Constraining Filtration With GFR and Renal Plasma Flow

Why GFR and Renal Plasma Flow Must Be Considered Together

A renal PBPK model needs a filtration input that is compatible with the kidney’s available plasma flow. The glomerular filtration rate (GFR) describes the volume of fluid filtered from plasma into the glomerular filtrate per unit time. Renal plasma flow (RPF) describes the volume of plasma delivered to the kidneys per unit time. Their ratio, the filtration fraction, is a compact physiological check on whether the two inputs can reasonably describe the same kidney, subject, and conditions.

This check matters even when the drug-specific filtered amount is calculated correctly. A model can use the appropriate unbound plasma concentration and still overstate filtration if its GFR is paired with an incompatible flow input, or if a blood-flow quantity is mistakenly treated as plasma flow. The introductory material on unbound drug filtration establishes the role of unbound drug in filtration; here the emphasis is on constraining that filtration with organ-level flows.

Definition: The filtration fraction (FF) is the ratio of glomerular filtration rate to renal plasma flow:

\mathrm{FF}=\frac{\mathrm{GFR}}{\mathrm{RPF}}.

GFR and RPF must refer to compatible conditions and use the same volume-per-time units. FF is dimensionless. It describes the fraction of incoming renal plasma flow represented by the filtered fluid volume; it is not, by itself, the fraction of a drug dose or body burden that is excreted.

In healthy adults, a filtration fraction around 0.15–0.25 is a useful broad orientation, not a universal acceptance interval. Values vary with physiology, measurement method, clinical state, and the definition and scaling of the reported quantities. A value outside that broad range should prompt review of the inputs and context rather than automatic rejection. A value above 1, however, means the stated GFR exceeds the stated incoming RPF; for simultaneous, compatible whole-kidney flows, that is not physiologically coherent.

Keep Plasma Flow and Blood Flow Distinct

Renal blood flow (RBF) is the volume of whole blood delivered to the kidneys per unit time. Whole blood includes both plasma and cells. If hematocrit (Hct) is expressed as a fraction, the plasma fraction of blood is \(1-\mathrm{Hct}\). The corresponding relationship is:

\mathrm{RPF}=\mathrm{RBF}(1-\mathrm{Hct}).

For example, if Hct is 0.45, plasma accounts for 0.55 of the blood volume. RPF is therefore 55% of RBF, not 100% of it. This conversion assumes the blood-flow and hematocrit values apply to the same circulation and condition. A hematocrit reported as 45% must be entered as 0.45 in the equation.

For drug filtration, concentration units also matter. Plasma concentration is mass per plasma volume, so multiplying it by GFR gives mass per time. A whole-blood flow cannot be substituted for RPF in FF, and a whole-blood concentration cannot be combined with a plasma flow without an explicit blood-to-plasma concentration relationship.

Model relationship: Let \(C_p\) be total drug concentration in plasma and \(f_{u,p}\) the unbound fraction in plasma. If unbound drug is freely filterable, the filtered drug mass rate is:

\mathrm{Filtered\ mass\ rate} =\mathrm{GFR}\, f_{u,p} C_p.

If a filtration sieving coefficient \(S_f\) is specified to represent incomplete passage of unbound drug, include it as \(\mathrm{GFR}\,S_f f_{u,p}C_p\). The freely filterable assumption corresponds to \(S_f=1\). Use an absolute GFR, not a body-surface-area-indexed value, when the model represents an individual’s amount rate.

Deriving and Interpreting the Constraint

The ratio follows directly from the meanings of the two flows. Over a short interval \(\Delta t\), the plasma volume delivered is approximately \(\mathrm{RPF}\Delta t\), while the volume filtered is \(\mathrm{GFR}\Delta t\). The ratio of filtered volume to delivered plasma volume is therefore:

\frac{\mathrm{GFR}\Delta t}{\mathrm{RPF}\Delta t} =\frac{\mathrm{GFR}}{\mathrm{RPF}} =\mathrm{FF}.

The time interval cancels, as do the volume units, leaving a dimensionless fraction. This interpretation relies on compatible whole-kidney values for the same subject and condition. A reported GFR indexed to body surface area, a flow from another subject, or a flow measured under a different physiological state does not automatically form a valid pair.

Filtration fraction constrains a physiological input; it does not determine GFR or RPF uniquely. Many pairs can have the same ratio. Nor does the ratio account for drug binding: the filtered drug rate additionally depends on plasma concentration and the unbound fraction. A drug with a low unbound fraction can have a low filtered rate even when FF is ordinary.

Worked Example: Checking a Paired GFR and RPF

Suppose a hypothetical adult PBPK parameter set specifies an absolute GFR of 120 mL/min and an RPF of 600 mL/min. Check the units and calculate FF.

Both values are whole-kidney volume flows in mL/min, so they can be divided directly:

\mathrm{FF} =\frac{120\ \mathrm{mL/min}}{600\ \mathrm{mL/min}} =0.200.

The filtration fraction is 0.200, or 20.0%. This falls within the broad adult orientation given above, so the pair is physiologically plausible as a preliminary check. It does not establish that either input is measured accurately or appropriate for a particular individual.

Worked Example: Converting Blood Flow to Plasma Flow

For a hypothetical subject, let RBF be 1.10 L/min and Hct be 0.45. A separately specified absolute GFR is 120 mL/min. Convert RBF to RPF, then calculate FF.

First convert the blood-flow value to mL/min: \(1.10\ \mathrm{L/min}=1{,}100\ \mathrm{mL/min}\). Then calculate plasma flow:

\mathrm{RPF} =1{,}100\ \mathrm{mL/min}(1-0.45) =1{,}100(0.55) =605\ \mathrm{mL/min}.

