A unified fractional flow framework for predicting the liquid holdup in two-phase pipe flows

Two-phase pipe flow occurs frequently in oil&gas industry,nuclear power plants,and CCUS.Reliable calculations of gas void fraction(or liquid holdup)play a central role in two-phase pipe flow models.In this paper we apply the fractional flow theory to multiphase flow in pipes and present a unified modeling framework for predicting the fluid phase volume fractions over a broad range of pipe flow conditions.Compared to existing methods and correlations,this new framework provides a simple,approximate,and efficient way to estimate the phase volume fraction in two-phase pipe flow without invoking flow patterns.Notably,existing correlations for estimating phase volume fraction can be transformed and expressed under this modeling framework.Different fractional flow models are applicable to different flow conditions,and they demonstrate good agreement against experimental data within 5%errors when compared with an experimental database comprising of 2754 data groups from 14literature sources,covering various pipe geometries,flow patterns,fluid properties and flow inclinations.The gas void fraction predicted by the framework developed in this work can be used as inputs to reliably model the hydraulic and thermal behaviors of two-phase pipe flows.

Unsteady rotating flows of a viscoelastic fluid with the fractional Maxwell model between coaxial cylinders

The fractional calculus is used in the constitutive relationship model of viscoelastic fluid. A generalized Maxwell model with fractional calculus is considered. Based on the flow conditions described, two flow cases are solved and the exact solutions are obtained by using the Weber transform and the Laplace transform for fractional calculus.

Flow Field-Flow Fractionation with Mass Spectrometry for Top-Down and Bottom-Up Lipidomics

As lipidomics has attracted increased attention in life science,advanced mass spectrometry(MS)technologies have been combined with other separation techniques to improve and expand the branch of study.This review intends to provide general knowledge of offline and online coupling of flow field-flow fractionation(FlFFF)—a technique that encompasses the separation of nano-to micro-scale biomolecules—with MS for analysis of blood plasma lipoproteins,processes that are considered bottomup and top-down approaches,respectively.The first part of this review focuses on the bottom-up method using multiplexed hollow fiber FlFFF(MxHF5)and nanoflow liquid chromatography electrospray-ionization tandem mass spectrometry(nLC-ESI–MS/MS)for non-targeted identification of lipids.In this protocol,plasma lipoproteins of different types are collected using MxHF5,and the lipids within the lipoproteins are then extracted and analyzed via nLC-ESI–MS/MS.The second part of the review describes the top-down approach,which uses online coupling of miniaturized FlFFF to ESI–MS for a fast screening of targeted lipids.Here,the separation of lipoproteins and detection of their component lipids are achieved simultaneously.While both methods aim to quantify the lipids within lipoproteins,the bottom-up approach provides an extensive lipidome,whereas the top-down method is suitable for high-speed targeted lipidomic analysis.This review discusses variants of FlFFF-ESI–MS/MS that offer effective analytical technologies for lipidomics.

Clinical applications of fractional flow reserve in bifurcation lesions

Pereutaneous coronary intervention （PCI） for coronary bifurcation lesions has been associated with lower procedural success rates and worse clinical outcomes compared with PCI for simple coronary lesions. Angiographic evaluation alone is sometimes inaccurate and does not reflect the fimctional significance of bifurcation lesions. The fractional flow reserve （FFR） is an easily obtainable, reliable, and reproducible physiologic parameter. This parameter is epicardial lesion specific and reflects both degree of stenosis and the myocardial territory supplied by the specific artery. Recent studies have shown that FFR-guided provisional side branch intervention strategy for bifurcation lesions is feasible and effective and can reduce unnecessary complex interventions and related complications. However, an adequate understanding of coronary physiology and the pitfalls of FFR is essential to properly use FFR for PCI of complex bifurcation lesions.

Distribution of void fraction for gas-liquid slug flow in aninclined pipe

In order to investigate the effect of inclination angle on the spatial distribution of phases, experiments on gas-liquid two-phase slug flow in an inclined pipe were carried out by using the optical probe and an EKTAPRO 1000 high speed motion analyzer. It has been demonstrated that the inclination angle and the mixture velocity are important parameters to influence the distribution of void fraction for upward slug flow in the inclined pipe. At high mixture velocity, the gas phase profile is axial symmetry in the cross-section of the pipe. This is similar to that for vertical slug flow. In contrast, most of the gas phase is located near the upper pipe wall at low mixture velocity. By measuring the axial variation of void fraction along the liquid slug, it can be concluded that there is a high void fraction wake region with length of 3～4D in the front of liquid slug. In the fully developed zone of liquid slug, the peak value of the void fraction is near the upper wall.

