Range Equation

The range equation is the calculation that the system performs to determine the depth of every echo.

In physics, distance is equal to velocity multiplied by time. However, in this case the system wants to calculate the distance to the reflector, not the total distance traveled by the pulse/echo, so the product of velocity and time must be divided by 2.

Here's an example given an echo that has a go-return time of 39 us:

D = (1.54 mm/us x 39 us)/2

= 60 mm / 2

= 30 mm

= 3 cm

This is a little complicated for us to do quickly. However, the ultrasound system is a computer, so it can instantly perform this calculation on every echo that returns to the transducer.

Luckily for us, there's a shortcut that can be useful. That shortcut is knowing that in soft tissue the go-return time for each centimeter of depth is approximately 13 us.

Thus, the go-return time in soft tissue for a reflector at 1 cm depth is 13 us, for a reflector at 2 cm depth it's 26 us, for a reflector at 3 cm depth, it's 39 us and so forth.

This is a handy value to remember for Registry questions that might ask:

"Given a pulse-echo time of 52 us, what is the reflector depth in soft tissue?"

The answer is 52 us divided by 13 us/cm = 4 cm.

Handy!

If you'd like to see the derivation of this shortcut, check out this page.