New method to measure coronary velocity and coronary flow reserve

Coronary flow reserve (CFR) is an important index of coronary microcirculatory function. The objective of this study was to validate the reproducibility and accuracy of intravascular conductance catheter-based method for measurements of baseline and hyperemic coronary flow velocity (and hence CFR). The absolute coronary blood velocity was determined by measuring the time of transit of a saline injection between two pairs of electrodes (known distance) on a conductance catheter during a routine saline injection without the need for reference flow. In vitro validation was made in the velocity range of 5 to 70 cm/s in reference to the volume collection method. In 10 swine, velocity measurements were compared with those from a flow probe in coronary arteries at different CFR attained by microsphere embolization. In vitro, the mean difference between the proposed method and volume collection was 0.7 ± 1.34 cm/s for steady flow and -0.77 ± 2.22 cm/s for pulsatile flow. The mean difference between duplicate measurements was 0 ± 1.4 cm/s. In in vivo experiments, the flow (product of velocity and lumen cross-sectional area that is also measured by the conductance catheter) was determined in both normal and stenotic vessels and the mean difference between the proposed method and flow probe was -1 ± 12 ml/min (flow ranged from 10 to 130 ml/min). For CFR, the mean difference between the two methods was 0.06 ± 0.28 (range of 1 to 3). Our results demonstrate the reproducibility and accuracy of velocity and CFR measurements with a conductance catheter by use of a standard saline injection. The ability of the combined measurement of coronary lumen area (as previously validated) and current velocity and CFR measurements provides an integrative diagnostic tool for interventional cardiology.     

Experimental analysis of the influence of stenotic geometry on steady flow.

We studied the flow behavior under steady flow conditions in four models of cylindrical stenoses at Reynolds numbers from 150 to 920. The flow upstream of the constrictions was always fully developed. The constriction ratios of the rigid tubes (D) to the stenoses (d) were d/D = 0.273; 0.505; 0.548; 0.786. The pressure drop at various locations in the stenotic models was measured with water manometers. The flow was visualized with a photoelasticity apparatus using an aqueous birefringent solution. We also studied the flow behavior at pulsatile flow in a dog aorta with a constriction of 71%. The flow through stenotic geometries depends on the Reynolds number of the flow generated in the tube and the constriction ratio d/D. At low d/D ratios, (with the increased constriction), the flow separation zones (recirculation zones, so-called reattachment length) and flow disturbances increased with larger Reynolds numbers. At lower values, eddies were generated. At high Re, eddies were observed in the pre-stenotic regions. The pressure drop is a function of the length and internal diameter of the stenosis, respective ratio of stenosis to the main vessel and the Reynolds numbers. At low Re-numbers and low d/D, distinct recirculation zones were found close to the stenosis. The flow is laminar in the distal areas. Further experiments under steady and unsteady flow conditions in a dog aorta model with a constriction of 71% showed similar effects. High velocity fluctuations downstream of the stenosis were found in the dog aorta. A videotape demonstrates these results.     

Novel method for measurement of medium size arterial lumen area with an impedance catheter: in vivo validation

There is no doubt that the transformation of a cardiac catheter into a conductance catheter that allows reliable and accurate assessment of lumen cross-sectional area (CSA) will provide a powerful diagnostic and treatment tool for the invasive cardiologist. The objective of this study was to develop a method based on the impedance catheter that allows accurate and reproducible measurements of CSA for medium size vessels (e.g., coronary, femoral, and carotid arteries). Two solutions of NaCl (0.5% and 1.5%) with known conductivities were injected directly into the lumen of the artery in eight swine. We showed that the CSA can be determined analytically from two Ohm's law-type algebraic equations that account for the parallel conductance of the current into the surrounding tissue. Excellent agreement was found between the conductance catheter with the proposed two-injection method and B-mode ultrasound (US). The root mean square error for the impedance measurements was 4.8% of the mean US diameter. The repeatability of the technique was assessed with duplicate measurements. The mean of the difference between the two measurements was nearly zero, and the repeatability coefficient was within 2.4% of the mean of the two measurements. The validated method was used to assess the degree of acute vasodilatation of the vessel in response to flow overload.     

