Advanced FE Modeling of Absorbable PLLA Screws Jorgen Bergstrom, Ph.D., David Quinn, Ph.D., Eric Schmitt jbergstrom@veryst.com, LLC September 14, 2011
Introduction Anterior cruciate ligament (ACL) reconstruction has become one of the most frequent procedures in arthroscopic surgery of the knee. About 50,000 ACL injuries occur each year in the United States. A graft (often tendon) is used as a replacement ACL and small interference (wedge) screws are used to hold the graft in place until it can heal. Both Titanium and bio-absorbable (PLLA) screws are used. Bio-absorbable screws do not require removal, and allow magnetic resonance studies. Screw breakage on insertion may occur in 10% of the operations. (Arthoscopy, Vol 16, 5, 2000) 2
ACL Reconstruction Surgery Four ligaments connect the femur to the tibia and allow for stabilization and control within the knee: the anterior cruciate ligament (ACL) the posterior cruciate ligament (PCL) the medial collateral ligament (MCL) the lateral collateral ligament (LCL) The ACL provide rotational stability and keeps the tibia from sliding in front of (anteriorly) the femur. (Avery) 3
Exemplar Interference Screws 4
Surgical Procedure (Bio-Core Interference Screw, Biomet Sports Medicine) 5
Known Issues 6
Pullout Strength of Interference Screws A common measurement for interference screw strength is its pullout (initial fixation) strength. Experiments are commonly performed using Polyurethane foam blocks [ASTM F-1839] The force can be applied using a nylon rope (Biomet Sports Medicine, Inc) or by pushing in a direction opposite to the screw insertion (Smith & Nephew). Type of Screw Average Pullout Strength Bio-Core 9x25 mm 746 N ± 105 N Arthrex 9x28 mm 794 N ± 128 N (Biomet Sports Medicine, Inc.) (Smith & Nephew) 7
Torsional Strength of PLLA Screws The torsional strength of both metallic and degradable screws has been measured The critical torque of PLLA screws is about 100 N-mm 8
PLLA Properties Poly-L-lactide (PLLA) is the product resulting from polymerization of L,L-lactide (also known as L-lactide). Physical properties: Crystallinity 37% Glass transition temperature: 60-65 C Melting temperature: 173-178 C Tensile modulus: 2.7-16 GPa PLLA has a modulus that is approximately equal to bone. PLLA degrades in-vivo in 2 to 3 years. 9
Experimental Data for PLLA Uniaxial tension to failure of pure PLLA fail Two different strain-rates fail Experiments performed by The applied strain rate strongly influences: the yield stress the failure stress 10
Experimental Data for PLLA Uniaxial tension with stress relaxation segments 3 min relaxation Applied strain rate approximately 0.002/s The experiments performed by The material is highly non-linear viscoelastic 11
Material Model for PLLA Intermolecular Resistance Network Intramolecular Flow Resistance Network Neo-hookean hyperelastic Powerlaw flow with double exponential yield evolution Neo-hookean hyperelastic (Simplified Rheological Representation) The Parallel Network Model (PNM) is commercially available from 12
Kinematics Deformation Gradients: Velocity Gradients (Network B): 13
Stress in Network A Cauchy Stress from Arruda-Boyce 8-chain model: Material parameters: shear modulus (μ), bulk modulus (κ), locking stretch (λl) Inverse Langevin function: Controls the large strain response 14
Stress in Network B Cauchy Stress from Arruda-Boyce 8-chain model: Total Stress: Controls the initial modulus and the plastic flow behavior 15
Rate Kinematics Network B Evolution in flow resistance: 16
Material Model Calibration For each material, the best material parameters were found using the NelderMead simplex algorithm implemented in a custom application The root-mean-square error (RMSE) was used as the objective function 17
Material Model Implementation The material model can be selected using the MCalibration software. MCalibration is commercially available from. 18
Material Model Calibration The material model calibration was performed using MCalibration. MCalibration is commercially available from. The calibrated material model was imported into ANSYS WB 13. 19
Calibration of PLLA Model The calibrated material model accurately captures the uniaxial tension data at different strain rates R2 fitness = 0.997 20
Calibration of PLLA Model The calibrated material model also accurately captures the stress relaxation data R2 fitness = 0.961 21
Calibration of PLLA Model Comparison between experimental and predicted stress relaxation behavior 22
FE Model Tibia The tibia and screw geometries were create in Solid Works FE mesh of the tibia (300k tet elements) Cancellous bone: E=1500 MPa nu=0.3 Screw location 23
FE Model Screw FE mesh of the PLLA screw (80k tet elements) 24
Boundary Conditions The interior of the screw head was pulled in tension to simulate a pullout Applied force = 600 N Load time = 1 sec The bottom of the tibia was held fixed Augmented-Lagrangian contact with a friction coefficient of 0.3 25
Results The simulation failed to converge past F=382 N The max Mises stress in the screw is 38.2 MPa 26
Results The simulation failed to converge past F=382 N The max Mises stress in the screw is 38.2 MPa The experimental failure stress at the applied strain rate is about 70 MPa. The predicted critical failure force is 700 N The experimental failure force is 740 to 790 N 27
Conclusions ACL reconstruction surgery often use PLLA interference screws. To optimize the design of the PLLA screws it is important to be able to run accurate FE simulations that incorporate the nonlinear viscoplastic response of the PLLA. The Parallel Network Model (PNM) from the PolyUMod library enable these important simulations. The simple pullout strength study presented illustrate how this approach can be used to determine the max stress and safety factors of different screw designs. In a future study we will study more advanced loading conditions and the influence of material degradation. 28
Founded 2006 www.veryst.com Located in Needham, MA (20 minutes west of Boston) Six Full-Time Engineers 5 PhD s (two former MIT faculty) is a software partner with ANSYS. Veryst provides the PolyUMod library of usermaterial models, and the material model calibration software MCalibration. 29