# Cardiac output

Cardiac output (Q or $\dot Q_{c}$ or CO ) is the volume of blood being pumped by the heart, in particular by a left or right ventricle in the time interval of one minute. CO may be measured in many ways, for example dm3/min (1 dm3 equals 1000 cm3 or 1 litre). Q is furthermore the combined sum of output from the right ventricle and the output from the left ventricle during the phase of systole of the heart. An average resting cardiac output would be 5.6 L/min for a human male and 4.9 L/min for a female.[1]

Q = Stroke Volume × Heart rate

## Clinical uses

The function of the heart is to transport blood to deliver oxygen, nutrients and chemicals to the cells of the body to ensure their survival and proper function and to remove the cellular wastes. Since the heart is a 'demand pump', that pumps out whatever blood comes back into it from the venous system, it is effectively the amount of blood returning to the heart that determines how much blood the heart pumps out (Q). This, in turn, is controlled principally by the demand for oxygen by the cells of the body and the capacitance of the arterio-venous system. If the body has a high metabolic oxygen demand then the metabolically-controlled flow through the tissues is increased, leading to a greater flow of blood back to the heart. This is also modified by the function of the vessels of the body as they actively relax and contract thereby increasing and decreasing the resistance to flow.

When Q increases in a healthy but untrained individual, most of the increase can be attributed to an increase in heart rate (HR). Change of posture, increased sympathetic nervous system activity, and decreased parasympathetic nervous system activity can also increase cardiac output. HR can vary by a factor of approximately 3, between 60 and 180 beats per minute, while stroke volume (SV) can vary between 70 and 120 ml, a factor of only 1.7.[2][3][4]

A parameter related to SV is Ejection Fraction (EF). EF is the fraction of blood ejected by the Left Ventricle (LV) during the contraction or ejection phase of the cardiac cycle or Systole. Prior to the start of Systole, the LV is filled with blood to the capacity known as End Diastolic Volume (EDV) during the filling phase or diastole. During Systole, the LV contracts and ejects blood until it reaches its minimum capacity known as End Systolic Volume (ESV), it does not empty completely. Clearly the EF is dependent on the ventricular EDV which may vary with ventricular disease associated with ventricular dilatation. Even with LV dilatation and impaired contraction the Q may remain constant due to an increase in EDV.

Stroke Volume (SV) = EDV – ESV
Ejection Fraction (EF) = (SV / EDV) × 100%
Cardiac Output (Q) = SV × HR
Cardiac Index (CI) = Q / Body Surface Area (BSA) = SV × HR/BSA
HR is Heart Rate, expressed as BPM (Beats Per Minute)
BSA is Body Surface Area in square metres.

Diseases of the cardiovascular system are often associated with changes in Q, particularly the pandemic diseases of hypertension and heart failure. Cardiovascular disease can be associated with increased Q as occurs during infection and sepsis, or decreased Q, as in cardiomyopathy and heart failure. The ability to accurately measure Q is important in clinical medicine as it provides for improved diagnosis of abnormalities, and can be used to guide appropriate management. Q measurement, if it were accurate and non-invasive, would be adopted as part of every clinical examination from general observations to the intensive care ward, and would be as common as simple blood pressure measurements are now. Such practice, if it were adopted, may revolutionise the treatment of many cardiovascular diseases including hypertension and heart failure. This is the reason why Q measurement is now an important research and clinical focus in cardiovascular medicine.

## Measuring cardiac output

Circulation is a critical and variable function of human physiology and disease. An accurate and non-invasive measurement of Q is the holy grail of cardiovascular assessment. This would allow continuous monitoring of central circulation and provide improved insights into normal physiology, pathophysiology and treatments for disease. Invasive methods are well accepted, but there is increasing evidence that these methods are neither accurate nor effective in guiding therapy, so there is an increasing focus on development of non-invasive methods.[5][6][7]

There are a number of clinical methods for measurement of Q ranging from direct intracardiac catheterisation to non-invasive measurement of the arterial pulse. Each method has unique strengths and weaknesses and relative comparison is limited by the absence of a widely accepted “gold standard” measurement. Q can also be affected significantly by the phase of respiration; intra-thoracic pressure changes influence diastolic filling and therefore Q. This is especially important during mechanical ventilation where Q can vary by up to 50% across a single respiratory cycle. Q should therefore be measured at evenly spaced points over a single cycle or averaged over several cycles.

