Why Conflicting Values Need Diagnosis
Reference physiology values are assembled from studies that may differ in participants, measurement methods, and definitions. Two values can look inconsistent while describing different quantities or populations. Conversely, two values with similar labels and units can differ because of how they were obtained. Selecting the larger, newer, or more precise-looking number without checking these distinctions can place a mismatch into a PBPK model.
The task here is not to force every source to agree. It is to decide whether the values are comparable for a stated modeling purpose, identify plausible reasons for disagreement, and document a choice that fits that purpose. The earlier material on evaluating sources of reference physiology data and representing uncertainty in physiological inputs provides useful context: source quality and parameter uncertainty are related, but resolving a source conflict first requires understanding what each source actually reports.
Start by stating the target parameter in operational terms. For example, “liver volume” should be specified as the anatomical volume of the liver in living reference adults, with a stated unit and any intended body-size basis. A different definition, such as volume estimated from a particular imaging boundary or volume per unit body mass, may be relevant but is not automatically interchangeable.
The comparison should then ask four questions: Are the populations alike? Do the measurements represent the same quantity? Are units and normalization bases aligned? Are the study methods suitable for the target use? These questions are not a mechanical score. A weakness in one dimension may matter greatly for a particular parameter, while a difference in another may be unimportant.
A Structured Comparison
Before calculating a discrepancy, record for each source the reported value, unit, population, measurement definition, normalization basis, method, and any qualifications that affect its interpretation. If a key feature is not reported, mark it as unknown rather than silently assuming it matches another source. The intended reference population also needs to be explicit: a healthy adult reference, a specified species and strain, or another defined group.
When two values do refer to the same quantity and basis, a signed relative difference can describe their numerical separation. Taking source A as the reference denominator, define the difference of B from A as follows:
This expression retains direction: a negative value means B is lower than A, and a positive value means B is higher. It is meaningful only when A is nonzero and both values are comparable on the same basis. The denominator must be named, because reversing A and B generally gives a different percentage. This calculation is a descriptive comparison, not a statistical test and not proof that one source is biased.
Normalization deserves particular care. A value per kilogram is not merely the original value with a different label: it uses body mass as a denominator and may change the comparison. Dividing by body mass is appropriate only when that basis is relevant to the intended parameterization. Similar normalized values do not prove that the underlying populations or body-size relationships are the same. If converting a value between body sizes requires a scaling assumption, that assumption must be supported and stated rather than smuggled into a unit conversion.
Method differences also require interpretation rather than ranking by a simple rule. A direct measurement may be closer to the target construct, but its sampling or measurement conditions may limit generalizability. An indirect method may cover a larger or more appropriate population, but rely on assumptions. The choice should reflect the target quantity and the evidence available, not a blanket preference for one method label.
Worked Comparisons
Worked Example: Liver Volume and Body-Mass Normalization
Hypothetical data. Source A reports a mean liver volume of 1.50 L in healthy adults with mean body mass 70 kg. Source B reports 1.72 L in healthy adults with mean body mass 84 kg. Both use the same stated anatomical definition and imaging approach. The target is a reference adult with body mass near 70 kg.
The raw volumes differ by \(1.72-1.50=0.22\) L. Relative to A, the signed difference is
That raw comparison does not account for the difference in mean body mass. As a descriptive check, calculate each cohort’s mean volume per kilogram:
Using A’s ratio as the denominator, the signed relative difference of B’s ratio from A’s is
Thus B is about 4.444% lower than A on this per-kilogram comparison. That does not establish that the two populations are interchangeable or that liver volume scales linearly with body mass. Because the target is near A’s mean body mass, A is a defensible direct reference choice, while B is useful as a sensitivity comparator. The documentation should state that choice and the limitation: this simple normalization is descriptive, not a justified body-size conversion.
Worked Example: A Per-Kidney Value Versus a Bilateral Total
Hypothetical data. Source A reports total renal blood flow of 1.05 L/min for both kidneys in healthy adults. Source B reports a mean flow of 0.54 L/min per kidney, based on measurements of both kidneys in a comparable adult population. The target parameter is total flow to both kidneys.
First align the basis. Since B’s reported mean is per kidney and the target is the sum for two kidneys, the corresponding bilateral value is
The signed difference of B’s bilateral value from A is
After aligning the units and organ basis, the estimates are numerically close. Before choosing one, check that both sources use compatible definitions of renal flow, comparable populations and measurement conditions, and that B really reports a mean per kidney rather than a one-sided value intended to represent both. Given the stated hypothetical details, Source B can be selected if its bilateral measurements and method are better documented; Source A remains a useful comparator. The small numerical difference does not by itself identify which method is more accurate.
