# Pressure flow and resistance relationship problems

### Putting it all together: Pressure, flow, and resistance (video) | Khan Academy

Ohm's law, relationship between flow, pressure and resistance blood flow inversely proportional to resistance . Blood viscosity changes in disease states. Heart; Cardiac cycle; Arteries; Blood flow; Vasodilation; Arterial Resistance; Cardiac output .. () Relationship between Fibroblast Growth Factor 21 and Extent of Left increases blood pressure in patients with coronary artery disease . Blood flow is a function of pressure difference and resistance (Darcy's law). Blood flow This equation is called Darcy's law or Ohm's law. Flow (F) is defined as .. Such problems are solved by Bernoulli's principle. Bernoulli's.

Various animals like mouse were used to detect the heart disease [ 14 ]. Cardiovascular disease is one of the most frequent causes of death of women in the world [ 15 - 17 ]. Stroke is the major healthcare problem with higher mortality and morbidity rates [ 18 ]. Women are more affected with Atherosclerosis [ 19 ]. At times increase in blood pressure may leads to various kinds of health problems [ 2021 ].

## Arterial Blood Pressure

Heart failure patients are at increased risk of sudden death due to ventricular problems [ 22 - 24 ]. Diabetes Mellitus DM is also a main risk factor for heart failure [ 25 - 27 ].

Ohm's Law and Hemodynamics (Fluid Mechanics - Lesson 9)

Most of the cardiovascular emergencies are caused by coronary artery disease [ 2829 ]. Echocardiography is the modality of choice for investigation of suspected congenital or acquired heart disease [ 30 - 32 ] Suspected heart disorders and related heart diseases can be investigated using Echocardiogram [ 33 - 35 ].

The frequency of the cardiac cycle is described by the heart rate [ 36 ]. There are two phases of the cardiac cycle. The heart ventricles are relaxed and the heart fills with blood in diastole phase [ 37 ]. The ventricles contract and pump blood to the arteries in systole phase [ 38 ]. When the heart fills with blood and the blood is pumped out of the heart one cardiac cycle gets complete.

The events of the cardiac cycle explains how the blood enters the heart, is pumped to the lungs, again travels back to the heart and is pumped out to the rest of the body [ 39 ].

The important thing to be observed is that the events that occur in the first and second diastole and systole phases actually happen at the same time [ 40 ]. During this first diastole phase, the atrioventricular valves are open and the atria and ventricles are relaxed. From the superior and inferior vena cavae the de-oxygenated blood flows in to the right atrium.

The atrioventricular valves which are opened allow the blood to pass through to the ventricles [ 41 ]. The Sino Atrial SA node contracts and also triggers the atria to contract. The contents of the right atrium get emptied into the right ventricle. During this first systole phase, the right ventricle contracts as it receives impulses from the Purkinje fibers [ 42 ].

The semi lunar valves get opened and the atrioventricular valves get closed. The de-oxygenated blood is pumped into the pulmonary artery.

## Hemodynamics (Pressure, Flow, and Resistance)

The back flow of blood in to the right ventricle is prevented by pulmonary valve [ 43 ]. The blood is carried by pulmonary artery to the lungs. There the blood picks up the oxygen and is returned to the left atrium of the heart by the pulmonary veins [ 44 ]. In the next diastolic phase, the atrioventricular valves get opened and the semi lunar valves get closed.

The left atrium gets filled by blood from the pulmonary veins, simultaneously Blood from the vena cava is also filling the right atrium. The Sino Atrial SA node contracts again triggering the atria to contract. The contents from the left atrium were into the left ventricle [ 45 ].

During the following systolic phase, the semi lunar valves get open and atrioventricular valves get closed. The left ventricle contracts, as it receives impulses from the Purkinje fibers [ 47 ]. Oxygenated blood is pumped into the aorta. The prevention of oxygenated blood from flowing back into the left ventricle is done by the aortic valve. Aortic and mitral valves are important as they are highly important for the normal function of heart [ 48 ].

The aorta branches out and provides oxygenated blood to all parts of the body. The oxygen depleted blood is returned to the heart via the vena cavae.

Left Ventricular pressure or volume overload hypertrophy LVH leads to LV remodeling the first step toward heart failure, causing impairment of both diastolic and systolic function [ 4950 ]. Coronary heart disease [CHD] is a global health problem that affects all ethnic groups involving various risk factors [ 5152 ].

