Question

X-RAY CT

a) Consider a 20 cm path through water, with a small piece of bone of thickness x. Assuming water has an attenuation coefficient of 0.3 cm-1, and bone of 1.0 cm-1, how thick would the bone have to be to reduce the number of photons detected by 10%?

b) Partial volume effects are troublesome when imaging some portions of the brain. Illustrate where partial volume effects lead to loss of tissue visualization. Suggest three independent ways to potentially reduce this effect by altering the way imaging is performed.

Answer 1

The total length is 20+x cm so, distance traveled in water is: 20 cm

The attenuation follows the exponential decay given by:

$I=I_oe^{-\mu_120}e^{-\mu_2x}$

here, I = [1 - 0.1] I_o

=> $0.9=e^{-(\mu_1(20)+\mu_2x)}$

taking natural log on both sides gives,

$ln(0.9)=-(\mu_1(20)+\mu_2x)$

$0.10536=0.3(20)+x$

=> x = - 6.105 cm.