Open Book Exam

Question #1 (25 Points)

(a) The presence of a metallic orthopaedic implant results in stress shielding which is generally thought to be deleterious. The level of compressive stress in an implant containing bone, sb  is affected by the bone cross-sectional area fraction, ab  and the stiffness of the bone and implant, Eb  and Ei

(i) Assuming that the bone and implant are loaded in uniaxial compression and the compression

normal strain is the same in both the bone and implant, show that

Where, s is the compressive stress averaged over the area of the bone and implant

(ii) If the stiffness of the metallic implant is orders of magnitude larger than the stiffness of the bone and the area fractions of the bone and the implant are approximately equal, show that the result in part (a) reduces to

How do changes in ai  and Ei/Eb  affect the compressive stress applied to bone? 6 points

(b) Comment on stress shielding and cell biomaterial interaction of trabecular tantalum metal reported in the following references listed below and what be your suggestions to minimize this problem? 6 points

Bencharit, S., Byrd, W. C., Altarawneh, S., Hosseini, B., Leong, A., Reside, G., Morelli, T. and Offenbacher, S., “ Development and Applications of Porous Tantalum Trabecular Metal-Enhanced Titanium Dental Implants” Clin. Implant Dent. Relat Res., 2014, 16(6): 817-826.

Keotsostathis, S.D., Tsakotos, G. A., Papakostas I., Mcheras, G. A. “Biological Processes at Bone – Porous Tantalum Interface. A Review.” J. Orthopedics, 6(4) e3 (2009).

Sevilla, P., Aparicio, C., Planell, J.A., Gil, F.J., Comparison of the Mechanical Properties between Tantalum and Nickel-Titanium Foams Implant Materials for Bone Ingrowths Applications, J. of Alloys and Compounds, 439, 67-73 (2007).

(c) Dental filling materials can readily experience a temperature differential on the order of 50°C in normal daily function. (Consider the consumption of a cold or hot beverage). Also consider a dental filling material that is cylindrical in shape as shown in the figure below. If this dental filling is 2 mm in diameter and 4 mm in length, what is the expected volumetric expansion for a filling material made of alumina with a thermal expansion αalumina  = 8.5 x 10-6 /°C? How does this compare to dental fillings made with resin, αresin  = 85 x 10-6  /°C and gold alloy, αgold alloy = 14 x 10-6  /°C? Assume a temperature change of 50 °C and the dental filling is assumed to deform isotropically. The thermal expansion coefficient for enamel is 8 x 10-6  /°C. The elastic modulus for alumina is 400 GPa, for the resin is 2.5 GPa and for the gold alloy is 95 GPa. Calculate the one-dimensional forces owing to these thermal expansions. Comment on the result of your calculations. 6 points

Question # 3 (25 Points)

Due to increasing incidence of peripheral arterial occlusive diseases and coronary heart diseases, there is a tremendous need for small diameter vascular grafts. To overcome the limitations of synthetic grafts and autologous grafts, two composite vascular grafts were developed (see the following table).

Circumferencial tests were performed on both grafts and porcine aorta till samples break, the following data was collected and displayed in the chart below.

1.   Plot the stress-strain curve for each specimen into one graph, determine the ultimate tensile stress strain at break for grafts and porcine aorta.

2.   Natural blood vessels have a nonlinear mechanical behavior where they exhibit a two-stage

behavior- a toe region followed by a linear region.

a.   Identify and label the two regions for all samples.

b.   Determine the elastic modulus for all samples.

3.   Consider the structure and composition of blood vessels.

a.   Explain why aorta exhibits a two-stage behavior under an increased strain.

b.   If the longitudinal or transverse tensile test is performed on the aorta, would you expect a similar mechanical behavior? What would be the change in elastic modulus?

c.   Justify the material selection and material combination (i.e., silk with gelatin and silk with polyurethane) for grafts # 1 and # 2. Justify the choice of your model.

4.   Several models have been proposed in the literature to fit the mechanical response of soft tissues, using an appropriate model to fit the data for grafts # 1 & # 2. Justify the choice of your model.

5.   Use the best fit model, determine the elastic modulus for graft # 1 # 2. Compare your results with the results from part 2b, which value(s) you think is more credible?

6.   Briefly  outline  experimental  procedure  for  the  circumferential  tensile  tests  for  vascular conduits.

7.   Ro complete the mechanical profile of the two grafts and evaluate the feasibility as vascular replacements, list any other mechanical properties you would like to study and

a.   Explain why these properties are crucial for vascular implant.

b.   Outline the testing that could be performed to evaluate the mechanical properties you selected.

8.   Compare the three graphs generated in part 1, which graft will you choose as an arterial graft? Considering the structure and properties differences between arterial and venous vessels, which synthetic graft would be more suitable for venous replacement? Use data/references from the literature to justify your choice.

9.   If the intended use of graft # 1 is an arterial replacement, suggest possible improvements in composition and fabrication techniques to closely  mimic  mechanical  behaviors  of  native arterial vessels.

Question # 4 (25 Points)

a. There  is a  new drug-eluting stent on the  market. This stent technology  uses diffusion- controlled release from a biostable polymer matrix to deliver an anti-inflammatory agent in the polymer matrix and the diffusion coefficients for the three formulations are 9.5 x 10- 11  cm2/s (slow), 7.0 x 10- 10  cm2/s (medium) and 5.2 x 10-9  cm2/s (fast).

i.          Assume that the complex geometry of a stent can be approximated as a planar slab with diffusion in one dimension and the coating thickness is 1 mm. Plot the release profiles on one graph. Determine the half-life of each formulation.

ii. A patient who has an arterial lesion that will require drug treatment for a duration of no less than 30 days, but complete by 2 months. Which formulation would you recommend?

b. A mixture of two polysaccharides (A and B) was prepared as polymer matrix to provide controlled release of therapeutic molecules. Nimesulide was selected as the model drug and suspended in the mixture. The resultant gel was dried and pressed into tablets.

Two tablet formulations were tested in the study. In the first formulation, A was cross-linked with B using sodium trimetaphosphate. In the second formulation, no cross-linker was used.

Liquid uptake capacity is important to a drug delivery system. The swelling degree of the tablets was studied by immersing the system in media at two pH values (pH 2.0 and pH 7.4). The results were presented below.