### The Fick Principle

The Fick principle was first described by Adolf Eugen Fick in 1870 and assumes that the rate at which oxygen is consumed is a function of the rate of blood flows and the rate of oxygen picked up by the red blood cells. The Fick principle involves calculating the oxygen consumed over a given period of time from measurement of the oxygen concentration of the venous blood and the arterial blood. Q can be calculated from these measurements:

• VO2 consumption per minute using a spirometer (with the subject re-breathing air) and a CO2 absorber
• the oxygen content of blood taken from the pulmonary artery (representing mixed venous blood)
• the oxygen content of blood from a cannula in a peripheral artery (representing arterial blood)

From these values, we know that:

VO2 = (Q×CA) - (Q×CV)

where

• CA = Oxygen content of arterial blood
• CV = Oxygen content of venous blood.

This allows us to say

Q = (VO2/(CA – CV))*100

and therefore calculate Q. Note that (CA – CV) is also known as the arteriovenous oxygen difference.[8]

While considered to be the most accurate method for Q measurement, Fick is invasive, requires time for the sample analysis, and accurate oxygen consumption samples are difficult to acquire. There have also been modifications to the Fick method where respiratory oxygen content is measured as part of a closed system and the consumed Oxygen calculated using an assumed oxygen consumption index which is then used to calculate Q. Other modifications use inert gas as tracers and measure the change in inspired and expired gas concentrations to calculate Q (Innacor, Innovision A/S, Denmark).

Additionally, the calculation of the arterial and venous oxygen content of the blood is a straightforward process. Almost all oxygen in the blood is bound to hemoglobin molecules in the red blood cells. Measuring the content of hemoglobin in the blood and the percentage of saturation of hemoglobin (the oxygen saturation of the blood) is a simple process and is readily available to physicians. Using the fact that each gram of hemoglobin can carry 1.34 ml of O2, the oxygen content of the blood (either arterial or venous) can be estimated by the following formula:

$Oxygen\ content\ of\ blood = \left [hemoglobin \right] \left ( g/dl \right ) \ \times\ 1.34 \left ( ml\ \mathrm{O}_2 /g\ of\ hemoglobin \right ) \times\ saturation\ of\ blood\ \left ( percent \right )\ +\ 0.0032\times\ partial\ pressure\ of\ oxygen \left ( torr \right )$

### Finapres Methodology

In 1967 the Czech physiologist Jan Peñáz invented and patented the volume clamp method to measure continuous blood pressure. The principle of the volume clamp method is to provide equal pressures dynamically on either side of the wall of an artery: inside pressure (= intra-arterial pressure) equals outside pressure (= finger cuff pressure) by clamping the artery to a certain volume. He decided that the finger was the optimal site to apply this volume clamp method.

In 1978 scientists at BMI-TNO, the research unit of Netherlands Organization for Applied Scientific Research at The University of Amsterdam, invented and patented a series of additional key elements to make the volume clamp work in clinical practice, among them: the use of modulated infra-red light in the optical system inside the sensor, the light-weight, easy to wrap finger cuff with Velcro fixation, a new pneumatic proportional control valve principle and last but not least the invention of a setpoint strategy for the determination and tracking of the correct volume at which to clamp the finger arteries – the Physiocal system. An acronym for PHYSIOlogical CALibration of the finger arteries, this Physiocal tracker turned out to be surprisingly accurate, robust and reliable and was never changed since its invention.

The Finapres methodology was developed to use this information to accurately calculate arterial pressure from the finger cuff pressure data. A generalized algorithm to correct for the pressure level difference between the finger and brachial sites within an individual patient was developed and this correction worked under all circumstances that it was tested, even when it was not designed for it, since it applied general physiological principles. The first implementation of this innovative brachial pressure waveform reconstruction was in the Finometer, the successor of Finapres that BMI-TNO introduced in the market in 2000.

