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It's All Downhill From Here

How Fast will your patient desaturate once you go to intubate?

Your patient has a high SPO2 but a low PO2 - should they receive BIPAP or CPAP?

Should you increase ventilation to improve oxygenation?

"And now we'll take some time to consider the Oxyhemoglobin desaturation curve."

And then, there is a collective eye roll from the audience. Why? Because barely anyone understands the curve (we'll refer to it as 'the curve' here to avoid making my fingers bleed from typing it 100x), and just as few understand why it's clinically relevant. Not only is this curve easy to understand, but it can also change how you practice. Stick with this blog all the way through and you'll leave with a solid knowledge base on the curve - as well as understand how to apply it clinically! Let's start off with understanding the curve itself, and then we'll throw in clinical application as we go.

Sigmoid - and I'm not talking about the colon.

Let's first understand the general shape of the curve. The shape of the curve is known as a sigmoidal curve (or sigmoidal function if you're solving a math problem). That means it's kind of shaped like an "s" that's been stretched out from left to right.

Pretty simple so far, right? Now let's take that sigmoid curve and add some values to it. We're going to add some values to the X and Y-axis. (X is on the bottom, Y is on the side.) The Y-axis (up the left side) is going to be the oxygen saturation in percent. Then, on the X-axis we'll put PO2.

Now that we've combined our sigmoid curve with our SPO2 and PO2, we can start to get some clinically relevant information. Look how flat the curve is going from 100 down to 80 on the X-axis (PO2). When you look at the SPO2 that correlates to those values, it barely changes! What about going down from 80 to 60 on the X-axis again (PO2)? Now we're on the edge of danger. A PO2 of 60 correlates with an SPO2 of 90. This is where the sigmoid curve comes into play - all of a sudden, our oxygen status isn't so stable! In fact, we're at the edge of a huge drop off in SPO2 value.

Going the other way on the curve (from left to right), Jardins, Burton, & Phelps (2016) note: "It is also interesting to note that very little oxygen combines with hemoglobin between a PO2 of 60 and 100 mmHg. In fact, a PO2 increase from 60 to 100 mmHg increases the total saturation of hemoglobin by only 7% (from 90% to 97% saturated)." That statement works the other way too. Going from 100 to 60 mmHG of PO2 will only change the SPO2 by ~7%. This means that if your patient's SPO2 falls from 98% to 90% really fast, they're going to drop from 90% (PO2 60 mmHg) to 25% (PO2 20 mmHg) much faster (Davis et al, 2008). 😬 Yikes!


Here's our first important clinical point. When our patient approaches the edge of that cliff, they're on the verge of a steep and swift fall. This is where we must be extremely careful not to let them drop any further. This is one reason why people say 'resuscitate before you intubate.' Resuscitate what? You need to ensure that the SPO2 is at or above ~93% for a few minutes before you can allow the patient to be apneic for any period of time. If you don't take this cliff of desaturation into account, you're putting the patient in serious danger of rapid desaturation and hypoxic arrest. Looking at this curve, is it any wonder why patients who aren't on that flat part of the curve (~93 and above) can desaturate so quickly?

Is there anything you can do to improve your preoxygenation phase? Here are a few general recommendations (Chang, 2014):

  1. Sit the patient up to improve lung compliance (at least 30º) and increase functional residual capacity

  2. Apneic Oxygenation (nasal cannula at high-flow)

  3. If needed, use positive pressure during pre-oxygenation (PEEP, CPAP, or BIPAP)

  4. Slow down your inspiratory time to spend more time on oxygen delivery

  5. Increase minute volume and FiO2


P50 and the 4,5,6,7,8,9 Rule

Lots of numbers, right? There are a couple of tricks to make sense of the curve in your head. One is called the P50, and the other is the 4,5,6,7,8,9 rule.