Disorder distal to modeled stenoses in steady and pulsatile flow

Measurements of the velocity and energy spectra were made in the distal region of modeled stenoses in a rigid tube with both steady and pulsatile water flows. Reynolds numbers of 318–2540 and a pulsatile flow frequency parameter of 15 were employed. The effects of the degree of stenosis, the stenosis geometry and the presence or absence of the downstream confining wall on the development of flow disturbances were investigated. Visualization of the distal flow patterns in stenotic and free jets illustrated the existence of complex fields which included vortex shedding, highly turbulent regions, and recirculation zones. Significant flow disorder was created by a mild stenosis in pulsatile, but not in steady, flow. Nondimensionalization employing the stenosis diameter and flow velocity in the throat of the constriction correlates the vortex shedding frequency and energy spectra within a limited postestenotic region.     

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.     

Impedance electrodes positioned on proximal portions of limbs quantify fluid compartments in dogs

Body resistance and reactance to the conduction of an alternating electrical current were measured using electrodes attached to distal and proximal portions of limbs in anesthetized dogs. Body impedance was calculated from these measurements obtained at 30-min time intervals during a control period and after intravenous administration of 0.9% saline. Extracellular (ECW) and total body water (TBW) were determined by bromide and heavy water dilution techniques, respectively. Baseline impedance obtained from proximal electrodes was related to ECW (r = 0.95, P less than 0.001) and TBW (r = 0.80, P less than 0.02). After saline infusion, proximal electrodes detected a significant fall in impedance (P less than 0.001), whereas distal electrodes did not (P = 0.06). Furthermore, ECW and TBW could be estimated from the drop of proximal impedance after this bolus infusion (r = 0.82, P less than 0.02, and r = 0.86, P less than 0.01, respectively), but not from distal impedance measurements. Proximally placed impedance electrodes are superior to traditionally used distal electrodes for assessment of body fluid changes in the dog.     

Flow in a catheterized curved artery with stenosis

The fluid mechanics of blood flow in a catheterized curved artery with stenosis is studied through a mathematical analysis. Blood is modelled as an incompressible Newtonian fluid and the flow is assumed to be steady and laminar. An approximate analytic solution to the problem is obtained through a double series perturbation analysis for the case of small curvature and mild stenosis. The effect of catheterization on various physiologically important flow characteristics (i.e. the pressure drop, impedance and the wall shear stress) is studied for different values of the catheter size and Reynolds number of the flow. It is found that all these flow characteristics vary markedly across a stenotic lesion. Also, increase in the catheter size leads to a considerable increase in their magnitudes. These results are used to obtain the estimates of increased pressure drop across an arterial stenosis when a catheter is inserted into it. Our calculations, based on the geometry and flow conditions existing in coronary arteries, suggest that, in the presence of curvature and stenosis, and depending on the value of k (ratio of catheter size to vessel size) ranging from 0.1 to 0.4, the pressure drop increases by a factor ranging from 1.60 to 5.16. But, in the absence of curvature and stenosis, with the same range of catheter size, this increased factor is about 1.74-4.89. These estimates for the increased pressure drop can be used to correct the error involved in the measured pressure gradients using catheters. The combined effects of stenosis and curvature on flow characteristics are also studied in detail. It is found that the effect of stenosis is more dominant than that of the curvature. Due to the combined effect of stenosis, curvature and catheterization, the secondary streamlines are modified in a cross-sectional plane. The insertion of a catheter into the artery leads to the formation of increased number of secondary vortices.     

In Vitro Shear Stress Measurements Using Particle Image Velocimetry in a Family of Carotid Artery Models: Effect of Stenosis Severity,Plaque Eccentricity,and Ulceration

Atherosclerotic disease, and the subsequent complications of thrombosis and plaque rupture, has been associated with local shear stress. In the diseased carotid artery, local variations in shear stress are induced by various geometrical features of the stenotic plaque. Greater stenosis severity, plaque eccentricity (symmetry) and plaque ulceration have been associated with increased risk of cerebrovascular events based on clinical trial studies. Using particle image velocimetry, the levels and patterns of shear stress (derived from both laminar and turbulent phases) were studied for a family of eight matched-geometry models incorporating independently varied plaque features – i.e. stenosis severity up to 70%, one of two forms of plaque eccentricity, and the presence of plaque ulceration). The level of laminar (ensemble-averaged) shear stress increased with increasing stenosis severity resulting in 2–16 Pa for free shear stress (FSS) and approximately double (4–36 Pa) for wall shear stress (WSS). Independent of stenosis severity, marked differences were found in the distribution and extent of shear stress between the concentric and eccentric plaque formations. The maximum WSS, found at the apex of the stenosis, decayed significantly steeper along the outer wall of an eccentric model compared to the concentric counterpart, with a 70% eccentric stenosis having 249% steeper decay coinciding with the large outer-wall recirculation zone. The presence of ulceration (in a 50% eccentric plaque) resulted in both elevated FSS and WSS levels that were sustained longer (∼20 ms) through the systolic phase compared to the non-ulcerated counterpart model, among other notable differences. Reynolds (turbulent) shear stress, elevated around the point of distal jet detachment, became prominent during the systolic deceleration phase and was widely distributed over the large recirculation zone in the eccentric stenoses.     

