Representing Residual Renal Function Across CKD Stages

From CKD Stage to Residual Renal Capacity

A chronic kidney disease (CKD) stage summarizes clinical information; it is not itself a PBPK parameter. A model needs quantities that describe the remaining function relevant to the drug, such as filtration or a particular tubular process. The same eGFR category can include people with different absolute filtration, different tubular function, and different degrees of compensation by surviving nephrons. Translating a stage into a model input therefore requires an explicit reference, a stated scaling assumption, and attention to what the available measurements can actually identify.

The earlier material on mapping eGFR and creatinine clearance to renal PBPK inputs distinguishes estimated clinical measures from the physiological quantities they approximate. The earlier material on separating glomerular filtration loss from tubular dysfunction establishes a second important distinction: filtration and tubular processes should not be treated as interchangeable. Here, the focus is how to represent the remaining capacities across CKD stages, including the distinction between having fewer functioning nephrons and having more work performed by each surviving nephron.

Stage Categories Are Context, Not Capacity Parameters

The G categories classify eGFR in mL/min/1.73 m²: G1 is at least 90; G2 is 60–89; G3a is 45–59; G3b is 30–44; G4 is 15–29; and G5 is below 15. These are filtration categories, not direct measurements of tubular secretion, reabsorption, or functioning nephron number. In addition, an eGFR in the G1 or G2 range does not by itself establish CKD; evidence of kidney damage or another qualifying abnormality is needed. CKD classification also presumes chronicity rather than a single transient result.

For PBPK scaling, the category can help organize a population or define a scenario, but it should not replace the actual value and units used in the model. eGFR is commonly indexed to a standard body surface area of 1.73 m². If the model requires an absolute rate in mL/min, de-index it using the patient’s body surface area (BSA):

This conversion changes the expression from a body-surface-area-indexed rate to an absolute rate; it does not make eGFR a direct measurement of true GFR. Use a matching reference when forming a ratio: an absolute disease-state value should be compared with an absolute reference, and an indexed value with an indexed reference. The reference should be appropriate to the model’s intended population and definition of normal function.

Whole-Kidney Function, Nephron Number, and Compensation

A useful conceptual decomposition is to express total capacity for a renal process as the number of functioning nephrons multiplied by the average capacity per nephron. For filtration, let \(N_0\) be the reference number of functioning nephrons and \(q_{G,0}\) the reference average filtration per nephron. In disease, let \(N\) and \(q_G\) denote the corresponding values. Define the remaining-nephron fraction \(r_N=N/N_0\) and the per-nephron filtration factor \(c_G=q_G/q_{G,0}\). Then the whole-kidney filtration ratio is:

This factorization is a bookkeeping representation, not a claim that nephron number or single-nephron filtration is routinely measured. A lower nephron fraction reduces total filtration; higher filtration by surviving nephrons can partly offset that reduction. Conversely, surviving nephrons may have lower average filtration, so the total decline can exceed what nephron loss alone would predict.

The same logic applies to a defined tubular capacity, but its per-nephron factor need not equal the filtration factor. For a tubular process \(j\), such as a specified secretory or reabsorptive capacity, write the whole-kidney ratio as \(r_j=r_Nc_j\), where \(c_j\) is the average per-nephron capacity factor for that process. Using a common \(r_N\) across processes is a simplifying assumption; using the filtration factor \(c_G\) as a substitute for \(c_j\) is a separate and usually unjustified assumption.

Scaling Filtration and Tubular Processes Separately

For a filtration-mediated drug-clearance component, a proportional scaling of the reference filtration component by \(r_G\) is a useful first model when the component is assumed to vary linearly with GFR and other relevant determinants are held fixed. That is a process-specific assumption: it does not establish that all renal clearance scales in the same proportion. A tubular secretion or reabsorption component should instead have its own residual-capacity ratio when evidence or a defensible assumption supports one.

For example, an illustrative additive renal-clearance representation can be written as a filtration component plus a tubular component. If the filtration component is scaled by \(r_G\) and tubular secretion by \(r_S\), then:

This form assumes the two reference components are defined consistently, the disease-state changes can be represented by the stated ratios, and the components add under the modeled conditions. It is not a universal renal-clearance equation. In particular, assigning \(r_S=r_G\) merely because eGFR is available is a convenience assumption, not a physiological consequence of CKD staging. A tubular ratio may be poorly known; in that case, represent the uncertainty with plausible scenarios or sensitivity analysis rather than implying that the stage uniquely determines it.

Choosing and Checking a Scaling Strategy

A transparent modeling workflow makes the distinction between clinical classification and physiological scaling visible. First select the actual renal measurement and verify its units, indexing, and chronic context. Then define a reference and calculate the residual filtration ratio. Finally, assign tubular capacities separately, documenting which are measured, estimated, or assumed. The process can be summarized as follows.

Useful diagnostics include checking that all ratios use compatible units and a clearly identified reference; confirming that the chosen eGFR value is not being confused with an absolute GFR; and checking whether predictions change substantially when the tubular ratio varies over plausible values. If a model predicts the same renal effect for every drug solely because each has the same eGFR scaling, despite different reliance on tubular processes, its structure may be too coarse. Likewise, a dramatic conclusion about nephron number based only on a low eGFR is not supported by the aggregate measurement.

A stage-based approach is practical when detailed process-specific data are unavailable: define representative filtration values or ranges for each stage and state that tubular capacities are held at reference levels, scaled proportionally, or varied in scenarios. A patient-specific approach uses available renal measurements and process-relevant evidence to set individual inputs. The former is more transparent and often more feasible for population simulations; the latter may be more physiologically informative but can require data that are not routinely available. Neither approach removes uncertainty, and a stage category should not be mistaken for an individual’s complete renal phenotype.

Common Pitfall and Limitations

Wrong reasoning: “This patient is in G3b, so every renal process has 40% of normal capacity, and the remaining 40% must represent the fraction of nephrons still functioning.” The correction is that G3b is a category for indexed eGFR, not a universal capacity ratio. Even after deriving a filtration ratio from a specific value and reference, it represents an aggregate filtration comparison. It cannot distinguish nephron number from per-nephron filtration, and it does not determine tubular capacity.

The product representation \(r_G=r_Nc_G\) clarifies the issue but does not solve it: many pairs of factors have the same product. Tubular capacity can vary independently in the model, but its true disease-state value may be uncertain. Estimates may also be affected by the limitations of eGFR as a proxy, differences between the reference and modeled population, and whether the disease state is stable. Treating the ratios as fixed constants can understate this uncertainty. Report the assumptions and, where they matter to predicted exposure, examine alternative values rather than presenting a single stage-derived number as uniquely determined.