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.