CFD analysis of pulsatile blood flow in an atherosclerotic human artery with eccentric plaques

Atherosclerosis is a slow vascular degeneration. It thickens the internal walls of a blood vessel locally depositing an atherosclerotic plaque. Such reduced lumen increases the resistance to blood flow. Plaques can be punctual (eccentric, here considered) or circumferential (symmetrical). Stenoses do not have a typical shape: we hypothesised here a reference geometry (trapezium) with its possible evolutions (semi-ellipse, triangle). Two criteria (Equivalent Area and Equivalent Dimensions) were then defined to compare the results among the 35 case studies numerically analysed with a Computational Fluid Dynamics code (Comsol Multiphysics 3.3). Blood was considered a Cassonian fluid with modified viscosity equation. The artery was cylindrical, rigid and straight, interested by a pulsatile blood flow. Among the variables: shape and dimensions of the stenoses; number of stenoses (single or coupled pathologies); mutual locations (3 possibilities). The main results were that the length of the consequent flow disturbance is due to the stenotic shape and height; blood flow recirculation, downstream of the pathology, is due to the slope of the stenotic walls; and the peak velocities depend on the shape and height of stenosis. The differences from case to case diminish in diastole.     

A self-calibrating telemetry system for measurement of ventricular pressure-volume relations in conscious, freely moving rats

Using Bluetooth wireless technology, we developed an implantable telemetry system for measurement of the left ventricular pressure-volume relation in conscious, freely moving rats. The telemetry system consisted of a pressure-conductance catheter (1.8-Fr) connected to a small (14-g) fully implantable signal transmitter. To make the system fully telemetric, calibrations such as blood resistivity and parallel conductance were also conducted telemetrically. To estimate blood resistivity, we used four electrodes arranged 0.2 mm apart on the pressure-conductance catheter. To estimate parallel conductance, we used a dual-frequency method. We examined the accuracy of calibrations, stroke volume (SV) measurements, and the reproducibility of the telemetry. The blood resistivity estimated telemetrically agreed with that measured using an ex vivo cuvette method (y=1.09x - 11.9, r2= 0.88, n=10). Parallel conductance estimated by the dual-frequency (2 and 20 kHz) method correlated well with that measured by a conventional saline injection method (y=1.59x - 1.77, r2= 0.87, n=13). The telemetric SV closely correlated with the flowmetric SV during inferior vena cava occlusions (y=0.96x + 7.5, r2=0.96, n=4). In six conscious rats, differences between the repeated telemetries on different days (3 days apart on average) were reasonably small: 13% for end-diastolic volume, 20% for end-systolic volume, 28% for end-diastolic pressure, and 6% for end-systolic pressure. We conclude that the developed telemetry system enables us to estimate the pressure-volume relation with reasonable accuracy and reproducibility in conscious, untethered rats.     

Intravascular ultrasound assessment of culotte stent deployment for the treatment of stenoses at major coronary bifurcations

