Cardiac Output, Stroke Volume, and Heart Rate

Why Cardiac Output Combines Two Measurements

A heart can pump more blood per minute by beating more often, by ejecting more blood with each beat, or by changing both. For a PBPK model, this makes cardiac output a useful whole-body physiological quantity: it describes the volume of blood pumped by the heart per unit time. Its value depends on the physiological state being represented, so a resting value should not automatically be treated as a value during a different condition.

Definition: Heart rate ($HR$) is the number of heartbeats per unit time. Stroke volume ($SV$) is the volume of blood ejected by a ventricle per beat. Cardiac output ($Q_{\mathrm{card}}$) is the volume of blood pumped by a ventricle per unit time. When $HR$ and $SV$ refer to the same state and time interval, cardiac output is $$ Q_{\mathrm{card}} = HR \times SV. $$

For example, if $HR$ is recorded in beats per minute and $SV$ in millilitres per beat, the units cancel as follows:

\frac{\mathrm{beats}}{\mathrm{min}} \times \frac{\mathrm{mL}}{\mathrm{beat}} = \frac{\mathrm{mL}}{\mathrm{min}}.

The result is a volume flow, not a volume per beat and not a count of beats. It can be converted to litres per minute by dividing millilitres per minute by 1,000. A PBPK parameter table may use either unit, but calculations and comparisons must use consistent units.

Resting Output and State-Specific Output

A resting cardiac output is an estimate for a person or animal under specified resting conditions. “Resting” does not identify one universal number: measured or selected values can vary across individuals and with conditions such as posture, recent activity, temperature, and measurement protocol. A reference value is therefore a parameter for a defined reference state, not an unchanging property that applies in every circumstance.

If heart rate or stroke volume changes, cardiac output may change too. The product equation gives the output for the inputs supplied; it does not by itself explain why those inputs changed or predict a particular response to activity, illness, or another condition. For a state-specific estimate, use heart rate and stroke volume that represent that same state. Combining a resting heart rate with a stroke volume from a different state can produce a number, but it does not generally describe cardiac output in either state.

In practice, $HR$ may be measured directly while $SV$ is measured or selected from a reference source. Consequently, a calculated cardiac output may be an estimate based on inputs rather than an independent direct measurement. The distinction matters when evaluating the result: uncertainty or state mismatch in either input carries through to the product.

Worked Example: Calculating a Resting Cardiac Output

Suppose a hypothetical adult has a resting heart rate of 72 beats/min and a resting stroke volume of 70 mL/beat. Estimate resting cardiac output.

The inputs describe the same resting state, and their units are compatible. Apply the product:

Q_{\mathrm{card}} = HR \times SV = (72\ \mathrm{beats/min})(70\ \mathrm{mL/beat}) = 5{,}040\ \mathrm{mL/min}.

Convert to litres per minute:

5{,}040\ \mathrm{mL/min} \times \frac{1\ \mathrm{L}}{1{,}000\ \mathrm{mL}} = 5.04\ \mathrm{L/min}.

The estimated resting cardiac output is therefore 5.04 L/min. The units cancel correctly, and the result is a flow per minute. This calculation is not evidence that every adult at rest has this output; it is the product of the stated hypothetical inputs.

How Changes in Heart Rate and Stroke Volume Combine

When comparing two states, both factors must be considered. Let state 1 have $HR_1$ and $SV_1$, and state 2 have $HR_2$ and $SV_2$. Applying the definition in each state and dividing gives a useful comparison:

Q_{\mathrm{card},1}=HR_1SV_1,\qquad Q_{\mathrm{card},2}=HR_2SV_2

\frac{Q_{\mathrm{card},2}}{Q_{\mathrm{card},1}} = \frac{HR_2SV_2}{HR_1SV_1} = \left(\frac{HR_2}{HR_1}\right) \left(\frac{SV_2}{SV_1}\right).

This follows because the ratio of the two products can be rearranged into a product of the two input ratios. It shows why a change in heart rate alone does not establish the direction or size of the change in output: stroke volume may also change. If only heart rate changes while stroke volume remains constant, output changes in the same proportion as heart rate. If both change, their ratios multiply.

Worked Example: Comparing Two Hypothetical States

In a hypothetical measurement, a person has $HR_1=70$ beats/min and $SV_1=75$ mL/beat in state 1. In state 2, the same person has $HR_2=88$ beats/min and $SV_2=62$ mL/beat. Assume each pair describes its own state consistently. Calculate and compare the outputs.

For state 1:

Q_{\mathrm{card},1} = (70\ \mathrm{beats/min})(75\ \mathrm{mL/beat}) = 5{,}250\ \mathrm{mL/min} = 5.25\ \mathrm{L/min}.

For state 2:

Q_{\mathrm{card},2} = (88\ \mathrm{beats/min})(62\ \mathrm{mL/beat}) = 5{,}456\ \mathrm{mL/min} = 5.456\ \mathrm{L/min}.