Vasodilation Vasodilation is increase in the internal diameter of blood vessels or widening of blood vessels that is caused by relaxation of smooth muscle cells within the walls of the vessels particularly in the large arteries, smaller arterioles and large veins thus causing an increase in blood flow [ 53 ].

When blood vessels dilate, the blood flow is increased due to a decrease in vascular resistance [ 54 ]. Therefore, dilation of arteries and arterioles leads to an immediate decrease in arterial blood pressure and heart rate hence, chemical arterial dilators are used to treat heart failure, systemic and pulmonary hypertension, and angina [ 55 ].

At times leads to respiratory problems [ 56 ]. The response may be intrinsic due to local processes in the surrounding tissue or extrinsic due to hormones or the nervous system. The frequencies and heart rate were recorded while surgeries [ 57 ].

The process is the opposite of vasodilation. The primary function of Vasodilation is to increase the flow of blood in the body, especially to the tissues where it is required or needed most. This is in response to a need of oxygen, but can occur when the tissue is not receiving enough glucose or lipids or other nutrients [ 61 ]. In order to increase the flow of blood localized tissues utilize multiple ways including release of vasodilators, primarily adenosine, into the local interstitial fluid which diffuses to capillary beds provoking local Vasodilation [ 62 ].

Vasodilation and Arterial Resistance The relationship between mean arterial pressure, cardiac output and total peripheral resistance TPR gets affected by Vasodilation.

Vasodilation occurs in the time phase of cardiac systole while vasoconstriction follows in the opposite time phase of cardiac diastole [ 63 ]. Cardiac output blood flow measured in volume per unit time is computed by multiplying the heart rate in beats per minute and the stroke volume the volume of blood ejected during ventricular systole [ 64 ]. TPR depends on certain factors, like the length of the vessel, the viscosity of blood determined by hematocrit and the diameter of the blood vessel.

Vasodilation works to decrease TPR and blood pressure through relaxation of smooth muscle cells in the tunica media layer of large arteries and smaller arterioles [ 6566 ]. A rise in the mean arterial pressure is seen when either of these physiological components cardiac output or TPR gets increased [ 67 ]. Vasodilation occurs in superficial blood vessels of warm-blooded animals when their ambient environment is hot; this diverts the flow of heated blood to the skin of the animal [ 68 ], where heat can be more easily released into the atmosphere [ 69 ].

Vasoconstriction is opposite physiological process. Systemic vascular resistance SVR is the resistance offered by the peripheral circulation [ 72 ], while the resistance offered by the vasculature of the lungs is known as the pulmonary vascular resistance PVR [ 73 ]. Vasodilation increase in diameter decreases SVR, where as Vasoconstriction i.

The Units for measuring vascular resistance are dyn. This is numerically equivalent to hybrid reference units HRUalso known as Wood units, frequently used by pediatric cardiologists. To convert from Wood units to MPa. Calculation of Resistance can be done by using these following formulae: Calculating resistance is that flow is equal to driving pressure divided by resistance. And 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'll be the superior vena cava. There's also an inferior vena cava. And the blood flow through this half is, as you would guess, continues to go around.

And if I was to try to figure out the pressures, the blood pressures, at different points along the 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 venue 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 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 is pretty normal.

It's somewhere around 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 Again, that's what you would expect-- somewhere between 80 and So 90 is the average, because it's going to be not exactlybecause 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, it'd probably be something like, let's say And then as you cross the arterial, the pressure falls dramatically. So it's somewhere closer to And then here it's about Here it's about Let's say 10 over here.

### Pressure and Blood Flow

And then at the very end, it's going to be close to a 5 or so. Let me just write that again. 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, right?

• Putting it all together: Pressure, flow, and resistance
• Effects of Vasodilation and Arterial Resistance on Cardiac Output

So from 95 all the way to five, 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. 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 want 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 want 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 is 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.

### CV Physiology: Hemodynamics (Pressure, Flow, and Resistance)

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; S is for start-- and the pressure at the end can be subtracted from one another.

The change in pressure is really the change from one part of tube 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 much volume-- how many liters of blood are flowing in a minute? 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. And for a 70 kilogram person, the stroke volume is about 70 milliliters.