If we would calculate things like starling forces
in the cardiovascular system,
we oftentimes use this kind of equation
where J is the flux,
[K sub F] is a filtration coefficient,
A is a surface area,
[P sub C] is the hydrostatic pressure within the capillary,
[P sub I] is the hydrostatic pressure within the interstitial space,
sigma is the reflection coefficient,
the [Pi sub C] is the oncotic pressure of the capillary,
and then [Pi sub I] is the oncotic pressure within the interstitial space.
So this is a very classic way of looking at how fluid travels
from the blood into the interstitial space.
The kidney is no different.
It’s utilizing this very same principle,
but we’re going to only focus on glomerular capillaries
rather than capillaries that are located throughout the body.
So when we break it down to glomerular capillaries,
now we’re talking about glomerular filtration rate,
so that’s replacing J.
[K sub F] is the same.
The area will be consistent,
so we can factor that out.
So we will have [K sub F] is the hydrostatic pressure
within the glomerular capillary
minus the hydrostatic pressure within Bowman’s space,
or also known as the glomerular space.
The [Pi sub GC] is the glomerular capillarity oncotic pressure,
and then the [Pi sub BS] is the oncotic pressure within Bowman’s space,
again also known as the glomerular space.
So this formula works very well looking at how fluid travels across a capillary.
What are the major principles or players in this?
Well, the [K sub F], which is the filtration coefficient --
that’s number 1.
Then we also have the hydrostatic pressures
within both the capillary
and within the glomerular space.
The third thing that’s important is the oncotic pressures,
and those would be located both
within the glomerular capillary
and also in the glomerular space.
So how do we break down this formula
so that it makes more sense intuitively?
I think for this one,
we can look at an afferent arteriole,
the glomerular capillaries,
and then the efferent arteriole.
If we understand how blood flow travels in through this system,
and then how much pressure is exerted,
we’ll be able to figure out how much filtration actually occurs.
So let’s use some examples.
When you start off on the afferent arteriole side,
you have a pretty high pressure.
This hydrostatic pressure within the glomerular capillary right as it enters
the afferent arteriole is high - 60 mmHg.
The oncotic pressure is about 25 mmHg
of the oncotic pressure within the glomerular capillary,
or [Pi sub GC].
As we travel along the capillaries,
through the glomerular capillary system,
let’s take a midpoint of going through the glomerular capillaries.
You noticed that hydrostatic pressure didn’t change very much.
It dropped from maybe 60 to 59.
But what did change was the oncotic pressure within the glomerular capillary.
It changed from 25, now to 32,
which is a pretty large increase.
You might ask yourself, “What caused this increase?”
Well, if you don’t have as much fluid traveling around,
you’re going to concentrate all of your solutes.
This is exactly what happens.
You’ve pushed some of the plasma out of the capillary
into the Bowman’s space or the glomerular space.
And what does that leave?
More concentrated substances, like proteins,
some concentrated substances like cells
that increases your oncotic pressure.
Let’s keep traveling around now towards the end of the glomerular capillary.
This is right before you get to the efferent arteriole.
You noticed that pressure again doesn’t change very much,
maybe 1 mmHg from the midpoint to the end,
going from 59 mmHg to 58 mmHg.
But once again, there is an increase in oncotic pressure.
It jumps all the way to 35.
So there's about a 10 mmHg change in the oncotic pressure between
what the glomerular capillaries saw
just at the start of the afferent arteriole,
to just right at the end before the efferent arteriole.
The reason that increase happens
is because you are concentrating your proteins and your cells
within the blood
because plasma has left the glomerular capillary
and traveled into Bowman’s space.
Now, let’s do a little bit of comparison
between the renal and systemic capillary forces.
If you remind yourself what the renal forces were,
it was glomerular filtration
equals the plasma filtration coefficient,
multiplied by the pressures within the glomerular capsule,
minus the pressure within Bowman’s space.
We subtract that quantity from the oncotic pressure within the glomerular capillary,
minus the oncotic pressure within Bowman’s space.
So if we look at now a systemic or a normal capillary,
we have this type of system.
We can replace the numbers with now Q
just being the flux of water
from inside the blood vessel
to outside the blood vessel.
[K sub F] is the same.
It’s a plasma coefficient.
But now, the plasma values will be in the capillary
versus the interstitial space,
versus the oncotic pressure within the capillary,
versus interstitial space.
So let’s look at what happens on the arterial side of a systemic capillary.
So this is how much water or plasma will be fluxed out of the blood vessel.
Let’s take an example of the hydrostatic pressure within a capillary of 37.
We subtract that from the hydrostatic pressure within the interstitial space,
which should yield 35.
We take that number,
subtracted from the quantity of the oncotic pressure
within the capillary,
minus the oncotic pressure in the interstitial space,
and that yields 24.
So then it will be 35 - 24 = +11.
That means that around 11 mmHg of fluid
left the capillary and is out in the interstitial space.
If we contrast that to the venous side of a normal capillary,
this is where the flux is [Q sub V],
or the flux of water or plasma,
back into the capillary now.
You take 16 as the pressure in the venous side of the capillary
minus 2, which is the pressure in the interstitial space,
that should yield 14.
We subtract that from the quantity of the oncotic pressure within the capillary,
which is around 25,
minus 1, which is the oncotic pressure within the interstitial space.
That, again, yields 24.
So now we have: 14 - 24 = -10.
So what does a negative number mean?
A negative number means the fluid is being pulled back into the capillary.
So on the arterial side of the circulation,
we pushed fluid out.
On the venous side, we pull it back in.
But notice these numbers don’t quite equal, do they?
There is 1 mmHg of fluid that’s left in the interstitial space.
That eventually will be picked up by the lymphatic system
and brought back into the circulation,
but it’s left out in the interstitial space.
That is the amount of filtration that occurred – 1 mmHg.
That’s a lot different than the types of glomerular filtration rates we got in the previous examples.
So once again, showing the difference between the renal capillaries
and the systemic capillaries is the amount of filtration.
There’s much less filtration in systemic capillaries versus the renal capillaries.