## Systemic Vascular Resistance: Radius, Length, Viscosity

The systemic vascular resistance is the resistance that blood “sees” as it travels throughout the circulatory system of the body.

It is controlled by three different factors: length of the blood vessel (l), radius of the blood vessel (r), and the viscosity of the blood (η). The equation that relates these three factors to resistance is known as Poiseuilles’ equation:

R ≈ (η x l) / r4

Let’s discuss how each of the factors above influences resistance. The longer the vessel, the more likely blood will sludge and stick up against the walls; this tendency intuitively causes an increase in overall resistance. Blood vessel length does not typically change during adulthood, therefore its contribution to vascular resistance in humans is relatively constant.

When blood is more viscous than usual the resistance also increases. For example, molasses flows very slowly because it is highly viscous; blood is no different. There are a few uncommon instances in human physiology where blood viscosity increases; therefore, like vessel length, its contribution to vascular resistance is also relatively constant.

The most important parameter is the radius of the vessel. When the radius of a vessel shrinks, the resistance increases; when the radius of a vessel dilates, the resistance drops. Imagine trying to pump a set amount of fluid through a small opening versus a larger opening. There is much less resistance encountered through the larger opening. The same is true for large and small blood vessels. Even more importantly, as indicated by Poiseuille’s equation above, when the radius of a vessel is halved, the resistance increases by 16 fold! Therefore, even small changes in blood vessel diameter can have dramatic consequences on the bodies’ vascular resistance.

How the Body Controls Resistance

How do you think the body controls resistance most effectively? You guessed it! By controlling the radius of blood vessels. When there is an abnormal drop in vascular resistance, the body compensates by pumping out hormones (ie: epinephrine and norepinephrine); these hormones cause muscle cells surrounding blood vessels to constrict. Constriction leads to a decreased radius of the vessel, which leads to increased resistance.

Clinical Measurements

How do you measure systemic vascular resistance? Well, first off, systemic vascular resistance is not measured, but is calculated from other cardiovascular vital signs such as the mean arterial pressure (MAP), cardiac output (CO), and central venous pressures (CVP). The equation that relates these three values to resistance is:

SVR = [(MAP – CVP) / CO] x 80

Mean arterial pressure is a sort-of average between the systolic and diastolic blood pressure readings. It can be calculated using blood pressures obtained from an arterial catheter or a blood pressure cuff.

Central venous pressures are normally low, and do not contribute much to vascular resistance, but when very accurate measurements are needed they can be obtained from a central venous and/or a pulmonary artery catheter.

Cardiac output can be obtained from a pulmonary artery catheter if accurate values are needed; it can also be roughly estimated from a cardiac echocardiogram (ie: an ultrasound of the heart).

Role in Disease

So what’s the big deal? Why all this talk about vascular resistance? Vascular resistance is important because it is one determinant of blood pressure, and therefore organ perfusion.

The mean arterial pressure is calculated by multiplying the cardiac output by the systemic vascular resistance, and then adding the result to the central venous pressure (MAP = CO x SVR + CVP, a reorganization of the equation above).

Since the mean arterial pressure is the driving force behind the delivery of blood and oxygen to the organs, it is of vital importance that it stays above a certain threshold. Otherwise organs will not receive enough oxygen and will eventually die. One way of ensuring that the mean arterial pressure stays within a set range is for the body to constrict and/or dilate the vessels as needed.

On the flip side, if systemic vascular resistance is too "clamped" down then hypertension occurs. If severe enough, the heart may not be able to generate enough force to eject an adequate amount of blood into the tightened arterial system, which over time could result in systolic heart failure.

Overview

Systemic vascular resistance is the resistance blood sees as it travels throughout the bodies blood vessels. It is influenced by the length and radius of the blood vessel(s), as well as the viscosity of blood. It is calculated from the mean arterial pressure, central venous pressure, and cardiac output. Systemic vascular resistance plays a vital role in maintaining blood pressures within set ranges so that organ perfusion is maximized.

