Anatomic and physiologic dead space

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Introduction0:00–0:29

The main job of the lungs is gas exchange, pulling oxygen into the body and getting rid of carbon dioxide. Normally, during an inhale - the diaphragm and chest muscles contract to pull open the chest and that sucks in air like a vacuum cleaner, and then during an exhale - the muscles relax, allowing the lungs to spring back to their normal size pushing that air out.

Anatomic dead space0:29–4:11

But as it turns out, not all the air that we breathe in, ends up participating in gas exchange. As we inhale, air enters the nasal cavity or the oral cavity and travels down the trachea and then splits into the two mainstem bronchi and enters the two lungs.
Within the lungs, the bronchi divide into progressively smaller and smaller bronchioles until air gets down to tiny thin-walled air-sacs called alveoli which are surrounded by tiny capillaries.
This is the site of gas exchange. So, the part of the respiratory tree prior to these alveoli, starting from the nose, or the mouth, right up to the tiny terminal tiny bronchioles without these alveoli, merely acts to conduct or transport air to the alveoli.
This part is known as the conducting zone and it does not take part in gas exchange. The volume of air contained in this conducting zone is known as anatomic dead space.
‘Dead’ sounds kind of ominous but it basically reflects the fact that this air is as good as dead to the body, because you can’t extract oxygen from it.
‘Anatomic’ means that this dead space is inbuilt within the anatomy of the respiratory system and doesn’t really change; no matter what we do, we cannot ever use this air for gas exchange.
Alright, so now let’s simplify all this—so this ball represents all the alveoli, and this portion represents all of the conducting zone, in other words the anatomic dead space.
So how much air is part of this anatomic dead space? A normal person, when breathing quietly without any active effort, takes in about 500 ml or half a liter of air - this is the tidal volume, represented by these three blocks.
Almost a third of this tidal volume or about 150 ml is trapped in this anatomic dead space, and the remaining 350 mL or so is used for gas exchange.
K so let’s go way back to when an infant is born, at this point there’s no air inside the lungs, so the alveolar air sacs are completely collapsed.
As the baby takes its first breath, new oxygenated air rushes in through the respiratory tree and inflates the alveoli, but about a third of the air is left in the anatomic dead space, shown in orange, but we’ll keep it half purple since it’s still oxygenated air.
Those purple blocks then participate in gas exchange, converting them to old deoxygenated air, shown in green. As the baby starts to exhale air for the first time, this dead space air which did not participate in gas exchange is the first to be exhaled out, and the conducting zone gets filled with air from the alveoli which has already taken part in gas exchange and given its oxygen to the body.
During the next inhalation, it’s this old green deoxygenated air that re-enters the alveoli first, and it’s joined by fresh oxygenated purple air from the new tidal volume.
The dead space gets filled with fresh air that has just been breathed in. This goes on for every subsequent breath cycle throughout the life of the person.
So to summarize, if you sample the dead space air after a person has just inhaled, then the dead space air would be fresh air from the environment, and if you sample the air sample of air from the dead space after a person has just exhaled, then the air would be from the alveoli.
So to gauge how effectively gas exchange is taking place in the lungs, it’s important to time it just right, and take an air sample from the dead space at the end of exhalation.

Physiologic dead space4:11–5:01

Now, so far, we’ve been assuming that the air that manages to reach the alveoli is able to participate in gas exchange. Unfortunately, that’s not always the case.
Some alveoli may have an inadequate blood supply, so when these alveoli get filled with air fresh purple air, they are well-ventilated, but not well perfused.
This is known as a ventilation-perfusion defect. In this situation, the oxygen in the air purple air doesn’t functionally make it’s way into the blood., so some of this air also ends up being dead space air, but this time we call it alveolar dead space, and together we call these the physiologic dead space.
The term ‘physiologic’ refers to all the air that is physiologically inaccessible to the body due to anatomic and functional reasons.

