Statistical analysis for measuring the effects of stenotic shapes and spiral flows on wall shear stress by using numerical simulations of physiological blood flow
Numerical simulations have been done for a statistical analysis to investigate the effect of stenotic shapes and spiral flows on wall shear stress in the three-dimensional idealized stenotic arteries. Non-Newtonian flow has been taken for the simulations. The wall of the vessel is considered to be rigid. Physiological, parabolic and spiral velocity profile has been imposed for inlet boundary condition. Moreover, the time-dependent pressure profile has been taken for outlet boundary condition. Reynolds number at the inlet has been ranged approximately from 86 to 966 for the investigation. Low Reynolds number k-w model has been used as governing equation. 120 simulations have been performed for getting the numerical results. However, the numerical results of wall shear stress have been taken for the statistical analysis. The simulations and the statistical analysis have been performed by using ANSYS-18.1 and SPSS respectively. The statistical analyses are significant as p-value in all cases are zero. The eccentricity is the most influencing factor for WSSmax. The WSSmin has been influenced only by the flow spirality. The stenotic length has an influence only on the WSSmax whereas the stenotic severity has an influence on the WSSmax and WSSave.
Simulation of Physiological Non-Newtonian Blood Flow through 3-D Geometry of ...Iwate University
Abstract: A numerical simulation has been performed to investigate blood flow behavior of three dimensional idealized carotid arteries. Non-Newtonian flow has been taken for the simulation. The wall of the vessel is considered to be rigid. Physiological and parabolic velocity profile has been imposed for inlet boundary condition. Reynolds number at the inlet has been ranged approximately from 86to 966 for the investigation. Low Reynolds number k-w model has been used as governing equation. The investigations have been carried out to characterize the flow behavior of blood. The numerical results have been presented in terms of wall shear stress distributions, streamlines contours and axial velocity contours. However, highest wall shear stress has been observed in the bifurcation area. Unexpectedly, transient or unstable flow has created flow disturbance regions in the arteries. Moreover, the disturbance of flow has risen as the severity of stenosis in the artery has been increased.
A One-Dimensional Model of a False AneurysmIJRESJOURNAL
ABSTRACT:A false aneurysm is a hematoma, i.e. collection of blood outside of a blood vessel, that forms due to a hole in the wall of an artery. This represents a serious medical condition that needs to be monitored and, under certain conditions, treated urgently. In this work a one-dimensional model of a false aneurysm is proposed. The new model is based on a one-dimensional model of an artery previously presented by the authors and it takes into account the interaction between the hematoma and the surrounding muscle material. The model equations are derived using rigorous asymptotic analysis for the case of a simplified geometry. Even though the model is simple it still supports a realistic behavior for the system consisting of the vessel and the hematoma. Using numerical simulations we illustrate the behavior of the model. We also investigate the effect of changing the size of the hematoma. The simulations show that our model can reproduce realistic solutions. For instance we show the typical strong pulsation of an aneurysm by blood entering the hematoma during the work phase of the cardiac cycle, and the blood returning to the vessel during the resting phase. Also we show that the aneurysm grows if the pulse rate is increased due to, e.g., a higher work load.
Simulation of Physiological Non-Newtonian Blood Flow through 3-D Geometry of ...Iwate University
Abstract: A numerical simulation has been performed to investigate blood flow behavior of three dimensional idealized carotid arteries. Non-Newtonian flow has been taken for the simulation. The wall of the vessel is considered to be rigid. Physiological and parabolic velocity profile has been imposed for inlet boundary condition. Reynolds number at the inlet has been ranged approximately from 86to 966 for the investigation. Low Reynolds number k-w model has been used as governing equation. The investigations have been carried out to characterize the flow behavior of blood. The numerical results have been presented in terms of wall shear stress distributions, streamlines contours and axial velocity contours. However, highest wall shear stress has been observed in the bifurcation area. Unexpectedly, transient or unstable flow has created flow disturbance regions in the arteries. Moreover, the disturbance of flow has risen as the severity of stenosis in the artery has been increased.
A One-Dimensional Model of a False AneurysmIJRESJOURNAL
ABSTRACT:A false aneurysm is a hematoma, i.e. collection of blood outside of a blood vessel, that forms due to a hole in the wall of an artery. This represents a serious medical condition that needs to be monitored and, under certain conditions, treated urgently. In this work a one-dimensional model of a false aneurysm is proposed. The new model is based on a one-dimensional model of an artery previously presented by the authors and it takes into account the interaction between the hematoma and the surrounding muscle material. The model equations are derived using rigorous asymptotic analysis for the case of a simplified geometry. Even though the model is simple it still supports a realistic behavior for the system consisting of the vessel and the hematoma. Using numerical simulations we illustrate the behavior of the model. We also investigate the effect of changing the size of the hematoma. The simulations show that our model can reproduce realistic solutions. For instance we show the typical strong pulsation of an aneurysm by blood entering the hematoma during the work phase of the cardiac cycle, and the blood returning to the vessel during the resting phase. Also we show that the aneurysm grows if the pulse rate is increased due to, e.g., a higher work load.
Shear stress Effects on Left Coronary Artery Saran A K
Throughout the last decade, many studies have found the effect of shear stress on coronary vasculature. Ischaemic Heart Disease is a leading cause of death worldwide, killing an Indian every minute. The most common cause of myocardial ischemia is Atherosclerosis and on the basis of several data, atherosclerosis appears to be more prevalent in the left coronary arterial system compared to the right. The reason for this has remained an enigma for a long while but can be explained by using shear stress. Now, we will see how the shear stress breaks the coronary circuit
Stanford Type A Aortic Dissection: a Complex Disease for Patients and Cardiot...Crimsonpublisherssmoaj
Acute type A aortic dissection is a catastrophic event in which blood exits the vascular lumen and dissects the media, creating a false lumen. Surgery is the best possible treatment but it is complex. The surgical team needs to understand the anatomy and physiopathology before dealing with the repair. While there are just a few surgical solutions for the repair of the dissected ascending aorta, debate is still ongoing about the best surgical option for the disease involving the arch and the descending aorta. Late reoperations are relatively common on the aortic valve and/or the distal aorta after primary repair. Results are excellent in specialized centers with high volume and complexity. Lifelong follow-up is required in survivors.
ANALYSIS OF FLOW CHARACTERISTICS OF THE BLOOD THROUGH CURVED ARTERY WITH MIL...indexPub
Narrowing of the arteries caused by atherosclerosis reduces blood flow to the heart, which results shows ischemia, angina pectoris, cerebral strokes, and other coronary artery disease signs and symptoms. Curvature is seen in blood vessels at various locations. The stenotic surface provides an additional curvature and the point of maximum shear which varies with the cross-section. A cylindrical form of the Navier-Stokes equations in polar coordinate system have been extended to include dynamic curvature along the axial direction. The blood flow behavior of taking different values of blood parameters like viscosity, the radius of the artery, and the thickness of the stenosis has been studied with and without curvature by using an extended blood flow model with dynamic curvature. Moreover, the aspects of blood flow, such as dynamic curvature velocity profile, volumetric flow rate, pressure drop, and shear stress, have been studied in relation to blood flow around curved arteries with stenosis, variations in the radii of the artery, thickness of the stenosis, and viscosity. The information may reveal that by increasing the values of curvature, viscosity, and thickness of stenosis, velocity, and volumetric flow rate can be quickly reduced. Increasing the curvature, viscosity, and thickness of stenosis also results in an increase in shear stress and a pressure drop. The presence of curved stenotic arteries has a significant impact on the flow parameters, and it is crucial to know about these dynamics in order to study the cardiovascular system.