The availability of a continuous, high-fidelity, calibrated blood pressure waveform opened up the perspective of beat-to-beat computation of integrated hemodynamics, based on two notions:

1. That pressure and flow are inter-related at each site in the arterial system by their so-called characteristic impedance and
2. That at the proximal aortic site, the 3-element Windkessel model of this impedance can be modeled with sufficient accuracy in an individual patient when age, gender, height and weight are known.

### Dilution methods

The output of heart is equal to the amount of indicator injected divided by its average concentration in the arterial blood after a single circulation through the heart.

This method was initially described using an indicator dye and assumes that the rate at which the indicator is diluted reflects the Q. The method measures the concentration of a dye at different points in the circulation, usually from an intravenous injection and then at a downstream sampling site, usually in a systemic artery. More specifically, the Q is equal to the quantity of indicator dye injected divided by the area under the dilution curve measured downstream (the Stewart (1897)-Hamilton (1932) equation):

$Cardiac\ output = \frac{Quantity\ of\ Indicator}{\int_0^\infty Concentration\ of\ Indicator\cdot {dt}}$

The trapezoid rule is often used as an approximation of this integral.

### Ultrasound Dilution method

Ultrasound dilution (UD) uses body temperature normal saline (NS) as an indicator introduced into an extracorporeal loop to create an AV circulation, with an ultrasound sensor used to measure the dilution and then calculate cardiac output using a proprietary algorithm. A number of other hemodynamic variables can also be calculated such as total end-diastole volume (TEDV), central blood volume (CBV) and active circulation volume (ACVI). The UD method was firstly introduced in 1995.,[9] and it was used extensively to measure flow and volumes with extracorporeal circuits condition such as ECMO[10][11] and Hemodialysis,[12][13] leading more than 150 peer reviewed publications, and now it has adapted to Intensive Care Units (ICU) settings as COstatus (Transonic System Inc. Ithaca, NY). The UD method is based on ultrasound indicator dilution.[14] Blood ultrasound velocity (1560–1585 m/s) is a function of total blood protein concentration (sums of proteins in plasma and in red blood red cells), temperature etc. Injection of body temperature normal saline (ultrasound velocity of saline is 1533m/sec) into a unique AV loop decreases blood ultrasound velocity, and produce dilution curves. UD requires establishment of an extracorporeal circulation through its unique AV loop with two preexisting arterial and central venous lines in ICU patients. When the saline indicator is injected into the A-V loop, it is detected by the venous clamp-on sensor on the AV loop before it enters the patient’s right heart atrium. After the indicator traverses the heart and lung, the concentration curve in the arterial line is recorded and displayed on the COstatus HCM101 Monitor. Cardiac output is calculated from the area of the concentration curve by the classic Stewart-Hamilton equation. It is a non-invasive procedure only by connection the AV loop and two lines of a patient. UD has been specialised for application in pediatric ICU patients, and has been demonstrated to be a relatively safe, although invasive, and reproducible tool.

### Pulmonary Artery Thermodilution (Trans-right-heart Thermodilution)

The indicator method was further developed with replacement of the indicator dye by heated or cooled fluid and temperature change measured at different sites in the circulation rather than dye concentration; this method is known as thermodilution. The pulmonary artery catheter (PAC), also known as the Swan-Ganz catheter, was introduced to clinical practice in 1970 and provides direct access to the right heart for thermodilution measurements.

The PAC is balloon tipped and is inflated, which helps "sail" the catheter balloon through the right ventricle to occlude a smaller branch of the pulmonary artery system. The balloon is deflated. The PAC thermodilution method involves injection of a small amount (10ml) of cold glucose at a known temperature into the pulmonary artery and measuring the temperature a known distance away (6–10 cm) using the same catheter.

The Q can be calculated from the measured temperature curve (The “thermodilution curve”). Low Q will change the temperature slowly, and High Q will change the temperature rapidly. The degree of change in temperature is directly proportional to the cardiac output. Usually three or four repeated measures are averaged to improve accuracy. However it is complex to perform and there are many sources of inaccuracy in the method.[15][16] Modern catheters are fitted with a heating filament which intermittently heats and measures the thermodilution curve providing serial Q measurement. However, these take an average of measurements made over 2–9 minutes, depending on the stability of the circulation, and thus do not provide continuous monitoring.