P50 (Jardins, 2013) is just a general reference point on the curve. It points out that when your SPO2 is 50%, your PO2 is 27 mmHg (26.6 mmHg if you're being all textbook about it). That's really low. Remember the PO2 levels that mark the different levels of hypoxemia? They go like this:

  • Normal: 80 - 100 mmHg

  • Mild Hypoxemia: 60 - 79 mmHg

  • Moderate Hypoxemia: 40 - 59 mmhg

  • Severe Hypoxemia: <40 mmHg


Let's make some clinical applications. What does all of this tell us? Something you might take note of is that by the time your SPO2 is at half-saturation (50%), you're at roughly a quarter of your normal PO2 (assuming you started at 100 mmHg). And, at the steep angle of the curve your on at 50% SPO2, you might be headed all the way down. This is why it's so important to maintain saturations any way you can, especially if you're planning on taking someone's airway via anesthesia anytime soon. It's also worth mentioning that there is such a thing as "pulse oximetry lag". This means that by the time you actually see 50%, you're way past that. In a normal, healthy patient you can expect a pulse oximetry lag of about 15 seconds (Cairo, 2014), and much longer if the patient is peripherally clamped down or cold. What's even scarier is that depending on the patient's status, and taking into account pulse oximetry lag time, your patient with an SPO2 of 80% might be in the severe hypoxemia range.

What do we do about this? First, back out and oxygenate when you see the patient getting down into the ~90% range (don't wait until it's too late). Apneic oxygenation and denitrogenation, improving our first pass success rates, and ensuring good positioning can also help maintain saturations.

Here's one quick, but very important side point to remember. We focus a lot on first-pass success (getting the intubation on the first attempt). However, did we almost kill the patient in the process? First-pass success isn't enough - we need first pass success without complications. Did they desaturate? Did they go hypotensive? Did they aspirate? Those are signs that we seriously need to evaluate our technique.


Some people have trouble correlating SPO2 and PO2 values on the curve. Before we move on, I'll just leave you with one quick memory aid called the '4,5,6,7,8,9' rule. 40, 50, 60 on the PO2, and 70, 80, 90 on the SPO2 (Jardins, 2013). On a normal curve:

  • 40 mmHg correlates with ~70%

  • 50 mmHg correlates with ~80%

  • 60 mmHg correlates with ~90%

Notice that any value less than 90% SPO2 already puts us in the moderate hypoxemia range.

Normal Curve Summary:

Hemoglobin has the highest affinity for oxygen in and around the lungs, and the lowest affinity in the distal tissues. This is very efficient because the hemoglobin are like a train that picks up passengers in the lungs (oxygen loads onto hemoglobin with ease) and drops passengers off in distal tissue (offloads oxygen with ease). Changing affinity ensures that passengers (oxygen molecules) get on and off at the appropriate time, even though this train never stops! (Tuck and roll!)

The most important beginning knowledge about the curve is that it's not linear. Your SPO2 is not going to go from 100% to 90% at the same rate you'll drop from 90% to 80% (and then likely even farther if you count pulse oximetry lag time).

This tells us that we must be extremely careful when doing any kind of anesthesia when a patient has a 'soft' SPO2. Trying to intubate someone 'real quick' when you can't get the SPO2 above 80% is not okay - they're already on the side of the cliff, ready to free-fall faster than you can imagine. Use the oxygenation tips from the clinical application sections above to raise the SPO2 as high as possible before performing a procedure that will interrupt breathing. Simply understanding the shape of this curve will save a life.

But, doesn't the curve kind of change shape sometimes?

Right Shift

Just when we think we have a good handle on the curve, it changes shape. You've likely heard of a "right shift" or a "left shift" on the curve. All this means is that the curve on the graph moves down and to the right, or up and to the left. Why do we focus so much on these shifts when talking about the curve?

Let's discuss how the body uses a right shift naturally before we jump into a pathological right shift. Imagine that you're doing leg extension. Your quadriceps are burning, they're hot, they're building up acid, and they need more oxygen at this point than any other area in your body in order to continue doing work. So, how does the body ensure that this muscle gets the oxygen it needs? The whole area is under a right shift on the curve. The curve may be normal in the chest, arms, liver, etc... However, the body ensures that oxygen is dropped off at the correct spot by altering the curve. As you'll note from the red curve, when the curve shifts to the right, hemoglobin has a decreased affinity for oxygen, and therefore drops the oxygen off where it needs to go.

This is a pretty smart system that the body has going on. The right shift allows for oxygen to get dropped off wherever it's needed most. Did you notice the triggers for oxygen to get dropped off? Heuer & Scanlan (2018) help us appreciate these triggers:

  • Increased Oxygen need (low PO2 in the tissue)

  • Decreased pH (acidosis)

  • Increased Temperature

  • Isn't "Increased 2,3 DPG" usually on this list?