BACKGROUND: The mechanism for the disappointing late outcome following stenting of bifurcation lesions is unclear. This prospective observational study aims to evaluate culotte stent deployment and dimensions with intravascular ultrasound (IVUS). PATIENTS AND METHODS: Patients with bifurcation stenoses were treated using two stents in a culotte configuration. After optimizing the angiographic appearance of both stents, IVUS was used to evaluate both limbs of the culotte. The main outcome measures were cross-sectional area (CSA) and minimal lumen diameter (MLD) assessed by IVUS. RESULTS: Within the culotte stent, the final mean CSA in the main limb was 6.1 mm(2) (97% of reference) and in the side-limb was 5.9 mm(2) (97% of reference). However, in each case, the minimum CSA and IVUS MLD of both limbs was at the bifurcation point. For all patients, the final mean CSA at the bifurcation point of the main limb was 4.3 mm(2) (70% of main stent) and of the side-limb was 4.4 mm(2) (75% of side stent). The IVUS MLD at the bifurcation point of the main limb was 2.1 mm (78% of main stent) and of the side-limb was 2.1 mm (84% of the side stent). Importantly, this significant residual stenosis was not detectable with quantitative coronary angiography. CONCLUSIONS: IVUS evaluation of culotte stents is feasible. The minimum IVUS CSA and MLD of both limbs of the culotte stent is at the bifurcation point. Despite an optimal angiographic appearance a significant residual stenosis was noted with IVUS at each bifurcation point.     

CO2 angiography: studies of gas filling of vessels and assessing the factors of influence on the injection process with a cardiovascular model]

Following the advent of digital subtraction angiography (DSA), carbon dioxide gas has become a useful contrast agent for arterial angiography. Former manual injection methods had precluded accurate dosing and reproducibility. An original gas injector was therefore developed and tested in a circulatory system model. This permitted an accurate evaluation of vascular gas-filling. it also proved possible to measure the injection parameters taking different influencing factors into account. It was shown that vessels up to 10 mm in diameter are virtually completely filled with gas. In vessels larger than 10 mm in diameter, a residual fluid level remains, which in turn reduces the possibility for complete vessel imaging. The injection flow is dependent primarily on the vascular circulation rate, vessel diameter and the inclination of the vessel. With respect to other factors examined, neither catheter size, number of holes nor the direction of the injection have any relevant influence.     

Real-time assessment of flow reversal in an eccentric arterial stenotic model

Plaque rupture is the leading cause of acute coronary syndromes and stroke. Plaque formation, otherwise known as stenosis, preferentially occurs in the regions of arterial bifurcation or curvatures. To date, real-time assessment of stenosis-induced flow reversal remains a clinical challenge. By interfacing microelectromechanical system (MEMS) thermal sensors with the high frequency pulsed wave (PW) Doppler ultrasound, we proposed to assess flow reversal in the presence of an eccentric stenosis. We developed a 3-D stenotic model (inner diameter of 6 mm, an eccentric stenosis with a height of 2.75 mm, and width of 21 mm) simulating a superficial arterial vessel. We demonstrated that heat transfer from the sensing element (2×80 μm²) to the flow field peaked as a function of flow rates at the throat of the stenosis along the center/midline of arterial model, and dropped downstream from the stenosis, where flow reversal was detected by the high frequency ultrasound device at 45 MHz. Computational fluid dynamics (CFD) codes are in agreement with the ultrasound-acquired flow profiles upstream, downstream, and at the throat of the stenosis. Hence, we characterized regions of eccentric stenosis in terms of changes in heat transfer along the midline of vessel and identified points of flow reversal with high spatial and temporal resolution.     

小口径血液导流管的实验研究

目的:探讨小口径血液导流管在动物离断肢体模型中快速恢复通血的实验基础应用,研究小口径血液导流管实验幼猪离断肢体维持通血效果的评价。方法:20只实验幼猪随机分为A、B两组,制成后肢完全离断模型模型,采用内径为2.0 mm、外径2.5mm的血液导流管,A组长度10 cm;B组长度20 cm,进行血管桥接后定期观察血液导流管通畅性,观察终点为血液导流管完全堵塞,血管超声探测仪无血流信号,远端血管搏动消失,离断肢体以远皮下毛细血管网无渗血。比较两组到达观察终点的时间有无差异。结果:建立临时血管通路后,离断肢体远端股动脉的远端有搏动,血管超声探测仪可检测到血液导流管内有血流信号,随着时间的延长,血液导流管动脉段逐渐由鲜红色变为暗红色,导流管段逐渐形成附壁血栓,远端血管搏动及皮下毛细管网渗血逐渐减弱直至消失,血流信号消失,两组到达观测终点的时间分别为A组365±47.4 min;B组359±31.5 min,两者比较其差异没有统计学意义(P0.05)。说明长度在10 cm-20 cm的小口径血液导流管在实验动物离断肢体血管通血方面无明显差异。结论:小口径血液导流管能够用于动物离断肢体的血管临时桥接,维持通血时间可达6-8小时,有效通血时间长。实验数据说明小口径血液导流管适合于动物离断肢体模型中的血管桥接,在下一步临床应用中在四肢复杂血管损伤中有着较为广阔的临床应用前景。     

