the importance of the non-newtonian characteristics of blood

7/28/2019 The Importance of the Non-newtonian Characteristics of Blood

1/25

The Importance of the Non-Newtonian Characteristics of Blood

in Flow Modelling Studies

THE UNIVERSITY of LIVERPOOL

Department of Engineering

Ieuan Owen, Jonathon Gray,Marcel Escudier, Rob Poole


2/25

Aim: to achieve dynamic similaritybetween flow in vivo and model invitro

Modelling the flow of blood through bypass

grafts...

Q can blood be modelled using a Newtonian liquid?

Q can blood be modelled using a non-Newtonian liquid?

Q can large scale models be used?

Measurements made in the modelcan then predict the flow

conditions in vivo (e.g. WSS,

stagnation points, residence time

etc.)

45

A

X

38.5mm

INTERNAL BORE

ORIGIN

Y

B


3/25

Conditions to be modelled typical of femoral

bypass

45

6 mm

Simplified distalAnastomosis:45 angle

6 mm diameter

-0.50

0.00

0.50

1.00

-0.1 0.1 0.3 0.5 0.7 0.9 1.1

Time

Flow

Biphasic flow waveform:

Mean flow rate = 120 ml/min

Pulsatility index = 5.56

Time period = 1 second

Fluid Properties:Density = 1060 kg/m3 Viscosity ~ ?

Newtonian or non-

Newtonian?

50 100%0 - 50%


4/25

St

ress

YieldStress

Shear rate

Bingham

Plastic

n > 1 shear thickening

n = 1 Newtonian

n < 1 shear thinning

Non-Newtonian Liquids

n

dr

duK=!

1n

dr

duK

!

=

Power-Law

Liquids Simplest

Model


5/25

Rheology of Human Blood

1

10

100

1000

0.01 0.1 1 10 100 1000

Shear Rate, ! (s-1

)

Viscosity,"

(mPa.s

)

Newtonian (3.5 mPa.s)

Non-Newtonian (Power

law)

Blood is a shear-thinning non-Newtonian

liquid

Power law: = K(n-1)

n, power law index ~ slope of line (0.63)

K, consistency ~ level of the line (16.1 mPa.s)


6/25

Dimensional Analysis

- for a power law fluid under pulsatile flow

conditions

!"

#$%

& '(=

(

) *

U

*U,

U

D,n,

K

UDf

U?

)n2(n

2

w

w = f(U, D, , K, n, , U* ) [U* = Umax Umin ]


7/25

Dimensionless groups:

w U2 Friction Coefficient (WSS)

DnU

(2-n)Generalised Re

K

n Power law index

D Strouhal number U

U max peak - U min peak Pulsatility index

U

Dimensional Analysis

- for a power law fluid under pulsatile flow

conditions


8/25

Experimental Testing Rig

Flow ControlValves

Rotameters

Reservoir

Wave formPump

EM Flowmeter

Settling Chamber

flowflow

flow

Schematic Diagram of Testing Apparatus

X

Y

45

Internal Bore38.5mm

Wall Shear Stress Estimates obtained

along AB - the bed of the GraftA

B

PIV Laser (Camera Positioned at90 to Laser Sheet)

Flowmeter SignalConverter

Computer

Trim Pump


9/25

Pulsatile Flow Rate

-5

0

5

10

15

20

25

0 1 2 3 4 5 6

Time (s)

Flow

Rate

(l/min)

Required Waveform

1st Cycle

2nd Cycle


10/25

Particle Image Velocimetry (PIV)

Refractive index matching

Calibration target placed

in junction

Laser sheet in central

plane

Fluorescent particles

added to fluid

Each image pair takenat a fixed point in the

cycle

100 measurements


11/25

Flow visualisation using PIV


12/25

Estimates of Axial Wall Shear Stress

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

-2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00

Non Dimensional Distance (x/D)

NonDimensionalWallShearStress.

A B

INTERNAL BORE38.5mm

45

ORIGIN

Y

X

Wall shear stress estimates obtained along AB - the bed of the artery

A BLocal velocity

recorded at d/D =

0.025

Non-dimensionalised

using 1/2U2

u

d

wall = K(u/d)n


13/25

Conditions to be modelled typical of femoral

bypass

45

6 mm

Simplified distalAnastomosis:

45 angle

6 mm diameter

-0.50

0.00

0.50

1.00

-0.1 0.1 0.3 0.5 0.7 0.9 1.1

Time

Flow

Biphasic flow waveform:

Mean flow rate = 120 ml/min

Pulsatility index = 5.56

Time period = 1 second

Fluid Properties:Density = 1060 kg/m3 Viscosity ~ ?