Before we get into what 2,3 DPG is, I want to make sure we're understanding the basics of why the oxygen chooses to offload from hemoglobin at this point.

The first and probably most important part is the difference in partial pressures between the oxygen on the hemoglobin and the tissue that needs the oxygen. Clearly, there is more oxygen on the hemoglobin than the tissue, so oxygen will go from the area of high concentration to the area of low concentration (the chief binding property being the bond with the Fe2+ iron in the hemoglobin). The second aspect is hydrogen and carbon dioxide. The relatively acidic environment that the hemoglobin is exposed to in the distal tissue is going to promote oxygen offloading. This will offload oxygen into the tissue because of processes that are triggered from carbon dioxide and hydrogen binding to alpha and beta subunits on the hemoglobin. Finally, heat tends to speed everything up. Heat makes everything want to fall apart, and it weakens all types of bonds that hold substances together. Think of the difference between frozen and boiling water - which one is breaking bonds? Obviously, the boiling water. Thus, an increased temperature is going to aid in the desaturation of the hemoglobin (desaturating the hemoglobin while saturating the surrounding tissue).

The Bohr Effect

The Bohr Effect is something you'll hear referenced a lot when it comes to the curve - what is it? The Bohr Effect basically states that acid and CO2 have an inverse relationship to hemoglobin's affinity for oxygen.

  1. High Acid and CO2 = Low oxygen affinity

  2. Low Acid and CO2 = High oxygen affinity

This puts a name to the phenomenon mentioned above. We know that the quadricep needed more oxygen and needed to get rid of acid and CO2, and now we know the name of the effect that occurs. I'm going to leave the Bohr Effect at that... let's not overcomplicate it.

Now let's circle back to this 2,3 DPG stuff!

2,3 DPG

I don't want to miss the forest for the trees when it comes to the role of 2,3 DPG. I'm going to try to summarize this process in the simplest way I can while not losing the accuracy of the chemistry.

The first thing to know is that 2,3 DPG is not a crowbar like it is often taught. This is something I've taught in the past and now must revisit and revise. The common teaching is that 2,3 DPG is like a crowbar that rips oxygen off of hemoglobin so that it can move on into whatever tissue it needs to get to. However, this isn't very accurate. So... what does it actually do?

2,3 DPG (also called 2,3 BPG) is 2,3-diphosphoglycerate (Two - Three - DIE - PHOS - PHO - GLYCER - ATE). 2,3 DPG is a byproduct of glycolysis, and it reduces hemoglobin's affinity for oxygen (shifts the curve to the right). However, it only reduces the affinity oxygen has for hemoglobin after oxygen has already been offloaded. The 2,3 DPG actually hops onto heme units as oxygen hops off. Alright, so if it doesn't help offload the oxygen, what's the point? And why do we include it as an essential part of understanding the curve?

The importance of 2,3 DPG binding to hemoglobin after oxygen is gone is to stabilize the hemoglobin in a tense state. That's a real term, by the way - "tense". When hemoglobin is loaded with oxygen, it's said to be in its "relaxed" state (R). When oxygen is carrying carbon dioxide, hydrogen, and a relatively small amount of oxygen, it's said to be in its "tense" state (T). In its tense state, hemoglobin also has carbon dioxide and hydrogen attached to it to carry back to the lungs from the distal tissues (carbaminohemoglobin). Maybe we should look at this in the first person to understand the process and give hemoglobin a voice of its own.


whew its gettin hot in here. im feelin like I could get rid of some stuff.. maybe all this oxygen ive got hangin out.

all this acid is startin to burn! hot potato!

is that an area without oxygen? let it fly!

there it goes... goodbye sweet sweet oxygen.

i should go back to the lungs and get some more.

might as well take this hydrogen and carbon dioxide with me while i'm headed that way.


Hemoglobin again:

i feel kinda tense and naked without all that oxygen.

.....maybe i should just... TAKE IT ALL BACK!!!

2,3 DPG chimes in:

BRUH! dont do that! the tissues need that oxygen more than you! you've got other things that should make you happy. look at all the carbon dioxide and hydrogen you got on your subunits! take that mess somewhere else. i know youre tense, but you need to chill. lemme stabilize your wild self until you get back to the lungs.


alright.... you're right. hop on.