References and Resources

## Cardiac Output: Pump, Pump, Squeeze

The cardiac output (CO) measures how much blood the heart pumps per minute. It is directly related to the stroke volume (SV) and heart rate (HR). The stroke volume is the amount of blood in the left ventricle of the heart just before it contracts. The cardiac output is calculated by multiplying the heart rate by the stroke volume (CO = HR x SV).

The cardiac output is related to Ohm’s law, which in electrical terms states that the change in voltage of a circuit is equal to the flow of current, I, multiplied by the resistance, R, of the circuit (ΔV = I x R).

Like electrical current in a circuit, blood flows in a circular pathway from the left ventricle, through the body, where it eventually ends up in the right ventricle. We can change Ohm’s law to govern hemodynamics by stating that the change in voltage is equivalent to the change in pressure between the aorta and right atrium (mean arterial pressure and central venous pressures, respectively), flow of current is equal to the amount of blood pumped per unit time (ie: cardiac output), and resistance is equal to the resistance the blood sees as it travels through the vessels of the body (aka: the systemic vascular resistance).

Therefore, if we re-write Ohm’s law for the hemodynamics of cardiac output we get: central venous pressure (CVP, measured in mmHg) subtracted from the mean arterial pressure (MAP, measured in mmHg) is equal to cardiac output (CO, measured in liters/minute) multiplied by the systemic vascular resistance (SVR, measured in dynes-s / cm5), or:

(MAP – CVP) = (CO x SVR) / 80
(ΔV = I x R)

Doing a simple mathematical rearrangement of the equation above we get:

CO = [(MAP – CVP) / SVR] x 80
*** The 80 in the equation is a conversion factor to convert Wood to metric units ***.

In essence, the cardiac output is directly proportional to the difference in blood pressure between the left (arterial side) and right (venous side) sides of the body, and inversely proportional to the vascular resistance. In other words, if the pressure difference between the arterial and venous side of the body decreases the cardiac output will fall. Along the same lines, if the systemic vascular resistance increases then cardiac output will decrease.

Clinical Measurements

How do you clinically measure the components that constitute the cardiac output?

The most reliable, but invasive way is to use a pulmonary artery catheter, also known as a "Swan Ganz" catheter. The catheter is inserted into the pulmonary artery and advanced until it “wedges” in a small branch of the pulmonary arterial tree. From there a balloon in the tip of the catheter is inflated to keep it in place. At this location the tip of the catheter is effectively measuring the pressure of blood in the left atrium (ie: the "pulmonary artery wedge pressure"). Using the catheter, and various methods such as the thermodilution technique, the cardiac output and/or stroke volume can be measured directly.

Unfortunately, the use of Swan-Ganz catheters are fraught with serious problems such as arrhythmias and infection. Therefore, other less invasive techniques such as echocardiography with doppler (ie: an ultrasound of the heart) can be used to estimate cardiac output and stroke volume.

The other elements of cardiac output can also be measured clinically. The mean arterial pressure is calculated from the systolic and diastolic blood pressures, which are measured from a cuff or arterial catheter. Central venous pressure can be measured with a central venous catheter (ie: a "central line").

Role in Disease

A normal cardiac output is roughly 5.5 L/min for an average sized male and 5.0 L/min for an average sized female. However, in individuals with diseased heart muscle the pumping ability of the heart is reduced. The result is a decrease in cardiac output.

So what’s the big deal? A fall in cardiac output means that the body sees less oxygenated blood per minute. Every organ in the body requires oxygen to function properly. If cardiac output is decreased the organs may not receive enough oxygen to do their job. In super severe cases, when cardiac output approaches zero, cardiogenic shock occurs. If no oxygen reaches the organs multi-organ failure occurs and the patient may die.

Overview

Cardiac output is related to the stroke volume, heart rate, systemic vascular resistance, and difference in pressure between the arterial and venous sides of the body. When cardiac output drops the bodies’ organs receive less oxygen per unit time. In severe cases this may lead to organ death.

