WEBVTT

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We had talked a little bit
about the resistance equation

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that we got from Dr. Poiseuille.

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And the equation looked
a little bit like this.

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Actually, let me
just replace this.

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We had 8 times eta, which
was the viscosity of blood

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times the length
of a vessel divided

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by pi times the radius of that
vessel to the fourth power.

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And all this put together gives
us the resistance in a vessel.

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So thinking about this
a little bit more,

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let's assume for the moment
that the blood viscosity is not

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going to change.

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It certainly won't change
from moment to moment,

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but let's say that, in
general, blood viscosity

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is pretty constant.

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Now, given that, if I want
to change the resistance,

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then I have two variables left.

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I've got the length of my
vessel and I've got the radius.

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So if I have a vessel--
like this-- and let's

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say it's got a certain
radius and length.

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And let's say that radius is
r, and the length is here.

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And I apply a number.

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Let's say the number is
2 for the resistance.

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Well, I have two options for
changing that resistance.

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If I want to increase
the resistance,

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I can do two things.

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So let's say I want to
increase that resistance.

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And you can look at the
equation and tell me

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what the answer would be.

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Two things.

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And I'll actually draw it out.

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So one thing would be to keep
the radius basically the same,

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but make it much longer.

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Because if I make it
longer, since the L is now,

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let's say, twice as
long and r is the same,

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now my resistance
is going to double.

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So now we go 2 times.

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And 2 times 2 is 4.

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So my resistance is 4.

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OK.

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Option 2.

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Let's say I don't want
to change the length.

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I keep the length the same.

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Instead, I could actually
maybe change the radius.

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And let's say I half the radius.

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I make it half of what it was.

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And I actually worked out
the math in the last one.

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And it turned out that,
if you half the radius--

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in the last video, that is--
then the resistance actually

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is 16 times higher.

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And you can see that because
the resistance equals

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r to the fourth power here.

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So because r is to the fourth
power when you half it,

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it goes 16-fold.

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And so 16 times 2 is 32.

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So our resistance is 32.

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So these are the two strategies,
if you think of it that way,

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that a blood vessel can
use to increase resistance.

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And of the two, you can
see that one of them

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is definitely more effective.

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I mean, I can see
that because it's

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raised to the fourth
power, this is

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going to work much more
effectively to raise

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the resistance than
changing the length.

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And additionally,
if you think of it

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kind of from a
practical standpoint,

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keep in mind that I
have smooth muscle.

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So it's actually pretty
easy to accomplish this--

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or at least possible
to accomplish this.

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Whereas trying to
actually change

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the length-- which is
option 1-- is not feasible.

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I mean, it's much, much more
complicated to actually expect

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a vessel to simply
double in its length

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because it wants to
raise the resistance.

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So for multiple reasons,
changing radius,

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again, becomes the
name of the game.

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OK.

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So let's complicate
this a little bit.

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Let's say instead of one
vessel, I've got three vessels.

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I've got, let's say,
one vessel here.

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And there's, let's say, 5.

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And then I've got, let's
see, a longer vessel here.

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And this one happens to have
a resistance of, let's say, 8

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because it's longer.

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And let's do the same radius
for all these, but shorter now.

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This one is 2.

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And I want blood to flow
through all three of these.

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What is my total resistance?

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And here we're talking
about the three vessels

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being in a series--
meaning that you actually

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expect the blood to
go through all three

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of the vessels or tubes.

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So if they're going to go
through all three tubes, what

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you have to do is
simply add up the total.

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So resistance total-- so
this is total resistance.

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And I just put a
little t to remind me

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that that means total.

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So total resistance equals
the resistance of one part

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plus the second part
plus the third part.

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And if you had a
fourth or fifth part,

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you just keep adding them up.

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So in this case, you
have 5, 8, and 2.

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So Rt becomes 5 plus 8
plus 2, and that equals 15.

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So total resistance would be 15.

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And actually, I'm going to
give you a general rule.

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Total resistance is
always, always greater

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than any component.

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And you can see how
this is very intuitive.

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I mean, how could you possibly
have a situation where--

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if you're just simply
adding them up,

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because we don't expect
any negative resistance

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in this situation.

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You're simply adding up all
these positive resistances.

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Of course, the total
will be always greater

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than any one component.

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Seems intuitive, but I just
wanted to spell that out.

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So now, let's take
a scenario where

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you have a human body,
a vessel in the body.

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And let's say you have
three parts to it,

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and these are equal parts.

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So let's say the resistance
here is 2, 2, and 2.

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Obviously, I want to calculate--
as before-- my total.

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So my total will be 2
plus 2 plus 2, which is 6.

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And then, an interesting
thing happens.

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So you have, let's say-- I'll
draw the same vessel again.

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A really interesting
thing happens.

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This is the same blood vessel,
but now you have a blood clot.

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And this blood clot is floating
through the blood vessels.

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And it kind of makes
its way to this one

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that we're working with.

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And it goes and
lodges right here.

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So right here you have
a lodged blood vessel.

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Wow.

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That's pretty big, but it's
right in that middle third

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of our vessel.

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So we have now a tiny
little radius here.

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It's about, let's say,
half of what we had before.

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The new radius equals half
of what the old radius was.

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And you know from
the last example

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that's going to increase the
resistance in that part by 16.

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So the resistance
here stays at 2.

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Here it stays at 2.

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But here in the middle,
it goes from 2 to 32

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because it's 16 times greater.

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So you end up increasing
the resistance

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in the middle section by a lot.

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So let me just write
that out for you.

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So 2 times 16 gets us to 32.

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So here the resistance is 32.

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And so if I wanted to
calculate the total resistance,

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I'd get something like this--
32 plus 2 plus 2 is 36.

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So I actually went from 6
to 36 when this blood clot

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came and clogged up
part of that vessel.

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So just keep that in mind.

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We'll talk about that
a little bit more,

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but I just wanted
to use this example

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and also kind of
cement the idea of what

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you do with resistance
in a series.

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Let's contrast that to
a different situation.

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And this is when you have
resistance in parallel.

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So instead of asking
blood to either kind of go

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through all of my vessels,
I could also do something

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like this-- I could
say, well, let's say,

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I have three vessels again.

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And this time, I'm
going to change

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the length and the radius.

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And let's say this
one's really big.

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And the resistance here,
let's say, is 5, here is 10,

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and here is 6.

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So you've got three
different resistances.

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And the blood now
can choose to go

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through any one of these paths.

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It doesn't have to
go through all three.

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So how do I figure out now
what the total resistance is?

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So what is the total resistance?

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Well, the total
resistance this time

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is going to be 1 over 1 R1,
plus 1 over R2, plus 1 over R3.

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And you can go on and
on just as before.

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But in this case,
we only have three.

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So let's just put that there,
that there, and that there.

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And I can figure this
out pretty easily.

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So I can say 1 over 1 over
6 plus 1 over 10 plus 1/5.

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And the common
denominator there is 30.

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So I could say 5/30.

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This is 3/30, and
this would be 6/30.

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And adding that up together,
I get 1 over 14/30 or 30

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over 14, which is 2
and let's say 0.1.

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So 2.1.

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So the total
resistance here is 2.1.

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Putting all three of these
together is pretty interesting.

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And I want you to realize
that the resistance in total

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is actually less than
any component part.

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So unlike before where we said
that the total resistance is

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greater than any component,
here an interesting feature

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is that you have
total resistance

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is always less
than any component.

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So a pretty cool set of rules
that we can kind of go forward

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with.

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