I hope you enjoyed the casually written dialog. In summary of this 2,3 DPG section, hemoglobin is stabilized by the 2,3 DPG so that it will not steal the oxygen back from the tissue. The 2,3 DPG will only bind to the heme group after the oxygen has left (it binds to deoxyhemoglobin).

Courtney Graham (@GrahamCourt23) helped me out by drawing out some notes on the Tense (pucker) or the Relaxed (flat) state. It really helps to visualize this, and she did it way better than I could. Courtney zoomed in on a heme group for us to show the transition:

In the normal right shift, we saw that it should really only be happening in areas of the body that locally need that oxygen, and simultaneously need to get rid of carbon dioxide and hydrogen. But, what would happen if a right shift occurred systemically?

Pathological Right Shift

When we have a form of acidosis (like sepsis) our whole body is hot and acidic. That sounds a lot like the influencing factors that made oxygen leave hemoglobin in our quadricep above, doesn't it? Also, sepsis is causing an increase in metabolism, which is increasing glycolysis. What's a byproduct of glycolysis that that affects our curve? 2,3 DPG! Further, that increased metabolism is using up what? Oxygen! So when we have a systemic right shift of our curve, we have trouble loading oxygen onto our hemoglobin and getting it to the tissue that actually needs it. A systemic right shift is a failure of loading and transporting oxygen. The patient will require more aggressive oxygenation strategies to increase the partial pressure of oxygen to attempt to maintain oxygenation to distal tissues.

Right Shift summary

A right shift is a good thing if you're an area of the body working really hard. It's like a help message to send more oxygen and get rid of waste. A right shift says:

"Hey! We need some oxygen! Drop it off here!"

"And take this H+ and CO2 with you while you're at it!"

However, a right shift can be pathological if it's systemic. This can lead to a failure of oxygen reaching far away tissues that need it since hemoglobin has only a little affinity (attraction) for oxygen. How is it managed?


Let's make some clinical applications. A right shift is pretty common since we see a lot of patients with varying forms of acidosis. Treatment should include altering both oxygenation and ventilation. We traditionally teach that oxygenation and ventilation are two separate processes, but as we learn more about the curve, we see they are a little more related than we may have initially thought.

To improve oxygenation we need to increase the partial pressure of oxygen - this the quantity of oxygen. Increase your FiO2, and perhaps increase the pressure in which you're delivering that oxygen if it seems clinically indicated. Positive pressure should help recruit more alveoli to participate in gas exchange. It's worth mentioning here that overpressurization can actually have the opposite effect by blanching the capillaries in the alveolar/capillary membrane and creating anatomical dead space.

Ventilation (the physical movement of volume) is our chief agent to combat acidosis. You may use a Winter's Correction formula and a CO2 correction formula in order to figure out how much minute volume you need to be moving. Another method for correcting acidosis is avoiding solutions such as 0.9% NS since this has a low pH and causes hyperchloremic acidosis. And yes, even bicarbonate might be indicated if the patient has severe renal failure or has depleted their bicarbonate via diarrhea.


Left Shift

If a right shift was a decreased affinity for oxygen, I'll bet you've already concluded that a left shift will be an increased affinity for oxygen - nice! At first, this seems like it would be the better of the two scenarios, but they're actually equally bad. Both end up in a scenario where oxygen is not being delivered to distal tissue. The right shift can't hold the oxygen, and the left shift holds oxygen way too tightly. Let's add our left shift to our graph.

I added that grey line to show how the same saturation is related to different shifts on the curve. On the right shift, a higher PO2 is required to maintain saturation. On the left shift, a lower PO2 will maintain the same saturation. Again, this left shift initially seems like it would not be that big of an issue - hemoglobin is saturated, right? That's actually the problem. When that hemoglobin floats by a tissue that needs that oxygen, it won't drop off because there is an affinity issue - the hemoglobin has too strong of an affinity to release the oxygen.

Remember those triggers for hemoglobin to drop off oxygen? They aren't as present in the left shift.

Again, Heuer & Scanlan (2018) help us appreciate these triggers are missing:

  • CO2? Decreased.

  • H+? Decreased

  • Temperature? Decreased.

So, not only does the main driver of oxygen delivery fail (the partial pressure differences between hemoglobin and the tissue), but the triggers for oxygen offloading fail as well. On top of this badness, the patient will have an SPO2 that doesn't look bad at all. This could paint a very misleading clinical picture and lead us to think that the patient doesn't need intervention.