Bohr equation5:01–10:36

Okay so now that one block of accessible fresh purple air gets exchanged, and then this gets exhaled, we can actually now use some fancy equations to calculate the volume of physiological dead space of the exhaled air, which we’ll say is V sub D for dead space, but first there are a couple important assumptions.
First, we assume that there’s no CO2 in the environment air, the actual figure is about 0.04%, so zero is not too far off the mark, and remember that this is the purple boxes here since that air came from the environment but was never exchanged.
Assumption number two is that none of the CO2 was contributed from the dead space, so based on assumptions 1 and 2, the purple and orange blocks have zero CO2.
That leads to the third assumption, all the CO2 in exhaled air comes only from functioning alveoli, i.e. this last green block.
Now, if the tidal volume is VT , the volume of air trapped in the physiological dead space is VD , and the volume of air present in the functioning alveoli is VA ,.
From this, it’s pretty clear that VT = VD + VA Let’s label the concentration of CO2 in the tidal volume as CT and the concentration of CO2 in the alveolar air as CA.
Now, if you take a volume in mL and multiply by the concentration in say mg / ml, then you end up with the total amount of that something M, in this case in mg.
Now, that means that the total amount of CO2 in the alveoli is the volume VA times the concentration, CA. CA X VA Similarly, the total amount of CO2 in an exhalation is the tidal volume Vt times the concentration of the tidal volume Ct.
CT x VT Remember, though, that one of our assumptions is that all the CO2 in the tidal volume is from the functioning alveoli, i.e.
the green block, we could add in the concentration Cd of the dead space, but it’s equal to zero, so really the total amount in the tidal volume is the same as the amount in the alveoli, so we have Ma = Mt, or CA x VA = CT x VT And with a little rearranging: VA = (CT/CA) x VT Now we can substitute that guy in our original equation, and we’ll end up with Vt = Vd + VtCt over Ca, which can be rearranged to be Vd = Vt - VtCt over Ca, which is equal to Vt times the quantity 1 minus Ct over Ca.
Now, let’s multiply it all by Ca over Ca, which we can do because anything over itself is just equal to one. After distributing Ca over Ca you get Vt times the quanitity Ca over Ca - Ct over Ca, and finally, at long last, we have Vt times the quantity Ca minus Ct all over Ca.
(VT - VD) = (CT/CA) x VT Or, -VD = -VT + (CT/CA) x VT Or, VD = VT - (CT/CA) x VT Or, VD = VT (1 - (CT/CA)) Or, VD = VT (CA/CA - CT/CA) Or, VD = VT [(CA- CT) / CA] Now any time there is a mixture of different gases, the partial pressure of any one of the gases is directly proportional to the concentration of the gas in the mixture.
So like, as the concentration of CO2, for example, increases, so too does the partial pressure. (Concentration of a gas in a mixture) α (Partial pressure of the gas in the mixture) To convert this proportionality into equality, we need to multiply by a proportionality constant k, so we get partial pressrue times k is equal to concentration.
(Concentration of the gas) = (Constant) X (Partial pressure of the gas) Now let’s apply this equation to our previous equation.
We end up with Vd equals Vt times (Pa times k - Pt times k all over Pa times k. Conveniently, you’ll notice all our constants cancel out, so you just end up with Vd equals Vt times Pa minus Pt all over Pa.
VD = VT x [(PA - PT) / PA] Where, PA = Partial pressure of CO2 in alveolar air PT = Partial pressure of CO2 in the tidal volume air In well-functioning alveoli with adequate blood supply, carbon dioxide quickly dissolves into the blood until the partial pressure of CO2 in the alveolar air is equal to the partial pressure of CO2 in the blood, or P little a CO2, little a for arterial.
So we can replace PA with PaCO2: VD = VT x [(PaCO2 - PT) / PaCO2] This is known as the Bohr equation for calculating physiological dead space, named after the Danish physician Christian Bohr, father to the more famous son, physicist Niels Bohr!
All right, as a quick recap… we can’t utilize all of the air we breathe in for gas exchange. About ⅓ of a normal tidal volume or 150ml is wasted en route to the alveoli and makes up the anatomic dead space.

Review10:36–11:10

In addition, some of the alveoli don’t get adequate blood supply and therefore they don’t participate in gas exchange. When we add this air wasted in non-functioning alveoli to the anatomical dead space, we get the physiological dead space.
The physiological dead space is calculated by using the Bohr equation: VD = VT x [(PaCO2 - PT) / PaCO2].