PHYSIOLOGICAL NON-NEWTONIAN BLOOD FLOW THROUGH SINGLE STENOSED ARTERYIwate University
Abstract. A numerical simulation to investigate the Non-Newtonian modeling effects on physiological flows in a three dimensional idealized artery with a single stenosis of 85% severity is given. The wall vessel is considered to be rigid. Oscillatory physiological and parabolic velocity profile has been imposed for inlet boundary condition. Determination of the physiological waveform is performed using a Fourier series with sixteen harmonics. The investigation has a Reynolds number range of 96 to 800. Low Reynolds number k − ω model is used as governing equation. The investigation has been carried out to characterize two Non-Newtonian constitutive equations of blood, namely, (i) Carreau and (ii) Cross models. The Newtonian model has also been investigated to study the physics of fluid. The results of Newtonian model are compared with the Non-Newtonian models. The numerical results are presented in terms of velocity, pressure, wall shear stress distributions and cross sectional velocities as well as the streamlines contour. At early systole pressure differences between Newtonian and Non-Newtonian models are observed at pre-stenotic, throat and immediately after throat regions. In the case of wall shear stress, some differences between Newtonian and Non-Newtonian models are observed when the flows are minimum such as at early systole or diastole. In general, the velocities at throat regions are highest at all-time phase. However, at pick systole higher velocities are observed at post-stenotic region. Downstream flow of all models creates some recirculation regions at diastole.
Mathematical Modeling of Bingham Plastic Model of Blood Flow Through Stenotic...IJERA Editor
The aim of the present paper is to study the axially symmetric, laminar, steady, one-dimensional flow of blood through narrow stenotic vessel. Blood is considered as Bingham plastic fluid. The analytical results such as pressure drop, resistance to flow and wall shear stress have been obtained. Effect of yield stress and shape of stenosis on resistance to flow and wall shear stress have been discussed through tables and graphically. It has been shown that resistance to flow and the wall shear stress increase with the size of stenosis but these increase are, however, smaller due to non-Newtonian behaviour of the blood.
EFFECTS OF STENOSIS ON POWER LAW FLUID FLOW OF BLOOD IN BLOOD VESSELSJournal For Research
In this paper we assume that the blood is to be a Non-Newtonian and incompressible and Homogeneous fluid. An investigation has been done for the resistance to flow across mild stenosis situated symmetrically on steady blood flow through arteries with uniform or non-uniform cross section. An analytical solution for Power law fluid has been obtained. For the physiological insight of the problem various parameters systemic and pulmonary artery are taken and the study reveals that as the height of the stenosis increases in uniform or non-uniform portion of the artery, the resistance parameter and shear stress also steadily increases, whereas, flow rate decreases steadily and we analyze some cases between flux, pressure gradient and radius and give some significant results.
Shear stress Effects on Left Coronary Artery Saran A K
Throughout the last decade, many studies have found the effect of shear stress on coronary vasculature. Ischaemic Heart Disease is a leading cause of death worldwide, killing an Indian every minute. The most common cause of myocardial ischemia is Atherosclerosis and on the basis of several data, atherosclerosis appears to be more prevalent in the left coronary arterial system compared to the right. The reason for this has remained an enigma for a long while but can be explained by using shear stress. Now, we will see how the shear stress breaks the coronary circuit
Stanford Type A Aortic Dissection: a Complex Disease for Patients and Cardiot...Crimsonpublisherssmoaj
Acute type A aortic dissection is a catastrophic event in which blood exits the vascular lumen and dissects the media, creating a false lumen. Surgery is the best possible treatment but it is complex. The surgical team needs to understand the anatomy and physiopathology before dealing with the repair. While there are just a few surgical solutions for the repair of the dissected ascending aorta, debate is still ongoing about the best surgical option for the disease involving the arch and the descending aorta. Late reoperations are relatively common on the aortic valve and/or the distal aorta after primary repair. Results are excellent in specialized centers with high volume and complexity. Lifelong follow-up is required in survivors.
Characterizing stable coronary plaques with msct angiography
Similar to Statistical analysis for measuring the effects of stenotic shapes and spiral flows on wall shear stress by using numerical simulations of physiological blood flow
ANALYSIS OF FLOW CHARACTERISTICS OF THE BLOOD THROUGH CURVED ARTERY WITH MIL...indexPub
Narrowing of the arteries caused by atherosclerosis reduces blood flow to the heart, which results shows ischemia, angina pectoris, cerebral strokes, and other coronary artery disease signs and symptoms. Curvature is seen in blood vessels at various locations. The stenotic surface provides an additional curvature and the point of maximum shear which varies with the cross-section. A cylindrical form of the Navier-Stokes equations in polar coordinate system have been extended to include dynamic curvature along the axial direction. The blood flow behavior of taking different values of blood parameters like viscosity, the radius of the artery, and the thickness of the stenosis has been studied with and without curvature by using an extended blood flow model with dynamic curvature. Moreover, the aspects of blood flow, such as dynamic curvature velocity profile, volumetric flow rate, pressure drop, and shear stress, have been studied in relation to blood flow around curved arteries with stenosis, variations in the radii of the artery, thickness of the stenosis, and viscosity. The information may reveal that by increasing the values of curvature, viscosity, and thickness of stenosis, velocity, and volumetric flow rate can be quickly reduced. Increasing the curvature, viscosity, and thickness of stenosis also results in an increase in shear stress and a pressure drop. The presence of curved stenotic arteries has a significant impact on the flow parameters, and it is crucial to know about these dynamics in order to study the cardiovascular system.
PHYSIOLOGICAL NON-NEWTONIAN BLOOD FLOW THROUGH SINGLE STENOSED ARTERYIwate University
Abstract. A numerical simulation to investigate the Non-Newtonian modeling effects on physiological flows in a three dimensional idealized artery with a single stenosis of 85% severity is given. The wall vessel is considered to be rigid. Oscillatory physiological and parabolic velocity profile has been imposed for inlet boundary condition. Determination of the physiological waveform is performed using a Fourier series with sixteen harmonics. The investigation has a Reynolds number range of 96 to 800. Low Reynolds number k − ω model is used as governing equation. The investigation has been carried out to characterize two Non-Newtonian constitutive equations of blood, namely, (i) Carreau and (ii) Cross models. The Newtonian model has also been investigated to study the physics of fluid. The results of Newtonian model are compared with the Non-Newtonian models. The numerical results are presented in terms of velocity, pressure, wall shear stress distributions and cross sectional velocities as well as the streamlines contour. At early systole pressure differences between Newtonian and Non-Newtonian models are observed at pre-stenotic, throat and immediately after throat regions. In the case of wall shear stress, some differences between Newtonian and Non-Newtonian models are observed when the flows are minimum such as at early systole or diastole. In general, the velocities at throat regions are highest at all-time phase. However, at pick systole higher velocities are observed at post-stenotic region. Downstream flow of all models creates some recirculation regions at diastole.
