BP in the arm is very different from BP in the brain. That is what plethysmography is for.
A stenosis in a neck vein will raise BP in the brain, independently of the arm BP.
Unequal sharing of vein drainage:
I have read that fluid flowing in pipes follows Ohm's Law (V = I times R), where voltage, V, is equivalent to the fluid's pressure (P), current, I, is equivalent to the fluid's flow (F), and resistance, R, is equivalent to fluid resistance to flow, again we'll call it R.
Again, V == P
I == F
R == R
Ohm's Law for electricity ===========> V = I x R
Ohm's Law for fluid in pipes ===========> P = F(rate) x R
Pressure is Flow (rate) times Resistance.
Any time you want to increase only the Flow rate, you have to increase the Pressure in by the same proportion. The increase in Pressure will be lost as the pipe's Resistance is overcome, resulting in a drop in Pressure as fluid flows through the pipe.
Any time you increase only the Resistance of the pipe to Flow of fluid, you get less Pressure in the fluid exiting the pipe, by the same proportion.
Etc. See http://alturl.com/3fqqn
) for examples of various transformations.
We could be so bold as to assign units: Pressure in pounds per square inch (PSI)
Flow in Gallons per Minute (GPM)
Resistance in PSI/GPM. That is why in electricity, they're just called Ohms.
Think of a garden hose - think of a smaller garden hose attached to it. Now attach a third hose, the same as the first one, to that. Now the hoses go Big, Small, Big, and you're watering through them In Series. They are Series-Connected. In series, Rtotal = R1 + R2 + R3.
Take my word for the fact that the smaller a hose gets, the more Resistance to Flow it has, and Vice Versa.
So let's let P, Pressure drop from inlet of tube to outlet = 10 PSI (pounds/square in)
F, Flow rate of fluid in tube = 10 GPM (gallons/minute)
R, Resistance to flow through the tube = F/P = 10/10 = 1 PSI/GPM
Things get slightly tricky when pipes are in parallel, as in veins and collaterals. Resistance is reduced to something always smaller than the Resistance of the pipe with the least Resistance.
1/Rtotal = 1/R1 + 1/R2 + 1/R3 ...
Each new pipe (collateral vein) added in parallel makes the Resistance of the combination smaller, stealing from the total flow. The largest resistance you can have, if you can only add in parallel, is the largest pipe alone. The Flow will preferentially go to the pipe with the least Resistance.
Resistance depends on several variables, independent of Pressure or Flow rate.
Resistance is higher proportional to the friction of the pipe, and similarly to the drag or viscosity of the fluid.
But Resistance is lower, the larger the pipe's diameter, by a factor of the 4th power of its diameter.
When we doubled the diameter, Flow Resistance 2, RF2, became lower than Flow Resistance 1, RF1.
Vein Diameter 2, DV2, is 2 times as large as Vein Diameter 1, DV1.
RF2 = RF1 times (DV1/DV2)^^4
Let RF1 = 2 PSI/GPM
And DV1 = 1 inch, DV2 = 2 inches
So RF2 = ? PSI/GPM
Because of doubling DV1, RF2 = RFI times ((DV1/DV2)^^4) = 1 x (1/2)^^4 = 1/16 PSI/GPM
Said another way, Resistance to flow is Very, Very, Very, Very sensitive to the diameter of the pipe. That is why ballooning a vein is so tricky. It is why choosing the balloon's size, and how you blow it up, is so important. It is also why collateral veins disappear on the fluoroscope. The dye prefers the largest vein by a factor of the fourth power of the ratio of the vein diameters (which is the same proportion as the CSAs, if the veins are round). This number can get very different very quickly, as diameters change. If stenosis occurs, same thing.
The sharing of drainage by veins of different diameters is very, very, very, very unequal.
Brain blood pressure is directly (and potentially gravely) influenced by stenosis of the largest neck veins.