# Resistance to blood flow

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A 50-year-old man presents for evaluation of right calf swelling. An ultrasound is performed and the patient is found to have a blood clot occluding half the luminal diameter of the right popliteal vein. At baseline, the patient’s right popliteal vein has a resistance of R. The pressure gradient across the vessel is P and the rate of blood flow is Q. Assuming the pressure gradient is unchanged, which of the following best characterizes the new vascular resistance and flow rate?

### External References

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#### Pulmonary vascular resistance (PVR) p. 684, 734

chest wall and p. 687

### Transcript

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#### Contributors

Blood flow refers to the volume of blood travelling through a blood vessel, an organ, or the entire body over a period of time, and it can be measured as liters per minute. As blood flows, it encounters various factors that resist flow and movement of blood, known as the vascular resistance.

The first factor to contribute to vascular resistance is blood viscosity, where you can think of viscosity as the fluid’s thickness, or how sticky it is. The relationship is directly proportional, which can be represented as resistance ∝ η which is the greek letter eta and represents viscosity. So this means that as viscosity goes up, the harder it is for the liquid’s molecules to slide past each other, and the resistance goes up. Think about a heaping stack o’ pancakes, then picture some maple syrup. Even on flipping the syrup upside down it doesn’t really come out right away and resists moving right away; slowly it gloops out and doesn’t splash but just coats those pancakes in a delicious film of sugary goodness, oh right. Now, with another stack, grab some orange juice and pour...it immediately comes out and pretty goes everywhere. This is because the juice is less viscous than the syrup, so there’s going to be less resistance to movement. Because blood is full of large proteins and cells, it’s pretty viscous and moves much more slowly than just plain water, or orange juice. Blood viscosity doesn’t change much over time, but certain conditions like polycythemia, where the person has too many red blood cells, can increase viscosity, and conditions like anemia, where the person doesn’t have enough red blood cells, can decrease viscosity.

A second factor that affects resistance is total blood vessel length. Just like with viscosity, the relationship is directly proportional, and this can be represented as resistance ∝ L, so, simply put, shorter vessels have less resistance and longer vessels have more resistance because there’s more friction resisting flow. This means that as a child grows into an adult, their blood vessels will get longer, and their peripheral resistance will go up.

A third factor that affects resistance is blood vessel radius, which in this case is inversely proportional to resistance...to the fourth power! Meaning that that as a vessel’s radius goes down, its resistance really goes up. Unlike viscosity and length, the radius can change from minute to minute, especially the radius of arterioles, which can vasoconstrict like when you’re lying at home on the couch, which would decrease diameter and increase resistance, or vasodilate like when you’re running outside playing frisbee, which would increase diameter and decrease resistance.

Now, the equation relating all these variables is resistance R is equal to 8 times viscosity eta times length L divided by pi times radius r to the fourth power.

### Summary

Resistance to blood flow refers to the opposition that the circulatory system presents to the flow of blood. It plays a critical role in regulating blood pressure and blood flow to different organs and tissues. This resistance is directly proportional to blood viscosity (η) and the blood vessel's length (L); and inversely proportional to the radius of the vessel (r). This resistance (R) is represented as R=8Lr4

### Sources

1. "Medical Physiology" Elsevier (2016)
2. "Physiology" Elsevier (2017)
3. "Principles of Anatomy and Physiology" Wiley (2014)
4. "Rheology" Biology and Mechanics of Blood Flows, Part II: Mechanics and Medical Aspects. Springer. pp. 119–123 (2007)
5. "Human Anatomy & Physiology" Pearson (2018)

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