Mathematical Modeling of Bingham Plastic Model of Blood Flow Through Stenotic...IJERA Editor
The aim of the present paper is to study the axially symmetric, laminar, steady, one-dimensional flow of blood through narrow stenotic vessel. Blood is considered as Bingham plastic fluid. The analytical results such as pressure drop, resistance to flow and wall shear stress have been obtained. Effect of yield stress and shape of stenosis on resistance to flow and wall shear stress have been discussed through tables and graphically. It has been shown that resistance to flow and the wall shear stress increase with the size of stenosis but these increase are, however, smaller due to non-Newtonian behaviour of the blood.
EFFECTS OF STENOSIS ON POWER LAW FLUID FLOW OF BLOOD IN BLOOD VESSELSJournal For Research
In this paper we assume that the blood is to be a Non-Newtonian and incompressible and Homogeneous fluid. An investigation has been done for the resistance to flow across mild stenosis situated symmetrically on steady blood flow through arteries with uniform or non-uniform cross section. An analytical solution for Power law fluid has been obtained. For the physiological insight of the problem various parameters systemic and pulmonary artery are taken and the study reveals that as the height of the stenosis increases in uniform or non-uniform portion of the artery, the resistance parameter and shear stress also steadily increases, whereas, flow rate decreases steadily and we analyze some cases between flux, pressure gradient and radius and give some significant results.
Casson flow of blood through an arterial tube with overlapping stenosisiosrjce
The objective of the present analysis is to study the effect of overlapping stenosis on blood flow
through an artery by taking the blood as Casson type non-Newtonian fluid. The expressions for flux and
resistance to flow have been studied here by assuming the stenosis is to be mild. The results are shown
graphically for different values of yield stress, stenosis length, stenosis height and discussed.
EFFECT OF NEGATIVE ANGLE CANNULATION DURING CARDIOPULMONARY BYPASS – A COMPUT...ijbesjournal
Creation of emboli in the aortic root and changes in flow distribution between supra-aortic arteries and descending aorta can lead to stroke and perfusion related tissue damage during cardiopulmonary bypass. A thorough understanding of how the angle of cannulation affects the overall success of cardiopulmonary bypass during cannulation of the ascending aorta is needed. Previous simulation research has observed the effect of outflow cannula position by changing the location of the cannulation site to the subclavian artery and other vessels, as well as positions for innovative cannula designs. The purpose of this study is to evaluate the success of the procedure while using a straight cannula, modulating the angle of cannulation below horizontal in the frontal plane. A simplified geometry of the aorta was used. The success of the procedure was quantified by observing wall shear stress, normal stress, intra-fluid shear stress, and flow distribution. A numerical study was performed to solve the Reynolds Averaged Naiver Stokes governing equations, which were used in conjunction with a constant density fluid to simulate blood, and a realizable two-layer k-ε turbulence model
Study on viscosity induced contrast in ultrasound color flow imaging of carot...IJECEIAES
Efficient imaging of blood flow disturbances resulted from carotid atherosclerosis plays a vital role clinically to predict brain stroke risk. Carotid atherosclerosis and its development is closely linked with raised blood viscosity. Therefore, study of viscosity changing hemodynamic effect has importance and it might be useful for improved examination of carotid atherosclerosis incorporating the viscosity induced contrast in conventional ultrasound imaging. This work considered the design of realistic models of atherosclerotic carotid artery of different stages and solved to compute the hemodisturbances using computational fluid dynamics (CFD) by finite element method (FEM) to investigate viscosity changes effect. Ultrasound color flow image of velocities of blood have been constructed using phase shift information estimated with autocorrelation of Hilbert transformed simulated backscattered radiofrequency (RF) signals from moving blood particles. The simulated ultrasound images have been compared with CFD simulation images and identified a good match between them. The atherosclerosis stages of the models have been investigated from the estimated velocity data. It has been observed that the blood velocities increase noticeably in carotid atherosclerotic growths and velocity distribution changes with viscosity variations. It is also found importantly that the viscosity induced contrast associated to atherosclerosis is detectable in ultrasound color flow imaging. The findings of this work might be useful for better investigation of carotid atherosclerosis as well as prediction of its progression to reduce the stroke risk.
Endovascular complications: Antiplatelet management for flow diversionbijnnjournal
Up to 3−5% of the general population is affected by cerebral aneurysms that are associated with both modifiable
as well as non-modifiable risk factors ranging from familial to acquired neurovascular conditions. The initial
treatment option was aneurysm clipping and evolved to including primary or adjuvant endovascular treatment.
Aneurysm re-rupture, although rare, can have devastating consequences such as intracranial bleeding and carotidcavernous fistula. Emergent surgery in view of delayed aneurysm rupture in patients maintained on dual antiplatelet
therapy presents with the need to carefully assess the procedure-related risk factors and evaluate the patients’
platelet function. With the advent of novel technology, flow diverters came into play
Similar to Statistical analysis for measuring the effects of stenotic shapes and spiral flows on wall shear stress by using numerical simulations of physiological blood flow (20)
The practical implication of Technical analysis with Bollinger Bands on empir...Iwate University
Abstract
Any trader or investor gets benefits to analyze the market by using the method of technical analysis. Bollinger Bands is one of the most important indicators of technical analysis. In this study I have discussed easily about technical analysis, various types of indicators especially Bollinger Bands with example so that any new or old trader or investor can get understand about these fact. Then I have focus on practical implications where I have implemented Bollinger Bands as indicator to analyze ten listed companies of DSE. These ten companies are- LankaBangla Finance Ltd., Meghna Petroleum Ltd., United Airways (BD) Ltd., Jamuna Oil Company Ltd., Padma Oil Company Ltd., Active Fine Chemicals Ltd, Bangladesh Submarine Cable Company Ltd., Islami Bank Bangladesh Ltd., Square Pharmaceutical Ltd., & Titas Gas Transmission & Dist. Co. Ltd.
I have also presented a regression analysis for each company. The regressions are done by two variables which are closing price of each company as dependent variable & Index of DSE as independent variable. These regression analyses are done to find dependence of company’s closing price on Index of DSE. Finally, I have presented the Bollinger Bands charts of Index of DSE to highlight the market condition of DSE.
At last I expect this study will be a conducive for any new or old trader or investor to analyze their markets.
The Barrier of Establishing Democracy in BangladeshIwate University
The Barrier of Establishing Democracy in Bangladesh
The term democracy is derived from the Greek words, demos and Kratos, the former meaning the people and the latter power. Democracy thus means power of the people. It is now regarded as a form of government in which the people rule themselves either directly or indirectly through their representatives. In the words of President Abraham Lincoln, “Democracy is a government of the people, by the people and for the people”. According to Bryce, “Democracy is that form of government in which the ruling power of a state is legally vested, not in any particular class or classes but in the members of the community as a whole”.
