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Biomechanics

Biomechanics - Poster Session D

Poster E1 - Modeling of Sensors Used to Validate FE models of Articular Joint Contact: A Comparison of Simulated Hertz Contact

Friday, October 25, 2024
3:30 PM – 4:30 PM EST
Location: Exhibit Hall E, F & G

Introduction:  Finite element (FE) models are frequently used in studies of articular joint contact, with verification and validation important steps prior to clinical applications (1, 2, 3), Frequently, thin film electrical sensors are inserted into the joint space in in vitro studies for validation (3). However, their application as a gold standard warrants careful consideration of calibration methods and other possible sources for error, including resolution and influence on contact patterns (4). Although these available sensors are thin and quite flexible, slipping such a layer between the curved and congruous joint surfaces may alter the very contact pressures they are trying to measure.
This study aims to evaluate the use of a flexible pressure sensor (Tekscan Inc, model 4011, Norwood, MA) in validating of FE models of frictionless joint contact, specifically in evaluating knee contact mechanics under static loads. In this study, we developed FE models that allow us to compare FE predictions to the analytical solution of Hertzian contact theory, while also reflecting the typical mesh density and contact parameters of our group’s knee joint models. Models were constructed with and without the sensor in place to evaluate its impact on contact behavior. Our models were designed to simulate a planned experiment for further validation. We hypothesized the FE model accurately reflects the analytical solution and integrating a flexible sensor does not substantially affect measurements of maximum contact pressure, contact radius, and maximum displacement.

Materials and

Methods:  An FE model comprised of a block, sphere, and sensor was created (Figure 1) using Abaqus software (Dassault Systèmes, Johnston, RI). The sensor matched the matrix dimensions (29 mm by 76.2 mm) and was modeled using continuum shell (SC8R) elements with a thickness of 0.2 mm and 0.4 mm (with protective film). To identify effective modulus of the sensor, we conducted a 3-point bend test with a 50 N load cell (MTS Systems, Eden Prairie, MN). The sphere, with diameter of 38mm (similar to curvature of a human knee), was assigned material properties of Delrin (E = 4400 MPa, ν = 0.3). The block was assigned properties similar to Neoprene to prepare for a planned experiment and to approximate human cartilage (E = 10.35 MPa, ν = 0.4) (4). The block and the sphere were meshed with C3D8 elements. Models without the sensor were run to compare to the analytical solution and analyze the convergence of the mesh size.

The sensor was fixed at both edges to simulate experimental boundary conditions. Frictionless contact was established between surfaces. Models were run up to 100N applied to the sphere, starting with a displacement step to establish contact. Contact pressures along two perpendicular paths were extracted and maximum displacement of the block’s surface was identified. To estimate the maximum contact pressure distribution reported by the sensor, FE results were discretized to represent the resolution and lower threshold (0.2 MPa) of the sensor, with top and bottom surface pressures averaged to estimate sensor output.

Results, Conclusions, and Discussions: Our model without the sensor predicted displacement and maximum pressure within 6.4% of the analytical solution and the pattern of pressure distribution was captured, however contact radius was overestimated. As the mesh was refined, the indentation and contact radius values approached the analytical solution.

Insertion of the sensor created irregularities in the contact pressure distribution, with large variations in nodal pressure values within the contact area; this effect was greater with the thicker sensor. However, using a polynomial fit (Figure 2, 3), to smooth the results and averaging the top and bottom surfaces resulted in pressures that were comparable to the analytical solution with an error of less than 3% for the average pressure in the central 1 mm of the sensor. The thickness of the sensor played an important role on the indentation of the block, decreasing by 2.3% and 6.5% for the models with the 2mm and 4mm thick sensor, respectively. The contact radius decreased by 8.4% when the sensors where inserted.

Limitations of this study should be considered. The irregular pressure patterns on the models with the sensor made the quantification of the contact radius challenging. The polynomial smoothing function provided an approximation, however other techniques could be considered. Further analysis on the impact of the boundary conditions on the sensor is needed. It was assumed the sensor reports the average pressure at the top and bottom surfaces; this cannot be confirmed until our planned experiment. In our future work the results from the FE model and the analytical solutions will be compared to experimental data. We plan to evaluate the insertion of a modeled sensor in one of our group’s knee FE models (4).

This study provides insight into the impact that using a flexible pressure sensor can have on the contact pressures. The sensor’s insertion on the model slightly decreased indentation, contact pressure and radius, allowing to interpret our validation studies.

(1) Bachus et al., 2006, Medical Engineering & Physics
(2) Brimacombe et al., 2009, J. Biomech. Eng.
(3) Chen et al., 2017, Experimental Methods in Orthopaedic Biomechanics
(4) Letendre et al., 2024, SB3C

Acknowledgements (Optional):  We thank Peter Torzilli, Eugene Anku and Kai Hua Lui for their initial guidance and help on this project.