prof., dr.hab. Jewhen Sheregii University of Rzeszow , Rzeszow - Poland
Synovial fluid. Rheology and modelling Rheology and modelling Anna Kucaba-Pietal Rzeszow University...
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Transcript of 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