Introduction to Biomaterials Engineering CBE 4421a
Problem #1
1. a. Determine the probability of failure of a hip joint arthroplasty after 15 and 30 years, assuming the following (t is in years).
b. Which factor is the most important for the longevity of the arthroplasty?
Infection fi = 0.05e–t
Loosening flo = 0.01e+0.15t
Fracture ffr = 0.01e+0.01t
Wear fw = 0.01e+0.1t
Surgical error fsu = 0.001
Pain fpn = 0.005
2. A polyethylene is made of the following weight distribution.
a. Calculate Mn, Mw, and Mw/Mn (polydispersity).
b. Plot Wi versus Mi and also Mw and Mn in the same plot.
c. Why is Mw always greater than Mn?
Wi (grams) 10 20 30 30 20
Mi (kg/mol) 10 20 30 40 50
3. (a) Show that the atomic packing factor for HCP is 0.74.
3. (b) Titanium (Ti) has an HCP crystal structure and a density of 4.51 g/cm3.
(i) What is the volume of its unit cell in cubic meters?
(ii) If the c/a ratio is 1.58, compute the values of c and a.