Long-term outcomes after fractional flow reserve-guided percutaneous coronary intervention in patients with severe coronary stenosis

Objective To explore the safety and efficacy of FFR-guided percutaneous coronary intervention (PCI) in vessels with severe diameter stenosis. Methods & Results Of 1090 patients undergoing fractional flow reserve (FFR) assessment from 2002 to 2009,we identified 167 patients in whom FFR was measured in at least one 70%–89% stenotic lesion. These patients were subdivided into an FFR-defer group (n = 49) if PCI was deferred (FFR > 0.80),and an FFR-perform group (n = 118) if PCI was performed (FFR ≤ 0.80). Comparatively,an additional 1176 patients undergoing PCI in at least one lesion with 70%–89% stenosis but without measurement of FFR served as a control (angiography- guided) group. Clinical outcomes were compared during a median follow-up of 49.0 months. The 5-year Kaplan-Meier estimated revascularization rates were 16% in the FFR-defer group and 33% in the FFR-perform group (P = 0.046). The incidence of major adverse cardiac events were comparable in these two groups (HR = 0.82,95% CI: 0.37–1.82,P = 0.63). The number of stents placed was significantly lower in the FFR-guided group (0.9 ± 0.8 vs. 1.4 ± 0.8,P < 0.001). Conclusions Functional revascularization for lesions with visually severe stenosis is clinically safe and associated with fewer stents use. This study suggests that extending the use of FFR to more severe coronary lesions may be reasonable.

UNSTEADY FLOWS OF A GENERALIZED SECOND GRADE FLUID WITH THE FRACTIONAL DERIVATIVE MODEL BETWEEN TWO PARALLEL PLATES

The fractional calculus approach in the constitutive relationship model of a generalized second grade fluid is introduced.Exact analytical solutions are obtained for a class of unsteady flows for the generalized second grade fluid with the fractional derivative model between two parallel plates by using the Laplace transform and Fourier transform for fractional calculus.The unsteady flows are generated by the impulsive motion or periodic oscillation of one of the plates.In addition,the solutions of the shear stresses at the plates are also determined.

Gamma-ray attenuation technique for measuring void fraction in horizontal gas-liquid two-phase flow

The measurement of void fraction is of importance to the oil industry and chemical industry. In this article, the principle and mathematical method of determining the void fraction of horizontal gas-liquid flow by using a sin- gle-energy γ-ray system is described. The γ-ray source is the radioactive isotope of 241Am with γ-ray energy of 59.5 keV. The time-averaged value of the void fraction in a 50.0-mm i.d. transparent horizontal pipeline is measured under various combinations of the liquid flow and gas flow. It is found that increasing the gas flow rate at a fixed liquid flow rate would increase the void fraction. Test data are compared with the predictions of the correlations and a good agreement is found. The result shows that the designed γ-ray system can be used for measuring the void fraction in a horizontal gas-liquid two-phase flow with high accuracy.

Fractional flow reserve: Current applications and overview of the available data

Flow fractional reserve(FFR) allows to evaluate the functional significance of coronary artery lesions, through the ratio of the mean coronary artery pressure after the stenosis to the mean aortic pressure duringmaximum hyperemia. The actual widely accepted cutoff value is 0.80. Below this value a coronary lesion is considered significant and therefore it requires invasive revascularization. Several studies [in particular Fractional Flow Reserve vs Angiography for Multivessel Evaluation 1(FAME-1) and FAME-2] have shown the relationship between FFR measurement and hard end-points(death, myocardial infarction, and urgent revascularization). Consequently, FFR evaluation represents the cornerstone in the decision-making in intermediate coronary lesions. Recent studies paved the way for further applications of FFR evaluation in complex and tricky clinical settings. In this paper, we perform an overview of the data regarding contemporary application of FFR. In particular, we review the use of FFR in: left main intermediate stenoses, serial stenoses, evaluation after stenting, guidance in coronary artery bypass surgery, and acute coronary syndrome. All the data presented in our overview confirm the essential role of FFR assessment in the daily clinical practice. The shift from "operator-dependent" to "FFR-dependent" evaluation in intermediate coronary artery stenosis is of paramount importance in order to improve the prognosis of our patients, through the discrimination of the functional role of every single coronary stenosis.

