In-Class Case Study: Determining the Mechanical Properties of Bone Using State-of-the-art Mechanical Testing System (MTS Bionix) Prepared by Prof. Deepak Vashishth Biomedical Engineering Department Rensselaer Polytechnic Institute Permission is granted for non-commercial use

Specific Aims Demonstrate tensile testing of cortical bone. Analyze the test data to extract the mechanical properties of the bone. Draw conclusions about –the mechanical properties of bone –limitations of linear elastic assumptions Use mechanical properties under tension, compression and torsion to analyze fracture surfaces of bone

In-Class Exercise Form the class into four groups of students Each group discusses and specifies one of the following four steps necessary to the study. –1. The hypothesis for experimental investigation –2. The testing required to validate the hypothesis –3. The physical design of test specimens –4. The experiment protocol and data analysis The next four slides show issues to be considered by each of the four groups.

Mechanical Properties of Cortical Bone 1. Possible Hypotheses a. Bone is weaker in tension than in shear. b. Bone is stronger in tension than in shear but: Tensile yield stress < 2(Yield stress in shear) c. Bone is stronger in compression than in tension. d. Bone is stronger in compression than in shear. e. Compressive yield stress > 2(Yield stress in shear)

Mechanical Properties of Cortical Bone 2. Required Testing Monotonic tests can determine the yield and ultimate strength under tension, compression and torsion. The properties vary with the rate at which specimens are tested. – (Use a fixed rate.) The rate should be similar to in vivo rates – i.e. rates at which the body loads the bone (Burr et al., 1996).

Mechanical Properties of Cortical Bone 3. Design of test specimen First alternative: testing of whole bone –Geometric variations occur in the bone and affect the measured mechanical properties. –The calculation of stress and strain is difficult if not impossible due to these variations. Second alternative: testing of specimens machined from whole bone, producing a standard geometry: –Test results vary with material properties only. –Fracture will be at a predictable site. –Stress and strain can be easily calculated. (continued)

Mechanical Properties of Cortical Bone 3. Design of test specimen Stress = Force/ [  *(0.003^2)/4] Strain = (  L/10)  L- measured via an extensometer Typical Dimensions (in mm) Reference: Vashishth et al., 2001

Preparation of test specimen

Mechanical Properties of Cortical Bone 4. Experimental set-up & data analyses See next slide for Lab image and Optional: Use NetMeeting to connect on-line to the Orthopaedic Biomechanics Laboratory Department of Biomedical Engineering Rensselaer Polytechnic Institute

MTS Testing RPI Specimen Grips Pod Controller MTS Signal Generator Multi-axial Load Cell Computer Interface

Mechanical Properties of Cortical Bone 4. Experimental set-up & data analyses The next two slides show the user interface screen display for the MTS during the experiment. The notes that accompany each slide are keyed to the numbers shown overlaying the screen display.

MTS Software

Running the Test See next slide for Lab image And link to A video file shows the fracture of the bovine bone specimen Optional: Use a WebCAM to connect on-line to the Orthopaedic Biomechanics Laboratory

Extensometer V-Groove Grips Keep eyes on fracture site Link: Username: biomed Password: guest

The data generated from this experiment is compiled in an Excel file. Link to this file to see data. There will be two sheets on this file. The first sheet will be the raw data and the second will be the calculated data. Link to wet bone tensile test Excel file Username: biomed Password: guest

The MTS Test Results Biomechanical Testing of Bone

Critical Points on a generalized stress- strain curve

Determining the Yield Stress (Y) using 2% offset

MTS Test Results Mechanical Properties of Cortical Bone

Is the assumption of linearity valid? 0.2% offset – Is it justified?

Case Study Wrap-up The results of experimental analysis for a large number of bone tests are shown in the next slide. We will look again at our initial hypotheses and draw conclusions based on the results. For homework, we will see if the results from the in-class case study appear similar to the large sample results.

Material Properties of Cortical Bone (Vashishth 1997) Loading E (GPa) G (GPa) Ystrain (%) Ystress (MPa) U.Strain (%) U.Stress (MPa) Tension 22.9 (2.2) 0.80 (0.03) 131 (5) 3.89 (0.79) 159 (8) Compression 22.4 (2.5) 1.19 (0.11) 207 (23) 1.22 (0.16) 210 (22) Torsion 5.6 (0.8) 1.39 (0.24) 68 (7) 2.0 (0.15) 84 (11)

Hypotheses Biomechanical Testing of Cortical Bone Looking again at each possible hypothesis, we can accept or reject as follows: 1:Bone is weaker in tension than in shear 2:Bone is stronger in tension than in shear but: Tensile yield stress < 2(Yield stress in shear) 3: Bone is stronger in compression than in tension. 4: Bone is stronger in compression than in shear. 5:Compressive yield stress > 2(Yield stress in shear)

Homework Exercise Using the data file generated from the dry bone tensile experiment, calculate: –Elastic Modulus –Yield stress and strain –Ultimate stress and strain Compare the differences between the wet bone experiment and dry bone experiment. Using the yield strength values obtained under tension, compression and shear, explain the failure of bone under tension and compression*. Link to Dry Bone Tensile Test File Username: biomed Password: guest