DIP Episode 600 - Intuition and Integrations With Select Equations (Step 1-3)

All right, welcome. My name is divine. This is episode 600 of the Divine Intervention Podcasts. In today's podcast, we're going to be discussing a topic that I like to call intuition and integrations with equations. Intuition and integrations with select equations. So what am I going to focus on here? In this podcast, I'm going to focus on a bunch of equations that pop up pretty frequently on the USMLA exams. And I'm going to try to give you some intuition on them and make some integrations with them. And this is episode 600 and I just want to say a big thank you. You know, grateful to God for the spot podcast. But I'm also grateful to the people that listen to this podcast. I hope you find it to be helpful, but thank you for listening to this podcast. Thank you for promoting the podcast. And again, I'm really committed to quality medical education. And I will keep doing everything, you know, God willing as the Lord helps me to keep teaching to the best of my abilities. All right, so let's jump right into it. So the first equation we're going to deal with today, which I think is really important is the diffusibility equation. The diffusibility equation equation. This is something that is going to make many things kind of basically clicking your brain. Right. So what's the equation for a diffusibility? Well, the equation is going to be the area, the surface area available. So the feasibility equals the air surface irrevailable divided multiplied by the pressure gradient.

So multiply by the pressure gradient divided by the thickness. Okay. So the feasibility is what it's the area. Right. Multiply by the pressure gradient divided by the thickness. So we're basically seeing that there are three things here that appear to control diffusibility. Right. There's literally three things here that appear to control divisibility, diffusibility. Right. Area and pressure gradient does that directly related to the diffusibility. And thickness is indirectly related indirectly proportional to the diffusibility. So why does this make sense? Why does this make sense? Or what are some integrations that can be made with this stuff? Well, the first thing is area. Let's look at area. Right. Area is different is directly related to diffusibility. That should make sense. If you have more surface area, more diffusion will happen. Right. More diffusion will happen. Right. So if you think about it, for example, many times when you want to have diffusion in the body, you have all these surface area modifications. Right. Many times you see them referred to as SA Ms surface area modifications. These modifications, they literally are targeted towards increasing surface area so that you can have more diffusion. Right. Like for example, if you look at the GI tract of an individual, you look at the enterocytes. What's that EPICO surface modification that we find on the surfaces of an enterocytes? It's the microvilli. Those microvilli, what do they do?

They pretty much increase surface area available for diffusion. They literally increase surface area available for diffusion. They have those EPICO surface modifications. Right. Because of those microvilli, you have more surface area, you can have more diffusion. Right. But say for example, if a person has an unabsorbed disorder, where those microvilli have been messed up. Right. So say for example, they've been messed up by Celiac disease where you have these anti-glyadine anti-indomacial or anti tissue transglutamines antibodies. You mess up the surface area by reducing the surface area. You have less diffusibility. You're going to have less absorption. Right. Or say for example, you are taking some kind of diabetes drug. Remember those alpha glucosides inhibitors, like acrabose and miglito, that inhibit brush border enzymes. When you shot those down, you're in a sense kind of reducing surface area. So you have less diffusion. Right. So the most surface area you have available, the more diffusion you can have. Right. And this is part of why it is very, very important, you know, to try to treat COPD or to tell the people that have COPD to stop smoking. What's the integration there? In COPD, what is the mechanism behind those people's hypoxia? The primary mechanism behind their hypoxia is a reduction in pulmonary surface area. Right. So for example, remember in COPD, you have a lot of proteases. These proteases are typically made by inflammatory cells.

They're trying to clear off the junk that's in your lungs. What can that junk be? That junk can be a lot of cigarette smoke because you're a smoker. Right. They want to clear out that junk in your lungs. Right. But the thing is as they're clearing out that junk, there's also other issues you're running to. What are these other issues? Well, the primary issue you're running to is that you have all these proteases that are elaborated by these white blood cells, these macrophages, these dust cells. And those proteases literally chop your lungs. As you chop your lung, parankham, you're literally killing surface area. As you kill surface area, there's going to be less diffusibility. This is why DLCO is decreased in a person that has an emphysema, for example, DLCO is decreased because surface area has been impaired. Right. Surface area has been impaired. So because you have a decrease in the surface area available for diffusion, right. The oxygen inside your viola, your PB-AO2 will not equilibrate with the oxygen inside your blood vessels, your PB-AO2. So because that is not happening, right. Your PB-AO2 will become low. You're going to become hypoxic. You're going to become hypoxic for that reason. Right. And that then explains why you have a low SEO2 in a person that has COPD because oxygen is not dissolving in their plasma because it cannot diffuse very well across the ovulum membrane. Right.