Intravascular ultrasound imaging of myocardial-infarction-related arteries after percutaneous transluminal coronary angioplasty reveals significant plaque burden and compensatory enlargement

We studied patients with acute myocardial infarction (MI) by intravascular ultrasound (IVUS) to elucidate the controversy as to the amount and severity of the atherosclerotic disease at the culprit lesion site in acute MI, as discrepancies exist between angiographic and pathological reports. Twenty-five consecutive patients (age 56 3 10.5 years), with acute MI, underwent IVUS study of the MI-related artery immediately following successful PTCA to the culprit lesion. The IVUS images were analyzed quantitatively and qualitatively and were compared with the angiography of the same arteries. At the PTCA site, 64% of the lesions had an area stenosis of 50-70% and the plaque cross-sectional area (CSA) averaged 0.5 3 0.18 of the arterial CSA. IVUS-defined atherosclerosis was found also in 72% of the segments proximal and distal to the culprit lesion with a plaque/artery CSA ratio of 0.25 3 0.2. The angiogram revealed only 30% of these segments to be abnormal (P 3 0.001). Sixty-nine per cent of all the plaques were defined as 'soft' (low echo-genecity) versus 31% 'hard' (high echo-genecity). The hard plaques were larger than the soft plaques (0.5 3 1.6 versus 0.37 3 0.19 CSA index, respectively, P 3 0.01). With the increase in plaque area there was a significant increase in arterial cross-sectional area. This was demonstrated for all the diseased segments with a correlation coefficient of 0.49 (P 3 0.0001) and for the diseased reference sites a similar correlation coefficient of 0.49 (P 3 0.003) was found. Contrary to coronary angiographic-based reports, this IVUS study revealed a significant atheromatous plaque burden at the culprit lesion of MI-related arteries as well as diffuse atherosclerosis in the reference segments proximal and distal to the lesion. The detection of compensatory enlargement may explain the discrepancies between the histopathological and the angiographic studies.     

Inhibitory Synapses on Pacemaker Neurons in the Heart Ganglion of a Stomatopod, Squilla oratoria

The pacemaker neurons of the Squilla heart ganglion are innervated from the CNS through three pairs of extrinsic nerves. One of them, the α-nerve, is inhibitory to the heart beat. The effect of α-nerve stimulation on the pacemaker potential was examined with intracellular electrodes. Without extrinsic nerve stimulation the membrane potential of the pacemaker cell fluctuated spontaneously. On application of a tetanic train of stimuli to the α-nerve the membrane potential was shifted and fixed to a steady level, which with K₂SO₄-filled electrodes was near the peak of hyperpolarization after a spontaneous burst, but was less negative with KCl-filled electrodes. The shift of the membrane potential was due to the summated IPSP's. By changing the level of the membrane potential with injection of the polarizing current the IPSP could be reversed in sign, and the size of the IPSP was linearly correlated with the membrane potential level. During inhibition the membrane conductance increased. The increase depended on divalent cation concentrations in the outside medium. In Ca-rich saline the IPSP was greatly enhanced. In Mg-rich saline it was suppressed. The amplitude of antidromic spikes was reduced during inhibition especially when the spike frequency was high.     

IVUS Validation of Patient Coronary Artery Lumen Area Obtained from CT Images

Aims

Accurate computed tomography (CT)-based reconstruction of coronary morphometry (diameters, length, bifurcation angles) is important for construction of patient-specific models to aid diagnosis and therapy. The objective of this study is to validate the accuracy of patient coronary artery lumen area obtained from CT images based on intravascular ultrasound (IVUS).

Methods and Results

Morphometric data of 5 patient CT scans with 11 arteries from IVUS were reconstructed including the lumen cross sectional area (CSA), diameter and length. The volumetric data from CT images were analyzed at sub-pixel accuracy to obtain accurate vessel center lines and CSA. A new center line extraction approach was used where an initial estimated skeleton in discrete value was obtained using a traditional thinning algorithm. The CSA was determined directly without any circular shape assumptions to provide accurate reconstruction of stenosis. The root-mean-square error (RMSE) for CSA and diameter were 16.2% and 9.5% respectively.