The difference is $5{,}456-5{,}250=206$ mL/min, or 0.206 L/min. Relative to state 1, the increase is $206/5{,}250=0.03924$, approximately 3.92%. Heart rate increased, but stroke volume decreased; the output rose modestly because the product of the two changes was greater than one:

\left(\frac{88}{70}\right) \left(\frac{62}{75}\right) \approx 1.039.

This is a numerical comparison of the stated hypothetical inputs. It does not establish what caused the changes or imply that the same response occurs in another person or condition.

Worked Example: Why Heart Rate Alone Is Not Enough

Consider two hypothetical states. In state A, $HR=60$ beats/min and $SV=80$ mL/beat. In state B, $HR=80$ beats/min and $SV=60$ mL/beat. Compare their cardiac outputs.

For state A:

Q_{\mathrm{card,A}} = (60\ \mathrm{beats/min})(80\ \mathrm{mL/beat}) = 4{,}800\ \mathrm{mL/min} = 4.80\ \mathrm{L/min}.

For state B:

Q_{\mathrm{card,B}} = (80\ \mathrm{beats/min})(60\ \mathrm{mL/beat}) = 4{,}800\ \mathrm{mL/min} = 4.80\ \mathrm{L/min}.

The heart rates differ, but the outputs are equal because the products are equal. Thus, a higher heart rate does not necessarily mean higher cardiac output. Without stroke volume, heart rate alone is insufficient to calculate the output.

Assumptions, Checks, and Common Failure Modes

The multiplication is straightforward, but its interpretation depends on the inputs. A sound calculation uses a representative heart rate and stroke volume for the same individual, state, and relevant time interval. Heart rate must be expressed as beats per time, and stroke volume as volume per beat. If stroke volume is provided in litres per beat, convert units as needed before comparing with a result in millilitres per minute.

When values vary from beat to beat, the product is best understood using the average beat rate over an interval and the average volume ejected per beat over that same interval. The total volume pumped over the interval equals the number of beats times the average volume per beat; dividing by the interval duration gives the corresponding average output. A single heart-rate reading paired with a stroke-volume value from another time may not meet this condition.

A calculated value can also be inaccurate if either input is uncertain, unrepresentative, or taken from an incompatible source. For instance, a reference stroke volume may not represent the modeled subject, while a heart rate may be taken during a transient state. Report the source and state represented by the inputs when that information is available. For a changing condition, a single product is a snapshot or interval average, not a description of every moment.

The product estimate is not the only way cardiac output can be obtained: direct measurement approaches are also used clinically and physiologically. Those approaches have their own measurement assumptions and uncertainty. The product is useful when suitable heart-rate and stroke-volume inputs are available, but it should not be described as a direct measurement merely because it yields a numerical output. Nor should one input, such as a reference heart rate, be used as a substitute for output.

Common pitfall: “Heart rate rose, so cardiac output must have risen by the same percentage.” This reasoning silently assumes stroke volume stayed constant. The correction is to calculate both state-specific products, or use the ratio equation with both the heart-rate and stroke-volume ratios. If stroke volume is unknown, the direction and size of the output change cannot generally be concluded from heart rate alone.

Using the Quantity in a PBPK Context

Cardiac output provides a whole-body flow quantity that helps define the physiological setting for a PBPK model. Before using an output as a model input, identify whether it represents a reference resting state or another specified state, and make sure its units agree with the model's required flow units. This tutorial concerns the whole-heart product $HR\times SV$; it does not determine how that total is assigned among organs.

A compact workflow helps prevent avoidable errors:

Define the state.
Record whether the inputs represent rest or another specified condition, and ensure they refer to the same subject and time period.

Check the units.
Express heart rate as beats per time and stroke volume as volume per beat so that beats cancel.

Multiply and convert.
Calculate $Q_{\mathrm{card}}=HR\times SV$, then convert to the desired volume-per-time unit.

Interpret in context.
Describe the result as an estimate for the stated inputs and state, not as a universal value or a conclusion about an unmeasured condition.

The main alternatives answer related but different questions. The product method calculates output from heart rate and stroke volume. A direct measurement approach estimates output through a separate measurement procedure. Treating heart rate alone as a proxy is not equivalent to either: it omits stroke volume and cannot identify output without additional information.

Check Your Understanding

Answer each question, then compare with the solutions below.

A hypothetical resting heart rate is 64 beats/min and stroke volume is 75 mL/beat. What is cardiac output in L/min?
Heart rate rises from 72 to 90 beats/min while stroke volume remains 60 mL/beat. By what percentage does cardiac output change?
Why is a resting heart rate paired with a stroke volume measured in a different state a questionable input pair?
Two states have the same cardiac output but different heart rates. What must be considered when explaining this result?

Solutions. 1. $64\times75=4{,}800$ mL/min, which is $4.80$ L/min. 2. With stroke volume fixed, the output ratio is $90/72=1.25$; output increases by 25%. 3. The values may not represent the same state or interval, so their product may not describe either state. 4. Stroke volume must also be considered: different heart-rate and stroke-volume combinations can produce the same product, as in the worked example.