# Relationship between pressure flow and resistance

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

pressure drives blood flow. Thus, we have an inverse relationship between blood vessel resistance and the blood flow rate - the higher the resistance, the. It also discusses resistance which is due to factors that impede or slow blood flow . . The relationship between blood volume, blood pressure, and blood flow is. The Relationship Between Pressure and Flow in the Systemic resistance increases markedly with moderate reductions in arterial pressure. When reflex.

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.

### Blood Flow, Blood Pressure, and Resistance | Anatomy & Physiology

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. 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. So for a 70 kilo person, you can expect about 70 milliliters per beat. And as I write this, let's say my heart rate is about 70 beats per minute. I feel pretty calm, and so it's not too fast. So the beats cancel as we said, and I'm left with 70 milliliters times 70 per minute. So that's about 4, milliliters per minute.

Or if I was to simplify, that's a 5, let's say about. So the flow is about 5 liters per minute. So I figured out the blood flow, and that was simply because I happen to know my weight, and my weight tells me the stroke volume. And I know that there's a change in pressure.

• Hemodynamics (Pressure, Flow, and Resistance)
• Pressure and Blood Flow

We've got to figure that out soon. And lastly, this last thing over here is resistance. And know I've said it before.

### Pressure and Blood Flow

I just want to point out to you again, the resistance is going to be proportional to 1 over R to the fourth. And so just remember that this is an important issue. And that's the radius of the vessel. So let's figure out this equation. Let's figure out the variables in this equation and how it's going to help us solve the question I asked you-- what is the total body resistance?

So if I have to figure out total body resistance-- let me clear out the board-- I've got, let's say, the heart.

I like to do the heart in red. And it's pumping blood at my aorta. So blood is going out of the aorta. And then it's going and branching here. And then it's going to branch some more. And you can see where this is going. It's going to keep branching. And eventually every branch kind of collects on the venous side.

All the blood is kind of filtering back in slowly into venules and veins. And finally into a vena cava. And I should really draw this going like that.

The blood is going to go back into the vena cava. So that's my system. And I got to figure out what the total body resistance is here. So if I have a system drawn out for myself, and I happen to know that here I said And here I said the pressure was 5. Then delta P equals 95 minus 5, which is And I know that there are 5 liters of blood flowing through per minute. And that was my Q. So I could say 90 equals 5 liters per minute.

Actually let me take a step back from that. Instead of 90, let me write the units. That was my flow. And I've got delta P here. And my resistance is the unknown. So I'll just leave that as R. So let's just solve for R. So I'll move my flow to the other side. The majority of hospitals and clinics have automated equipment for measuring blood pressure that work on the same principles.

The patient then holds the wrist over the heart while the device measures blood flow and records pressure. Cardiac output Volume of the blood Resistance Recall that blood moves from higher pressure to lower pressure.

It is pumped from the heart into the arteries at high pressure. Since pressure in the veins is normally relatively low, for blood to flow back into the heart, the pressure in the atria during atrial diastole must be even lower. It normally approaches zero, except when the atria contract see Figure Cardiac Output Cardiac output is the measurement of blood flow from the heart through the ventricles, and is usually measured in liters per minute.

Any factor that causes cardiac output to increase, by elevating heart rate or stroke volume or both, will elevate blood pressure and promote blood flow. These factors include sympathetic stimulation, the catecholamines epinephrine and norepinephrine, thyroid hormones, and increased calcium ion levels.

Conversely, any factor that decreases cardiac output, by decreasing heart rate or stroke volume or both, will decrease arterial pressure and blood flow. These factors include parasympathetic stimulation, elevated or decreased potassium ion levels, decreased calcium levels, anoxia, and acidosis.

Compliance Compliance is the ability of any compartment to expand to accommodate increased content. A metal pipe, for example, is not compliant, whereas a balloon is.

The greater the compliance of an artery, the more effectively it is able to expand to accommodate surges in blood flow without increased resistance or blood pressure. Veins are more compliant than arteries and can expand to hold more blood.

When vascular disease causes stiffening of arteries, compliance is reduced and resistance to blood flow is increased. The result is more turbulence, higher pressure within the vessel, and reduced blood flow. This increases the work of the heart. Blood Volume The relationship between blood volume, blood pressure, and blood flow is intuitively obvious. Water may merely trickle along a creek bed in a dry season, but rush quickly and under great pressure after a heavy rain.

