Given a Helium-Neon laser-based fiber optic Doppler probe at an angle of 60¡C with a blood vessel that registers a frequency shift of 63KHz, what is the velocity of the blood? Is this a reasonable number from a physiologic point of view when compared to the average velocity in the major and minor blood vessels in the human body?
The subjects of this question are laser velocimetry and physiology.
Social Studies are things like history, geography and sociology
How serious can you be about taking this course when you don't even know what the subject is?
To determine the velocity of the blood using the given information, we need to apply the Doppler effect formula. The Doppler effect is the change in frequency of a wave observed by an observer moving relative to the source of the wave.
The formula for the Doppler effect in cases of relative motion between the source of the wave and the observer is as follows:
Δf/f₀ = v/c
Where:
- Δf is the change in frequency (in this case, 63KHz)
- f₀ is the original frequency emitted by the source
- v is the velocity of the blood (what we want to find)
- c is the speed of light (approximately 3 x 10^8 m/s)
In this case, the original frequency emitted by the source is the frequency without any velocity-induced shift, so we can take f₀ as the frequency of the source (laser) itself.
Now, we can rearrange the formula to solve for v:
v = (Δf/f₀) * c
First, we need to convert the angle from Celsius to radians. As 1 radian = 180/π degrees, the angle in radians = (60 * π) / 180 = π/3 radians.
Now let's assume the laser has a wavelength of 632.8 nm (typical for a Helium-Neon laser).
Using the formula for Doppler shift due to an angle between the source and the observer:
Δf/f₀ = 2v/c * cos(θ)
Where:
- θ is the angle between the blood vessel and the laser probe (π/3 radians)
- Δf/f₀ is the frequency shift (63KHz)
- v is the velocity of the blood (what we want to find)
- c is the speed of light (approximately 3 x 10^8 m/s)
Rearranging the formula to solve for v:
v = (Δf/f₀) * (c/2) * (1/cos(θ))
Substituting the given values:
v = (63KHz) * (3 x 10^8 m/s) / (2 * cos(π/3))
Calculating cos(π/3):
cos(π/3) = 0.5
Substituting this value back into the formula:
v = (63KHz) * (3 x 10^8 m/s) / (2 * 0.5)
v ≈ 945 m/s
Now, as for determining if this velocity is reasonable from a physiologic point of view, the average velocity in the major arteries of a human body is around 0.3-0.5 m/s, while in the major veins, it ranges from 0.1-0.3 m/s. However, in microvessels (capillaries), the velocity can be much lower, typically at a few mm/s.
Therefore, a blood velocity of approximately 945 m/s seems extremely high and unrealistic from a physiological standpoint. It's important to review the calculations or ensure that the provided data is accurate to evaluate further.