So since oxygen cannot dissolve in the plasma very well, then there's not enough oxygen to jump on hemoglobin and saturate it. Right. Okay. So now let's talk about this whole concept of pressure gradient. Right. What's this whole concept of pressure gradient? We see that pressure gradient is directly related to the feasibility. Well, why is that important? Well, the thing is, for example, think of a person that has a, think of a person that is on a mechanical ventilator. Right. Think of a person that's on a mechanical ventilator. Mechanical ventilation is literally called invasive positive pressure ventilation. And just as an FYI, we know that our friends at the MVM Es, they love to give alternate names to things. Right. They may not give you the name you're familiar with just to shake you up a little bit on your exams. Right. So pressure gradient. Right. Pressure gradient. Let's talk about mechanical ventilation. Mechanical ventilation when you're placed on an, when you're intubated is basically invasive positive pressure ventilation, invasive positive pressure ventilation. So a tube is rammed down your throat. But why do you think we put people on mechanical ventilation? Well, one of the things it does is that it literally increases pressure gradient. Right. It literally increases pressure gradient. Because if you have a higher pressure gradient, then you can bring in oxygen into the lungs from the high pressure.

And if the oxygen you have your lie is under higher pressure, it's going to be a lot easier to diffuse because it's just a simple pressure principle. What's the direction of flow? The direction of flow is that flow happens from regions of high pressure to regions of low pressure. So the thing is by delivering that's why it's called positive pressure ventilation, positive pressure ventilation. Right. You're literally delivering oxygen under high pressures to the person's lungs. When you do that, you're increasing the pressure gradient across the ovular membrane. And when you increase the pressure gradient across the ovular membrane, you're going to have more diffusion. When you have more diffusion, right, you're pretty much trying to increase the DLC. Right. When a person is placed on invasive positive pressure ventilation, remember, another kind of positive pressure ventilation that's very common on the USMLE is non-invasive positive pressure ventilation. That's something we find in people that have like bi-PAP or people that own bi-PAP or CPAP. Right. Remember, we tend to use bi-PAP in people that have like CHF exacerbations. We also use them more commonly on the USMLE scene. People that have a COPD exacerbations. If they are not responding to the institution of IV steroids and in heel bronchordi leaders, you can use bi-PAP non-invasive positive pressure ventilation. Again, it delivers oxygen on the high pressures. By doing that, you're making the oxygen tension of the...

You're making the oxygen tension of the blood. I mean, sorry, of the oxygen in the avial eye higher, much higher than the oxygen tension of the oxygen dissolved in your plasma. So you're increasing that pressure gradient. That's going to encourage the fusibility. All right. Now, the final thing in this diffusibility equation is thickness. And we see that there's an inverse relationship. There's an inverse relationship between thickness and the fusibility. Right. So basically, as the membrane gets thicker, as the avial membrane gets thicker, you're essentially increasing the diffusion distance. Right. And the fusion gets less efficient as you put distance between yourself and the source of the thing that's diffusing. Right. A very poignant example is if a person farts around you. Right. If a person farts around you, you run away from them very quickly. Why do you run away from them very quickly? Have you ever thought about that? Because as you put more distance between yourself and those people, as you put more distance between yourself and those people, you kind of run away. Right. Or a person's perfume smells a lot better when you get closer to them. Right. Because the thickness, the distance between you and the source is smaller. But as you go far away from them, you don't really smell that perfume anymore. Right. You want to drive away from bad smells and drive closer to good smells. Right. So thickness. So thickness, in this case, let's talk about the avial membrane.