PAC use is complicated by arrhythmias, infection, pulmonary artery rupture, and right heart valve damage. Recent studies in patients with critical illness, sepsis, acute respiratory failure and heart failure suggest use of the PAC does not improve patient outcomes.[5][6][7] PAC use is in decline as clinicians move to less invasive technologies for monitoring hemodynamics.

### Doppler ultrasound method

This method uses ultrasound and the Doppler effect to measure Q. The blood velocity through the heart causes a 'Doppler shift' in the frequency of the returning ultrasound waves. This Doppler shift can then be used to calculate flow velocity and volume and effectively Q using the following equations:

• Q = SV × HR
• SV = vti × CSA

where:

• CSA = valve orifice cross sectional area; use pr²
• vti = the velocity time integral of the trace of the Doppler flow profile

Doppler ultrasound is non-invasive, accurate and inexpensive and is a routine part of clinical ultrasound with high levels of reliability and reproducibility having been in clinical use since the 1960s.

#### Echocardiography

Echocardiography uses a conventional ultrasound machine and a combined two dimensional (2D) and Doppler approach to measure Q. 2D measurement of the diameter (d) of the aortic annulus allows calculation of the flow CSA (cross-sectional area) which is then multiplied by the vti of the Doppler flow profile across the aortic valve to determine the flow volume or SV. Multiplying SV by HR produces Q. Echocardiographic measurement of flow volume is clinically well established and of proven accuracy but requires training and skill, and may be time consuming to perform effectively. The 2D measurement of the aortic valve diameter is challenging and associated with significant error, while measurement of the pulmonary valve to calculate right sided Q is even more difficult.

#### Transcutaneous Doppler: USCOM

An Ultrasonic Cardiac Output Monitor (USCOM) (Uscom Ltd, Sydney, Australia) uses Continuous Wave Doppler (CW) to measure the Doppler flow profile vti, as in echocardiography, but uses anthropometry to calculate aortic and pulmonary valve diameters so both the right and left sided Q can be measured. Real time Automatic tracing of the Doppler flow profile allows for beat to beat right and left sided Q measurement. This single method has been used in neonates, children and adults for low and high Q measurement.

#### Transoesophageal Doppler: TOD

Transoesophageal Doppler (TOD), also known as esophageal Doppler monitor (EDM), supports a CW sensor on the end of a probe which can be introduced via the mouth or nose and positioned in the oesophagus so the Doppler beam aligns with the descending thoracic aorta (DTA) at a known angle. Because the transducer is close to the blood flow the signal is clear, however correct alignment may be difficult to maintain, especially during patient movement. This method has good validation, particularly for measuring changes in blood flow. As it only measures DTA flow and not true Q, it may be potentially influenced by disproportionate changes in blood flow between upper and lower body though this does not appear to be problematic in most clinical situations. This method generally requires patient sedation and is accepted for use in both adults and children.

### Pulse Pressure Methods

Pulse Pressure (PP) methods measure the pressure in an artery over time to derive a waveform and use this information to calculate cardiac performance. The problem is that any measure from the artery includes the changes in pressure associated with changes in arterial function (compliance, impedance, etc..).

Physiologic or therapeutic changes in vessel diameter are assumed to reflect changes in Q. Put simply, PP methods measure the combined performance of the heart and the vessels thus limiting the application of PP methods for measurement of Q. This can be partially compensated for by intermittent calibration of the waveform to another Q measurement method and then monitoring the PP waveform. Ideally, the PP waveform should be calibrated on a beat to beat basis.

There are invasive and non-invasive methods of measuring PP:

#### Non-invasive PP – Sphygmomanometry and Tonometry

The sphygmomanometer or cuff blood pressure device was introduced to clinical practice in 1903 allowing non-invasive measurements of blood pressure and providing the common PP waveform values of peak systolic and diastolic pressure which can be used to calculate mean arterial pressure (MAP). The pressure in the arteries, measured by sphygmomanometry, is often used as a guide to the function of the heart. Put simply, the pressure in the heart is conducted to the arteries, so the arterial pressure approximately reflects the function of the heart or the Q.

