Investigating Cartilage Stress Dennis Cody November 22, 2004

Outline History  PTC & Pro/Engineer  Stanford VA – Investigation of Stress in Cartilage  Description of Patellofemoral Pain.  Determine when bone can be assumed rigid.  Understand apparent discrepancies in literature. PTCStanfordVA

Parametric Technology Corporation 5 years in Quality Assurance – Senior QAE Software: Pro/Engineer, Pro/Mechanica, Pro/Intralink Transition to new defect tracking database Desire to enhance people’s lives and health PTC

Stanford – Design and Prototype Tools for Surgical Procedure Implant pegs: placement, depth, diameter, angle Method of creating peg holes Tools:  Cutting Block  Depth Resection Gauge  Drilling Template  Template Impactor  Posterior Peg Impactor  Tibial Trial  Tibial Spacer PTCStanford

Outline History  PTC & Pro/Engineer  Stanford VA – Investigation of Stress in Cartilage  Description of Patellofemoral Pain.  Determine when bone can be assumed rigid.  Understand apparent discrepancies in literature. PTCStanfordVA

Outline  Determine when bone can be assumed rigid.  Understand apparent discrepancies in literature. When looking at stresses in cartilage: PTCStanfordVA

Motivation - PFPS What is PF Pain Syndrome?  Anterior knee pain  Associated with repetitive exercise  Cause difficult to determine  Muscle imbalance  Attachment  Bone shape, alignment… BackgroundMethodsResults

Objective Obtain PF joint data in young adult volunteers using non-invasive techniques.  Kinematics  Kinetics  Contact areas  Stresses Focus: From static MR Images, create a finite element model that can be used for analyses BackgroundMethodsResults VA

Hypothesis Subjects with PF pain will have elevated cartilage stresses (compared to age and activity matched subjects without PF Pain), either because of increased PF forces and/or decreased PF contact areas. Assumption to test: When looking at patellar and femoral cartilage stresses due to physiological loads, the underlying bone can be treated as a rigid material. BackgroundMethodsResults VA

Background Modeling and solving models with bone elements is expensive. Some studies consider bone as a rigid material. (Li et al., 2001, Zhang et al., 1999) Others consider the bone elements. (Beaupré et al., 2000, Brown et al., 1984) BackgroundMethodsResults VA

Background – Previous Work 3D Model of tibio-femoral joint (Donahue et al., 2002)  Model with bone  Model with rigid backing  No difference of more than 2% BackgroundMethodsResults VA

Background – Previous Work Ideal model with plug and indentor (Brown et al., 1984)  Cancellous bone modulus value impacts effect of rigid implant in bone  Impactor has small radius  smaller than in PF joint? BackgroundMethodsResults VA

Background – Previous Work AuthorSectionThickness (mm)Modulus (MPa) Beaupré Cartilage36 Subchondral12000 Cancellous16200 Brown Cartilage~ Subchondral~ Cancellous~ Donahue Cartilage 3D model of 30 yr old specimen, varying thickness 15 Subchondral Cancellous400 BackgroundMethodsResults VA

Methods Contact formulation Plane Strain Cancellous modulus Subchondral bone thickness Cartilage bone interface radius BackgroundMethodsResults Figure modified from Beaupré et al., VA

Model Model hemisphere contacting a plate (axisymmetric) Allows curved and flat surface Two models:  Cartilage and bone elements BackgroundMethodsResults VA

Model Model hemisphere contacting a plate (axisymmetric) Allows curved and flat surface Two models:  Cartilage and bone elements  Cartilage with rigid backing BackgroundMethodsResults VA

Methods – Plane Strain Master-Slave surface BackgroundMethodsResults VA

Methods – Plane Strain Master-Slave surface Hertz contact BackgroundMethodsResults Remove ABAQUS Series VA

Master-Slave surface Hertz contact Compare with results from Beaupré’s PE model Methods – Plane Strain BackgroundMethodsResults VA

Methods – Plane Strain Master-Slave surface Hertz contact Comparison with results from Beaupré’s PE model. PE vs. BackgroundMethodsResults VA

Methods – Axisymmetric Master-Slave surface Hertz contact Comparison with results from Beaupré’s PE model. PE vs. Axisymmetric BackgroundMethodsResults VA

 Stress With  Radius σ 1-max = 432 kPa σ 2-max = 396 kPa σ 3-max = 401 kPa σ 4-max = 407 kPa σ 7-max = 414 kPa σ 8-max = 420 kPa r 2r r F F F F  1-max  5-max  3.8%  2-max  6-max  4.4%  3-max  7-max  3.2%  4-max  8-max  3.2%  1-max  3-max = 1.08  5-max  7-max = 1.08  0%  2-max  4-max =.97  6-max  8-max = 0.98  1% = ? = ? r = 20.5 mm 2r = 40.5mm F = 230N Cart thk = 3.5 mm Subch bone = 0.5 mm Canc modulus = 600 MPa BackgroundMethodsResults ? = ? = ? = ? = VA σ 5-max = 449 kPa σ 6-max = 413 kPa

 Stress With  Load  Stress With  Load σ 5-max = 300 kPa σ 6-max = 294 kPa σ 7-max = 414 kPa σ 8-max = 420 kPa σ 3-max = 401 kPa σ 4-max = 407 kPa F σ 1-max = 292 kPa σ 2-max = 286 kPa F 2F  1-max  5-max  2.8%  2-max  6-max  2.6%  3-max  7-max  3.2%  4-max  8-max  3.2%  1-max  3-max = 0.73  5-max  7-max = 0.72  1%  2-max  4-max = 0.70  6-max  8-max = 0.70  0% = ? = ? r = 40.5 mm F = 115N 2F = 230N Cart thk = 3.5 mm Subch bone = 0.5 mm Canc modulus = 600 MPa BackgroundMethodsResults ? = ? = ? = ? = VA

Stress Patterns BackgroundMethodsResults VA

Trends in Results BackgroundMethodsResults Modulus (MPa) Thickness (mm) Octahedral ShearHydrostaticOI %0.68%0.53% %1.32%0.87% %1.36%0.30% %3.36%1.12% %3.47%0.34% %15.8%4.21% OI : Osteogenic Index = k * σ Octahedral Shear + σ Hydrostatic (k = 0.35) VA

Summary Contact model ran successfully in Abaqus Rigid assumption valid for healthy young subjects, probably not for osteoporotic subjects Model differences explain difference in results

Thank You