Newtonian or non-

Newtonian?


14/25

Fluid Properties

0.63

60.6

-

-

70

0.63

35.1

-

-

70

-

-

13.4

130

-

-

-

6.1

130

-

0.63

16

3.5

130

70

n

K

Re(N)

Re(PL)

0.06%

XG

35% Gly

0.07% XG63% Gly50% GlyBlood


15/25

-3.00

-2.00

-1.00

0.00

1.00

2.00

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0

Axial Distance x/D

NonDimensionalWallShearStress. Re(N) = 130 (63% Gly.)

Re(N) = 130 (50% Gly.)

Re(PL) = 70 (0.07% XG)

Re(PL) = 70 (0.06% XG / 35% Gly.)

.1 0.4 0.9

Dimensionless wall shear stress measured along the bed of

the model artery at peak systole (50% distal flow split)

Scaling procedure validated


16/25

Dimensionless wall shear stress measured along the bed of

the model artery at end systole (50% distal flow split)

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0

Axial Distance x/D

NonDimensionalWallShearStress. Re(N) = 130 (50% Gly.)

Re(PL) = 70 (0.07% XG)

Re(N) = 130 (63% Gly.)

Re(PL) = 70 (0.06% XG/35% Gly.)

0

0

0

0

0.1 0.4 0.9

Scaling procedure validated


17/25

Measured velocity profiles (normalised)

Two fluids with same n, but different K, scaled for Re

-20

-10

0

10

20

30

40

50

0 10 20 30 40 50 60

-0.50

0.00

0.50

1.00

-0.1 0.4 0.9


18/25

Dynamic Scaling

Experiments have confirmed that the flow of a power-lawfluid can be accurately represented by another power-law

fluid with a different K provided they have the same n

Because the dynamic scaling is valid the physical size of

the model can be varied and the non-dimensional resultsare still valid i.e. large-scale models can be used

We can now use the measured non-dimensional WSS to

predict the WSS values in a life-scale artery assuming the

fluid is Newtonian or non-Newtonian


19/25

Predictions of life-scale WSS based on Newtonian

and non-Newtonian assumption

Peak Systole 50% Distal split

-8.0

-4.0

0.0

4.0

8.0

-2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00

WallShearStress

(Pa) 3.5mPa.s

Power-law.

.

.

.

. . .

b)


20/25

Predictions of life-scale WSS based on Newtonian

and non-Newtonian assumption

Peak Systole 100% Distal split

-4.0

-2.0

0.0

2.0

4.0

6.0

8.0

-2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00

WallShearStress

(Pa)

3.5mPa.s

Power-law

.

.

.

.

. . .

b)


21/25

Aim: to achieve dynamic similaritybetween flow in vivo and model invitro

Modelling the flow of blood through bypass

grafts...

Measurements made in the modelcan then predict the flow

conditions in vivo (e.g. WSS,

stagnation points, residence time

etc.)

45

A

X

38.5mm

INTERNAL BORE

ORIGIN

Y

B

Q can blood be modelled using a Newtonian liquid? NO

Q can blood be modelled using a non-Newtonian liquid?

YES


22/25

Conclusions

Use of a Newtonian fluid to model blood can give WSSvalues three times those produced by a shear-thinningfluid

Non-Newtonian analogue fluid and scaling procedures

have been shown to work

Experiments need to be designed properly

Future??????


23/25

What are we doing now?

Carrying out similar large-scale experiments for astenosis

Using Fluent with power-law viscosity to comparewith experiments

Blood Rheology (RJP & TVH)

Shear viscosity variation with shear rate

Oscillatory measurements G, G (relaxation time)

Extensional properties (CaBER, capillary break-upextensional rheometer


24/25

Future Work

o 3-D time-resolved PIV

o Develop more realistic analogue fluids

o Computational Fluid Dynamics (in house finite-

volume code)

o Shear-thinning, viscoelastic, thixotropic effects (inisolation & in combination


25/25

The Importance of the Non-Newtonian Characteristics of Blood

in Flow Modelling Studies

THE UNIVERSITY of LIVERPOOL

Department of Engineering

Ieuan Owen, Jonathon Gray,Marcel Escudier, Rob Poole

the importance of the non-newtonian characteristics of blood

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