Similarly, as blood volume decreases, pressure and flow decrease. As blood volume increases, pressure and flow increase. Under normal circumstances, blood volume varies little.

Low blood volume, called hypovolemia, may be caused by bleeding, dehydration, vomiting, severe burns, or some medications used to treat hypertension. It is important to recognize that other regulatory mechanisms in the body are so effective at maintaining blood pressure that an individual may be asymptomatic until 10—20 percent of the blood volume has been lost.

Treatment typically includes intravenous fluid replacement. Hypervolemia, excessive fluid volume, may be caused by retention of water and sodium, as seen in patients with heart failure, liver cirrhosis, some forms of kidney disease, hyperaldosteronism, and some glucocorticoid steroid treatments.

Restoring homeostasis in these patients depends upon reversing the condition that triggered the hypervolemia. Resistance The three most important factors affecting resistance are blood viscosity, vessel length and vessel diameter and are each considered below. Blood viscosity is the thickness of fluids that affects their ability to flow. Clean water, for example, is less viscous than mud. The viscosity of blood is directly proportional to resistance and inversely proportional to flow; therefore, any condition that causes viscosity to increase will also increase resistance and decrease flow.

For example, imagine sipping milk, then a milkshake, through the same size straw. You experience more resistance and therefore less flow from the milkshake. Conversely, any condition that causes viscosity to decrease such as when the milkshake melts will decrease resistance and increase flow.

Normally the viscosity of blood does not change over short periods of time. The two primary determinants of blood viscosity are the formed elements and plasma proteins. Since the vast majority of formed elements are erythrocytes, any condition affecting erythropoiesis, such as polycythemia or anemia, can alter viscosity.

Since most plasma proteins are produced by the liver, any condition affecting liver function can also change the viscosity slightly and therefore decrease blood flow. Liver abnormalities include hepatitis, cirrhosis, alcohol damage, and drug toxicities. While leukocytes and platelets are normally a small component of the formed elements, there are some rare conditions in which severe overproduction can impact viscosity as well. Blood vessel length is directly proportional to its resistance: As with blood volume, this makes intuitive sense, since the increased surface area of the vessel will impede the flow of blood.

Likewise, if the vessel is shortened, the resistance will decrease and flow will increase. The length of our blood vessels increases throughout childhood as we grow, of course, but is unchanging in adults under normal physiological circumstances. Further, the distribution of vessels is not the same in all tissues. Adipose tissue does not have an extensive vascular supply. One pound of adipose tissue contains approximately miles of vessels, whereas skeletal muscle contains more than twice that.

Overall, vessels decrease in length only during loss of mass or amputation. An individual weighing pounds has approximately 60, miles of vessels in the body.

Gaining about 10 pounds adds from to miles of vessels, depending upon the nature of the gained tissue. One of the great benefits of weight reduction is the reduced stress to the heart, which does not have to overcome the resistance of as many miles of vessels. In contrast to length, the blood vessel diameter changes throughout the body, according to the type of vessel, as we discussed earlier.

The diameter of any given vessel may also change frequently throughout the day in response to neural and chemical signals that trigger vasodilation and vasoconstriction.

The vascular tone of the vessel is the contractile state of the smooth muscle and the primary determinant of diameter, and thus of resistance and flow. The effect of vessel diameter on resistance is inverse: Given the same volume of blood, an increased diameter means there is less blood contacting the vessel wall, thus lower friction and lower resistance, subsequently increasing flow.

A decreased diameter means more of the blood contacts the vessel wall, and resistance increases, subsequently decreasing flow. The influence of lumen diameter on resistance is dramatic: A slight increase or decrease in diameter causes a huge decrease or increase in resistance.

## Arterial Blood Pressure

This means, for example, that if an artery or arteriole constricts to one-half of its original radius, the resistance to flow will increase 16 times.

A Mathematical Approach to Factors Affecting Blood Flow Jean Louis Marie Poiseuille was a French physician and physiologist who devised a mathematical equation describing blood flow and its relationship to known parameters. The same equation also applies to engineering studies of the flow of fluids.