But what is the present status of democracy in our country???..
We have passed about forty-one years since independence but our achievements in the spheres of democracy and development are not noteworthy. In Bangladesh every political leader or party, civil or military, popular or unpopular, big or small, in or out of power, talks about democratic incessantly. Even so the nation has failed to put it into practice. Parties voted into power to strengthen democracy have all failed to encourage its values. Taking advantage of this situation, military leaders intervened to practice their own version of democracy, which only exacerbated the crisis. The country today is riddle with numerous problems threatening the very development of democracy.
What is the reason for this???..
THE PROSPECT OF BOND MARKET: BANGLADESH PERSPECTIVEIwate University
There are a lot of impediments to the development of bond market in Bangladesh. The bond market is still at a budding stage. It is attributed by a limited supply of debt instruments, especially long-term instruments. Consequently, the reliable benchmark for long-term bonds or debentures does not exist. The market is illiquid and trading is motionless. It is slowed down by the relatively high interest rate bearing risk-free national savings scheme, though interest has been reduced a little bit in recent years. In addition, the issuance process of bond is burdensome and costly, which becomes a disincentive to the development of effective bond market. Finally, the investor base has to be extended in parallel with a suitable investor education. Recommended measures must be undertaken for developing the bond market.
A study on five model of organisational behaviorIwate University
Top management’s models are particularly important to identify, for the underlying model that exists within a firm’s chief executive officer tends extend throughout that firm. For this reason, models of organizational behavior are highly significant.
A STUDY ON JOB SATISFACTION IN BANKING SECTOR IN BANGLADESHIwate University
This report study is aimed at finding the relationship between the overall satisfaction and the various factors of job satisfaction such as payment, promotion, security, treatment, bonus etc. taking bank of Bangladesh into consideration. It overviews some theoretical literature on these satisfaction factors and presents the regression outputs and their interpretation.
The findings of the study are:
1. Position of the various satisfaction level of factors of bank.
2. The regression output has components:
o Regression statistics table
o Correlation table
o Model summery
o ANOVA table
o Regression coefficients table
3. And their interpretation.
Quantitative data is taken by conducting the survey two banks in savar such as Dutch-Bangla Bank Lt. and Sonali Bank Lt.
AN ASSAIGNMENT ON FINANCIAL RATIO ANALYSIS OF M.I. CEMENT FACTORY LIMITEDIwate University
Financial analysis is the selection, evaluation, and interpretation of financial data, along with other pertinent information, to assist in investment and financial decision-making.
In our study we will try to measure the risk and profitability of M.I. Cement Factory Limited by the financial ratio analysis.
M.I. cement factory was introduced on 11 December, 1994 under the Companies Act 1994 as a public Limited company. The plant, equipped with world famous O’Sepa Separator, initially went into operation with the daily production capacity of 600 metric tons in the year 2000 and marketed its product with the brand name Crown cement. From the very beginning, it has maintained an uncompromising policy of producing high quality cement. As a result, it has gained huge popularity in the market. Due to increase of demand, the company has set up its second unit with the production capacity of 800 metric tons per day in 2002 and third unit with capacity of 1400 tons per day in 2007.
Gradually with the increase of demand the management undertook further expansion program for 4th unit of the plant raising the total production capacity to 5800 metric tons per day. The 4th unit expansion would be completed within 2011.
In our study we have shown the statement of financial position, statement of comprehensive income, liquidity ratio, solvency ratio, profitability ratio and their analysis.
Energy can exist in numerical forms such as thermal, mechanical, kinetic, potential, electrical, magnetic, chemical, and nuclear their sum constitutes the total energy E (or e on a unit mass basis) of a system. The forms of energy related to the molecular structure of a system and the degree of the molecular activity are referred to as the microscopic energy. The sum of all microscopic form of energy is called the internal energy of a system, and is denoted by U.
This report is aimed at finding the relationship between the net income and the current asset, current liability, working capital, debt ratio, current ratio, quick ratio, taking cement companies of Bangladesh into consideration. It overviews some theoretical literature on these financial factors and presents the regression outputs and their interpretation.
The findings of the study are:
1. Position of the various financial performances of these companies.
2. The regression output has components:
o Regression statistics table
o Correlation table
o Model summery
o ANOVA table
o Regression coefficients table
o Excluded Variables table.
3. And their interpretation.
Quantitative data is taken from company’s annual reports, business research companies’ archives and financial websites. The findings from the study can either have a positive or negative impact on financial performance.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
AIRCRAFT GENERAL
The Single Aisle is the most advanced family aircraft in service today, with fly-by-wire flight controls.
The A318, A319, A320 and A321 are twin-engine subsonic medium range aircraft.
The family offers a choice of engines
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Event Management System Vb Net Project Report.pdfKamal Acharya
In present era, the scopes of information technology growing with a very fast .We do not see any are untouched from this industry. The scope of information technology has become wider includes: Business and industry. Household Business, Communication, Education, Entertainment, Science, Medicine, Engineering, Distance Learning, Weather Forecasting. Carrier Searching and so on.
My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
In my system we have to make a system by which a user can record all events coordinated by a particular faculty. In our proposed system some more featured are added which differs it from the existing system such as security.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
COLLEGE BUS MANAGEMENT SYSTEM PROJECT REPORT.pdfKamal Acharya
The College Bus Management system is completely developed by Visual Basic .NET Version. The application is connect with most secured database language MS SQL Server. The application is develop by using best combination of front-end and back-end languages. The application is totally design like flat user interface. This flat user interface is more attractive user interface in 2017. The application is gives more important to the system functionality. The application is to manage the student’s details, driver’s details, bus details, bus route details, bus fees details and more. The application has only one unit for admin. The admin can manage the entire application. The admin can login into the application by using username and password of the admin. The application is develop for big and small colleges. It is more user friendly for non-computer person. Even they can easily learn how to manage the application within hours. The application is more secure by the admin. The system will give an effective output for the VB.Net and SQL Server given as input to the system. The compiled java program given as input to the system, after scanning the program will generate different reports. The application generates the report for users. The admin can view and download the report of the data. The application deliver the excel format reports. Because, excel formatted reports is very easy to understand the income and expense of the college bus. This application is mainly develop for windows operating system users. In 2017, 73% of people enterprises are using windows operating system. So the application will easily install for all the windows operating system users. The application-developed size is very low. The application consumes very low space in disk. Therefore, the user can allocate very minimum local disk space for this application.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
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Statistical analysis for measuring the effects of stenotic shapes and spiral flows on wall shear stress by using numerical simulations of physiological blood flow
1. Series on Biomechanics, Vol.33, No.1 (2019), 16-29
16
Statistical analysis for measuring the effects of stenotic shapes and spiral
flows on wall shear stress by using numerical simulations of
physiological blood flow
K. Mamuna
, K. Funazakia
, M. N. Akhterb
a
Mechanical Engineering Department, Iwate University, Morioka, Iwate, Japan; presidentmamun@gmail.com
b
Department of Mathematics, Dhaka University of Engineering and Technology, Dhaka, Bangladesh
_____________________________________________________________________________________
Abstract
Numerical simulations have been done for a statistical analysis to investigate the effect of stenotic shapes and
spiral flows on wall shear stress in the three-dimensional idealized stenotic arteries. Non-Newtonian flow has been
taken for the simulations. The wall of the vessel is considered to be rigid. Physiological, parabolic and spiral
velocity profile has been imposed for inlet boundary condition. Moreover, the time-dependent pressure profile has
been taken for outlet boundary condition. Reynolds number at the inlet has been ranged approximately from 86 to
966 for the investigation. Low Reynolds number k-w model has been used as governing equation. 120 simulations
have been performed for getting the numerical results. However, the numerical results of wall shear stress have been
taken for the statistical analysis. The simulations and the statistical analysis have been performed by using ANSYS-
18.1 and SPSS respectively. The statistical analyses are significant as p-value in all cases are zero. The eccentricity
is the most influencing factor for WSSmax. The WSSmin has been influenced only by the flow spirality. The stenotic
length has an influence only on the WSSmax whereas the stenotic severity has an influence on the WSSmax and
WSSave.
