Why Parameter Provenance Matters
A PBPK simulation can be numerically reproducible yet difficult to review if its inputs cannot be traced to evidence. A value copied into a model may have originated as a laboratory measurement, a literature estimate, a calculation from several measurements, or a value selected during model development. Those origins are not interchangeable. A reviewer needs to know what was measured, under which conditions, how it was transformed, and why it is suitable for the model’s intended use.
A parameter evidence table is not simply a list of model inputs and citations. It records the chain from source evidence to the value actually implemented, including units and any conversions or scaling. This makes it possible to detect errors such as mixing species, confusing a measured quantity with a scaled quantity, or applying an in vitro estimate without accounting for the assay conditions that produced it.
The earlier material on mapping evidence to PBPK model components establishes why evidence should be linked to the model feature it informs. Here the emphasis is the auditable parameter-level record. A useful table normally identifies the model parameter and its role, the value used and units, the source, the conditions under which evidence was obtained, any calculations or scaling, the reported uncertainty, and the selection rationale. If several measurements are plausible, retain their separate records rather than silently replacing them with one unexplained number.
From Measurement to Model Input
A reported number is not automatically the model parameter. For example, an assay may measure apparent intrinsic clearance per milligram of microsomal protein, while the model requires clearance per kilogram of body weight. The table must preserve both the measured quantity and the conversion. Likewise, an unbound fraction measured in plasma is not the same parameter as an unbound fraction in an in vitro incubation. Names that sound similar do not make values interchangeable.
Before entering a value, check that the evidence matches the parameter’s definition and context: species, population, matrix, temperature, pH, substrate concentration, assay system, and whether the reported quantity is total or unbound. Record the units as reported and the units required by the model. If a conversion is needed, show its equation and factors. A numerical value without units or conditions is not a complete parameter record.
State what the parameter represents, its model location or process, and the population or species to which it applies.
Record the source, method, assay conditions, sample or system, and the quantity as originally reported.
Write each unit conversion, correction or scaling step explicitly, with factors and assumptions.
Explain why the evidence is relevant, what uncertainty was reported, and which limitations remain.
State which value was implemented, why it was preferred to alternatives, and whether any discrepancy remains unresolved.
Worked Examples of Parameter Evidence
Worked Example: Selecting a Plasma Unbound Fraction
Suppose a hypothetical human PBPK model requires the plasma unbound fraction, \(f_{u,p}\), for compound Q. Two fictional laboratory reports give different estimates. Report A used equilibrium dialysis of human plasma at 37 °C and pH 7.4, with three replicate determinations; it reports \(f_{u,p}=0.080\), replicate SD \(=0.006\), and recovery of 94%. Report B used ultrafiltration at 25 °C, reports \(f_{u,p}=0.13\), and does not provide recovery or replicate variability. These are hypothetical values, not results from a real study.
The values differ by \(0.13-0.080=0.050\), so the difference should not be hidden by reporting a simple average. First check whether each measurement addresses the model quantity. Both concern human plasma, but the assay conditions differ; Report A is at physiological temperature and provides replicate variation and a recovery check. Report B’s lower temperature and missing recovery information make its result harder to assess for this purpose.
The evidence table can therefore record \(0.080\) as the selected value, with its source conditions and replicate SD, while retaining \(0.13\) as a conflicting estimate. The selection is based on documented relevance and completeness, not on which value gives a preferred simulation result. The SD describes variation among Report A’s replicates; it is not, by itself, a confidence interval for the true human population value.
A suitable record would identify the model parameter as \(f_{u,p}\) (dimensionless), the selected value as 0.080, the matrix as human plasma, the assay as equilibrium dialysis, the conditions as 37 °C and pH 7.4, and the reported uncertainty as replicate SD 0.006 with \(n=3\). It would also state the alternative value and why it was not selected. If the discrepancy could materially affect the model’s use, it should remain visible for scientific review rather than being treated as resolved by the table alone.