Comparative efficacy and safety of adenosine and regadenoson for assessment of fractional flow reserve:A systematic review and meta-analysis

BACKGROUND Adenosine is a coronary hyperemic agent used to measure invasive fractional flow reserve(FFR)of intermediate severity coronary stenosis.AIM To compare FFR assessment using adenosine with an alternate hyperemic agent,regadenoson.METHODS PubMed,Google Scholar,CINAHL and Cochrane databases were queried for studies comparing adenosine and regadenoson for assessment of FFR.Data on FFR,correlation coefficient and adverse events from the selected studies were extracted and analyzed by means of random effects model.Two tailed P-value less than 0.05 was considered significant.Heterogeneity was assessed using I2 test.RESULTS Five studies with 248 patients were included in the final analysis.All included patients and coronary lesions underwent FFR assessment using both adenosine and regadenoson.There was no significant mean difference between FFR measurement by the two agents[odds ratio(OR)=-0.00;95%confidence interval(CI):(-0.02)-0.01,P=0.88].The cumulative correlation coefficient was 0.98(0.96-0.99,P<0.01).Three of five studies reported time to FFR with cumulative results favoring regadenoson(mean difference 34.31 s;25.14-43.48 s,P<0.01).Risk of adverse events was higher with adenosine compared to regadenoson(OR=2.39;95%CI:1.22-4.67,P=0.01),which most commonly included bradycardia and hypotension.Vast majority of the adverse events associated with both agents were transient.CONCLUSION The performance of regadenoson in inducing maximal hyperemia was comparable to that of adenosine.There was excellent correlation between the FFR measurements by both the agents.The use of adenosine,was however associated with higher risk of adverse events and longer time to FFR compared to regadenoson.

Fractional flow reserve measured via left internal mammary artery after coronary artery bypass grafting:Two case reports

BACKGROUND The fractional flow reserve(FFR)has made the treatment of coronary heart disease more precise.However,there are few reports on the measurement of FFR via the left internal mammary artery(LIMA).Herein,we described the determination of further treatments by measuring FFR via the LIMA in 2 cases after coronary artery bypass grafting(CABG).CASE SUMMARY Case 1 was a 66-year-old male who was admitted due to“chest tightness after CABG.”The patient underwent CABG 7 years prior due to coronary heart disease.Coronary artery angiography showed complete occlusion of the left anterior descending artery(LAD),and subtotal occlusion of the third segment of the right coronary artery.On arterial angiography,there was 85%stenosis at the distal end of the anastomosis of the LIMA-LAD graft.FFR via LIMA was determined at 0.75.Thus,balloon dilation was performed in Case 1.FFR after balloon dilation was 0.94.Case 2 was a 60-year-old male who was admitted due to“chest tightness after CABG.”The patient underwent CABG 6 years prior due to coronary heart disease.There was 60%segmental stenosis in the middle segment of LAD and 75%anastomotic stenosis.FFR measured via LIMA was 0.83(negative);thus the intervention was not performed.Case 2 was given drug treatments.At the 3-mo follow-up,there was no recurrence of chest tightness or shortness of breath in both cases.They are currently under continual follow-up.CONCLUSION We provided evidence that FFR measurement via grafted blood vessels,especially LIMA,after CABG is a good method to determine the intervention course.

Fractional flow reserve and non-hyperemic indices:Essential tools for percutaneous coronary interventions

Hemodynamical evaluation of a coronary artery lesion is an important diagnostic step to assess its functional impact.Fractional flow reserve(FFR)received a class IA recommendation from the European Society of Cardiology for the assessment of angiographically moderate stenosis.FFR evaluation of coronary artery disease offers improvement of the therapeutic strategy,deferring unnecessary procedures for lesions with a FFR>0.8,improving patients'management and clinical outcome.Post intervention,an optimal FFR>0.9 post stenting should be reached and>0.8 post drug eluting balloons.Non-hyperemic pressure ratio measurements have been validated in previous studies with a common threshold of 0.89.They might overestimate the hemodynamic significance of some lesions but remain useful whenever hyperemic agents are contraindicated.FFR remains the gold standard reference for invasive assessment of ischemia.We illustrate this review with two cases introducing the possibility to estimate also non-invasively FFR from reconstructed 3-D angiograms by quantitative flow ratio.We conclude introducing a hybrid approach to intermediate lesions(DFR 0.85-0.95)potentially maximizing clinical decision from all measurements.

