I'm going to talk to you about pressure, resistance and flow.
We're going to try to make sure you feel
real comfortable with all three of these things
by the time we're done.
So we start with the heart, and
off of the heart is the aorta.
This is the largest artery in the body.
And, this is one branch of the aorta.
I didn't draw a lot of the other ones.
This is the brachial artery.
And the blood is flowing from the aorta
into the brachial artery.
And let's say that the blood is trying to make its way out to
our finger tips,
for example.
So on its way out there it makes its way
to an arterial
and the blood continues flowing
and it goes into a capillary bed
and the vessels are too small
to draw so I just kind of do that thing
and it then goes into
the other half of the capillary bed
where now the blood is deoxygenated.
So I'm going to draw that as blue.
That's the part where
now the blood is without oxygen
and then it continues to
go and get collected
into a venule which
sounds a little bit like the arterial
on the other side, right?
We've got a vein over here
and then finally the blood gets
collected in a large vein
called the vena cava.
And there are actually
two vena cavas, so this will be the
superior vena cava.
There is also an inferior vena cava.
And the blood flow
through this half
is, as you would guess, kind of
continues to go around.
And if I was to try to figure out
the pressures, the blood pressures,
at different points along this system
I'm going to choose some points
that I think would be interesting ones to check.
So it would be good probably to check
what the pressure is right at the beginning
and then maybe at all the branch points
so what the pressure is
as the blood goes from the aorta to the
brachial artery.
Maybe as it ends the brachial artery and enters the arterial,
maybe the beginning and the end of the capillaries
also from the venule
to a vein and
also, wrapping it up,
what the pressure is at the end.
Now these numbers
or these pressures can be
represented as numbers, right? Like, what is the millimeters
of mercury
that the blood is exerting on the wall
at that particular point.
in the system.
And earlier we talked about
systolic versus diastolic pressure.
And there we wanted to use two numbers
because that's kind of the range.
The upper and the lower range of a pressure.
But now I'm going to do it with one number.
And the reason I'm using one number instead of two
is that this is the average pressure over time.
So the average pressure over time, for me,
keep in mind my blood pressure's pretty normal
somewhere around 120 over 80 in my arm.
So, the average pressure
in the aorta kind of coming out
would be somewhere around 95.
And in the artery, in the arm,
probably somewhere around 90.
Again that's what you would expect,
somewhere between 80 and 120.
So 90 is the average because
it's going to be not exactly 100.
Because, remember, it's spending more time
in diastole and relaxation
than in systole.
So it's going to be closer to 80 for that reason.
And then if you check the pressure
over here by this X,
probably be something like, let's say, 80.
And then as you cross the arterial
the pressure falls dramatically.
So it's somewhere closer to 30.
And there here it's about 20.
Here it's about 15.
Let's say 10 over here.
And then, at the very end,
it's going to be close to a 5 or so.
Here, let me try that again. 10 and 5.
And the units here are millimeters of mercury.
So I should just write that: pressure in millimeters of mercury.
That's the units that we're talking about.
So, the pressure falls dramatically
from 95 all the way to 5.
And the heart is a pump, so it's going to
instill a lot of pressure in that blood again
and pump it around and around
and that's what keeps the blood flowing in one direction
So now let me ask you a question and let's see if we can figure this out.
Let's see if we can figure out what the resistance is
in all of the vessels in our body, combined.
So we talked about resistance before
but now I wanted to pose this question.
See if we can figure it out. So what is
total body resistance.
And that's really
the key question I wanted to try to figure out with you.
We know that there is some relationship between radius and resistance
and we talked about vessels and tubes and things like that,
but let's really figure this out
and make this a little bit more intuitive for us.
So to do that
let's start with an equation.
And this equation's really going to walk us through this puzzle.
So we've got pressure P equals Q times R.
Really easy to remember because
the letters follow each other in the alphabet.
And, here actually instead of P let me put delta P
which is really "change in pressure".
So this is change in pressure.
And a little doodle that I always keep in my mind
to remember what the heck that means is
if you have a little tube, the pressure at the beginning --
Let me say "start". The s is for start.
