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ABHIRUP ROY CHOUDHURY1, KRITTIKA DASGUPTA2, ABHIJIT CHANDA1,2, DEBABRATA NAG1
1DEPARTMENT OF MECHANICAL ENGINEERING 1DEPARTMENT OF MECHANICAL ENGINEERING &
2SCHOOL OF BIOSCIENCE AND ENGINEERING
JADAVPUR UNIVERSITYKOLKATAKOLKATA
Presented at the COMSOL Conference 2010 India
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HAEMODYNAMICS AND ITS NEED
Study of the flow of blood through arteries from a fluid mechanicsarteries from a fluid mechanics point of view
Needed to enrich the knowledge of the bloodfl d i i diflow pattern due to recent uprise in cardiacdiseases
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STENOSISAbnormal narrowing of bloodAbnormal narrowing of blood
vessels
Deposition of
cholesterolcholesterol
and other fatty matter
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Doppler Ultrasound Image of the CAROTID ARTERY ofDoppler Ultrasound Image of the CAROTID ARTERY of 130 patients of varying age:
To determine the location of the stenosis To determine the geometry of constriction To study the actual blood flow pattern30
40
1020
0CCA ICA ECA Bifurcation
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N t i f l t i i l di Newtonian for large arteries, including the common carotid artery
Non‐Newtonian for narrower channels Density : 1050 Kg/m3y g Dynamic viscosity: 0.00345 Pa.s
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MODELLING USING COMSOLMODELLING USING COMSOL
VERSION: COMSOL 3.5a
FLUID MECHANICS MODULE
INCOMPRESSIBLE NAVIER‐STOKES SECTION
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MODELLING THE GEOMETRY
Assumption: The artery is a long straight pipe(AXIS‐SYMMETRIC MODEL)
CURVED GEOMETRY
DIAMETER(D0)=0.0057 m
CONSTRICTION= 62% of the diCURVED GEOMETRY radius
RECTANGULAR GEOMETRY8
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The artery wall is rigid
Bl d fl i Blood flow is Newtonian Laminar LaminarSteady‐state Incompressible Incompressible
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GOVERNING EQUATIONS & GOVERNING EQUATIONS & BOUNDARY CONDITIONSBOUNDARY CONDITIONS
I ibl N i St k E tiIncompressible Navier‐Stokes Equation:
]).(.().( Tνp uuI.[-uu ])(()( p[
0u .
AXIAL SYMMETRY
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1Rruu(r)INLET: OUTLET: ZERO PRESSURE
WALL (NO‐SLIP)WALL (NO‐SLIP)
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MESHINGMESHING IN COMSOLIN COMSOL Free mesh using triangular elements
Adaptive refinement near the constriction
SOLVER USEDSOLVER USED•SOLVER TYPE: STATIONARY•NAME OF SOLVER: DIRECT(PARDISO)
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SUMMARY OF VALUES USEDSUMMARY OF VALUES USEDFLUID PROPERTIES VALUES
DENSITY 1050 kg/m3
DYNAMIC VISCOSITY 0.00345 Pa.s.
GEOMETRICAL PROPERTIES VALUES
DIAMETER OF ARTERY 5.7 mm.
MAXIMUM CONSTRICTION 62%
FLOW PARAMETERS VALUES
REYNOLDS NUMBER 100, 400, 800, 1000
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Close similarities between clinical and computationalclinical and computational results
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RADIAL VELOCITY PLOT
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POINT OF SEPARATION
LENGTH OF REATTACHMENT
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REATTACHMENT LENGTH VS. REYNOLDS NUMBERREATTACHMENT LENGTH VS. REYNOLDS NUMBER
• The reattachment length increases with increase in Re
•The length of reattachment is 10% higher for thehigher for the rectangular stenosis than the curved one
HIGHER REATTACHMENT LENGTH Direction of propagation
Direction of flow
HIGHER RATE OF PROPAGATION OF STENOSIS16
Of Stenosis
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•Shows that irreversible pressure rise increasespressure rise increases with increase in Re
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•Shows that irreversible pressure rise increasespressure rise increases with increase in Re
•Shows that the pressure rise is higher for the rectangular stenosis by g y23%.
HIGHER LOAD ON HEART
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CONCLUSIONSCONCLUSIONSSeverity increases with increase in Reynolds number i.e. increase in blood velocityincrease in blood velocity.
The length of the stenosis gradually increases.
A rectangular constriction is more severe than a curved oneone.
A curved geometry gradually approaches a rectangular shape
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THETHE CONDITIONCONDITION ESSENTIALLY WORSENSWORSENSWITH TIMEWITH TIME
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1. Ku D.N., Blood flow in arteries, Ann. Rev. Fluid Mech, 29, 399‐434 (1997)2. Wootton D.M. and Ku D.N., Fluid mechanics of vascular systems, diseases, and2. Wootton D.M. and Ku D.N., Fluid mechanics of vascular systems, diseases, and
thrombosis. Annu. Rev. Biomed. Eng, 01, 299‐329 (1999)3. Johnston P.R. and Kilpatrick D., Mathematical modeling of flow through an
irregular arterial stenosis, Journal of Biomechanics, 24, 1069‐1077 (1991)4 Anderson H I Halden R Glomsaker T 2000 Effects of surface irregularities4. Anderson H.I., Halden R., Glomsaker T., 2000, Effects of surface irregularities
on flow resistance in differently shaped arterial stenosis, Journal of Biomechanics 33, 1257‐1262 (2000)
5. Tang D., Yang C., Ku D.N., A 3‐D thin‐wall model with fluid‐structure interaction for blood flow in carotid artery with symmetric and asymmetricinteraction for blood flow in carotid artery with symmetric and asymmetric stenosis, Computers and Structures 72, 357‐377 (1999)
6. Bertolotti C., Deplano V., Three‐dimensional numerical simulation of flow through stenosed coronary bypass, Journal of Biomechanics, 33, 1011‐1022 (1999)(1999)
7. Mandal P.K., An unsteady anaysis of Non‐Newtonian blood flow through tapered arteries with stenosis, International Journal of Non‐Linear Mechanics,40, 151‐164 (2005)
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OTHANK YOU
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CAROTID ARTERYCAROTID ARTERY
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