Why a Reference Table Needs More Than Numbers
A PBPK model may require organ volumes, organ blood flows, and tissue composition as inputs. Collecting one number for each quantity is not enough to make a usable reference table. A value depends on its population, measurement basis, units, and physiological conditions; two values that look comparable can refer to different things. A table that omits those details is difficult to audit and easy to misuse.
The aim here is a coherent reference-adult input table: a documented set of values for a defined adult reference, with each value linked to its conditions, source, and uncertainty. “Coherent” does not mean that all values must come from one publication. It means their definitions and bases are explicit, and that any combination or reconciliation is visible rather than hidden.
The earlier material on reference physiological profiles, body-size metrics, tissue composition, organ blood-flow values, source evaluation, uncertainty, and source conflicts provides the necessary background. This tutorial focuses on assembling those kinds of information into one auditable artifact.
Specify the Reference Before Filling the Table
A reference profile should be written in words before values are entered. For the examples below, use a hypothetical reference adult of 70 kg, described as healthy, awake, resting, and supine. Treat the values as illustrative teaching data, not as recommended clinical constants or observations from a real study. A different modeling question may require a different reference profile.
Record what “adult” means for the intended application, and include any available details that could affect the values, such as sex, age range, posture, activity, feeding state, or temperature. Do not silently assign a value from one condition to a different one. If a source does not report a relevant condition, record it as unreported rather than guessing.
Use one row per anatomical region and quantity type, or a clearly defined set of columns with the same effect. Make explicit whether a volume is an organ volume or a model compartment volume, and whether a flow is a flow through an organ bed or a value defined on another basis. Tissue composition also needs a stated basis; the example table uses mass fractions of wet tissue. These fractions need not sum to one when only water, lipid, and protein are listed: the remaining fraction represents other constituents.
A Compact, Traceable Table
The table below demonstrates a compact view of a larger master record. Each row is a non-overlapping region for this illustrative bookkeeping scheme. “Remaining tissues” is the residual compartment, not a separately measured organ. The volume entries sum to a stipulated total tissue volume for this example; that accounting convention should not be assumed for a different model. Flow entries are assigned to the listed regions once, so the liver entry is a total liver-bed flow, not an additional flow to be added to a separately listed portal contribution.
| Region | Volume (L) | Flow (L/min) | Water fraction | Lipid fraction | Protein fraction | Illustrative source records |
|---|---|---|---|---|---|---|
| Brain | 1.40 (1.30–1.50) | 0.70 (0.55–0.85) | 0.78 | 0.10 | 0.08 | V1, F1, C1 |
| Heart | 0.33 (0.28–0.38) | 0.25 (0.20–0.30) | 0.76 | 0.04 | 0.17 | V1, F1, C1 |
| Liver | 1.50 (1.30–1.70) | 1.45 (1.10–1.80) | 0.71 | 0.04 | 0.18 | V1, F1, C1 |
| Kidneys | 0.31 (0.27–0.35) | 1.00 (0.80–1.20) | 0.79 | 0.03 | 0.16 | V1, F1, C1 |
| Skeletal muscle | 28.0 (24.0–32.0) | 0.90 (0.60–1.20) | 0.76 | 0.03 | 0.19 | V1, F1, C1 |
| Skin | 3.30 (2.80–3.80) | 0.35 (0.20–0.50) | 0.64 | 0.10 | 0.20 | V1, F1, C1 |
| Adipose tissue | 18.0 (14.0–22.0) | 0.20 (0.10–0.30) | 0.20 | 0.78 | 0.02 | V1, F1, C1 |
| Remaining tissues | 15.16 (11.0–19.0) | 0.15 (0.05–0.25) | 0.60 | 0.15 | 0.15 | V1, F1, C1 |
The ranges in parentheses are illustrative bookkeeping ranges only. They are not asserted to be confidence intervals, prediction intervals, or jointly attainable values. In a real table, the source record must state what an uncertainty range represents. A master record should also preserve source details such as title, version, page or table, and any transformation applied. Here V1, F1, and C1 are hypothetical identifiers for volume, flow, and composition source records, respectively; they are not references to real publications.
The values are rounded for display. Store a suitable precision in the working record, then round for communication. Keep units in the column headings and retain the condition and basis alongside the value so they remain attached if the table is copied or filtered.
Worked Example: Converting and Recording One Flow Value
Suppose a hypothetical source reports a brain-bed flow of 700 mL/min for the stated resting reference condition. The table uses L/min. Convert the value, record the basis, and show the arithmetic.
Since 1 L = 1,000 mL:
The table entry is therefore 0.700 L/min, with the source record retaining the original 700 mL/min, its measurement basis, conditions, and location. The units cancel correctly. This conversion does not establish that the value applies to a different posture or activity state; that would require a separate justification.
Check Accounting Without Hiding Assumptions
A table can be checked for internal consistency, but a check is meaningful only if its accounting boundaries are defined. For the example, suppose the eight listed regions are declared to partition a total model tissue volume of 68.0 L, without overlap. The residual volume can then be checked by subtraction. Similarly, suppose these flow entries are intended as a complete, non-overlapping allocation of a reference total flow of 5.00 L/min. The sum is a bookkeeping check, not a derivation of the physiological distribution.