Right. So the thing is there are many things that can thicken your avial membrane. So like for example, if a person has a fibrodeclone disease, for a person has fibrodeclone disease, right, from anything, you know, like sarcoidosis or pneumoconylis or whatever, that literally thickens the that literally thickens the avial membrane. Right. And if that happens, then it's going to be really hard for oxygen to effectively diffuse from the avial line to the pulmonary vessels. So your p-litre ill too, which is the oxygen tension within your pulmonary vessels is going to plummet. Because again, literally, you just, it's just too thick. It's just literally too thick. That's how those people become hypoxemic. Right. That's how they become hypoxemic. Right. Well, if you even think about a person that has very wet lungs, right. Person that has very wet lungs. Right. So for example, a person that has a, um, arides, person that has arides. When a person has arides, a acute respiratory distress syndrome, there's all this inflammation going on. So there's all these histamines and bradykines that are released. When those histamines and bradykines are released, um, your, your pulmonary vasculopremibility increases. And as your pulmonary vessels get more permeable, as they get more permeable, as they get more permeable, uh, you're going to leak a lot of fluid into your pulmonary interstitial. Right. As that happens, you are pretty much coating the walls of the person's avial line with fluid.

That's going to increase the thickness of the avial wall. And as that happens, diffusion is going to get a lot less efficient. Right. So those people are going to become hypoxemic. That's why ARDS is so dangerous. And this is why one of the reasons we treat ARDS is to put your mechanical ventilation. If not, you're, you're probably going to die. Right. By placing your mechanical ventilation, we're taking advantage of the numerator in this diffusibility equation. You're increasing the pressure gradient as I've already discussed. All right. So I think I've made enough integrations with this equation. So hopefully this equation now makes intuitive sense in your brain. That's why the title of this podcast is literally intuition and integrations with equations, intuition and integrations with equations. All right. So what's the next equation I want to discuss? The next one I want to discuss is a Poiseau's law. Right. Poiseau's law is one that is really, really common is one that is discussed in many different settings. Some people don't even realize that Poiseau's law is being tested on the US Emily exam that they're taking. Right. But many of us know that that Poiseau's law has to deal with, has to deal with a prefer resistance. Right. Poiseau's law has to deal with prefer resistance. And we know that prefer resistance is so so so what's the equation? Right.

So our resistance is directly is equal to viscosity multiplied by the length of the vessel divided by the radius to the fourth power. I'm going to say that equation again. Right. So Poiseau's law is the the prefer resistance is the equal to the viscosity multiplied by the length of the vessel divided by the radius to the fourth power. So what do we learn from this? Right. The thing we learn is that the resistance is directly proportional to the viscosity. And the resistance is directly proportional to the length of the vessel. And the resistance is inversely proportional to the radius to the fourth power. Many people sadly forget that radius to the fourth power part of the whole of the whole Shebang. Right. So let's make some integrations with this. Right. Let's let's pick the one that many people ignore most of the time. And that is viscosity. Right. There's actually many implications for viscosity that you want to keep at the back of your mind. Right. So for example, think of a person that has an hypocycidine tumor. Right. So a person that has like renal cell carcinoma or a person that has a hemangioplastoma that we find in the posture force of the brain or a person that has a paracelolacarcinoma. And also just think of a person that has viscous blood for any other reason. Right. Let's say for example, you have polycythemia there where you have some kind of jack two mutation.

When you have these jack two mutations, it causes an ipo independent proliferation of your ribloxel of your ribloxel precursors. Right. So we can turn our right cells. Right. All these things are going to make your blood very thick. All these things are going to make your blood very viscous. Right. Well, if a person is hypothermic, for example, if a person is hypothermic, the blood gets very, very viscous because it's almost like their blood is turning to ice. It doesn't exactly turn to ice, but it gets pretty close. Right. So when those things happen, your blood viscosity increases. So if your blood viscosity increases, what do you think is going to happen to your total perfor resistance? It's going to increase, right, because it's like your blood has become sludge. Your blood has literally become sludge. Your blood has literally become sludge. Right. So there is less resistance to flow. Sorry, there is more resistance to flow of that blood. So you're going to raise that vascular resistance. You're literally going to raise that vascular resistance. Right. That's why many times when people have polycythemia, those people tend to have very high blood pressures. Right. Their blood pressures are literally high because the resistance has been increased because their blood is very, very viscous. Their blood is very, very viscous. Right. Their blood is very, very viscous.