A left shift isn't all bad. Just like the right shift, it happens for a reason in a healthy patient. If the tissue has a pretty normal or cold temperature, isn't producing much CO2, and doesn't have a lot of H+ floating around it, it probably doesn't need the oxygen as much as a tissue that's hot and acidic (because it likely isn't doing much work). This is the body's own physiological mechanism for triaging where oxygen should be dropped off. Imagine if our workout dude up above had no ability to triage oxygen to his legs, and his pectoralis major was getting the same amount of oxygen dropped off as his quadriceps. That wouldn't be very efficient, would it? That's why most of his body is probably on a normal or left shift, but his legs are on a right shift. Just like we had a really interesting effect to look at on the right shift (Bohr Effect), we also have an effect called the Haldane Effect on the left shift. What's this one all about?

The Haldane Effect and Positive Cooperativity

Remember how in the Bohr effect the presence of CO2 and H+ had an inverse relationship to oxygen affinity in the Hemoglobin? It went like this:

  1. High Acid and CO2 = Low oxygen affinity

  2. Low Acid and CO2 = High oxygen affinity

Do you think the opposite is true for oxygen? It is, and this effect is called the Haldane Effect. The Haldane Effect states that when there is a high partial pressure of oxygen, it displaces CO2 from hemoglobin. This takes place in the lung when that deoxyhemoglobin (full of CO2) meets a high partial pressure of oxygen in the pulmonary circulation. This high PO2 causes CO2 to be released from the subunits attached to the hemoglobin, and then the hemoglobin is free to onboard oxygen.

The opposite is true as well. A Deoxygenated hemoglobin has an increased ability to carry CO2 away from distal tissues. In summary of the Haldane Effect:

  1. Oxygenated Hemoglobin = Decreased affinity for CO2

  2. Deoxygenated hemoglobin = Increased affinity for CO2

One other thing I want to mention about oxygen onboarding in the lungs is positive cooperativity. Positive cooperativity is a process in which oxygen likes to follow other oxygen. Let's illustrate this. Imagine that you're at the school dance, but no one is dancing. Everyone is scared to be the first one out there on the dance floor. Then, one brave soul ventures out onto the dance floor and starts showin' their moves. Once there is at least one person out there, it's much easier for the next person to join in. Then another, and so on. If lots of people are dancing, there's barely any resistance to even the shyest person to get out there and joining in on the party. Oxygen is the exact same way. It's hard for oxygen to be the first person out on the dance floor. But, if some brave oxygen molecule gets on hemoglobin, the rest want to join in. The hemoglobin actually changes its structure to make it easier for other oxygen molecules to join in. The hemoglobin is like a DJ switching up the music to get more people dancing. As one oxygen molecule joins, the hemoglobin opens up the rest of its oxygen-binding spots even wider to make it more inviting for more oxygen to hop on - it's like the music they can't resist. (If your imagination allows it, this dance floor illustration would work in reverse as well.)

However, just like the right shift, the left shift can turn pathological as well. How does this occur, and what do we do about it?

Pathological Left Shift

What would cause our body to shift the curve to the left? Maybe the first thing that comes to mind is hypothermia, or perhaps hyperventilation. Hypothermia makes the whole body cold, thus tricking the hemoglobin into hanging onto oxygen. After all, how is the body supposed to know what areas need oxygen if it can't tell who's doing work (lack of heat from the cellular engine and entropy)? Hyperventilation physically moves a large amount of minute volume, which eliminates a lot of CO2. CO2 is globally reduced in hyperventilation, which means there is a lack of one of the main triggers that cause hemoglobin to let go of oxygen. As I mentioned before, this can trick us into thinking that just because the SPO2 is adequate, that tissue is actually being oxygenated. So, what can we do about a left shift?


Let's make some clinical applications. Your patient comes in COVID and has a relatively high SPO2, but their PO2 is hypoxemic. Let's say the patient is not intubated yet, and you're trying to decide between CPAP and BIPAP. The patient is moving adequate volumes, and they're on a left shift. Which treatment might you choose? You would likely pick CPAP over BIPAP because the patient is already on a left shift. If you remove CO2 when you don't need to, and perhaps put the patient into a respiratory alkalosis, you would exacerbate the left shift and cause even less oxygen to be dropped off at the tissue sites. If the patient has an advanced airway, beware of overly aggressive minute volumes on a ventilator or BVM - they can cause alkalosis. Again, while the SPO2 might look good, we might not actually be dropping that oxygen off at the tissue level.

