Scenario: You are the principal design biomedical engineer for the Hanoi University of Technology College of Medical Hospital. As a result of recent governmental initiatives their is a new country-wide project to provide on-demand bone plates that are custom manufactured at on-site regional hospitals to repair long-bone fractures. There is great pressure to keep costs contained. You have observed that during some surgical procedures to repair/plate long-bone fractures, there is uncertainty and waste regarding the selection and use of the best bone plate. Your job is to work with the surgeon to identify in advance of, and during the surgical procedure, the best choice for the size of the plate based on patient anthropometric data. For this particular case, the patient is YOU!
Patient data: weight__________kg height____________cm
For this case the bone to be plated is the tibia. The length of the tibia is 25% of your height. There is a small amount curvature (bowing) in the tibia that results in a 1% of body height mid-bone displacement from the vertical (and thus creating a bending moment even when just standing). The outside diameter of the tibia at mid-length is 1.5% of body height.
Your job is to select the cross-sectional dimensions of a bone plate to stabilize the fracture. You know that a realistic approach to achieving this is to select/design a bone plate whose cross-sectional dimensions result in the situation where the neutral axis is located at the interface between the plate and the bone. As you do this, you notice that you are actually calculating Ip, and that quantity by itself does not uniquely determine both the thickness (t) and width (b) of the plate. You use your smarts to know that you do not want the plate to protrude through the skin (requiring a relatively small thickness) and that you want the BUCMH machinist to largely be able to use relatively standard stock metal, which comes in 0.25-cm widths and thicknesses (so you may slightly be rounding up/down your dimensions). So with this information you are able select a plate thickness and corresponding width.
Second, you plan to locate the plate on the tensile side of the fracture. Assume the installation of the plate itself results in a compressive force of one half body weight. What degree of bending (displacement at the transverse axis of the plate kind of related to the radius of curvature) is required to assure that the fracture site remains under compression when the bone is subjected to four times body weight (in case you accidentally stumble down the stairs while you are rehabilitating). Assume the plate length is ten times its width (while this is a reasonable value, it is not based on any engineering rationale). For this portion of the problem you will also need to know the Young’s Modulus of the plating material (for the previous portion of the problem, you can get away with using an Ep/Eb ratio =10, I think; Eb=10x109 N/m2 and Ep=100x109 N/m2).
In providing your design, use an application software package with clearly identifies inputs, units, remarks, and other documentation that explains your approach from beginning to end. Most specifically your solution must clearly identify the dimensions you select for your plate, the degree of plate mid-point displacement (curvature). If you correctly approach the problem but encounter unrealistic assumptions or dimensions, adjust and justify them accordingly. Your full design report must provide full documentation so that the Chief Orthopedic Surgeon can present your results and report to the Minister of Health, whose education is in politics and not medicine or engineering. Good luck!
Instructor: Professor and Dean Benjamin S. Kelley, Ph.D., P.E.
Baylor University, Waco, Texas (USA)
This collection contains:
Benjamin S. Kelley.