Worked Example: Scaling Microsomal Intrinsic Clearance
A hypothetical human liver microsome assay reports apparent intrinsic clearance of 12 µL/min/mg microsomal protein, with a replicate SD of 2 µL/min/mg. For this example, assume the selected scaling factors are 40 mg microsomal protein/g liver and 25 g liver/kg body weight. The model requires a body-weight-normalized intrinsic clearance.
The conversion is the measured clearance per milligram multiplied by microsomal protein per gram liver and liver mass per kilogram body weight:
The units cancel as follows: mg in the first denominator cancels mg in the second numerator, and g in the second denominator cancels g in the third numerator. The arithmetic is \(12\times40\times25=12{,}000\), giving \(12{,}000\ \mu\mathrm{L}/(\mathrm{min}\cdot\mathrm{kg})\). Since \(1{,}000\ \mu\mathrm{L}=1\ \mathrm{mL}\), the scaled value is \(12.0\ \mathrm{mL}/(\mathrm{min}\cdot\mathrm{kg})\).
The table should preserve the original assay value and SD, not just the scaled result. It should list both scaling factors, their units and sources, and make clear that they are assumed inputs to this calculation. This example does not propagate uncertainty in the scaling factors; therefore the SD from the microsome replicates must not be presented as the complete uncertainty of the scaled parameter. The record should also identify the assay species and conditions from the hypothetical report before the value is used in a human model.
Worked Example: Reconciling Apparent Clearance Across Assays
Two hypothetical microsomal assays estimate clearance for compound R under different incubation conditions. Assay A reports apparent clearance of 18 µL/min/mg protein and an incubation unbound fraction, \(f_{u,inc}=0.60\). Assay B reports apparent clearance of 12 µL/min/mg protein and \(f_{u,inc}=0.40\). For this example, the assay reports define unbound intrinsic clearance as apparent clearance divided by the incubation unbound fraction.
For Assay A, \(18/0.60=30\ \mu\mathrm{L}/(\mathrm{min}\cdot\mathrm{mg})\). For Assay B, \(12/0.40=30\ \mu\mathrm{L}/(\mathrm{min}\cdot\mathrm{mg})\). Thus the apparent values differ, but the corrected values agree under the stated correction convention.
The table should show each assay’s apparent value, \(f_{u,inc}\), conditions, correction equation and resulting unbound clearance. The agreement supports using 30 µL/min/mg as a reconciled estimate in this hypothetical example, provided the assay systems and correction definitions are comparable. It does not establish that the value is exact: any uncertainty in apparent clearance and \(f_{u,inc}\), as well as between-assay differences, should be retained as evidence-level limitations. If the source reports do not define the same correction convention, the arithmetic agreement alone is not sufficient to combine them.
Choosing Among Conflicting Measurements
Conflicts should be assessed on the evidence, not settled by averaging automatically or by selecting whichever value makes the simulation agree with an expected answer. Ask whether the candidate measurements have the same parameter definition, units, species, matrix, and conditions. Then consider whether the method is documented well enough to interpret, whether its conditions match the model’s use, and whether any transformations are justified. These checks provide a rationale; they do not guarantee that the selected value is true.
A direct measurement may be more relevant than an indirect estimate, but “direct” does not mean free of limitations. Conversely, a scaled value can be appropriate if its source measurement and scaling factors are well supported and transparently shown. Literature values can provide useful evidence, but the report should give enough identifying information and context for the reviewer to locate and evaluate the source. A value tuned during model development should be labelled as such, rather than presented as an independently measured physiological or drug-specific quantity.