Keywords: Haemodynamic, non-Newtonian flows, regression analysis, turbulent flows, spiral flow
____________________________________________________________________________________________
1. Introduction
The cardiovascular system actually maintains blood flow to all cells such as the artery, capillary and
vain in the body. Thus, cardiovascular diseases are the types of disease that involve heart or blood
vessels. Stenosis is one of the most devastating cardiovascular diseases which are formed by depositing
fatty substances on the wall of the blood vessels because, it may lead to total vessel blockage in some
instances and therefore poses a serious medical problem. However, arterial stenosis is an abnormal
constriction of the artery. Arteries are generally strong and flexible blood vessels that can expand and
contract with heartbeats. They contain a thin layer of cells called endothelium that keeps the artery
smooth and allows blood to flow easily. Excessive accumulation of Lower Density Lipoprotein or LDL
cholesterol in the artery wall is the main cause for damaging the endothelium. Thus, the arterial wall loses
its flexibility which decreases the area of artery which is called arterial stenosis.
The initial research on blood flow within stenosed arteries concentrated on experimental simulations.
Numerous experimental studies have been carried out in animals, stenosis models, and humans by
Giddens et al. [1]; Saad and Giddens [2]; and strandness et al. [3]. Clark [4] and Saad and Giddens [2]
showed that transitional flow or turbulence can be expected distal to the constriction even with relatively
mild stenoses. However, numerical simulation of blood flow can help to obtain detailed flow patterns,
such as wall shear stress distributions which are very difficult to obtain experimentally. Thus, numerical
modelling of stenotic blood flow has been being popular day by day.
However, moderate and severe stenoses may create a highly disturbed flow region in the downstream
area of the stenotic artery. These disturbed flows may either remain laminar or may undergo transition to
turbulent flow depending upon the flowrate through the stenotic geometry. Besides, turbulence represents
an abnormal flow condition, which is related to several vascular disorders such as post-stenotic dilatation
described by Cassanova and Giddens [5]. Thus, the development of turbulent flow has important clinical
2. K. Mamun et al./ Statistical analysis for measuring the effects of stenotic shapes and spiral flows on wall shear
stress by using numerical simulations of physiological blood flow
17
consequences. It may also significantly decrease in pressure and abnormally increase wall shear stresses
in the artery, which may result in haemolysis and the activation of platelets.
Smith [6] conducted extensive studies of steady flows through an axisymmetric stenosed artery using
an analytical approach where he described that the resulting flow patterns were highly dependent on
geometry of the stenosis and the overall Reynolds number of the flow. Deshpande et al [7] analysed the
finite difference scheme to solve the flow through an axisymmetric stenosis under steady flow and arrived
at similar conclusions. Besides, Young and Tsai [8] conducted experimental analysis on steady flow
through stenosed arteries with varying severity, stenosis length, axisymmetric and asymmetric conditions,
and with a range of Reynolds numbers from laminar to turbulent flows. Talukder et al. [9] investigated
the effects of double stenoses and the influence of the distance between stenoses on pressure drops in
steady and Newtonian flows through the solid artery and found that the pressure drop is linearly related to
the number of stenoses. Kumar and awasthi [10] analytically examined the laminar and Newtonian blood
flows in a solid artery with multiple stenoses. They also studied the effect of haematocrit percentage on
pressure drop and wall shear stress. Stenosis eccentricity is another important key characteristic of
stenosis that contributes to the extent of physiological disturbance [11]. A. Javadzadegan et al., [12, 13]
have found the significant roles of stenotic severity and eccentricity in coronary hemodynamic. Besides,
the presence of a helical spiral type blood flow with varying direction of rotation within the aorta has
been well confirmed [14-17] and has been shown by several CFD studies to be beneficial for reducing
hemodynamic anxiety in human arteries [18-23]. In addition to these computational studies, several
experimental investigations have also confirmed the beneficial impacts of aortic spiral flow in the
cardiovascular system [24-26].
There are some locations in the artery where blood flow has low Reynolds number or shear rate.
However, it has been described that Newtonian behaviour to blood flow is only valid when shear rates is
greater than 100s-1, which tends to occur only in larger arteries, according to Pedley [27]. Besides, if the
shear rate is high, the blood behaves like a Newtonian fluid whose viscosity be 0.00345Pa.
s, according to
Berger and Jou [28]. However, if the shear rate of blood flow falls down, the blood flow exhibits Non-
Newtonian property. In addition, blood exhibits remarkable Non-Newtonian properties in some diseased
condition like severe myocardial infarction, cerebrovascular diseases and hypertension, described by
Chien [29]. Thus, non-Newtonian blood models would provide a more accurate representation of blood
flow behaviour within the arteries.
Wall shear stress (WSS) is the frictional force generated by the blood flow in the blood vessels. It is
one of the main hemodynamic forces to influence vascular endothelial cells, which plays avital role in the
development and progression of atherosclerotic plaques and arterial aneurysms [30]. Besides, it works
directly on the endothelium as a biological stimulator by controlling the cellular function [31, 32].
However, high wall shear stress in normal arteries is believed to have protective roles to form stenosis,
but it enhances platelet activation and subsequent aggregation and even plaque rupture in stenotic arteries
[33, 34]. In addition to high WSS, regions of relatively low WSS in normal arteries are also believed to
have a higher propensity to form the stenosis [35, 36]. Thus, stenosis can be formed for both in high and
low wall shear stress in the arteries.