Conclusions

The image segmentation and CSA extraction algorithm for reconstruction of coronary arteries proved to be accurate for determination of vessel lumen area. This approach provides fundamental morphometric data for patient-specific models to diagnose and treat coronary artery disease.     

Numerical simulation of steady turbulent flow through trileaflet aortic heart valves—II. Results on five models

Turbulent flow simulations are run for five aortic trileaflet valve geometries, ranging from a valve leaflet orifice area of 1.1 cm² (Model A1—very stenotic) to 5.0 cm² (Model A5—natural valve). The simulated data compares well with experimental measurements made downstream of various aortic trileaflet valves by Woo (PhD Thesis, 1984). The location and approximate width and length of recirculation regions are correctly predicted. The less stenotic valve models reattach at the end of the aortic sinus region, 1.1 diameters downstream of the valve. The central jet exiting the less stenotic valve models is not significantly different from fully developed flow, and therefore recovers very quickly downstream of the reattachment point. The more stenotic valves disturb the flow to a greater degree, generating recirculation regions large enough to escape the sinuses and reattach further downstream. Peak turbulent shear stress values downstream of the aortic valve models which approximated prosthetic valves are 125 and 300 N m⁻², very near experimental observations of 150 to 350 N m⁻². The predicted Reynolds stress profiles also present the correct shape, a double peak profile, with the location of the peak occuring at the location of maximum velocity gradient, which occurs near the recirculation region. The pressure drop across model A2 (leaflet orifice area 1.6 cm²) is 20 mmHg at 1.6 diameters downstream. This compares well with values ranging from 19.5 to 26.2 mmHg for valves of similar orifice areas. The pressure drop decreases with decreasing valve stenosis, to a negligible value across the least stenotic valve model. Based on the good agreement between experimental measurements of velocity, shear stress and pressure drop, compared to the simulated data, the model has the potential to be a valuable tool in the analysis of heart valve designs.     

Numerical modeling of pulsatile turbulent flow in stenotic vessels

Pulsatile turbulent flow in stenotic vessels has been numerically modeled using the Reynolds-averaged Navier-Stokes equation approach. The commercially available computational fluid dynamics code (CFD), FLUENT, has been used for these studies. Two different experiments were modeled involving pulsatile flow through axisymmetric stenoses. Four different turbulence models were employed to study their influence on the results. It was found that the low Reynolds number k-omega turbulence model was in much better agreement with previous experimental measurements than both the low and high Reynolds number versions of the RNG (renormalization-group theory) k-epsilon turbulence model and the standard k-epsilon model, with regard to predicting the mean flow distal to the stenosis including aspects of the vortex shedding process and the turbulent flow field. All models predicted a wall shear stress peak at the throat of the stenosis with minimum values observed distal to the stenosis where flow separation occurred.     

Measurement of pharyngeal cross-sectional area by finite element analysis.

A noninvasive measurement of pharyngeal cross-sectional area (CSA) during sleep would be advantageous for research studies. We hypothesized that CSA could be calculated from the measured pharyngeal pressure and flow by finite element analysis (FEA). The retropalatal airway was visualized by using a fiber-optic scope to obtain the measured CSA (mCSA). Flow was measured with a pneumotachometer, and pharyngeal pressure was measured with a pressure catheter at the palatal rim. FEA was performed as follows: by using a three-dimensional image of the upper airway, a mesh of finite elements was created. Specialized software was used to allow the simultaneous calculation of velocity and area for each element by using the measured pressure and flow. In the development phase, 677 simultaneous measurements of CSA, pressure, and flow from one subject during non-rapid eye movement (NREM) and rapid eye movement (REM) sleep were entered into the software to determine a series of equations, based on the continuity and momentum equations, that could calculate the CSA (cCSA). In the validation phase, the final equations were used to calculate the CSA from 1,767 simultaneous measurements of pressure and flow obtained during wakefulness, NREM, and REM sleep from 14 subjects. In both phases, mCSA and cCSA were compared by Bland-Altman analysis. For development breaths, the mean difference between mCSA and cCSA was 0.0 mm2 (95% CI, -0.1, 0.1 mm2). For NREM validation breaths, the mean difference between mCSA and cCSA was 1.1 mm2 (95% CI 1.3, 1.5 mm2). Pharyngeal CSA can be accurately calculated from measured pharyngeal pressure and flow by FEA.