1. MINIMIZING STRESS SHIELDING IN
FEMORAL HIP IMPLANTS THROUGH
MATHEMATICAL MODELING AND
EXPERIMENTAL VERIFICATION
Justin Fisher, Tyler Grubb, Phuong Huyen, Rohan Yadav
Dr. Abdellah Ait Moussa, Dr. Morshed Khandaker

2. OVERVIEW
Objective:
• Reduce stress shielding and interface stress in a hip replacement
by controlling stem stiffness, which is a function of stem
geometry and its material properties.
How:
• Create a self-regulated software package to optimize the stem
geometry by mathematically modeling and controlling the stem
geometry using a fixed number of design parameters, create a
solid model of the stem assembly, and conduct the finite
element simulation.
• Design and build experimental apparatus to benchmark and
confirm the numerical results.

3. DELIVERABLES
• Numerical analysis method for minimization of stress
shielding on a femoral hip implant under static and
dynamic loads through geometrical manipulation
• Experimental verification and benchmark of the numerical
analysis results.

4. OSTEOPOROSIS
• Secondary Osteoporosis
• Bone fragility due to bone
density reduction
• Caused by a variety of factors

5. STRESS SHIELDING
Femur Bone Bone with Implant

6. MATHEMATICAL MODEL
𝑥
𝑎
𝑝
+
𝑦
𝑏
𝑝
= 1

7. FINITE ELEMENT ANALYSIS
ANSYS Static Structural in Workbench.
Engineering Data- Titanium, PMMA Cement and Cortical Bone.
The IGES model imported into Design Modeler.
1. Meshing
Medium mesh with Tetrahedral elements.
Elements – About 90,000-100,000
Grid Independent Test
2. Contact Region
Stem- Cement: Rough
Bone-Cement: Bonded

8. FINITE ELEMENT ANALYSIS
3. Boundary Conditions
• Abductor Muscle force of 1.5 KN at 15° with
vertical.
• Joint Reaction force of 2.5 KN at 10° with
vertical.
• Fixed Support at Distal End
• Simulates average walking conditions.
• Fatigue Tool
• Goodman Theory
• Text file of equivalent alternating stress.

9. NUMERICAL ANALYSIS RESULTS
Compare stress over the surface of bone.
Stress Diff =
(σ′1 −σ1)2 +(σ′2 −σ2)2 +(σ′3 −σ3)2 +..+(σ′ 𝑛 −σ 𝑛)2
𝑛

10. NUMERICAL OPTIMIZATION OF STEM GEOMETRY
Design of Experiments Method
• Developed by Genichi Taguchi from Japan during late 1940.
• Suggested fractional factorial experiments using orthogonal
arrays.
• Type of orthogonal array based on the number of variables and
their levels.
• Best design parameters will identified from orthogonal arrays.
• About 20 variables for cross section of stem geometry.
• L32 orthogonal array was used.

11. TYPE OF SENSOR
Sensor Electrical Strain
gage
Piezoelectric
Sensor
Fiber Bragg Sensor
Temperature
effect on zero
point
Low NA High
Drift Small Large Small
Temperature
coefficient of
sensitivity
High but
compensable
Low High
Linearity High Low NA
Static
measurement
Applicable NA Applicable
Dynamics
measurement
Applicable Applicable Applicable

12. MEASUREMENT SYSTEM
The system consists of
• Power supply provides ± 15 V, 12V, and 5V
• 6 strain gage modules
• DAQ device

13. MEASUREMENT SYSTEM – POWER SUPPLY

14. MEASUREMENT SYSTEM

15. MEASUREMENT SYSTEM
LabVIEW Program for DAQ
• Measuring the Output voltage of the strain gage
module.
• Measuring the Excitation Voltage.
• Smoothing the measurement with the Moving
Average Filter.
• Computing strain and stress value.
• Exporting the data to Excel.

16. MECHANICAL DESIGN
Designed for Little Tensile Tester
Machined
Force Applied Part
Hip Cup Part
Base Plate

17. MECHANICAL FORCE ANALYSIS
• Sum of moment about L
to solve for Fa and Xl
such that the give forces
for the test condition are
met.

18. BUDGET
Total Budget: $1,000.00
Expenses:
Electronic Components: $232.74
Instrumentation Amplifiers (6)
Circuit Components
Strain Gages (6)
Mechanical Components: $22.98
Crimps and Cable
Total Sent: $255.72
Budget Left: $744.28

19. FUTURE WORK
• Experimentally measure Stress Array in Femur Bone
• Experimentally measure Stress Array in Non-
Optimized Implant
• Experimentally measure Stress Array in Optimized
Implant

20. REFERENCES
[1] Kurtz S, Ong K, Lau E, Mowat F, Halpern M, Projections of primary and revision hip and
knee arthroplasty in the United States from 2005 to 2030, J Bone Joint Surg Am. 2007
Apr;89(4):780-5.
[2] Raut, V. V., Siney, P. D., and Wroblewski, B. M., 1995, ‘‘Revision for Aseptic Stem Loosening
Using the Cemented Charnley Prosthesis,’’ J. Bone Joint Surg. Br., 77-B, pp. 23–27.
[3] Raut, V. V., Siney, P. D., and Wroblewski, B. M., 1995, ‘‘Cemented Revision for Aseptic
Acetabular Loosening,’’ J. Bone Joint Surg. Br., 77-B, pp 357-361.
[4] Ali Abdulkarim, Prasad Ellanti, Nicola Motterlini, Tom Fahey, and John M. O'Byrne,
Cemented versus uncemented fixation in total hip replacement: a systematic review and meta-
analysis of randomized controlled trials, Orthop Rev (Pavia). Feb 22, 2013; 5(1): e8
[5] Li C, Granger C, HD. Progressive failure analysis of laminated composite femoral prostheses
for total hip arthroplasty. Biomaterials 2002;23:4249–62.
[6] Wolfram Mathematica, http://www.wolfram.com/mathematica/
[7] SolidWorks Corporation, http://www.solidworks.com/
[8] ANSYS Corporation, http://www.ansys.com/
[9] Lennon, A.B., McCormack, B.A.O., Prendergast, P.J., 2003. The relationship between cement
fatigue damage and implant surface finish in proximal femoral prostheses. Medical
Engineering and Physics 25, 833-841.
[10] Jeffers, J.R.T., Browne, M., Taylor, M., 2005b. Damage accumulation, fatigue and creep of
vacuum mixed bone cement. Biomaterials 26 (27), 5532-5541.