What about a patient who is hypothermic? They're on a left shift due to their temperature. This might actually be an okay time to use warmed 0.9% NS because the fluid will move the pH slightly more acidic (assuming the patient is perhaps alkalotic) and warm the patient at the same time.



In emergency and critical care medicine (especially EMS) we have the greatest ability to impact the respiratory and cardiovascular systems of our patients. Most of our skillsets, medications, and equipment are designed to handle pathologies involving these two systems. Understanding the oxyhemoglobin curve is a cornerstone in understanding internal respiration, which we have a great ability to change - for better, or for worse. Although this blog may have seemed like a heavy subject, this really only scratched the surface of what you can learn about oxygen saturation, transport, and delivery. We didn't even talk about the roles of anemia, fetal hemoglobin, dishemoglobins, or the formulas for total oxygen delivery, extraction, and what influence these factors. Keep learning! There is much more to oxygenation than just looking at the SPO2, and they're applicable to your care no matter what type of clinician you are. I hope this blog served as an aid in helping you understand this initial and essential part of oxygenation!

Peer Review

I thoroughly enjoyed reading this blog. The 4,5,6,7,8,9 relationship is new to me, but I will now never forget it! Sam asked me to weigh in on some considerations relative to this subject when involving other gases. I’m not sure how I feel about being the guy he asks about gas?!?

Combustion in a closed space can consume significant amounts of oxygen, decreasing the ambient concentration of oxygen to as low as 10-13%. Think about the immediate short term effects this will have on tissues that are particularly sensitive to compromised oxygen delivery (heart and brain). At the same time, large amounts of carbon monoxide is produced. Carbon monoxide (CO) is a colorless, odorless gas produced by the incomplete combustion of carbon-containing compounds, such as wood, coal, and gasoline. It is a major component of the smoke produced in open fires. CO causes tissue hypoxia by decreasing the oxygen-carrying capacity of the blood. Hemoglobin binds CO with an affinity more than 200 times greater than the affinity for oxygen. CO causes a left shift in the oxyhemoglobin dissociation curve, which reduces the ability of hemoglobin to unload oxygen. The heart is particularly affected because CO binds with the heme molecules in myoglobin, decreasing facilitated diffusion of oxygen into muscle. Interaction of CO with myocardial myoglobin results in decreased myocardial contractility.

Also remember pulse oximetry readings can be misleading in the setting of carbon monoxide (CO) exposure or methemoglobinemia because these devices use only 2 wavelengths of light (the red and the infrared spectrum), which detect oxygenated and deoxygenated hemoglobin only and not any other form of hemoglobin. Readings are falsely elevated by CO-bound hemoglobin (carboxyhemoglobin). CO-oximeters use 4 wavelengths of light and are capable of detecting carboxyhemoglobin and methemoglobin.

Mike Brown


Note: Please don't be bothered by the slightly older references. The most current textbooks of respiratory physiology are listed here that I used for research. Luckily for us the curve hasn't changed in a long time ;)

Davis, D. P., Hwang, J. Q., & Dunford, J. V. (2008). Rate of decline in oxygen saturation at various pulse oximetry values with prehospital rapid sequence intubation. Prehospital emergency care : official journal of the National Association of EMS Physicians and the National Association of State EMS Directors, 12(1), 46–51.

Cairo, J. (2014). Mosby's respiratory care equipment. St. Louis, Mo: Elsevier.

Chang, D. (2014). Clinical application of mechanical ventilation. Clifton Park, New York: Delmar Cengage Learning.

Heuer, A. & Scanlan, C. (2018). Wilkins' clinical assessment in respiratory care. St. Louis, Missouri: Elsevier.

Jardins, T. (2013). Cardiopulmonary anatomy & physiology : essentials of respiratory care. Clifton Park, NY: Delmar Cengage Learning.

Jardins, T., Burton, G. & Phelps, T. (2016). Clinical manifestations and assessment of respiratory disease. St. Louis, Mo: Mosby Elsevier.


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