Why Blood-Flow Data Need an Audit
A cardiac-output value and a list of organ flows can each look plausible while being incompatible as a set. The discrepancy may be as simple as liters per minute being mixed with milliliters per minute. It may also reflect measurements made in different physiological states, fractions calculated using different denominators, or organ categories that overlap. Checking these issues before using the numbers helps prevent a bookkeeping error from becoming a physiological assumption.
The audit is not a procedure for deciding which of two conflicting measurements is correct. Its purpose is to establish whether the reported values can be compared under a stated set of definitions and conditions. A mismatch is a reason to investigate the source, timing, or measurement basis—not a license to adjust values until they add up.
Conditions for a Valid Comparison
A circulation-wide total is meaningful only when the quantities being summed have compatible units and definitions. Organ flows should refer to the same type of flow (for example, blood flow rather than a mixture of blood and plasma flow), the same time window or physiological state, and a set of distinct beds that covers the circulation being audited. The cardiac-output value used as the reference must correspond to that same state and time window.
The basic conservation check assumes a steady or suitably time-averaged circulation: blood is not accumulating or being depleted in the vascular compartments over the comparison interval. It also assumes that the listed beds form a complete partition of the relevant systemic flow, with no bed counted twice. Under these conditions, systemic organ flows sum to systemic cardiac output. In the circulation as a whole, mean pulmonary and systemic flows are also equal at steady state if there is no important shunt or other pathway that bypasses the series circulation. These equalities do not require every individual measurement to be exact; measurement uncertainty can explain small differences.
The definition of an organ flow matters as much as its numerical value. For example, reported liver perfusion may mean hepatic arterial flow alone or combined hepatic arterial and portal venous inflow. Portal blood has already passed through the gastrointestinal circulation; counting it once as gut flow and again as a separate new input to the whole-body circulation can double-count flow. Before summing, identify the accounting boundary and whether each reported value is an independent inflow or a transfer within the circulation.
A Practical Audit
Use a sequence of checks rather than beginning with the total. First standardize units. Next check measurement times and conditions, including rest versus exercise, posture, or a disease state. Then verify what each value represents and what denominator was used for any reported fraction. Only after those checks should you compare totals. If the total does not agree, calculate the discrepancy and identify whether omitted beds, overlaps, uncertainty, or timing could account for it.
Convert every flow to a common unit before adding or taking a ratio. Keep track of whether a value is blood flow, plasma flow, or another quantity.
Check that cardiac output and organ flows refer to the same time window and physiological state. A resting output is not automatically an appropriate denominator for exercise flows.
Confirm that fractions share a denominator and that organ categories are neither omitted nor double-counted.
Sum compatible flows, compare with the matching cardiac output, and investigate the discrepancy in light of rounding and measurement uncertainty.
Why Fractions Must Share a Denominator
Suppose a set of distinct, exhaustive organ beds has flows \(Q_1,\ldots,Q_k\), and all fractions are defined relative to the same cardiac output \(Q_{\mathrm{CO}}\). Under the flow-conservation assumptions, \(Q_{\mathrm{CO}}=\sum_{i=1}^{k}Q_i\). Dividing both sides by the same positive \(Q_{\mathrm{CO}}\) gives:
This result is a diagnostic, not a rule for forcing reported fractions to total one. If the listed beds are incomplete, their fractions can sum to less than one; the difference represents unlisted flow only if the denominator and definitions really are compatible. If fractions sum above one, look for overlapping categories, different denominators, or incompatible measurements. Rounding can also cause a small departure from one. The acceptable size of that departure depends on the reported precision and measurement uncertainty; there is no universal tolerance that makes every discrepancy acceptable.
Worked Example: Converting Mixed Flow Units
Hypothetical data. A report gives \(Q_{\mathrm{CO}}=5.2\) L/min. It lists brain flow as 700 mL/min, kidney flow as 0.9 L/min, liver flow as 1.3 L/min, muscle flow as 1.6 L/min, and other systemic flow as 700 mL/min. Are the reported organ flows compatible with cardiac output?
The values cannot be summed as written because some are in mL/min and others in L/min. Since 1 L = 1,000 mL, convert the two values in mL/min: 700 mL/min = 0.700 L/min for each. The organ-flow total is therefore:
The total equals the reported cardiac output of 5.2 L/min at the precision shown. This is an arithmetic compatibility check, not proof that the measurements are accurate. It also assumes that the organ categories are complete, non-overlapping, and measured for the same physiological state as the cardiac output.
Worked Example: Fractions That Exceed a Complete Partition
Hypothetical data. For one reported state, \(Q_{\mathrm{CO}}=5.0\) L/min. Six fractions, all stated to be percentages of that cardiac output, are reported as brain 0.14, kidneys 0.20, liver 0.25, skeletal muscle 0.18, skin 0.05, and other organs 0.22. The report describes these categories as a complete, non-overlapping partition. Check their consistency.
The fractions sum to:
The implied total flow is \(1.04(5.0)=5.20\) L/min, which exceeds the stated cardiac output by \(5.20-5.0=0.20\) L/min, or 4% of cardiac output. If each fraction was rounded to the nearest 0.01, each individual rounding error can be at most 0.005 in magnitude. For six fractions, the largest possible total rounding error is \(6(0.005)=0.030\). Even allowing that maximum in the direction that reduces the sum, the underlying total would be at least \(1.04-0.03=1.01\), still above one.