Related Articles

References and Resources

## A Simple Approach to Hemodynamic Instability

What is “hemodynamic instability”? Hemodynamics is the study of blood movement; when this movement is compromised in some way you get hemodynamic instability. If left untreated it can cause multi-organ failure and death.

You can think of hemodynamic instability as the collapse of the cardiovascular system. This collapse causes a significant drop in blood pressure.

There are many causes of hemodynamic instability and fortunately you don’t need to know all of them to manage a patient who is acutely experiencing cardiovascular collapse. A few basic tenets of physiology, when examined in the right order, will help you manage a patient who is unstable.

The tenets are as follows: preload (volume status), afterload (systemic vascular resistance), heart rate, heart rhythm, and contractility.

The first component of cardiovascular physiology that should be assessed in a hemodynamically unstable patient is preload and intravascular volume. Intravascular volume measures how much blood is present in the circulatory system. If a patient is volume deplete (ie: has a decreased intravascular volume) then hemodynamic instability can occur. An easy way to visualize this is to imagine someone bleeding. If the bleeding is not stopped, the cardiovascular system will eventually collapse. In the hospital this is often referred to as a patient being "dry".

Preload is one way to estimate a patient’s intravascular volume. Measuring preload is easy if you have a central venous catheter, and even easier if you have a Swan Ganz catheter, although these are used less frequently nowadays. These types of catheters can measure central venous and pulmonary artery pressures, which provide a good estimate of intravascular volume status.

If a patient does not have a central line you have to rely on clinical clues. One way to assess intravascular volume is to measure urine production. If urine output is less than normal, then the patient is trying to “hold on” to fluid, and therefore may be volume deplete. Urine that is dark amber in color is another clue. Decreased skin turgor is another clinically useful sign. Examining a patient’s neck veins (ie: jugular venous pulsations) can also be useful under certain circumstances.

In essence, if a patient’s preload, and therefore intravascular volume status is decreased it can be quickly corrected by giving the patient intravenous fluids. The type of fluid given is dictated by the clinical situation, but the most commonly used fluids for hemodynamic resuscitation are normal saline, lactated Ringer’s solution, and good old fashioned blood (especially when blood loss is responsible for the decreased volume!).

That’s great! But what do we do if we assess the patient’s volume status and come to the conclusion that it is sufficient, and the patient is STILL hemodynamically unstable? Not to fear… Let’s move on to the next tenet – systemic vascular resistance.

Systemic Vascular Resistance (SVR) and Afterload

The systemic vascular resistance is the resistance that blood sees as it travels through the arterial system. The vascular resistance varies depending on the etiology and time frame of the hemodynamic instability.

For example, patients in the initial stages of hypovolemic shock (ie: acute blood loss) the SVR will be elevated as the arteries constrict to maintain blood pressure; however, once the blood volume reaches critically low levels even constriction of the arteries is not enough to maintain the SVR. At this point the blood pressure will drop precipitously.

In contrast, patients in septic shock have a decreased systemic vascular resistance as the blood vessels dilate pathologically in response to infection. The result is the same as the above example: the blood pressure drops.

So how do we treat a decrease in systemic vascular resistance? Assuming intravascular volume (ie: preload) is adequate we sometimes need to "help" the patient constrict their blood vessels so they can maintain an adequate blood pressure. We do this using medications known as "pressors". The most commonly used pressors are norepinephrine (Levophed®), phenylephrine (Neosynephrine®), vasopressin, and dopamine.

Pressors should only be used once a patient has been treated with volume resuscitation. In other words, it does not make sense to help someone constrict their blood vessels when they have no intravascular volume to constrict around! This is why SVR is the 2nd (and not the 1st) tenet of managing someone with hemodynamic instability.