And if you think about it, if you have this very viscous blood, you're basically in by increasing that resistance, you're increasing the afterload that the heart has to deal with. You're literally increasing the afterload that the heart has to deal with. So it's going to be harder for blood to get out of the heart. It's going to be harder for blood to get out of the heart. Right. So if you want to think about this from an even different perspective, how about low viscosity? Well, if you think about low viscosity, think of anemia when the president is anemic, their blood has low viscosity. Right. Their blood has low viscosity. So think about it. If you have like a hemoglobin of three, for example, your blood has low viscosity, but that's kind of a problem as well. Because by your blood having low viscosity, by your blood having low viscosity, you're basically reducing the vascular resistance. And if you're reducing the vascular resistance, your any effect reducing the afterload, and when you reduce the afterload, what happens to your cardiac output? Well, your cardiac output is going to rise. Your cardiac output is going to rise. That's one bad thing that happens when you have really bad anemia. But also when you have really bad anemia as well, another bad thing that happens is that your tissues are not getting enough oxygen because there's fewer, there's fewer hemoglobin in your bloodstream because there's fewer hemoglobin because there's fewer hemoglobin. Right.

Because there's fewer hemoglobin. There's fewer oxygen careers. So your tissues get hypoxic whenever your tissues get hypoxic, your cardiac output actually rises in response. I'm really hoping God willing that that I get reminded mentally to talk about this equation. There is some equation there somewhere. I know I know there's some equation there somewhere. But as as a person gets hypoxic, right, as the oxygen tension in your blood goes down, your cardiac output rises. There's an inverse relationship between those two things. So when your cardiac output rises, your heart keeps raising its cardiac output just to deal with this hypoxia situation, just to deal with this hypoxia situation. The thing is over time that's that's going to cause some problems, right? Because the thing is your heart is a muscle. It's trident muscle. It can only work that hard for so long. Over time, your heart is going to get very tired, right? Because it's like, man, I'm always at high cardiac output because of tissue hypoxia because of this chronic reduced reduced afterload. That can lead to problems, right? That can actually cause something called high output heart failure. It's a heart failure that arises because you have chronically elevated cardiac output, right? That's actually the pathophage behind that, right? So that's one of the reasons why when a person, for example, has, when a person has a proverb virus B19, that's one of the reasons why they develop a demon.

Many people don't think about this, right? But you see like a fetus that has a hydroxyitalis. How do you think that hydroxyitalis arises? That hydroxyitalis arises because basically, basically, the child has really bad anemia from the proverb B19 infection. Remember, it infects the red blood cell precursors. When that happens, when that happens, you develop an anemia that anemia decreases blood oxygen content. That's going to raise the cardiac output. Over time in utero, you're going to develop high output heart failure. If the heart fails, it's going to stop pumping as well after a while, right? And then fluid, the person basically has like a CHF exacerbation in utero. So fluid kind of builds up all around the child's body and the child becomes hydropic. There's other reasons behind that, but that's actually one important reason, right? And another integration of this viscosity of a thing is if you really think about it in the context of, if you think about it in the context of screening the child for anemia, right? So one of the ways we screen fetuses for anemia is to get a Doppler ultrasound of the middle cerebral artery of the fetus. This is actually one way you can screen to see like, oh, does this child have anemia from like, araging compatibility or whatever? Because the thing is if blood is viscous, if blood is viscous, it flows slow. If blood is viscous, it flows slow. But if blood is not viscous, it flows fast.

So if you notice that the velocity of blood is very high in the fetal middle cerebral artery, that's a surrogate for the blood flowing fast. And if the blood is flowing fast, the child probably has anemia. That's a very good non-invasive way to screen fetuses for anemia, but if you look at things from another perspective of, oh, because your blood is very viscous, because you have a polycythemia for whatever reason, right? Your blood is flowing slow. If your blood flows slow, if your blood flows slow, right? That's going to cause bloodstasis. And where have we heard about bloodstasis? We have heard about bloodstasis from Verkho's triad, right? When you have Verkho's triad, you literally have bloodstasis. That bloodstasis, right? Makes your clotting factors interact with each other more and more. And it's the interact with each other more and more. You're going to become hyperquaglable. You're literally going to become hyperquaglable. And as you become hyperquaglable, you can develop all these thrombotic issues, right? Like for example, a person that has p-veir, there's a reason why people that have p-veir tend to develop botcaric syndrome. That's thrombosis of the hepatic vein. Because again, those people are polycythemic. Their blood is very viscous. So their blood flows slow, right? Their blood flows slow. And this is also why people that have other disorders that can increase blood viscosity, like warden, thrombomacroglobulinemia, right?

