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 micro-EHL 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 | |
MoMR | 20–30 | 75–150 | |
Ellipsoidal surface [29] | a, b, c are the three semi-axis lengths of an ellipsoid | ||
Alpharabola surface [33] | a is the parameter to control the variation rate of the radius of curvature | ||
Pre-worn surface [34] | are curve-fitted parameters based on rotational Gaussian distribution function. |
Components | Magnitudes (mm) |
---|---|
Femoral radius in ML direction, RF, ML | 18 |
Femoral radius in AP direction, RF, AP | 24–33 |
Tibial radius in ML direction, RT, ML | 21 |
Tibial radius in AP direction, RT, AP | 45 |
Tibial liner thickness, d | 10 |
Materials | Example | Elastic Modulus (GPa) | Poisson’s Ratio | Density (kg/m3) | 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 Steady-State Solution | Accuracy | Applicable Geometries |
---|---|---|---|
Column model [24,54] | A few seconds to minutes | Good accuracy for hard-on-soft bearings | Ball-in-socket; large conformity |
Multi-Grid [63] | Minutes to hours | High | Ball-on-plan or ball-in-socket |
Spherical FFT [63] | Minutes to hours | High | Ball-in-socket |
FEA [60] | Hours | High | Ball-on-plan or ball-in-socket |
Lubricants | Zero Shear-rate Viscosity (Pa·s) | Plateau Viscosity (Pa·s) | (the Constant, Unit·s) | (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] | Ball-in-Socket | MoP/cup: 1.05/0.4 | Non-Newtonian/40 (base) and 0.0009 (plateau) | ISO 14242-3 | Deterministic; wear model |
Ruggiero and Sicilia [9] | Ball-in-Socket | CoP/cup: 1.0/0.47 | Non-Newtonian/ 0.0015 (base)– (plateau) | Measured from patients [70] | Deterministic; wear model |
Ford et al. [49] | Ball-in-Socket | MoP/cup: 0.024/0.49; 0.7/0.4; 1.0/0.4 | Newtonian/0.002 | ISO 14242-1 | Deterministic model |
Gao et al. [85] | Ball-in-Socket | MoM 210/0.3 | Non-Newtonian/40 (base) and 0.0009 (plateau) | Leeds ProSim; Measured from patients [70] | Deterministic model |
Gao et al. [92] | Ball-in-Socket | MoM 210/0.3 | Newtonian/0.0009 | ISO 14242-1 | Deterministic; wear model |
Gao et al. [91] | Ball-in-Socket | MoM 210/0.3 | Newtonian/0.001 | ISO 14242-1 | Deterministic model; surface texturing |
Chyr et al. [98] | Ball-on-Plane | MoP (no deformation in modelling) | Newtonian/not explicitly specified | Steady-state | Stochastic model |
Knee implants | |||||
Butt et al. [99] | Real geometry from CAD model | MoP/cup: 1.0/0.4 | Newtonian/0.1 | ISO 14243-3 | Stochastic model |
Marian et al. [40] | Elliptical ball-in-socket | MoP/cup: 3.5/0.34; 0.66/0.46 | Non-Newtonian/0.05 (base) and 0.002 (plateau) | ISO 14243-3 | Deterministic model |
Gao et al. [55] | Spherical ball-in-socket | MoP/cup: 1.0/0.4 | Non-Newtonian/40 (base) and 0.005 (plateau) | Subject-specific 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