Nomenclature.
x Axial location of the flow field r Radial location of the flow field
t Time period of the inlet flow cycle R Radius of the healthy artery
u Instantaneous velocity U Average velocity
WSSmax Maximum wall shear stress WSSmin Minimum wall shear stres
WSSave Average wall shear stress Constant viscosity of blood
Density of blood Shear rate
Turbulent kinetic energy Shearing stress
Kinematic viscosity of the fluid Closure coefficient
Specific dissipation rate δ Kronecker delta
e Statistical error 3-D Three Dimension
Although the individual effects of aortic spiral blood flow as well as stenotic severity, stenotic
length and stenotic eccentricity on the wall shear stress and on other hemodynamic parameter has been
3. K. Mamun et al./ Statistical analysis for measuring the effects of stenotic shapes and spiral flows on wall shear
stress by using numerical simulations of physiological blood flow
18
investigated, combinational effects of them are unknown. Therefore, the present study investigates to find
out the effects of flow spirality and stenotic shape on wall shear stress.
2. Methodology
2.1. Geometry
One hundred twenty idealized 3-D stenotic arteries have been used as the geometric model for this
study; whereas only four among them have been shown in the Fig. 1. These models have been
differentiated by their stenotic shape such as Stenotic severity, eccentricity and length; which are changed
with model to model. Various stenotic severities (by area), which were changed from 25% to 85%, have
been randomly selected for the models in the study. Stenotic eccentricity has been quantified by the
eccentricity index (EI) ranging from 0 to 0.9 where EI of 0 corresponds to a concentric stenosis whereas
EI of 0.9 corresponds to a highly eccentric stenosis. Besides, stenotic lengths 1D, 1.5D, 2D, 2.5D and 3D
have been taken in the models where D means diameter of the artery. The diameter of the models is 6
mm. The geometry of generated models have been divided by three parts such as pre stenotic length (4D),
stenotic length isn’t fixed and has been changed from 1D to 3D for different models and post stenotic
length (6D). The wall is considered to be rigid. These arteries are modeled by using ANSYS Workbench.
However, the flow field meshing nodes and elements number are different for the different models,
because the shape and size of the stenosis are not the same.
Fig. 1. Different stenotic arteries with the different stenosis's shapes.
2.2. Blood properties
Blood has been taken as fluid where the density of the blood is 1050kg/m3
. Moreover, blood has been
considered Non-Newtonian fluid, so the viscosity of the blood is calculated from cross model. Malcolm
M. Cross [39] proposed a shear rate dependent viscosity model called Cross model. The Cross model is
defined by the equation (1).
(1) = + ( − ) 1 +
| ̇ |
Where, = 0.0364 . is the usual molecular blood viscosity for zero shear rates, =
0.00345 . when shear rates is high, = 2.63 is the reference shear rate, ̇ is the instantaneous
shear rate, and m=1.45 is the constant.
4. K. Mamun et al./ Statistical analysis for measuring the effects of stenotic shapes and spiral flows on wall shear
stress by using numerical simulations of physiological blood flow
19
2.3. Governing equation
In the present study, numerical calculation has been done to simulate blood flows through stenotic
arteries with low Reynolds numbers ranging approximately from 86 to 966. In this range of Reynolds
numbers, the viscous sub-layer is very much thick, so flow should be laminar theoretically. However, for
highly eccentric and severe stenotic arteries, the blood passes through the very critical region with high
velocity. Naturally the Reynolds number of blood flow will increase during passing through the highly
eccentric and severe throat. Thus, the flow may undergo transition to turbulent for this condition. Neither
laminar flow neither modelling nor standard two-equation models are suitable for this kind of blood flow.
We therefore chose the Wilcox low-Re k-w turbulence model for our simulation. However, the Navier-
Stokes equations can be given by (2) and (3).
(2) = 0
(3) + = − +
Since each term of this equation is time averaged, the equation is referred to as a Reynolds averaged
Navier-Stokes (RANS) equation. During this procedure, several additional unknown parameters appear
which require additional equations to be introduced as turbulence models. The set of RANS equations
have been presented by the equations (4) and (5).
(4) = 0
(5) + = − + + + (− )
In this equation (−ρui
′uj
′) is an additional term known as the Reynolds’s stress tensor, which can be
approximated by using Boussinesq’s hypothesis, (6).
(6) − = + −
The k equation -
(7) − = + −
The equation –
(8) = + + −
Turbulent viscosity –
(9) =
The generation rate of turbulence kinetic energy-
(10) = +
5. K. Mamun et al./ Statistical analysis for measuring the effects of stenotic shapes and spiral flows on wall shear
stress by using numerical simulations of physiological blood flow
20
The values of the Wilcox model constants were -
(11) = 0.555, = 0.8333, = 0.09, = 2 and = 2
2.4. Boundary condition
Physiological, parabolic and spiral velocity profile has been imposed for the inlet boundary condition.
Moreover, time dependent pressure profile has been taken for outlet boundary condition. For this purpose
one user defined function has been written in C++ programming language to demonstrate the inlet and
outlet boundary conditions. Axial velocity profile -
(12) = 1 −
2+ 2
2
Tangential velocity profile -
(13) =
2+ 2 1/2
The tangential velocity ( ) has been applied in the inlet as the spiral component and constant (c)
determines the intensity of the flow spirality. Besides, the values of ‘c’ have been changed from 0 to 2.5
for different simulations, which have been presented in table 5 in the appendix. However, the spiral
velocity has been shown by the Fig. 3(c). Where –
(14) = ∑ ( ( ) + ( ))
Pressure outlet profile –
(15) = ∑ ( ( ) + ( ))
Where, An, Bn, Cn and Dn are the coefficients, which have been presented in the Table 1 and 2. Since
cardiac pulse cycle is 0.82sec, f is found from the equations (14, 15). Where –
(16) =
.
= 7.66 rad/sec
Table 1
Harmonic coefficients for physiological waveform of velocity profiles
n A B n A B n A B
0 0.166667 0 6 0.01735 0.01915 12 -0.00341 0.005463
1 -0.03773 0.0985 7 -0.00648 0.002095 13 -0.00194 0.000341
2 -0.10305 0.012057 8 -0.01023 -0.0078 14 -0.00312 -0.00017
3 0.007745 -0.06763 9 0.008628 -0.00663 15 0.000157 -0.00299
4 0.025917 -0.02732 10 0.002267 0.001817 16 0.001531 0.000226
5 0.037317 0.024517 11 0.005723 0.003352
Table 2
Harmonic coefficients for physiological waveform of pressure profiles
n C D n C D n C D
0 90 0 6 1.4574 1.6086 12 -0.28644 0.458892
1 -3.16932 8.274 7 -0.54432 0.17598 13 -0.16296 0.028644
2 -8.6562 1.012788 8 -0.85932 -0.6552 14 -0.26208 -0.01428
6. K. Mamun et al./ Statistical analysis for measuring the effects of stenotic shapes and spiral flows on wall shear
stress by using numerical simulations of physiological blood flow
21
3 0.65058 -5.68092 9 0.724752 -0.55692 15 0.013188 -0.25116
4 2.177028 -2.29488 10 0.190428 0.152628 16 0.128604 0.018984
5 3.134628 2.059428 11 0.480732 0.281568
Fig. 2(a) and 2(b) show physiological waveform of inlet velocity and pressure outlet profiles
respectively and Fig. 2(c) depicts the graph of the parabolic inlet velocity profile. Wall shear stress was
measured at the peak systole (at time 0.1804) of the cardiac cycle.