Anything that kind of donks up your blood with so many antibodies, like even multiple myeloma, that can ultimately cause these people's blood to become more viscous. As your blood becomes more viscous, it's going to flow slow. That's slow flow is going to lead to the person having, it's going to lead to the person having blotsstasis. That's going to make them hyperquaglable. Again, think about Verkho's triad. And also, this is why a person that is hypothermic. This is why being hypothermic is extremely dangerous. Because again, when you're hypothermic, your blood becomes like ice. It becomes more viscous, and that can cause a lot of problems. That's why sometimes we give patients a warmed fluid. Because by giving warm fluids, you're giving fluids that are less viscous. So they're going to flow better and they're going to produce the person's tissues even better, right? I never imagine I'll be talking about viscosity this much, but I guess viscosity is pretty high or to know for you exams. And then I know that integration, you can even make with viscosity, because we're just thinking about this from the blood vessel perspective. How about from a biliary tract perspective, right? If for example, you lose a, you have a lot of himoleses, right? You have a lot of himoleses. You're going to generate a lot of indirect bilirubin. As you generate a lot of indirect bilirubin, right? That's going to saturate your bile.

It's going to make your bile even more concentrated, even more viscous. And if it gets more viscous, there's going to be less flow of that bile. There's going to be what less flow of that bile. And if that bile does not flow as well, right? Because it's slower, because it's thicker, because it's more viscous, that can certainly cause a lot of problems for you. That can certainly cause a lot of problems for you. So that's number one. So those people can begin to develop ghost stones, right? If you see a person that has rapid weight loss, when you lose a lot of weight, one of the ways your body gets rid of fat is as cholesterol. So that cholesterol, that excess cholesterol you're losing can super saturate your bile. And when you super saturate your bile, I'm again, that's going to make it thicker, that's going to make it more viscous. So you're going to have like a colistatic pattern. You're going to have a lot of colistases. And although you can also think about this constantly from a biliary tract perspective, it's a triaxone. There's a reason why we don't really give subtraction to like newborns, right? We try to avoid that for a very simple reason. You know why? Because if we give them subtraction, subtraction is a calcium collider. It can bind calcium very effectively. And by binding calcium, it makes the, so it can bind the calcium in your biliary fluid. It's going to make it thicker.

That's the thing that actually explains the introipartic polystases that we find in people that take, in people that take that takes a triaxone, right? That's why instead of using safe triaxone as the third generation sephalus brain of choice in newborns, we use sephaltaxine instead, right? We use sephaltaxine instead. So I think that's all I'm going to say about viscosity. The other parts of this, of this equation are kind of straightforward, right? So we know that length is directly related to to resistance, right? There's a reason why you are the order is probably like the most important ordering your body because it's probably like one of the longest vessels in your body, right? So because it's very long, it's the one that generates a lot of the resistance that you see in your body because it's a very lengthy vessel, right? As you have a longer vessel, right? You're going to have a more, more resistance. And then the final part of this equation is the radius to the fourth power, right? Basically, as you have a smaller radius, right? You have bigger resistance, which makes sense, right? It's much easier for fluids to come out through a holes than through a straw, right? It's just more efficient because you just have like, it's almost like you have more surface here available, right? So there's less resistance to flow. So more things just kind of flow, flow through, right? So, but don't forget that part about the fourth power. That's one thing that many people forget.

So say, for example, if you if you if you double the resistance, if you, I mean, sorry, if you double the radius, if you double the radius, you're actually reducing resistance by by a factor of 16, by a factor of 16, right? Because two to the fourth, right? So two times two is four, four times two is eight and eight times two is 16, right? So you're literally increasing the decreasing resistance by by 16 points, right? By by a, not 16 points, but by a factor of 16 by 16, by 16, for the reducing resistance by that, that much, right? So please just kind of keep that at the back of your mind. They love to test these things on the exams. There's a few more equations, I think I kind of have on my mind. But again, if I start talking about the next one is because this podcast is in short, but it's kind of a lot of detail packed into it. Right? So I want you to kind of spend some time thinking through it on packing God willing. We'll have another podcast like this, go through some intuition, go through some more integrations with equations, right? So again, the two equations we discussed today, the feasibility is equal to area times the pressure gradient divided by the thickness and then Poisson's law where the resistance to flow is equal to the viscosity multiplied by the length of the vessel divided by the radius to the fourth power, divided by the radius to the fourth power, right?