• The pressure in the heart rises as blood is forced into the aorta
• The more stretched the aorta, the greater the pulse pressure (PP)
• In healthy young subjects, each additional 2 ml of blood results in a 1 mmHg rise in pressure
• Therefore:
SV = 2 ml × Pulse Pressure
Q = 2 ml × Pulse Pressure × HR

By resting a more sophisticated pressure sensing device, a tonometer, against the skin surface and sensing the pulsatile artery, continuous PP wave forms can be acquired non-invasively and analysis made of these pressure signals. Unfortunately the heart and vessels can function independently and sometimes paradoxically so that changes in the PP may both reflect and mask changes in Q. So these measures represent combined cardiac and vascular function only. Another similar system that uses the arterial pulse is the pressure recording analytical method (PRAM).

#### Invasive PP

Invasive PP involves inserting a manometer (pressure sensor) into an artery, usually the radial or femoral artery and continuously measuring the PP waveform. This is usually done by connecting the catheter to a signal processing and display device. The PP waveform can then be analysed to provide measurements of cardiovascular performance. Changes in vascular function, the position of the catheter tip, or damping of the pressure waveform signal will all affect the accuracy of the readings. Invasive PP measurements can be calibrated or uncalibrated.

##### Calibrated PP – PiCCO, LiDCO

PiCCO (PULSION Medical Systems AG, Munich, Germany) and PulseCO (LiDCO Ltd, London, England) generate continuous Q by analysis of the arterial PP waveform. In both cases, an independent technique is required to provide calibration of the continuous Q analysis, as arterial PP analysis cannot account for unmeasured variables such as the changing compliance of the vascular bed. Recalibration is recommended after changes in patient position, therapy or condition.

In the case of PiCCO, transpulmonary thermodilution is used as the calibrating technique. Transpulmonary thermodilution uses the Stewart-Hamilton principle, but measures temperatures changes from central venous line to a central arterial line (i.e. femoral or axillary) arterial line. The Q derived from this cold-saline thermodilution is used to calibrate the arterial PP contour, which can then provide continuous Q monitoring. The PiCCO algorithm is dependent on blood pressure waveform morphology (i.e. mathematical analysis of the PP waveform) and calculates continuous Q as described by Wesseling and co-workers.[17] Transpulmonary thermodilution spans right heart, pulmonary circulation and left heart; this allows further mathematical analysis of the thermodilution curve, giving measurements of cardiac filling volumes (GEDV), intrathoracic blood volume, and extravascular lung water. While transpulmonary thermodilution allows for less invasive Q calibration, the method is also less accurate than PA thermodilution and still requires a central venous and arterial line with the attendant infection risks.

In the case of LiDCO, the independent calibration technique is lithium dilution, again using the Stewart-Hamilton principle. Lithium dilution uses a peripheral vein to a peripheral arterial line; however, it does not provide information on cardiac filling volumes and extravascular lung water. Calibration measurements cannot be performed too frequently, and can be subject to error in the presence of certain muscle relaxants. The PulseCO algorithm used by LiDCO is based on pulse power derivation and is not dependent on waveform morphology.

##### Self Calibrating PP — FloTrac/Vigileo

FloTrac/Vigileo (Edwards Lifesciences LLC, U.S.A.) is a pulse contour analysis-based hemodynamic monitoring tool that measures cardiac output (Q) utilizing a standard arterial catheter. The device consists of a special high fidelity pressure trandsducer which, when used with a supporting monitor (Vigileo or EV1000 monitor), derives left-sided cardiac output (Q) from a sample of arterial pulsations. The device works by utilizing an algorithm that is based on the physiological principle that pulse pressure (PP) is proportional to stroke volume (SV).[18] The algorithm calculates the product of the standard deviation of the arterial pressure wave (AP) (over a sampled period of time of 20 seconds) and a vascular tone factor (Khi) to generate stroke volume. The equation in simplified form is as follows: SV=std(AP) * Khi. Khi which accounts for the effects of arterial resistance, and compliance is a multivariate polynomial equation that continuously quantifies arterial compliance and vascular resistance. Khi does so by analyzing the morphologic change of the arterial pressure waveforms on a bit by bit basis (based on the principle that changes in compliance or resistance affect the shape of the arterial pressure waveform). By analyzing the shape of the arterial pressure waveform, we can indirectly assess the effect of vascular tone allowing calculation of SV. Cardiac Output (Q) is then derived utilizing the equation Q=heart rate(HR)*SV. With this system only perfused beats that generate an arterial waveform are counted for HR.