(a) (b) (c)
Fig. 2. Physiological waveform of (a) velocity and (b) pressure profiles; (c) parabolic velocity profile.
(a) (b) (c)
Fig. 3. (a) Comparison of the numerical and experimental result of the steady velocity profile, (b) pressure
distributions of a stenotic artery with different mesh sizes, and (c) streamlines and vector distribution of the spiral
flow at inlet.
2.5. Validation and grid independence checking
Before starting of present investigation the numerical simulation is needed to be validated. Validation
of the present numerical computation has been done by plotting the steady velocity profile at 2.5D
downstream from the stenosis throat and comparing it with the velocity profile of Varghese and Frankel
[38]. For this case, a parabolic velocity profile has been assumed as inlet boundary condition. The mean
inlet velocity corresponds to Reynolds number 500 and the flow has been assumed to be steady. The
results have been shown in the Fig. 3(a), where a good agreement can be found with Varghese and
Frankel [38].
An extensive test has been carried out in a stenotic artery with different mesh sizes such as mesh0
(175511 element), mesh1 (282580 element) and mesh2 (490227 element) respectively. Fig. 3(b) shows
the pressure distributions of a stenotic artery with mentioned mesh sizes. In all cases, the pressure
distributions are same. It implies that the solution is grid independence.
7. K. Mamun et al./ Statistical analysis for measuring the effects of stenotic shapes and spiral flows on wall shear
stress by using numerical simulations of physiological blood flow
22
2.6. Numerical analysis
The numerical simulations are performed by well-known software ANSYS Fluent 18.1. A pressure
based algorithm is chosen as the solver type. This solver is generally selected for an incompressible fluid.
As there is no heat transfer in the blood flow process, energy equation is not solved. Since turbulent is
expected in 85% stenotic artery at post stenotic region, a low Reynolds number k − ω turbulent model is
used throughout the work. The SIMPLE algorithm is selected for pressure-velocity coupling. First Order
Upwind scheme is employed as a numerical scheme for discretization of the momentum equation. The
time step is set to 0.0041 sec with 200 number of total time steps. Maximum 100 iterations are performed
per each time step.
2.7. Statistical analysis
Ansys fluent has been used for calculation to get statistical data such as maximum, minimum and
average wall shear stress. The main objective of this study is to find out relationship among the
maximum, minimum and average wall shear stress with the stenotic shape and flow spirality. The
maximum, minimum and average wall shear stresses are considered as the dependent variables, whereas
the stenotic severity, eccentricity, length and flow spirality are taken as independent variables to analyse
the relationship among them. However, stenotic severity, eccentricity, length and flow spirality are taken
as non-dimensional variables. Well known statistical software SPSS has been used for the analysis. Two-
way ANOVA and multivariable linear regression analyses have been used to determine the relationships
among them. However, P value less than 0.05 has been considered as significant level for the study.
3. Results and Discussions
Wall shear stress is a flow-induced stress that can be described as the frictional force of viscous blood.
Arterial endothelium is highly sensitive to hemodynamic shear stresses that act at the vessel surface in the
direction of blood flow. High prolonged high wall shear stress elongates the endothelial cells and force to
align in the direction of the flow. Consequently, it fragments the internal elastic layer of the arteries and
initially starts to form an atherosclerosis or an aneurysm. On the other hand, low WSS had negligible
effect on the cell but increases intercellular permeability and consequently increases the plaque formation
in the arteries. Thus, endothelial cells react differently to the high and low WSS. As the WSS is mostly
responsible for creating a new stenotic throat, this study investigated the effect of stenotic shape and flow
spirality on wall shear stress.
Three regression cases have been presented in this study. WSSmax, WSSmin and WSSave are the
dependent variable for the first, second and third cases respectively, whereas independent variables are
same in all three cases. However, the independent variables are stenotic severity, eccentricity, length and
flow spirality. The residual sum of squares and significant level of the cases have been presented in Table
3. Residual sum squares in first case is 0.734 which means 73.4% of the variation of WSSmax can be
explained by the stenotic severity, eccentricity, length and flow spirality. Similarly, it can be said that
WSSmin and WSSave are dependent on stenotic severity, eccentricity, length and flow spirality by 55.6%
and 63.6% respectively. Besides, p-value in all three cases is zero which is less than 0.05, so null
hypothesis must be rejected and it can be said that the cases are statistically significant. Actually, the p-
value for each term tests the null hypothesis that the coefficient is equal to zero (no effect). A low p-value
which is less than 0.05 indicates that the null hypothesis can be rejected. In other words, a predictor that
has a low p-value is likely to be a meaningful because changes in the predictor's value are related to
changes in the response variable. Conversely, a larger (insignificant) p-value suggests that changes in the
predictor are not associated with changes in the response. In the Table 4 it is found that p-value of the
flow spirality is greater than 0.05 in first and third cases, which indicates that changes in the flow spirality
are not associated with changes in the WSSmax, and WSSave. Similarly, stenotic eccentricity in second case
and stenotic length in second and third cases are also statistically insignificant.
8. K. Mamun et al./ Statistical analysis for measuring the effects of stenotic shapes and spiral flows on wall shear
stress by using numerical simulations of physiological blood flow
23
Table 3
Residual sum of squares and significant level or P-value of the cases
Case Dependent Variable Residual sum of squares Significant Level
p-value
1 WSSmax 0.734 0.00<0.05
2 WSSmin 0 .556 0.00<0.05
3 WSSave 0.636 0.00<0.05
Besides, regression coefficients represent the mean change in the response variable for one unit of
change in the predictor variable while holding other predictors constant. From the Table 4, first case
presented that the coefficients of severity, eccentricity and length are 1.225, 10.426 and -6.363
respectively, whereas spirality is negligible because of the higher p-value. Thus, the stenotic severity and
eccentricity have positive relationship, but the stenotic length has inverse relationship with WSSmax
distribution and flow spirality has no influence on the WSSmax. That means, if the stenotic severity and
eccentricity increase, the WSSmax distribution will also increase, whereas if the stenotic length increases,
the WSSmax distribution will decrease. However, when the stenotic severity is raised by 1% keeping
others predictors unchanged, the WSSmax will expect to increase by 1.225 Pa. The stenotic eccentricity is
the most influencing factor for WSSmax in the first case, as if it increases by 0.1 keeping others predictors
constant, the WSSmax will be expected to increase by 10.426 Pa. On the other hand, stenotic length has
inverse relationship with the WSSmax of the first case. Thus, the WSSmax will expect to decrease by 6.363
Pa when the length increases by 0.1 D and other predictors are constant.