You can already begin to think of Poisson's law in, for example, you're trying to give fluid to a patient, right? If you want to give fluid to a patient, it probably makes sense to, it probably makes sense to use a shorter, shorter tube, right? Because a shorter tube will present less resistance. I want to use a wider tube, right? A wider tube will present less resistance as well, right? We'll present less resistance as well, right? Because by increasing that radius, you're decreasing resistance, right? To the fourth power, right? Again, there are so many ways they can integrate this, right? And there are so many ways they can really integrate this stuff. So just make sure you understand these things. I know you may be like, wow, divine, we only talked about like six, two equations today. But do you see how many different ways they can test these two equations, right? So just kind of keep these things at the back of your mind. And I think it's going to help you be very successful on your exams. There are so many ways they can test these things. I probably talked about like 20 or 25 different concepts today, just from these two equations, right? So there's a lot more equations where this came from. So God, will you now discuss them in another podcast? So if you like the way I teach, I think you're going to love my classes. You're going to absolutely love my classes. I have a bunch of classes starting on the 20th of this month. First step one, all the way to step three, right?

So I have a two and a half artistic in class, I have a four-hour bio stats class, I have a five-hour social sciences, quality improvement, healthcare systems, ethics class. Those are for step one to three. And then for step two, and step three, specifically, I have a last minute review, right? Later this month, and then have a 20-hour step two, step three review. And then in the first two weeks of June, this class is going to only be held once this year. It's an epic class. My 50 hours step two, step three review, I've literally meet podcasts where I talk about these classes and what you get from them and how they are different from my podcast. So just listen to those. And if you need more information, just shoot me and email through the website. These classes are going to be held through soon, right? But these classes, so you imagine getting these kinds of integrations and this level of teaching and understanding for like 50 hours, for example, for 20 hours, for example, you're going to get a ton of benefit from it, right? Many people have taken these classes done extremely well on their exams. So I also offer one, I want you to do it for all the US Million complex exams. And also I have this podcast on Apple Google and Spotify, have a You Tube channel, you can check out Divine Intervention, US Million Podcasts and videos. And then I also help with ERA's applications, personal statements, more interviews and things of that nature.

And also I have another website called Divine Intervention Life Lessons.com. Divine Intervention Life Lessons.com, right? Every week, you know, many of you know my question. Every week I post like 203 podcasts, where from a biblical perspective, I address a life lesson. There's actually an Apple podcast associated with that called the Divine Intervention Life Lessons podcast. So thank you for listening to me today. I really hope you found this podcast to be helpful. I will see you in episode 601. So God bless you, have a wonderful day and bye for now. Thank you.

Area (directly proportional), Pressure Gradient (directly proportional), and Thickness (inversely proportional).

Reduction in total surface area due to alveolar wall destruction by proteases.

Polycythemia or hypothermia (blood becomes sludge-like).

Resistance is inversely proportional to the fourth power of the radius ($\text{R} \propto 1/r^4$).

Anemia (low hemoglobin concentration).

Calcium chloride is a calcium collider that binds calcium in the bile, increasing its viscosity and causing intrahepatic cholestasis.

$F = \frac{Area \times \text{Pressure Gradient}}{Thickness}$

Increases diffusion, as Area is directly proportional to $F$.

Increased viscosity ($\eta$) and increased length ($L$).

Thickness (the alveolar-capillary membrane becomes thicker).

Polycythemia vera or chronic venous stasis (Virchow's triad).

Resistance increases by a factor of 16 ($2^4$).

$F = \frac{Area \times \text{Pressure Gradient}}{Thickness}$

Increases diffusion, as Area is directly proportional to $F$.

Increased viscosity ($\eta$) and increased length ($L$).

Thickness (the alveolar-capillary membrane becomes thicker).

Polycythemia vera or chronic venous stasis (Virchow's triad).

Resistance increases by a factor of 16 ($2^4$).