software was developed to allow analysis of the pulses using a modification of the backward extrapolation technique. This allowed calculation of the forward arterial blood flow and noninvasive derivation of the resting arterial flow waveform. There is good reproducibility of the technique, with 8% variability between pairs of measurements at rest and 4% variability after hand exercise. Direct comparison made with blood flows measured by venous occlusion plethysmography showed good average agreement. The mean blood flow for venous occlusion (rest and exercise) was 0.76 +/- 0.07 mL/beat (mean +/- SEM), and the mean blood flow for backward extrapolation (rest and exercise) was 0.74 +/- 0.09 mL/beat (mean +/- SEM). This corresponds to 3.86 +/- 0.36 mL/min/100 mL and 3.76 +/- 0.46 mL/min/100 mL, respectively. Important assumptions when using this method are that venous return is constant and that forward arterial flow is over before the end of the cardiac cycle.     

Endotoxin-induced reduction in biliary indocyanine green excretion rate in a chronically catheterized rat model

Using a nonstressed chronically catheterized rat model in which the common bile duct was cannulated, we studied endotoxin-induced alterations in hepatic function by measuring changes in the maximal steady-state biliary excretion rate of the anionic dye indocyanine green (ICG). Biliary excretion of ICG was calculated from direct measurements of biliary ICG concentrations and the bile flow rate during a continuous vascular infusion of ICG. Despite significant elevations in mean peak serum tumor necrosis factor-alpha (TNF-alpha) concentrations (90.9 +/- 16.2 ng/ml), there was no effect on mean rates of bile flow or biliary ICG clearance after administration of 100 microg/kg endotoxin at 6 or 24 h. Significant differences from mean baseline rates of bile flow and biliary ICG excretion did occur after administration of 1,000 microg/kg endotoxin (mean peak TNF-alpha 129.6 +/- 24.4 ng/ml). Furthermore, when rats were treated with up to 16 microg/kg of recombinant TNF-alpha, there was no change in mean rates of bile flow or ICG biliary clearance compared with baseline values. These data suggest that the complex regulation of biliary excretion is not mediated solely by TNF-alpha.     

Neuropeptide Y reduces ovarian blood flow in the rabbit

Neuropeptide Y-containing nerve fibers have previously been demonstrated to innervate the mammalian ovary. These nerve fibers innervate primarily the vasculature. In this study we have developed a method for in vivo measurement of the ovary blood flow rate by means of the 133Xe method. Using this technique we measured the ovary blood flow rate and investigated the dose-response relationship between close intraarterial-injected NPY and the ovary blood flow rate. A monoexponential washout curve for 133Xe was found for the whole washout process, ensuring that the blood flow rate at any time could be calculated from the curve. We found a mean blood flow rate in the nonpregnant rabbit ovary at 43.6 +/- 4.4 ml.(100 g)-1.min-1 (mean +/- SEM). Injection of NPY (20, 200, 2000 pM) in the aorta close to a. ovarica resulted in a dose-dependent decrease in the ovarian blood flow rate with a maximum reduction to 40.7 +/- 6.3% (mean +/- SEM) of the control blood flow rate. These findings make it likely that receptors able to interact with NPY are present in the vasculature of the rabbit ovary.     

Maximum airflow through the nose in humans

Inspiratory and expiratory flow via the nose and via the mouth during maximum-effort vital capacity (VC) maneuvers have been compared in 10 healthy subjects. Under baseline conditions maximum flow via the nose was lower than that via the mouth in the upper 50-60% of the VC on expiration and throughout the VC on inspiration. The mean ratio of maximum inspiratory to maximum expiratory flow at mid-VC was 1.38 during mouth breathing and 0.62 during nasal breathing. Inspiratory flow limitation with no increase in flow through the nose as driving pressure was increased above a critical value (usually between 12 and 30 cmH2O) was found in all six subjects studied. Stenting the alae nasi in seven subjects increased peak flow via the nose from a mean of 3.49 to 4.32 l/s on inspiration and from 4.83 to 5.61 l/s on expiration. Topical application of an alpha-adrenergic agonist in seven subjects increased mean peak nasal flow on inspiration from 3.25 to 3.89 l/s and on expiration from 5.03 to 7.09 l/s. Further increases in peak flow occurred with subsequent alan stenting. With the combination of stenting and topical mucosal vasoconstriction, nasal peak flow on expiration reached 81% and, on inspiration, 79% of corresponding peak flows via the mouth. The results demonstrate that narrowing of the alar vestibule and the state of the mucosal vasculature both influence maximum flow through the nose; under optimal conditions, nasal flow capacity is close to that via the mouth.     

Effect of injectable or inhalational anesthetics and of neuroleptic, neuroleptanalgesic, and sedative agents on tumor blood flow

Among other parameters, varying blood flow values may be responsible for tumor-to-tumor variabilities in the radiobiologically hypoxic cell fraction of experimental rodent tumors. To test whether changes in tumor blood flow may be caused by anesthetic agents often used in radiobiology, the effect of injectable and inhalational anesthetics and of neuroleptic, neuroleptanalgesic, and sedative agents on blood flow in subcutaneous DS-carcinosarcomas implanted in Sprague-Dawley rats has been investigated using the 85Kr clearance technique. In conscious rats, 20-100 min after animal instrumentation mean blood flow is 0.62 +/- 0.17 ml/g/min (mean +/- SD) in 0.75 +/- 0.15 g tumors at a mean arterial blood pressure of 125 +/- 12 mm Hg. In animals receiving thiobutabarbital, chloral hydrate, or methoxyflurane tumor blood flow is somewhat higher than that measured in conscious rats. Tumor blood flow in animals receiving etomidate, ketamine-xylazine, fentanyl-fluanisone, or urethane is significantly lower than that in the thiobutabarbital group and somewhat lower than in the conscious animals. Blood flow values observed with midazolam, ketamine-midazolam, fentanyl-droperidol, droperidol, diazepam, and pentobarbital are similar to those measured in conscious rats. Virtually no flow alterations with time are detectable in conscious rats and with most of the drugs used. In animals anesthetized with urethane or methoxyflurane, tumor blood flow increases and tumor vascular resistance diminishes slightly with time.     

Distributions of positive signals in pyrosequencing

Pyrosequencing is one of the important next-generation sequencing technologies. We derive the distribution of the number of positive signals in pyrograms of this sequencing technology as a function of flow cycle numbers and nucleotide probabilities of the target sequences. As for the distribution of sequence length, we also derive the distribution of positive signals for the fixed flow cycle model. Explicit formulas are derived for the mean and variance of the distributions. A simple result for the mean of the distribution is that the mean number of positive signals in a pyrogram is approximately twice the number of flow cycles, regardless of nucleotide probabilities. The statistical distributions will be useful for instrument and software development for pyrosequencing and other related platforms.