synovial fluid. rheology and modelling rheology and modelling anna kucaba-pietal rzeszow university...

Synovial fluid. Rheology and modelling

Anna Kucaba-PietalRzeszow University of Technology

Poland

purpose of the work

• To examine whether the use of an isotropic micropolar model to describe the liquid crystal synovial fluid is appropriate

• Performing calculations tribological size biobearings on the basis of the theory of micropolar fluids for physiological data and comparison with the results of clinical observations

coefficient of friction cx ~ 0.001-0.03,It works about 70 yearsTransfer the load from a few to 18MP

cartilage

Synovial fluid

Biobearing hip joint

cartilage

5

Contents value

Dry matter 0,133,5

Density(20oC)

1,00811,015

pH 7,27,4

viscosity (20oC)

water, g/kg 960988

hyaluronic acid(HA )

2-3%

The content of dry matter g/kg1240

Albumins, globulins g/lPhospholipids,glycoprotein's

10,721,310,20,5

Mucyns, g/l 0,681,35

Glucoses, g/l jak w surowicy krwi

Urynial Acid, mg/l

73,4

Synovial Fluid

6

Sodium Hyaluronate, Hyaluronan• Made up of repeating glucuronic acid and N-acetylglucosamine subunits• High molecular weight: 0.2 to 10 million Dalton• Major component of synovial fluid• Exhibits viscoelastic properties

Synovial Fluid

Main Factors affecting the rheological properties:a) Hyaluronic Acid concentationc) Molecular weigh of Hyaluronic Acidd) temperature

7

efekt przędliwości własności lepkosprężyste – efekt

Barusa

The influence of HA concentration on viscosity coefficient of synovial fluid

HA concentration effect on Synovial fluid rheology

8

In normal joints synovial fluid shows higher elastic properties.

For diseases such as Rheumatoid arthritis, seropositive and seronegative, it is observed to decrease in the elastic and viscous properties of synovial fluid

In the elderly peoples and competitive athletes, a decrease in viscosity and reduced HA chain length is observed.

Rheumatic Diseases

9

• Pathophysiological significance of biofluid rheology

• Develop an understanding of how the micro- and nano-structure of blood influences its rheology

• Explore to use of rheological parameters in diagnostics and menagement of clinical disorders and inoptimisation of blood processing

• Explore new methods of measurement suited for clinical application

• Maintain new type apparatus for such measurements

Perspectives

d,

d i,iVt

d

dkl

km lm lm km

jj j

t

,

d

d i

ij j i

VT f

t

,

d( )

dij j

ijk kj ij j i

jT C g

t

, , ,

d( )

d i j ijk k ij i j ij i i

eV T C q Q

t

ikik Ij

0ij

nlk = –nkl

TTTCCC DRDR ,

OThe mathematical description of the liquid crystal medium versusmicropolar fluid model

0 0

00

k

0

( 10) ( 0,5)

100fH c

Cartilage - construction

20 mm 5 mm

20 mm50 mm

2 mm 2 mm

The coefficient of friction during

movement along (1) and

perpendicular to Microgroove (2).

(Kupchinov)

Cartilage surface waviness exhibits

Magn. X 300

Synovial fluid - rheological properties

dynamic viscosity coefficient of a HA solution

coefficient of dynamic viscosity of synovial

viscoelastic properties - Barus effect

Cartilage - the construction

20 mm 5 mm

20 mm50 mm

2 mm 2 mm

Model Rivlina-Ericksena

21 1 2p I A A A

gdzie: t –stress tensor p – pressure

I – tensor jednostkowy,A1 i A2 – shear tensor Rivlina-Ericksena,

h, a, b – material constants of synovial

Tij = (-p +lV k,k)dij + m(Vi,j + V j,i) + k(V j,i - eijkWk) ,

 Cij= d Wk,kdij + bWi,j + gWj,i .

D

DtV

DV

DtT f

ID

DtC g T

DE

Dtq T V C T

,

,

,

:( ) :( ) .

Micropolar fluid equations

Micropolar fluid equations

d,

d i,iVt

,

d,

di

ij j i

VT f

t

,

d

d ij j i ijk kjI C g Tt

i

, , ,

d( )

d i j k ijk ij i j ij i i

eV T C q Q

t

, , ,ij k k ij i j j iC

, , , ,( ) ( ) ( )ij k k ij i j j i j i ijk kT p V V V V

' / , ' / , ' , ' / , ' / , '( )

c c c c

c

pU t t T L L U x x L p

μ κ U

L

V V ω ω

N N

, ,2 4

cLκN L l

μ κ l μ

The dimensionless form of the m.f. equations

21 'Re( ' ' ') ' ' ' ' ' 2 ' '

St '

p N

t

VV V V ω

2

2 2 2

1 'Re ( ' ' ')

St '

2 ( 2 ' ' ') 2(1 )( ' ' ' ' ' ')

I

tl

L N N

ωV

ω V ω ω

N4,

ll

hL

Lmin = h/lmin = 1000 Lmax

= h/lmax = 90.

·     h = 40 mm,·     a = 0.04 m = R/2 ·     U = 0.01 m/s  

Effect legth of HA molecules on load   N parameter N showing the synovial fluid

concentrations of HA: L1, L2 - HA molecules long, L3, L4 - short molecules

The calculated bearing capacity W for different lengths Lof HA molecules pozaslaniaj synku na rysunkach polskie napisy

Ten slajd proszę rozbi mi na dwa slajdy , tytul taki sam,Na jednym dwa z boku na drugim wykres.

HA concentration effect on Synovial fluid rheology

Effect of HA molecules on the surface of bone approaching time in biołożysku? Parameter N as a function of the synovial fluid: L1, L2 - HA molecules

long, L3, L4 - short molecules

Calculation of time approaching the surface of the bone s as a function of concentration and lenth of HA

Nośność stawu biodrowego w funkcji parametru N

dla pięciu wartości temperatury mazi

Calculation of load capacity as a function of temperature

Conclusions

  The calculation of the tribological joint quatities obtained under micropolar model applied to synovial fluid are qualitatively consistent with clinical observations.

Mikropolarny fluid model of synovial remains in compliance with confirmed experimentally LCD model synovial fluid both in terms of physics of liquid crystals, as well as mathematical description.Describes the synovial fluid phase transitions.

Thank you for your attention