Heart Rate

Once intravascular volume status and vascular resistance have been dealt with, the next step is to monitor the heart rate. Patients who are excessively tachycardic (ie: high heart rate) or bradycardic (ie: low heart rate) can also be hemodynamically unstable. Let’s explain…

During tachycardia the left ventricle does not have as much time to fill with blood. Therefore, each beat of the heart ejects less blood than normal. If the tachycardia is severe enough this can cause hemodynamic instability and decreased blood flow. Likewise, in patients who are excessively bradycardic the amount of blood ejected over a specific unit of time (aka: cardiac output) may not be enough to sustain the bodies need for blood.

Patients who are excessively tachycardic can be treated with beta blockers assuming there is no other cause readily identified. It is also important to remember that tachycardia may be a sign of decreased intravascular volume! Therefore, the patient’s excessive heart rate may correct when the preload is corrected (again, always start at tenet number 1!).

Bradycardia can be treated with atropine. Atropine is a molecule that stimulates heart rate by blocking the actions of acetylcholine. It is also important to note that bradycardia is sometimes a "physiologic" response to the administration of pressors. For example, phenylephrine often causes a "reflex" bradycardia.

Heart Rhythm

Just like abnormal heart rates, abnormal heart rhythms can also cause hemodynamic instability. The most commonly encountered abnormal rhythms in hemodynamically unstable patients are atrial fibrillation, atrial flutter, heart block, ventricular fibrillation, and ventricular tachycardia.

Abnormal heart rhythms contribute to hemodynamic instability by decreasing the filling capacity of the heart. For example a patient in rapid atrial fibrillation will not have enough time between heart beats to load their left ventricle with blood.

The treatment of the various cardiac arrhythmias depends on the type of rhythm. It is important to note that abnormal rhythms may not have a significant impact on hemodynamic instability, and may need no additional treatment. This is most commonly encountered in people who are in atrial fibrillation, but their rate is well controlled.

Contractility

You’ve fixed intravascular volume, corrected the systemic vascular resistance, examined the heart rate and rhythm and you still can not stabilize the patient. Under these circumstances you have to think about the heart itself. It may not be ejecting blood efficiently or effectively enough to ensure cardiovascular stability.

Under these circumstances you need to order an echocardiogram to assess the heart’s function. If the heart is not holding its own it may need a little help. Medications such as epinephrine, dopamine, dobutamine, milrinone, and digoxin can help give the heart a little extra “squeezing power” to improve cardiac output.

Overview

The management of hemodynamic instability always begins with an assessment of intravascular volume (preload). If repleting intravascular volume does not fix the problem then the next step is to look at systemic vascular resistance. Does the patient need a little help constricting those blood vessels? If not, than you have to move quickly to assessing heart rate and rhythm. Finally, when all else fails, we have to assess the contractility of the heart. Maybe it isn’t pumping as hard or as efficient as it should be.

Correcting hemodynamic instability in the above order is both a quick and efficient framework for thinking about the unstable patient. Often times the physician will drop quickly down the list as they recognize a problem immediately (ie: rapid atrial fibrillation) and this is ok!!! The important thing is to have a framework for thinking about cardiovascular instability.

References and Resources

• Stiell IG, Macle L. Canadian Cardiovascular Society atrial fibrillation guidelines 2010: management of recent-onset atrial fibrillation and flutter in the emergency department. CCS Atrial Fibrillation Guidelines Committee. Can J Cardiol. 2011 Jan-Feb;27(1):38-46.
• Bozza FA, Carnevale R, Japiassú AM, et al. Early fluid resuscitation in sepsis: evidence and perspectives. Shock. 2010 Sep;34 Suppl 1:40-3. Review.
• Price S, Uddin S, Quinn T. Echocardiography in cardiac arrest. Curr Opin Crit Care. 2010 Jun;16(3):211-5.
• Naeem N, Montenegro H. Beyond the intensive care unit: a review of interventions aimed at anticipating and preventing in-hospital cardiopulmonary arrest. Resuscitation. 2005 Oct;67(1):13-23.
• Sevransky J. Clinical assessment of hemodynamically unstable patients. Curr Opin Crit Care. 2009 Jun;15(3):234-8.