-- and the pressure at the end
can be subtracted from one another.
And that gives you Ps minus Pe equals delta P.
The change in pressure is really
the change from one part of the tube to the end of the tube.
And that's the first part of the equation.
So next we've got Q.
So what is Q? This is flow.
And more specifically it's blood flow.
And this can be thought of in terms of a volume.
of blood over time.
So let's say minutes.
So how many liters of blood
are flowing in a minute. Or two minutes,
or whatever number of minutes you decide.
And that's kind of a hard thing to figure out actually.
But what we can figure out
is that Q, the flow, will equal the stroke volume.
And I'll tell you what this is just after I write it.
The stroke volume times the heart rate.
So what that means is that basically if you can know
how much blood is in each heartbeat--
so if you know the volume per heartbeat
and if you know how many beats there are per minute,
then you can actually figure out the volume per minute, right?
Because the beats would just cancel each other out.
And it just turns out, it happens to be
that I'm about 70 kilos.
That's me.
I'm 70 kilos.
And for a 70 kilogram person
the stroke volume is about 70 milliliters.
So, for a 70 kilo person you can expect
about 70 milliliters per beat
And, as I write this, let's say
my heart rate is about 70 beats per minute.
I feel pretty calm
and so it's not too fast.
So the beats cancel, as we said,
and I'm left with 70 milliliters
times 70 per minute.
So that's about 4900 milliliters per minute.
Or, if I was to simplify that's a 5. Let's say, about.
So the flow is about 5 liters per minute.
OK. So I figured out the blood flow
and that was simply because I happened to know my weight.
And my weight tells me the stroke volume.
And I know that there's a change in pressure.
We've got to figure that out soon.
And lastly, this last thing over here is resistance.
And I'm just going to-- I know I've said it before.
I just want to point out to you again
that resistance is going to be proportional to 1/r to the fourth.
And so just remember that this is an important issue.
r is radius, and that's the radius of the vessel.
So let's figure out this equation, and how--
Let's figure out the variables in this equation.
and how it's going to help us solve
the question I asked you.
What is the total body resistance?
OK. So if I have to figure out total body resistance--
Let me clear out the board.
I've got, let's say, the heart over here.
I like to do the heart in red.
And it's pumping blood out my aorta.
Right? So blood is going out. Out of the aorta.
And then it's going and branching,
branching here, branching here, let's say.
And then it's going to branch some more
and it's going to branch some more,
and you can see where this is going.
It's going to keep branching.
And eventually every branch
kind of collects on the venous side.
All the blood is kind of filtering back in,
solely into venules and veins.
and finally into a vena cava.
And I should really draw this going like that.
The blood is going to go back into the vena cava.
So that's my system,
and I've got to figure out
what the total body resistance is here.
So, if I have a system drawn out for myself
and I happen to know that--
here I said 95 and here I said the pressure was 5--
then delta P equals 95 minus 5
which is 90.
And I know that there are 5 liters
of blood flowing through per minute,
and that was my Q.
So I could say 90
equals 5 liters per minute.
Actually let me take a step back from that.
Instead of 90 let me write the units.
90 millimeters of mercury
equals 5 liters per minute. That was my flow.
That's my Q.
And I've got delta P here.
and my resistance is the unknown
so I'll just leave that as R.
So let's just solve for R.
So I'll move my flow to the other side.
So R equals-- I'll put it here--
90 divided by 5 which is 18.
And the units are a little funky
but I'll just write them out anyway.
Millimeters of mercury times minutes divided by liters.
So this is the answer to my question.
What is the total body resistance?
Well we know what the pressures are
at the beginning and end of our system.
And we know that the flow has to be around 5 liters per minute
because that's based on my weight and my heart rate.
Therefore the resistance must be
18 millimeters of mercury times minutes over liters.
Whatever that set of units means to you.
It's kind of an abstract thing.
But basically I want to demonstrate to you
that this powerful equation helps us solve
for what would otherwise be kind of a tricky problem to figure out.