Worked Example: Converting Tissue-Water Measurement Bases
Hypothetical data. Two sources describe water content in comparable human liver samples. Source A reports 72.0% water by wet tissue mass. Source B reports 2.60 g water per gram of dry solids. The target table requires the fraction of wet tissue mass that is water. Assume for this conversion that wet mass consists of water plus the reported dry solids.
For each gram of dry solids, B reports 2.60 g water, giving total wet mass \(2.60+1.00=3.60\) g. The water fraction of wet mass is therefore
Using the unrounded conversion, the value is approximately \((2.60/3.60)\times100\%-72.0\%=0.2222\) percentage points higher than A. As a signed relative difference from A, it is
The conversion makes the reported bases comparable under the stated mass-balance assumption. For a table requiring wet-mass fraction, A is already in the target format and can be selected, with B recorded as a converted corroborating value. If the sources used different tissue preparation or definitions of dry solids, however, the arithmetic conversion would not resolve that methodological difference.
Justifying and Recording a Choice
A defensible decision can be organized as a short chain of reasoning. First define the intended parameter and population. Next determine whether the apparent conflict survives unit and definition harmonization. Then assess whether the remaining values differ in a way plausibly explained by population composition or study method. Finally choose a value, or retain distinct alternatives if the evidence does not support a single choice.
State the physiological quantity, target population, unit, and whether a normalized basis is required.
Convert units and compatible measurement bases, recording any assumptions needed for the conversion.
Compare populations, methods, sampling conditions, and reporting details; distinguish observed facts from plausible explanations.
Record the selected value, source, rationale, excluded alternatives, and unresolved uncertainty relevant to model use.
A compact record might state: “Selected 1.50 L from Source A for the reference adult because the source reports the target anatomical definition in a cohort whose mean body mass is near the intended 70 kg. Source B reported 1.72 L in a heavier cohort; its descriptive per-kilogram ratio was 4.444% lower than A’s. No linear conversion between cohort body sizes was assumed.” This preserves both the decision and the reasoning that could matter during later model review.
Do not use a numerical cutoff as a substitute for this judgment. A 5% discrepancy may be important when the target definition is precise and the parameter strongly affects model behavior, while a larger difference may be expected between distinct populations or measurement constructs. Likewise, a reported standard error or uncertainty interval can describe sampling or measurement uncertainty but does not repair a mismatch in definitions. Source conflict and within-source uncertainty should be recorded as different issues.
Diagnostics, Alternatives, and Limitations
Several signs indicate that a comparison may be going wrong. Values may be compared before checking whether one is per organ and the other is a bilateral total; a percentage may be reported without naming its denominator; or a ratio may be treated as proof that body-size differences are resolved. Another warning is a choice justified only by publication date, sample size, or the fact that one number is closer to a familiar value. Each can be relevant evidence, but none alone establishes suitability for the target.
When sources are compatible, one can select the source best aligned with the target and retain other estimates for comparison, or summarize several estimates if they genuinely measure the same quantity and population. When sources are not compatible, preserve them as separate parameterizations or use the value most directly matched to the intended model population, while documenting the mismatch. A simple average is not a neutral compromise: it can create a value that no source measured and that corresponds to no defined population.
This process has limits. Source reports may omit details needed to assess population characteristics, measurement boundaries, or methods. A descriptive relative difference cannot determine whether a discrepancy exceeds expected sampling or measurement variation without suitable uncertainty information. Even with complete metadata, a chosen reference value is a modeling decision, not proof that it is the uniquely correct physiological value. Unresolved conflicts should remain visible in the parameter record rather than being hidden by false precision.
Check Your Understanding
For each question, identify the relevant comparison issue before reading the brief solution.
- Source A reports 0.80 L and Source B reports 0.92 L for an organ. What is the signed relative difference of B from A, and what does its sign mean?
- One source reports a value per kilogram and another reports a total value. What must be checked before comparing them?
- Two sources report tissue water in different mass bases. When is a mathematical conversion sufficient to align them?
- Why is averaging values from sources with different target populations not automatically justified?
- What should be recorded if missing method details prevent a confident choice?
Solutions. (1) \((0.92-0.80)/0.80\times100\%=15.00\%\); B is 15.00% higher than A, using A as the denominator. (2) Check that the population and parameter definition match and that the per-kilogram basis is appropriate; do not assume a ratio supplies a valid body-size conversion. (3) A conversion is sufficient only when the definitions and mass components are known and the assumptions needed for conversion are defensible. (4) The sources may describe different physiological targets, so their average may not represent either population. (5) Record the unknown details, the resulting limitation, the selected value and rationale, and any alternative retained for sensitivity assessment.