Although understanding the math behind the relationships among the factors affecting blood flow is not necessary to understand blood flow, it can help solidify an understanding of their relationships. Please note that even if the equation looks intimidating, breaking it down into its components and following the relationships will make these relationships clearer, even if you are weak in math.

Focus on the three critical variables: It may commonly be represented as 3. One of several things this equation allows us to do is calculate the resistance in the vascular system. Normally this value is extremely difficult to measure, but it can be calculated from this known relationship: The important thing to remember is this: Two of these variables, viscosity and vessel length, will change slowly in the body.

Only one of these factors, the radius, can be changed rapidly by vasoconstriction and vasodilation, thus dramatically impacting resistance and flow. Further, small changes in the radius will greatly affect flow, since it is raised to the fourth power in the equation. The Roles of Vessel Diameter and Total Area in Blood Flow and Blood Pressure Recall that we classified arterioles as resistance vessels, because given their small lumen, they dramatically slow the flow of blood from arteries.

In fact, arterioles are the site of greatest resistance in the entire vascular network. This may seem surprising, given that capillaries have a smaller size. How can this phenomenon be explained? Although the diameter of an individual capillary is significantly smaller than the diameter of an arteriole, there are vastly more capillaries in the body than there are other types of blood vessels. Part c shows that blood pressure drops unevenly as blood travels from arteries to arterioles, capillaries, venules, and veins, and encounters greater resistance.

However, the site of the most precipitous drop, and the site of greatest resistance, is the arterioles. This explains why vasodilation and vasoconstriction of arterioles play more significant roles in regulating blood pressure than do the vasodilation and vasoconstriction of other vessels. Part d shows that the velocity speed of blood flow decreases dramatically as the blood moves from arteries to arterioles to capillaries.

This slow flow rate allows more time for exchange processes to occur. As blood flows through the veins, the rate of velocity increases, as blood is returned to the heart. The relationships among blood vessels that can be compared include a vessel diameter, b total cross-sectional area, c average blood pressure, and d velocity of blood flow. Disorders of the…Cardiovascular System: Arteriosclerosis Compliance allows an artery to expand when blood is pumped through it from the heart, and then to recoil after the surge has passed.

This helps promote blood flow. In arteriosclerosis, compliance is reduced, and pressure and resistance within the vessel increase. This is a leading cause of hypertension and coronary heart disease, as it causes the heart to work harder to generate a pressure great enough to overcome the resistance. Arteriosclerosis begins with injury to the endothelium of an artery, which may be caused by irritation from high blood glucose, infection, tobacco use, excessive blood lipids, and other factors.

Artery walls that are constantly stressed by blood flowing at high pressure are also more likely to be injured—which means that hypertension can promote arteriosclerosis, as well as result from it. Recall that tissue injury causes inflammation. As inflammation spreads into the artery wall, it weakens and scars it, leaving it stiff sclerotic. As a result, compliance is reduced. Moreover, circulating triglycerides and cholesterol can seep between the damaged lining cells and become trapped within the artery wall, where they are frequently joined by leukocytes, calcium, and cellular debris.

Eventually, this buildup, called plaque, can narrow arteries enough to impair blood flow. When this happens, platelets rush to the site to clot the blood.

## Putting it all together: Pressure, flow, and resistance

This clot can further obstruct the artery and—if it occurs in a coronary or cerebral artery—cause a sudden heart attack or stroke. Alternatively, plaque can break off and travel through the bloodstream as an embolus until it blocks a more distant, smaller artery.

Ischemia in turn leads to hypoxia—decreased supply of oxygen to the tissues. Hypoxia involving cardiac muscle or brain tissue can lead to cell death and severe impairment of brain or heart function. A major risk factor for both arteriosclerosis and atherosclerosis is advanced age, as the conditions tend to progress over time. However, obesity, poor nutrition, lack of physical activity, and tobacco use all are major risk factors.

Treatment includes lifestyle changes, such as weight loss, smoking cessation, regular exercise, and adoption of a diet low in sodium and saturated fats. Medications to reduce cholesterol and blood pressure may be prescribed. For blocked coronary arteries, surgery is warranted. In angioplasty, a catheter is inserted into the vessel at the point of narrowing, and a second catheter with a balloon-like tip is inflated to widen the opening.

To prevent subsequent collapse of the vessel, a small mesh tube called a stent is often inserted.