Tissue Specific Imaging – examples in numbers
This page is a continuation of the discussion on Tissue Specific Imaging.
Accurate measurement of fat depth and muscle thickness is very important in certain applications. If the speed of sound is assumed to be traveling at 1540m/s, but is in fact traveling at 1430m/s through fat, a hypothetical 10cm fat thickness would be overestimated by 0.77cm. The mathematics of this is as follows:
Speed = distance/time, so time = distance/speed
- When scanning through 10cm of soft tissue:
t = (2*0.10m) / 1540m/s (speed of sound through soft tissue)
t = (2*0.10) / 1540 = 0.00012987s.
Distance is multiplied by two because the ultrasound waves must go and return.
In other words, it takes 0.00012987s (0.13 miliseconds) for ultrasound to travel to a depth of 10cm and return in soft tissue.
- When scanning the same distance through fat:
Sound travels a little more slowly through fat, at 1430m/s.
t = (2*0.10) / 1430 = 0.00013986s.
It takes ultrasound 0.14 miliseconds to go and return through a depth of 10cm in fat.
The significance of this becomes apparent when you consider that the ultrasound machine assumes a constant speed of sound. Unless you adjust the TSI value, this will be assumed to be 1540m/s.
Since distance = speed x time, the ultrasound machine will calculate the distance traveled as follows:
- IN SOFT TISSUE: d = (1540 x 0.00012987)/2 = 0.10m
Clearly, this is the answer we would expect, as the go and return time was already calculated for a depth of 10cm.
- IN FAT: d = (“1540” x 0.00013986s)/2 = 0.107m, or 10.77cm
This is the origin of the 0.77cm inaccuracy stated above. The machine, not knowing that the sound waves are traveling through fat, of course continues to assume that they are traveling at a speed of 1540m/s. Since the sound waves are in reality traveling slower than this, they take longer to get back to the transducer. Due to the relationship between distance and time, the machine displays this extra time taken as 0.77cm of additional depth.
For interest’s sake, this is what would happen through 10cm of bone (clearly an unlikely scenario!):
Sound travels through bone very fast, at around 3200m/s. t = (2*0.10)/3200 = 0.0000625s.
It takes only 0.06 miliseconds for ultrasound waves to go and return for a depth of 10cm through bone, but the ultrasound machine will assume:
d = (“1540” x 0.0000625)/2 = 0.048m, or 4.8cm.
Due to the fact that the sound waves return to the transducer so quickly, the machine assumes that they are reflecting back from an interface only 4.8cm away – not 10cm away. This scenario is impossible in reality due to the amount of attenuation that would occur traveling through 10cm of bone there and back, but it should hopefully get you thinking about the way sound waves travel through different media.
Understanding this is important in interpreting artifacts.
February 19, 2021
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