42-101 Intro to BME (Przybycien)

Spring 2005

PROBLEM SET No. 10

Posted:

4/23/05

Due:

4/29/05 in class

Note: Final team evaluation due in class on Friday, 29 April.

1.

Biomaterials – Stress-Strain behavior.  A cancellous bone specimen (8 mm long, 5 mm wide, 6 mm thick) was subjected to compression testing; results from this testing are listed in the table below.  Plot the stress-strain curve (Microsoft Excel would be particularly convenient for this).  Determine the ultimate tensile stress and the elastic modulus (the “slope” function in Microsoft Excel would be particularly convenient for this).  Use the value of the elastic modulus to make an approximate estimate of the shear modulus.

displacement
(mm)   

0

force

(N)

0

0.05

21

0.1

49

0.15

118

0.2

190

0.25

301

0.3

399

0.35

503

0.4

602

0.45

700

0.5

810

0.55

960

0.6

1090

0.65

1200

0.7

1298

0.75

1390

0.8

1487

0.85

1523

0.9

1490

0.95

1350

2.

MRI.  MMD problem 14.9

3.

MRI.  Find the energy difference, in J, and corresponding photon frequency, in MHz, between the two spin states for 1H if the MRI instrument has a magnetic field strength of 0.75 T.  Compute the fractional excess of spin-up 1H nuclei ([N+ - N-]/N+) for room temperature samples in this instrument.  How might the fractional excess be improved so that a larger signal could be observed?

4.

Signal Processing.  A 360 Hz signal is sampled at 200 samples/sec.  What frequency will the “aliased” digital signal look like?

Updated on 4/23/05 by TMP