| Approach | Strength | What the evidence table should make clear |
|---|---|---|
| Use one directly measured value | Simple chain from assay to input | Whether conditions, population and parameter definition match the model use |
| Use a scaled or corrected value | Can translate experimental evidence to the model’s required quantity | Each factor, unit conversion, assumption and source in the transformation |
| Combine multiple estimates | May represent more than one relevant evidence source | Why combination is justified and how differences and uncertainty are handled |
| Select one value from conflicting evidence | Provides an explicit model input | Why it was preferred, what alternatives were considered, and what discrepancy remains |
Derivation: Why Scaling Factors Must Be Visible
The microsomal scaling calculation follows from multiplying quantities that express the same clearance at successive levels. Suppose the assay clearance is \(a\ \mu\mathrm{L}/(\mathrm{min}\cdot\mathrm{mg})\), the microsomal protein content is \(b\ \mathrm{mg}/\mathrm{g}\) liver, and liver mass is \(c\ \mathrm{g}/\mathrm{kg}\) body weight. Multiplication gives:
The units demonstrate why each factor is needed: protein units and liver-mass units cancel, leaving clearance per body mass. Omitting either factor leaves a quantity on the wrong scale. This dimensional check can reveal a missing conversion, but it cannot establish that the scaling factors themselves are biologically appropriate. Their provenance and applicability still require justification.
Diagnostics, Limitations, and Common Pitfalls
A parameter record is likely inadequate if its value has no units; if it cites a source but omits the assay conditions; if a scaled value cannot be reconstructed; or if the stated uncertainty refers to a different quantity than the one implemented. Other warning signs include comparing total and unbound quantities as though they were equivalent, applying a value from one species without explaining its use in another, or listing a single “best” value while omitting materially different candidate measurements.
A table improves transparency, but it does not resolve weak evidence. A precise source record cannot compensate for a poorly matched assay, uncertain scaling factors, or an unrepresentative population. Nor should a reported SD, range, or confidence interval be relabelled as generic uncertainty: preserve the source’s definition and units. Where evidence is sparse or conflicting, state the limitation and the selection rationale; do not imply more certainty than the evidence supports.
- Wrong reasoning: “The two \(f_{u,p}\) values are 0.080 and 0.13, so their average, 0.105, is the most objective input.”
Correction: Averaging is justified only if the estimates are sufficiently comparable and a combination rule is appropriate. First examine assay conditions, quality and relevance; retain and explain the competing evidence. - Wrong reasoning: “The scaled clearance is reported, so the original assay number and scaling factors are unnecessary.”
Correction: Without the original units and factors, a reviewer cannot reproduce the conversion or assess whether it applies. - Wrong reasoning: “The value that best matches the clinical observation is the correct measured parameter.”
Correction: Agreement with an outcome does not establish measurement provenance. Keep measured inputs distinguishable from values adjusted during model development, and justify each on its own evidence.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions below.
- A source reports clearance in µL/min/mg protein, but the model requires mL/min/kg. What information must be recorded to make the conversion reviewable?
- Two assays report apparent clearances of 16 and 10 µL/min/mg, with incubation unbound fractions of 0.50 and 0.25, respectively. Using the correction convention in this tutorial, calculate both unbound clearances.
- A measurement reports a mean and replicate SD but no confidence interval. Which uncertainty statement may be entered, and what should not be claimed?
- Two sources report different values for the same named parameter. Give two checks that should precede choosing or combining them.
Solutions. (1) Record the original value and units, microsomal protein per gram liver, liver mass per kilogram, the source and units of both factors, and the multiplication and unit conversion. (2) The first corrected value is \(16/0.50=32\ \mu\mathrm{L}/(\mathrm{min}\cdot\mathrm{mg})\); the second is \(10/0.25=40\ \mu\mathrm{L}/(\mathrm{min}\cdot\mathrm{mg})\). They do not agree, so the difference remains visible and requires assessment rather than automatic averaging. (3) Report the replicate SD with its units and replicate context. Do not call it a confidence interval or claim it quantifies all uncertainty in the model parameter. (4) Check whether the parameter definitions, units, species or matrix, and assay conditions match; also inspect method documentation and any transformations before deciding whether selection or combination is defensible.