Non-invasive Angiographic-based Fractional Flow Reserve:Technical Development,Clinical Implications,and Future Perspectives

New non-and less-invasive techniques have been developed to overcome the procedural and operator related burden of the fractional flow reserve(FFR)for the assessment of potentially significant stenosis in the coronary arteries.Virtual FFR-techniques can obviate the need for the additional flow or pressure wires as used for FFR measurements.This review provides an overview of the developments and validation of the virtual FFR-algorithms,states the challenges,discusses the upcoming clinical trials,and postulates the future role of virtual FFR in the clinical practice.

Linear Plus Linear Fractional Capacitated Transportation Problem with Restricted Flow

In this paper, a transportation problem with an objective function as the sum of a linear and fractional function is considered. The linear function represents the total transportation cost incurred when the goods are shipped from various sources to the destinations and the fractional function gives the ratio of sales tax to the total public expenditure. Our objective is to determine the transportation schedule which minimizes the sum of total transportation cost and ratio of total sales tax paid to the total public expenditure. Sometimes, situations arise where either reserve stocks have to be kept at the supply points, for emergencies or there may be extra demand in the markets. In such situations, the total flow needs to be controlled or enhanced. In this paper, a special class of transportation problems is studied where in the total transportation flow is restricted to a known specified level. A related transportation problem is formulated and it is shown that to each basic feasible solution which is called corner feasible solution to related transportation problem, there is a corresponding feasible solution to this restricted flow problem. The optimal solution to restricted flow problem may be obtained from the optimal solution to related transportation problem. An algorithm is presented to solve a capacitated linear plus linear fractional transportation problem with restricted flow. The algorithm is supported by a real life example of a manufacturing company.

Usefulness of Fractional Flow Reserve during Routine Clinical Procedures in All-Comer Coronary Artery Disease Patients

Background: Fractional flow reserve (FFR)-guided interventions, though proved to be safe, continue to be a much-underutilized modality in determining treatment strategy, and data is lacking in Indian population. Objective: We aimed to determine the use of FFR-guided PCI and assess the overall impact on treatment decisions and clinical outcomes in patients with acute coronary syndrome (ACS) or chronic coronary syndromes (CCS). Methods: In this single-center retrospective and prospective observational study, FFR had been performed for the evaluation of treatment reclassification and clinical outcomes, as per physician’s clinical practice. Results: Data was obtained for 250 subjects (mean age 60.45 ± 9.6 years) with 324 lesions. The treatment plan based on angiography alone changed in 28% of lesions post-hyperemic FFR. The initial treatment plan based on angiography vs. the final treatment plan post-FFR (>0.80) was medical management 56.5% vs. 66.0%;CABG 11.1% vs. 7.7%;and PCI 32.4% vs. 26.2%. In subjects initially assigned to medical management, 14% had changed to PCI, and for subjects initially assigned to PCI, 44% had changed to medical therapy. Receiver operating characteristics (ROC) curve analysis revealed a good correlation between a resting FFR value of <0.87 and hyperemic FFR value of <0.80. The rate of 2-year major adverse cardiovascular events (MACE) was 0.9%. Conclusion: This study supports the use of FFR in determining treatment strategy in ACS or CCS patients with low MACE. Resting FFR value of <0.87 may be an alternative to intracoronary nitroglycerine/adenosine/Nikorandil-induced FFR in predicting positive FFR particularly in hemodynamically unstable patients, and who are intolerant to hyperemic drugs.

Modes of failure with fractional flow reserve guidewires:Insights from the manufacturer and user facility device experience database

BACKGROUND Fractional flow reserve(FFR)measurement is commonly used in the cardiac catheterization laboratory to assess the functional significance of coronary arterial plaques.Robust real-world data on complications and modes of failure of FFR guidewires are limited.AIM To characterize these outcomes by analyzing the post-marketing surveillance data from the United States Food and Drug Administration Manufacturer and User Facility Device Experience(MAUDE)database for commonly used FFR guidewires.METHODS The MAUDE database was queried from January 2010 through April 2020 for 3 FFR guidewires[PressureWireTM X(Abbott),CometTM(Boston Scientific),and VerrataTM(Philips)]by searching for the following events:“Injury”,“malfunction”,“death”,and“other”.This yielded 544 reports.After excluding incomplete reports,486 reports were analyzed.RESULTS Guidewire tip fracture was the most commonly reported mode of failure,in 174(35.8%)cases followed by guidewire kinking(n=152,31.3%),communication failure(n=141,29.0%),and shaft fracture(n=67,13.8%).In total,133(27.4%)device failures resulted in patient adverse events.The most common adverse event was retained guidewire tip,in 71(53.4%)cases,followed by freshly deployed stent dislodgment(n=26,19.6%)and coronary artery dissection(n=23,17.3%).Seven deaths were reported.CONCLUSION FFR guidewire failures can occur because of various mechanisms and cause patient adverse events.The MAUDE database serves as an important platform for improved collaboration among clinicians,device manufacturers,and regulators to improve device performance and optimize patient outcomes.Our analysis provides mechanistic insights of FFR guidewire failure and associated adverse events but cannot verify causality or provide a comparison among different guidewires.