Thus rounding to two decimal places alone cannot explain the excess under the stated assumptions. Check whether the categories overlap, whether one value used a different denominator, or whether some measurements came from a different source or condition. The arithmetic identifies an incompatibility; it does not identify which reported fraction should be changed.
Timing and Circulation-Wide Checks
A sum can fail to match cardiac output without indicating a conservation violation if the measurements describe different states. Cardiac output and regional flows can change with exercise, posture, or illness. A flow report should therefore be checked for its measurement time and conditions, not just its units. Even “same visit” may be insufficient if measurements were taken during different stages of a changing condition.
A comparison between pulmonary and systemic flow needs the same care. In a steady circulation without a significant shunt, their mean flows through the series circuit should agree. During a transient, or when measurements use different averaging windows, instantaneous or short-window estimates may differ. A small difference may also reflect measurement error. The relevant question is whether the methods, timing, and uncertainty justify treating the discrepancy as meaningful—not whether the two printed numbers are identical.
Worked Example: A Flow Total From a Different State
Hypothetical data. Cardiac output is reported as 5.0 L/min at rest. A separate regional-flow report, taken during exercise, lists brain 0.75 L/min, kidneys 0.65 L/min, liver 1.10 L/min, skeletal muscle 4.40 L/min, skin 0.35 L/min, and other organs 0.35 L/min. A pulmonary-flow measurement during the exercise period is 7.8 L/min, while a systemic cardiac-output measurement during that period is 7.6 L/min. What can be concluded?
First, the exercise organ flows are all in L/min. Their sum is:
That total matches the reported exercise systemic cardiac output of 7.6 L/min. It is 2.6 L/min greater than the resting cardiac output, but comparing those values does not establish an inconsistency: they refer to different physiological states. The exercise pulmonary and systemic measurements differ by \(7.8-7.6=0.2\) L/min. Without information about their timing, averaging windows, methods, or measurement uncertainty, it is not possible to decide whether that difference is meaningful. At steady state, with matched measurements and no important shunt, the expected mean flows through the pulmonary and systemic circuits are equal; the report as given does not establish those conditions well enough to diagnose a violation.
How to Interpret a Mismatch
A useful alternative to demanding exact equality is to calculate and report the residual between the compatible organ-flow total and cardiac output. For example, if organ flows sum to 4.8 L/min and the matched cardiac output is 5.0 L/min, the residual is \(5.0-4.8=0.2\) L/min. That residual could reflect an unlisted bed, measurement uncertainty, rounding, or a definition mismatch. It should not automatically be assigned to a particular organ. If measurement uncertainty is documented, assess whether the residual is plausible relative to it; if it is not documented, record that limitation rather than inventing a tolerance.
A strict sum check is easy to apply but can be misleading when categories overlap or measurements are asynchronous. A definition-and-timing audit is more informative because it tests whether the sum is meaningful in the first place. Where uncertainty estimates are available, comparison with those estimates is more defensible than imposing an arbitrary percentage cutoff. These approaches complement one another: first establish comparability, then assess the size of any remaining difference.
Common Mistakes and Failure Signals
- Adding before converting units. A numerical total made from mixed units has no interpretable meaning. Convert all values to a common unit first.
- Using any available cardiac output as the denominator. A fraction is meaningful only relative to its stated denominator. Do not use a resting output to normalize exercise flows without a clear reason.
- Treating a total of one as proof of consistency. Fractions can sum to one while being based on mismatched measurements or overlapping definitions. Check what they represent as well as their arithmetic.
- Calling every difference a conservation failure. Different times, states, or averaging windows prevent a direct comparison. Establish comparability before interpreting a residual.
- Double-counting internal transfers. A flow that moves between beds is not automatically a new input from the heart. Check the accounting boundary, especially when definitions include both upstream and downstream flow.
- “Fixing” a mismatch by rescaling all organ flows. Rescaling makes the numbers add by construction but hides the source of the discrepancy. Preserve the reported values, document the mismatch, and investigate their provenance.
Check Your Understanding
For each item, decide what can be concluded and identify the next useful check. Solutions follow the questions.
- A cardiac output is 4.8 L/min. Two reported organ flows are 900 mL/min and 1.2 L/min. What is their combined flow in L/min?
- Four fractions are reported as 0.20, 0.25, 0.30, and 0.15. If these are all the beds in a complete partition, what does their sum imply?
- Organ flows measured during exercise sum to 7.0 L/min, while the only reported cardiac output is 5.0 L/min at rest. Is a conservation violation established?
- At a matched steady state with no important shunt, pulmonary flow is 6.1 L/min and systemic cardiac output is 6.0 L/min. What should be checked before interpreting the 0.1 L/min difference?
Solutions. (1) Convert 900 mL/min to 0.900 L/min, then add: \(0.900+1.2=2.10\) L/min. (2) The fractions sum to \(0.20+0.25+0.30+0.15=0.90\). If they truly describe only part of the circulation, 0.10 remains unlisted; if they are claimed to be complete, the shortfall requires checking coverage, definitions, and rounding. (3) No. The cardiac output and organ flows refer to different states, so they cannot be used for a direct conservation comparison. Obtain or identify a cardiac-output measurement for the exercise period, and check the measurement windows and definitions. (4) Check the methods, units, averaging windows, and stated measurement uncertainty. A 0.1 L/min difference is not automatically meaningful or automatically negligible; its interpretation depends on those details.