Advantages of this system include its ability to measure Cardiac Output using an existing arterial catheter, and its automatic calibration features. Enhanced patient safety when obtaining CO data compared to traditional pulmonary artery catheterization along with minimal time required for set up and data acquisition are additional benefits of this technology. Disadvantages include its inability to provide data regarding right-sided heart pressures, or mixed venous oxygen saturation.[19][20] Intrinsic to this technology is the measurement of Stroke Volume Variation (SVV) which predicts volume responsiveness and is used for managing fluid optimization in high risk surgical or critically ill patients. A Physiologic Optimization Program based on hemodynamic principles that incorporates the data pairs SV and SVV has been published.[21]

##### Uncalibrated, pre-estimed demographic data-free — PRAM

Pressure Recording Analytical Method (PRAM), exclusively available in MostCare device (Vytech, Padova, Italy) estimates Q just from the analysis of the pressure wave profile, mininvasively obtained from an arterial catheter (choice of radial or femoral access); thanks to Physic Perturbation theory application to the physiology issue, all the elements determining Q can be simultaneously and beat-to-beat taken in consideration. Uniquely sampled at 1000 Hz, the detected pressure curve is so precise to be effectively submitted to an equally sophisticated analysis; the result is the calculation of the real (relative to the patient under examination) and actual (beat-to-beat) Stroke Volume; no constant value of impedance, deriving from an external calibration neither form pre-estimated in vivo/in vitro data are needed.
PRAM has been validated against the considered gold standard methods in stable condition[22] and in various hemodynamic states;[23] it can be used to monitor pediatric[24] and mechanically supported[25] patients.
A part to generally monitored hemodynamic values and to fluid responsiveness parameters, an exclusive reference is also provided by PRAM: Cardiac Cycle Efficiency (CCE). Expressed by a pure number ranging from 1 (the best) and -1 (the worse) it indicates the overall heart-vascular response coupling; the ratio between the heart performed and consumed energy, represented as CCE “stress index”, can be of paramount importance in understanding patient present and next future course.[26]

### Impedance cardiography

Impedance cardiography (often related as ICG or TEB) is a method that measures changes in impedance across the thoracic region over the cardiac cycle. Lower impedance indicates greater the intrathoracic fluid volume and blood flow. Therefore, by synchronizing fluid volume changes with heartbeat, the change in impedance can be used to calculate stroke volume, cardiac output, and systemic vascular resistance.[27]

Both invasive and non-invasive approaches are being used.[28] The noninvasive approach has achieved some acceptance with respect to its reliability and validity.[29][30][31][32] although there is not complete agreement on this point.[33] The clinical use of this approach in a variety of diseases continues.[34]

Noninvasive ICG equipment includes the Bio-Z Dx[35][verification needed] (Sonosite Inc, Bothell, WA) and the niccomo[36][verification needed] (medis GmbH, Ilmenau, Germany).

### Electrical Cardiometry

Electrical Cardiometry is a non-invasive method similar to Impedance cardiography, in the fact that both methods measure thoracic electrical bioimpedance (TEB). The underlying model is what differs, being that Electrical Cardiometry attributes the steep increase of TEB beat to beat to the change in orientation of red blood cells. Four standard ECG electrodes are required for measurement of cardiac output. Electrical Cardiometry is a method trademarked by Cardiotronic, Inc., and shows promising results in a wide range or patients (is currently US market approved for use in adults, pediatrics, and neonates). Electrical Cardiometry monitors have shown promise in postoperative cardiac surgical patients (both hemodynamicially stable and unstable).[37]

### Magnetic Resonance Imaging

Velocity encoded phase contrast Magnetic Resonance Imaging (MRI)[38] is the most accurate technique for measuring flow in large vessels in mammals. MRI flow measurements have been shown to be highly accurate compared to measurements with a beaker and timer[39] and less variable than both the Fick principle[40] and thermodilution.[41]

