Question

A) If the thickness of the chest is 20 cm, what percentage of X-rays are transmitted through the chest at a certain incident X-ray energy assuming HVL values of 3.5 and 1.8 cm for muscle and bone, respectively, and the bone thickness to be 4 cm and muscle thickness 16 cm.

B) If CT images are acquired at the same X-ray energy as above, calculate the CT numbers for muscle and bone voxels assuming the linear attenuation coefficient of water is 0.1 cm-1

Answer 1

A) Given, HVL of muscle = 3.5 cm

HVL of bone = 1.8 cm

muscle thickness = 16 cm

bone thickness = 4 cm

thickness of chest = 20 cm

HVL = ln2 / = 0.693 / - linear attenuation coefficient

Now, we are considering muscle,

HVL = 3.5 = 0.693/

hence, muscle = 0.693 / 3.5 = 0.198

Now considering bone,

HVL = 1.8 = 0.693 /

bone = 0.693/1.8 = 0.385

now, we have to calculate the percentage of X-rays transmitted through chest,

N = No x e ^( - x), x- thickness

In muscle,

HVL = N/No = e ^ ( - 0.198 x 16) = e ^ (3.168) = 0.042

In bone,

HVL = N/No = e^ (- 0.385 x 4) = e^ ( -1.54) = 0.214

Now, the overall percentage = 0.042 x 0.214 x 100 = 0.89%

B) Given, water = 0.1 cm-1

CT number = K x (tissue - water) / water , K- constant = 1000

in muscle,

CT number = 1000 x ( 0.198 - 0.1) / 0.1 = (0.098 x 1000) /0.1 = 98/0.1 = 980 HU

In bone,

CT number = 1000 x (0.385 - 0.1 ) / 0.1 = (0.285 x 1000 ) / 0.1 = 285/0.1 = 2850 HU