Worked Example: Checking the Volume and Flow Totals
Using the displayed central values, first sum the seven named tissue volumes:
Under the stated 68.0 L partition, the remaining-tissue entry is:
The listed volumes therefore sum to \(52.84+15.16=68.00\) L. This verifies arithmetic under the assumed partition; it does not show that the chosen total or component values are universally correct.
Now check the flow entries:
The central values match the stipulated total of 5.00 L/min. If the regions overlapped, if a flow were omitted, or if the total referred to a different circulation basis, this equality would not be a valid check. The table must state those boundaries rather than relying on a sum that happens to match.
Central values should not be expected to satisfy every constraint when each input has uncertainty. In particular, adding all upper or all lower range limits does not usually describe a coherent joint scenario. Preserve the marginal uncertainty information and document any constraints or dependencies known to apply; do not make the individual ranges appear more precise than their source supports.
Record Uncertainty and Source Decisions
An uncertainty field should say what kind of information it contains. A standard deviation, a reported interval, a range across sources, and an analyst-selected sensitivity range are not interchangeable. Record the type, numerical value or limits, units, and source for each. If a source provides no uncertainty estimate, write “not reported” rather than treating the point estimate as exact.
Keep provenance at the level of each quantity. A volume, flow, and composition value in the same row may come from different sources and may have different conditions. A concise source register can identify each record’s bibliographic details, definition, reference profile, and any conversion or adjustment. If a value is derived rather than directly reported, preserve the calculation and inputs so another analyst can reproduce it.
Worked Example: Resolving a Source-Condition Mismatch
Suppose a hypothetical source record F1 gives a flow of 1.00 L/min for the kidneys in the stated resting, supine reference condition. Another hypothetical record F2 gives 1.20 L/min but describes a different, incompletely specified condition. For this teaching example, treat the displayed ranges as illustrative and do not claim either record is a real source.
The values differ by \(1.20-1.00=0.20\) L/min, but the numerical difference alone does not identify a conflict: the condition and measurement basis must first be compared. If F1 matches the declared reference and F2 does not document a comparable condition, the table can use 1.00 L/min as the reference entry and retain F2 as a non-comparable alternative with its condition limitation noted. It should not average the two into 1.10 L/min, because that would create a value with no documented source or defined condition.
If both records were later shown to describe comparable conditions, the difference would need explicit evaluation and documentation rather than automatic selection or averaging. In either case, preserve both source records and the rationale for the table choice. The example illustrates the table-building decision, not a general rule that one source type is always preferable.
Choosing a Table Structure and Diagnosing Problems
A single wide table, like the compact view above, is convenient for review: related values for one region appear together. It can become awkward when different quantities have different source details, conditions, or uncertainty formats. A normalized master table with one record per region and quantity makes those differences easier to preserve; a wide display can then be generated for users. Separate volume, flow, and composition tables can also work, provided they share unambiguous anatomical labels and reference-condition identifiers.
| Approach | Useful when | Main risk |
|---|---|---|
| One wide display table | Rapid review of a fixed set of inputs | Different provenance or uncertainty details may be compressed or obscured |
| Separate domain tables | Each quantity type needs its own fields and source metadata | Region names or conditions can become inconsistent across tables |
| Master records plus display views | Traceability and multiple reporting views are important | Requires disciplined identifiers and maintenance |
Several warning signs indicate that the table is going wrong. Units that change within a column, fractions without a stated mass or volume basis, duplicate anatomical regions, and flow values with unclear boundaries all prevent reliable interpretation. A total that fails to match a declared partition calls for investigation; a matching total is not proof that the component values are biologically appropriate. Also check whether an uncertainty range is being presented as a formal interval when the source did not define it that way.
- Do not substitute a label for a definition. “Liver flow” needs an anatomical and measurement basis, not just a familiar organ name.
- Do not combine unlike conditions silently. Resting and non-resting values should remain distinguishable unless an explicit, documented transformation is justified.
- Do not infer exactness from a single value. Record missing uncertainty as missing, rather than as zero.
- Do not force a total by altering entries without a record. Any reconciliation must state the constraint, adjustment, and rationale.
A reference table is a practical model specification, not a definitive map of all human variability. Values may be population averages, estimates, or model conventions; the table should distinguish these where the evidence allows. It also cannot, by itself, make a table suitable for every age, body size, health state, or physiological scenario. The intended population and conditions delimit its use.
Check Your Understanding
Answer each question using the definitions and bookkeeping rules above.
- Why should “resting, supine” be recorded beside a flow value rather than assumed from the phrase “reference adult”?
- A tissue-composition row lists water, lipid, and protein fractions that sum to 0.94. Is that necessarily an error? Explain.
- A table reports 600 mL/min, but the flow column is in L/min. What value should be entered, and what information should remain in the source record?
- When is it valid to check whether organ volumes sum to a whole-body total?
- Two flow sources report different values, but one does not state the posture. Why is their average not automatically a sound reference value?
Solutions. (1) Conditions qualify the value; an unstated condition cannot be assumed to match the intended reference. (2) No. If the fractions cover only water, lipid, and protein, the remaining 0.06 may represent other constituents; the fraction basis must be stated. (3) \(600/1{,}000=0.600\) L/min. Preserve the original value, original unit, source location, basis, and conditions. (4) Only when the regions form a defined, non-overlapping partition and the total uses the same volume basis. (5) The records may refer to different conditions or bases; an average could describe neither source. Compare definitions and conditions, document the choice, and retain the source records.