Velocity encoded MRI is based on detection of changes in the phase of proton precession. These changes are proportional to the velocity of the movement of those protons through a magnetic field with a known gradient. When using velocity encoded MRI, the result of the MRI scan is two sets of images for each time point in the cardiac cycle. One is an anatomical image and the other is an image where the signal intensity in each pixel is directly proportional to the through-plane velocity. The average velocity in a vessel, i.e. the aorta or the pulmonary artery, is hence quantified by measuring the average signal intensity of the pixels in the cross section of the vessel, and then multiplying by a known constant. The flow is calculated by multiplying the mean velocity by the cross-sectional area of the vessel. This flow data can be used to graph flow versus time. The area under the flow versus time curve for one cardiac cycle is the stroke volume. The length of the cardiac cycle is known and determines heart rate, and thereby Q can be calculated as the product of stroke volume and heart rate. MRI is typically used to quantify the flow over one cardiac cycle as the average of several heart beats, but it is also possible to quantify the stroke volume in real time on a beat-for-beat basis.[42]

While MRI is an important research tool for accurately measuring Q, it is currently not clinically used for hemodynamic monitoring in the emergency or intensive care setting. Cardiac output measurement by MRI is currently routinely used as a part of clinical cardiac MRI examinations.[43]

## Cardiac Output and Vascular Resistance

The vascular beds are a dynamic and connected part of the circulatory system against which the heart must pump to transport the blood. Q is influenced by the resistance of the vascular bed against which the heart is pumping. For the right heart this is the pulmonary vascular bed, creating Pulmonary Vascular Resistance (PVR), while for the systemic circulation this is the systemic vascular bed, creating Systemic Vascular Resistance (SVR). The vessels actively change diameter under the influence of physiology or therapy, vasoconstrictors decrease vessel diameter and increase resistance, while vasodilators increase vessel diameter and decrease resistance. Put simply, increasing resistance decreases Q; conversely, decreased resistance increases Q.

This can be explained mathematically:

By simplifying Darcy's Law, we get the equation that

Flow = Pressure/Resistance

When applied to the circulatory system, we get:

Q = (MAP – RAP)/TPR

Where MAP = Mean Aortic (or Arterial) Blood Pressure in mmHg,

RAP = Mean Right Atrial Pressure in mmHg and

TPR = Total Peripheral Resistance in dynes-sec-cm-5.

However, as MAP>>RAP, and RAP is approximately 0, this can be simplified to:

Q ˜ MAP/TPR

For the right heart Q ˜ MAP/PVR, while for the left heart Q ˜ MAP/SVR.

Physiologists will often re-arrange this equation, making MAP the subject, to study the body's responses.

As has already been stated, Q is also the product of the heart rate (HR) and the stroke volume (SV), which allows us to say:

Q ˜ (HR × SV) ˜ MAP / TPR

## Cardiac Output and Respiration

Q is affected by the phase of respiration with intra-thoracic pressure changes influencing diastolic heart filling and therefore Q. Breathing in reduces intra-thoracic pressure, filling the heart and increasing Q, while breathing out increases intra-thoracic pressure, reduces heart filing and Q. This respiratory response is called stroke volume variation and can be used as an indicator of cardiovascular health and disease. These respiratory changes are important, particularly during mechanical ventilation, and Q should therefore be measured at a defined phase of the respiratory cycle, usually end-expiration.

## Combined cardiac output

Combined cardiac output (CCO) is the sum of the outputs of the right and left side of the heart. It is a useful in fetal circulation, where the cardiac output from both sides of the heart partly work in parallel by the foramen ovale and ductus arteriosus, both directly supplying the systemic circulation.[44]

## Example values

Measure Typical value Normal range
end-diastolic volume (EDV) 120 ml[45] 65 - 240 ml[45]
end-systolic volume (ESV) 50 ml[45] 16 - 143 ml[45]
stroke volume (SV) 70 ml 55 - 100 ml
ejection fraction (Ef) 58% 55 to 70%[46]
heart rate (HR) 70 bpm 60 to 100 bpm[47]
cardiac output (CO) 4.9 L/minute 4.0 - 8.0 L/min[48]

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