Numerical simulation on centrifugal pump compressible flow field with different gas volume fractions

In order to study the influence of gas-liquid two-phase flow on the performance and internal flow field of a centrifugal pump,the steady three-dimensional flow with different gas volume fractions was simulated by applying the Reynolds-average N-S equation and mixture gas-liquid two-phase flow model,and the compressibility of gas was taken into consideration in the simulation. Then the centrifugal pump characteristic and the gas distribution law in different gas volume fractions were analyzed. The computational results show that gas volume fraction has a certain influence on the performance of the centrifugal pump,and the efficiency and head of the pump are on the decline with the increase of it.Static pressure in the impeller increases in the radial direction,but the pressure gradient in the flow direction is different under the different gas volume fractions. The gas volume is distributed mainly in the ipsilateral direction of impeller back shroud in the flow channel of the volute. On the suction side of the blade inlet there is an obvious low-pressure area,which causes bubbles agglutination and higher gas volume fraction. With the gas entering passage flow,gas volume fraction in the suction decreases and the pressure surface rises gradually. Higher gas volume fraction causes air blocking phenomenon in the flow passage and the discharge capacity reduces. The increase of gas volume makes the turbulent motion within the impeller more and more intense,which leads to more and more energy loss.

Comparison of Fractional Flow Reserve-Guided Revascularization Strategies in Isolated Proximal Left Anterior Descending Coronary Artery Disease

The data about FFR-guided revascularization in isolated proximal LAD disease are limited and studies comparing long-term outcomes of FFR-guided PCI versus FFR-guided CABG in single-vessel proximal LAD disease are lacking. We aimed to assess the 4-year long-term safety and effectiveness of fractional flow reserve (FFR)-guided percutaneous coronary intervention (PCI) and FFR-guided coronary artery bypass graft surgery (CABG) for the treatment of proximal left anterior descending (LAD) lesions. The study included 129 patients with functionally significant (FFR ≤ 0.80) isolated proximal LAD stenosis (PCI, 88 patients vs. CABG, 41). Clinical endpoints were assessed by Kaplan-Meier method and compared by the log-rank test. At a mean follow-up time of 47 ± 12 months, a higher incidence of myocardial infarction in the PCI group (PCI: 32% vs. CABG: 15%;p = 0.003) and a higher incidence of stroke in the CABG group (CABG: 3 (7%) vs. PCI 0 (0%);p = 0.031) were observed. However, there were no significant differences in the primary composite endpoint, death and target vessel revascularization between PCI and CABG groups. The PCI and CABG in isolated proximal LAD lesions yielded similar long-term outcomes regarding the primary composite clinical endpoints. However, stroke was more frequent in the CABG group than in the PCI group.

Exact analytical solutions for axial flow of a fractional second grade fluid between two coaxial cylinders

The velocity field and the adequate shear stress corresponding to the longitudinal flow of a fractional second grade fluid,between two infinite coaxial circular cylinders,are determined by applying the Laplace and finite Hankel transforms.Initially the fluid is at rest,and at time t=0^+, the inner cylinder suddenly begins to translate along the common axis with constant acceleration. The solutions that have been obtained are presented in terms of generalized G functions.Moreover, these solutions satisfy both the governing differential equations and all imposed initial and boundary conditions.The corresponding solutions for ordinary second grade and Newtonian fluids are obtained as limiting cases of the general solutions.Finally,some characteristics of the motion,as well as the influences of the material and fractional parameters on the fluid motion and a comparison between models,are underlined by graphical illustrations.

Exact Solution of Unsteady Flow of Viscoelastic Fluid in a Pipe with Fractional Maxwell Model

The unsteady flow of viscoelastic fluid in a cylindrical pipe was investigated using the fractional Maxwell model. Two special cases of unsteady pipe flow were expressed. The first is start-up flow, and the second is oscillating flow. The exact solution of start-up flow under a constant pressure gradient was obtained by using the theories of Laplace transform and Fourier-Bessel series for fractional derivatives. The exact solution of oscillating flow was obtained by utilizing the separation of variables.