Table 4
Coefficients and P-value of the predictors in the cases
Case Dependent Variable Independent Variables Coefficients
(Pa)
Significant Level
p-value
1 WSSmax Constant -33.641 0.00 < 0.05
Severity 1.225 0.000<0.05
Eccentricity 10.426 0.037<0.05
Length -6.363 0.001<0.05
Spirality 5.440 0.712>0.05
2 WSSmin Constant 0.023 0. 000<0.05
Severity 0.000 0.000<0.05
Eccentricity 0.001 0. 842>0.05
Length -0.001 0. 482>0.05
Spirality 0.128 0.000 <0.05
3 WSSave Constant -1.402 0.00<0.05
Severity 0.047 0.00<0.05
Eccentricity 0.797 0.002<0.05
Length 0.165 0.072>0.05
Spirality 0.697 0.349>0.05
In addition, Figs. 4, 5 and 6 show the changing of WSSmax distributions with the variation of stenotic
contraction, eccentricity and length respectively. According to Fig. 4, the stenotic contraction or severity
has been changed in the models whereas the stenotic eccentricity and length are zero and 2D respectively
in all three models. The figure has shown that the WSSmax distribution has increased with the increase of
stenotic severity. From the Fig. 5, the stenotic eccentricity has been changed in the models taking 50%
stenotic severity and 2D length. It is clear from the figure that the WSSmax distribution has increased with
the increase of stenotic eccentricity. Fig. 6 has shown that the stenotic length has been changed in the
9. K. Mamun et al./ Statistical analysis for measuring the effects of stenotic shapes and spiral flows on wall shear
stress by using numerical simulations of physiological blood flow
24
models with 50% stenotic severity and 0 eccentricity. It is found that the WSSmax distribution decreases, if
the stenotic length increases.
In case 2 of the Table 4, it is observed that the P-value of Stenotic severity, eccentricity, and length
and flow spirality are 0, 0.842, 0.482 and 0 respectively. Thus, the stenotic eccentricity and length have
no influence on the WSSmin due to higher P-value. However, the regression coefficient of the stenotic
severity is zero. Thus, the WSSmin has no response for the variation of the severity which is also revealed
by the figure 7 (a). Thus, the flow spirality has only an influence on the WSSmin distribution and the
regression coefficient of it has shown that they are positively related to each other which is observed in
the Fig 7 (b). According to the regression coefficient it can be said that the WSSmin will expect to increase
by 0.128 Pa when the flow spirality increases by one unit but other predictors are constant.
Fig. 4. Contour representation of changing of WSSmax (Pa) distributions with the variation of stenotic contraction
keeping the other predictors unchanged.
Fig. 5. Contour representation of changing of WSSmax (Pa) distributions with the variation of stenotic eccentricity
keeping the other predictors unchanged.
10. K. Mamun et al./ Statistical analysis for measuring the effects of stenotic shapes and spiral flows on wall shear
stress by using numerical simulations of physiological blood flow
25
Fig. 6. Contour representation of changing of WSSmax (Pa) distributions with the variation of stenotic
length keeping the other predictors unchanged.
In case 3 of the Table 4, it is observed that the P-value of Stenotic severity, eccentricity, and length
and flow spirality are 0, 0, 0.072 and 0.349 respectively. Thus, the stenotic length and flow spirality have
no influence on the WSSave due to higher P-value. Thus, the Stenotic severity and eccentricity have an
influence on the WSSave distribution and the regression coefficient of them have revealed that they have
positive relationship with the WSSave which is also observed in the Fig. 8 (a, b). According to the
regression coefficient it can be said that if the stenotic severity and eccentricity will be increased by one
unit, the WSSave will expect to increase by 0.047 Pa and 0.797 Pa respectively.
(a) (b)
Fig. 7. Graphical representations of changing of WSSmim (Pa) distributions with the variation of (a) stenotic
contraction keeping the other predictors unchanged, and (b) flow spirality keeping the other predictors unchanged.
11. K. Mamun et al./ Statistical analysis for measuring the effects of stenotic shapes and spiral flows on wall shear
stress by using numerical simulations of physiological blood flow
26
(a) (b)
Fig. 8. Graphical representations of changing of WSSave (Pa) distributions with the variation of (a) stenotic
contraction keeping the other predictors unchanged, and (b) stenotic eccentricity keeping the other predictors
unchanged.
According to Table 4, it is clear that stenotic severity and eccentricity have an influence on both of the
WSSmax and WSSave whereas stenotic length and flow spirality have an influence only on the WSSmax and
WSSmin respectively. Besides, the fitted lines for WSSmax, WSSmin and WSSave are presented by the
following equations –
(17) = −33.641 + 1.225 ∗ + 10.426 ∗ − 6.363 ∗ ℎ +
(18) = 0.023 + 0.128 ∗ +
(19) = −1.402 + 0.047 ∗ + 0.797 ∗ +
4. Conclusions
From the study it can be concluded that the analysis cases are statistically significant as p-value in all
three cases are zero which is less than 0.05. Besides, 73.4%, 55.6% and 63.6% of the variation of the
WSSmax, WSSmin and WSSave respectively can be explained by the stenotic severity, eccentricity, and
length and flow spirality. The eccentricity is the most influencing factor for WSSmax. The WSSmax has
been influenced by the stenotic severity, eccentricity and length, whereas the WSSmin has been influenced
only by the flow spirality. The stenotic length has an influence only on the WSSmax whereas the stenotic
severity has an influence on the WSSmax and WSSave.
Acknowledgements
The Mechanical Engineering Department of Iwate University, Morioka, Japan is gratefully
acknowledged.
13. K. Mamun et al./ Statistical analysis for measuring the effects of stenotic shapes and spiral flows on wall shear
stress by using numerical simulations of physiological blood flow
28
39 42 0.4 2.5 0.158 99 70 0.2 2.5 0.143
40 40 0.4 3 0.241 100 73 0.2 3 0.226
41 50 0.2 1 0.01 101 82 0.8 1 0.025
42 53 0.2 1.5 0.093 102 76 0.8 1.5 0.028
43 48 0.2 2 0.157 103 80 0.8 2 0.142
44 55 0.2 2.5 0.24 104 85 0.8 2.5 0.225
45 48 0.4 3 0.011 105 82 0.7 3 0.026
46 50 0.4 1 0.094 106 80 0.7 1 0.029
47 53 0.4 1.5 0.156 107 76 0.7 1.5 0.141
48 55 0.4 2 0.239 108 85 0.7 2 0.224
49 50 0.6 2.5 0.012 109 80 0.9 2.5 0.027
50 55 0.6 3 0.095 110 85 0.9 3 0.03
51 48 0.6 1 0.155 111 76 0.9 1 0.14
52 53 0.6 1.5 0.238 112 82 0.9 1.5 0.223
53 55 0.5 2 0.013 113 85 0.1 2 0.028
54 48 0.5 2.5 0.096 114 82 0.1 2.5 0.031
55 53 0.5 3 0.154 115 80 0.1 3 0.139
56 50 0.5 1 0.237 116 76 0.1 1 0.222
57 48 0 1.5 0.014 117 76 0.3 1.5 0.029
58 55 0 2 0.097 118 82 0.3 2 0.032
59 53 0 2.5 0.153 119 80 0.3 2.5 0.138
60 50 0 3 0.236 120 85 0.3 3 0.221
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