Synovial fluid.
Rheology and modelling
Anna Kucaba-Pietal
Rzeszow 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
Biobearing hip joint
Synovial fluid
coefficient of friction cx ~ 0.001-0.03,
It works about 70 years
Transfer the load from a few to 18MP
cartilage
cartilage
Synovial Fluid
Contents
Dry matter
Density(20oC)
pH
value
0,133,5
1,00811,015
7,27,4
viscosity
(20oC)
water, g/kg
hyaluronic acid
(HA )
960988
The content of dry matter g/kg
1240
Albumins,
globulins g/l
Phospholipids,
glycoprotein's
10,721,3
10,2
0,5
Mucyns, g/l
0,681,35
Glucoses, g/l
jak w surowicy
krwi
Urynial Acid,
mg/l
73,4
2-3%
5
Synovial Fluid
Main Factors affecting the rheological properties:
a) Hyaluronic Acid concentation
c) Molecular weigh of Hyaluronic Acid
d) temperature
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
6
HA concentration effect on Synovial fluid rheology
efekt przędliwości
własności
lepkosprężyste – efekt
Barusa
The influence of HA concentration
on viscosity coefficient of synovial fluid
7
Rheumatic Diseases
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.
8
Perspectives
•
Pathophysiological significance of biofluid rheology
• Develop an understanding of how the micro- and nanostructure 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
9
OThe mathematical description of the liquid crystal medium versus
micropolar fluid model
d
  Vi,i ,
dt
dV
 i  Tij , j   fi
dt
djkl
  k m jlm  l m jkm
dt


d( jij j )
dt
  ijk Tkj  Cij , j   gi
de
 (Vi , j  ijkk )Tij  i, j Cij  qi ,i  Q
dt
C  RC  DC , T  RT  DT
lk = –kl
jik  I ik
 ij  0
  0  k 
 0
0 
 0
 0
( H  10)  (c f  0,5)
100
Cartilage - construction
50 mm
20 mm
20 mm
5 mm
2 mm
2 mm
Cartilage surface waviness exhibits
The coefficient of friction during
movement
along
(1)
and
perpendicular to Microgroove (2).
(Kupchinov)
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
50 mm
20 mm
20 mm
5 mm
2 mm
2 mm
 Model Rivlina-Ericksena
   pI  A1   A12   A2
gdzie:
 –stress tensor
p – pressure
I – tensor jednostkowy,
A1 i A2 – shear tensor Rivlina-Ericksena,
, ,  – material constants of synovial
Micropolar fluid equations
D
   V ,
Dt
DV

  T   f ,
Dt
DW
I
  C  g  T ,
Dt
DE

   q  T :(V )  C :(W)  T W.
Dt
Tij = (-p +lV k,k)ij + m(Vi,j + V j,i) + k(V j,i - ijkWk) ,
Cij=  Wk,kij + Wi,j + Wj,i .
Micropolar fluid equations
d
  Vi,i ,
dt
dVi

 Tij , j   fi ,
dt
di
I
 Cij , j   gi  ijkTkj
dt
de
  (Vi, j  k ijk )Tij  i, j Cij  qi,i  Q
dt
Tij  ( p  lVk ,k ) ij  m (Vi , j  V j ,i )  k (V j ,i  ijkk )
Cij  k ,k  ij  i , j   j ,i
The dimensionless form of the m.f. equations
p
V '  V / U , t '  t / Tc ,  '  Lc, ω '  ωLc /U, x '  x / Lc , p ' 
( μ  κ )U
Lc
Re(
1 V '
 V '  'V ')   ' p '  ' 'V '  2 N 2 ' ω'
St t '
I 1 ω '
Re 2 (
 V '  ' ') 
l St t '
2 2
2    
 2L N (2ω '  'V ')  2(1  N )(
 '  ' ω '  ' ' ω ')

N
κ
Lc
, L
, l
2 μN  κ
l

4 μN
The calculated bearing capacity W for different lengths L
of 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.



h = 40 mm,
a = 0.04 m = R/2
U = 0.01 m/s
L
h

, l
l
4m N
Lmin = h/lmin = 1000
Lmax = h/lmax = 90.
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
HA concentration effect on Synovial fluid
rheology
Calculation of time approaching the surface of the bone s
as a function of concentration and lenth of HA
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 load capacity as a function of temperature
Nośność stawu biodrowego w funkcji parametru N
dla pięciu wartości temperatury mazi
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