Lubrication Modelling of Artificial Joint Replacements: Current Status and Future Challenges
Abstract
:1. Introduction
2. Lubrication Modelling of Hip and Knee Replacements
2.1. Geometries of Contact Surfaces
2.2. Materials
2.3. The Bearing Surface Deformations
2.4. Loading and Motions of Human Daily Activities
2.5. Measurement of Film Thickness
2.6. The Synovial Fluids and Rheology Models
3. Mixed Lubrication Modelling of Hip and Knee Replacements
3.1. The Mixed Lubrication Regime
3.2. The Mixed Lubrication Models
3.2.1. Deterministic Model
3.2.2. Stochastic Models
3.2.3. Homogenisation Methods
4. Discussion
4.1. The Mixed Lubrication Theory
 (1)
 Is the negative film thickness proper to determine the asperity contact?
 (2)
 Is the unified Reynolds equation adequate to solve the microEHL problems?
4.2. Methods to Address the Realistic Geometry, Design, and Materials
4.3. Individual Physiological Diversities
4.4. Lubrication Analysis towards Design Optimisation
4.5. Joint Simulators and Validation of Numerical Models
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Component  Femoral Head Radius R (mm)  Radial Clearance (μm)  

Spherical bearing [27,35,36,37]  MoP  11–18  80–200 
MoM  14–24  30–150  
CoC  14–18  10–50  
MoM_{R}  20–30  75–150  
Ellipsoidal surface [29]  $\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}+\frac{{z}^{2}}{{c}^{2}}=1$ a, b, c are the three semiaxis lengths of an ellipsoid  
Alpharabola surface [33]  $\frac{{x}^{2}}{{R}^{2}/\alpha}+\frac{{\left(yR+R/\alpha \right)}^{2}}{{R}^{2}/{\alpha}^{2}}+\frac{{z}^{2}}{{R}^{2}/\alpha}=1,0\alpha 1$ a is the parameter to control the variation rate of the radius of curvature  
Preworn surface [34]  $R={R}_{0}+a\xb7{e}^{\frac{{\left(\phi {\phi}_{0}\right)}^{2}+{\left(\theta {\theta}_{0}\right)}^{2}}{2{\sigma}^{2}}}$ ${R}_{0}$$\mathrm{is}\mathrm{the}\mathrm{original}\mathrm{cup}\mathrm{inside}\mathrm{radius};\theta and\phi aresphericalcoordinates;$$a,\sigma ,{\phi}_{0}and{\theta}_{0}$ are curvefitted parameters based on rotational Gaussian distribution function. 
Components  Magnitudes (mm) 

Femoral radius in ML direction, R_{F, ML}  18 
Femoral radius in AP direction, R_{F, AP}  24–33 
Tibial radius in ML direction, R_{T, ML}  21 
Tibial radius in AP direction, R_{T, AP}  45 
Tibial liner thickness, d  10 
Materials  Example  Elastic Modulus (GPa)  Poisson’s Ratio  Density (kg/m^{3})  Advantages  Disadvantages 

Metals  Stainless steel  210  0.3  7900 


Titanium alloys  110  0.3  4500  
CoCrMo/CoCr alloys  230  0.3  8900  
Ceramics  Alumina  380  0.26  3900 


Zirconia  210  0.3  5600  
Polymers  PEEK  3–4  0.25  1300 


UHMWPE  0.5–1  0.4–0.46  900  
PCU  0.024  0.49  1200 
Approaches  Speed for a Full SteadyState Solution  Accuracy  Applicable Geometries 

Column model [24,54]  A few seconds to minutes  Good accuracy for hardonsoft bearings  Ballinsocket; large conformity 
MultiGrid [63]  Minutes to hours  High  Ballonplan or ballinsocket 
Spherical FFT [63]  Minutes to hours  High  Ballinsocket 
FEA [60]  Hours  High  Ballonplan or ballinsocket 
Lubricants  Zero Shearrate Viscosity ${\mathit{\eta}}_{0}$ (Pa·s)  Plateau Viscosity ${\mathit{\eta}}_{\mathit{\infty}}$ (Pa·s)  $\mathit{\alpha}$ (the Constant, Unit·s)  $\mathit{\beta}$ (the Rate Index Constant) 

Healthy synovial fluid [83,85]  40  0.0009  9.54  0.73 
TKA [82]  0.087–25  0.0094–11  0.047–35  0.44–0.64 
Revision TKA [82]  0.0087–4.0  0.0043–0.77  0.0043–10.8  0.37–0.59 
Calf serum (protein concentration 20 g/L for knee wear test) [86]  0.018  0.00085  13  0.85 
Calf serum (protein concentration 30 g/L for hip wear test) [86]  0.004  0.00088  11  0.6 
References  Geometry Type  Material Combination/Young’s Modulus (GPa)/Poisson’s Ratio  Fluid Rheology Properties/Viscosity (Pa·s)  Operating Conditions  Further Details 

Hip implants  
Ruggiero and Sicilia [10]  BallinSocket  MoP/cup: 1.05/0.4  NonNewtonian/40 (base) and 0.0009 (plateau)  ISO 142423  Deterministic; wear model 
Ruggiero and Sicilia [9]  BallinSocket  CoP/cup: 1.0/0.47  NonNewtonian/ 0.0015 (base)–$\infty $ (plateau)  Measured from patients [70]  Deterministic; wear model 
Ford et al. [49]  BallinSocket  MoP/cup: 0.024/0.49; 0.7/0.4; 1.0/0.4  Newtonian/0.002  ISO 142421  Deterministic model 
Gao et al. [85]  BallinSocket  MoM 210/0.3  NonNewtonian/40 (base) and 0.0009 (plateau)  Leeds ProSim; Measured from patients [70]  Deterministic model 
Gao et al. [92]  BallinSocket  MoM 210/0.3  Newtonian/0.0009  ISO 142421  Deterministic; wear model 
Gao et al. [91]  BallinSocket  MoM 210/0.3  Newtonian/0.001  ISO 142421  Deterministic model; surface texturing 
Chyr et al. [98]  BallonPlane  MoP (no deformation in modelling)  Newtonian/not explicitly specified  Steadystate  Stochastic model 
Knee implants  
Butt et al. [99]  Real geometry from CAD model  MoP/cup: 1.0/0.4  Newtonian/0.1  ISO 142433  Stochastic model 
Marian et al. [40]  Elliptical ballinsocket  MoP/cup: 3.5/0.34; 0.66/0.46  NonNewtonian/0.05 (base) and 0.002 (plateau)  ISO 142433  Deterministic model 
Gao et al. [55]  Spherical ballinsocket  MoP/cup: 1.0/0.4  NonNewtonian/40 (base) and 0.005 (plateau)  Subjectspecific gait cycle [66]  Deterministic; wear model 
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Gao, L.; Lu, X.; Zhang, X.; Meng, Q.; Jin, Z. Lubrication Modelling of Artificial Joint Replacements: Current Status and Future Challenges. Lubricants 2022, 10, 238. https://doi.org/10.3390/lubricants10100238
Gao L, Lu X, Zhang X, Meng Q, Jin Z. Lubrication Modelling of Artificial Joint Replacements: Current Status and Future Challenges. Lubricants. 2022; 10(10):238. https://doi.org/10.3390/lubricants10100238
Chicago/Turabian StyleGao, Leiming, Xianjiu Lu, Xiaogang Zhang, Qingen Meng, and Zhongmin Jin. 2022. "Lubrication Modelling of Artificial Joint Replacements: Current Status and Future Challenges" Lubricants 10, no. 10: 238. https://doi.org/10.3390/lubricants10100238