Now use plasma flow, not blood flow, in the filtration-fraction ratio:

\mathrm{FF} =\frac{120\ \mathrm{mL/min}}{605\ \mathrm{mL/min}} =0.1983.

The resulting FF is about 19.8%, a plausible value under the broad check. Dividing GFR by RBF instead would give \(120/1{,}100=0.1091\), but that is not the defined filtration fraction because its denominator is whole-blood flow rather than plasma flow.

Use Absolute Flows for Individual PBPK Amount Rates

GFR is sometimes reported indexed to a standard body surface area of 1.73 m². Indexing supports comparisons across people of different body sizes, but it does not itself give the volume per time filtered in a particular individual. When an individual model requires an absolute flow, convert the indexed value using that individual’s body surface area (BSA):

\mathrm{GFR}_{\mathrm{absolute}} = \mathrm{GFR}_{\mathrm{indexed}} \frac{\mathrm{BSA}}{1.73\ \mathrm{m^2}}.

This conversion is valid when the reported indexed GFR and BSA refer to the same individual and the indexing convention is as shown. It does not adjust the GFR for disease or other physiological differences; it simply reverses the body-surface-area indexing.

Worked Example: De-Indexing GFR Before Calculating FF

A hypothetical subject has an indexed GFR of 105 mL/min/1.73 m² and a BSA of 2.10 m². RPF is 625 mL/min. Convert GFR to an absolute flow and calculate FF.

The absolute GFR is:

\mathrm{GFR}_{\mathrm{absolute}} =105\ \frac{\mathrm{mL}}{\mathrm{min}\cdot1.73\ \mathrm{m^2}} \left(\frac{2.10\ \mathrm{m^2}}{1.73\ \mathrm{m^2}}\right) =127.5\ \mathrm{mL/min}.

The ratio can now be calculated using absolute flows with matching units:

\mathrm{FF} =\frac{127.5\ \mathrm{mL/min}}{625\ \mathrm{mL/min}} =0.2040.

The estimated FF is 20.4%. Comparing the indexed value 105 directly with the absolute RPF of 625 would mix units and produce a ratio with no valid filtration-fraction interpretation.

Calculate the Drug-Specific Filtered Rate

Once the flow pair has passed a basic consistency check, the filtered drug rate can be computed using the unbound plasma concentration. For the freely filterable assumption, filtered clearance referenced to total plasma concentration is \(\mathrm{GFR}f_{u,p}\). This is a filtration contribution; it is not necessarily the same as observed renal clearance, because processes beyond glomerular filtration can affect the amount ultimately appearing in urine.

Worked Example: From Filtration Inputs to Filtered Drug Rate

Suppose a hypothetical model uses GFR \(=120\ \mathrm{mL/min}\), RPF \(=600\ \mathrm{mL/min}\), \(f_{u,p}=0.20\), and \(C_p=5.0\ \mathrm{mg/L}\). Assume unbound drug is freely filterable. Calculate FF and the filtered mass rate.

The flow check gives \(\mathrm{FF}=120/600=0.200\), as in the first example. Convert GFR to L/min so it matches the concentration’s volume unit:

120\ \mathrm{mL/min}=0.120\ \mathrm{L/min}.

The unbound plasma concentration is \(f_{u,p}C_p=0.20(5.0)=1.0\ \mathrm{mg/L}\). Thus:

\mathrm{Filtered\ mass\ rate} =0.120\ \mathrm{L/min}\times1.0\ \mathrm{mg/L} =0.120\ \mathrm{mg/min}.

The hypothetical filtered mass rate is 0.120 mg/min. Its units follow because L/min multiplied by mg/L gives mg/min. The result is conditional on the stated free-filtration assumption and does not, by itself, predict urinary excretion.

Diagnostics, Alternatives, and Limitations

A filtration-fraction check is most useful as a consistency diagnostic before interpreting drug-specific renal predictions. Review the inputs when the ratio is unexpectedly high or low, or when changing one parameter produces an implausible pair. Check units, indexing, hematocrit conversion, subject and condition matching, and whether a reported flow is renal or systemic. A very high ratio can result from mixing indexed GFR with absolute RPF or from comparing GFR with an incorrectly low plasma-flow estimate. A ratio above 1 for compatible simultaneous whole-kidney flows indicates a contradiction that must be resolved before using the pair.

Several approaches provide different information. Using GFR alone is sufficient to calculate a filtration rate under specified concentration and binding assumptions, but it cannot show whether the input is compatible with plasma delivery. Using RPF alone establishes a delivery-flow input but does not specify how much plasma is filtered. When RBF rather than RPF is available, converting with a matched Hct provides an estimate of plasma flow, but adds uncertainty from both inputs. Paired GFR and RPF give the direct FF check; they do not make the measurements error-free or replace evaluation of the drug-specific filtration assumptions.

The filtration fraction is an approximate physiological summary, not a complete renal hemodynamic model. It does not specify regional variation, transient changes, measurement uncertainty, or how flow and filtration change with time. The broad adult orientation should not be used as a rigid cutoff across populations or conditions. In a PBPK model, document whether inputs are measured, estimated, indexed, or converted, and preserve their units through every calculation.

Common pitfall: “GFR is 120 mL/min and renal blood flow is 1,100 mL/min, so FF is 10.9%.” The arithmetic is correct, but the denominator is the wrong quantity. Convert RBF to RPF using hematocrit first; with Hct 0.45, RPF is 605 mL/min and FF is 19.8%. Filtration fraction is GFR divided by renal plasma flow, not renal blood flow.

Put inputs on a common basis.
Confirm that GFR and RPF apply to the same subject and condition, use compatible time units, and are both absolute whole-kidney flows.

Convert if needed.
Convert RBF to RPF with \(1-\mathrm{Hct}\), or de-index GFR using the individual’s BSA when an absolute flow is required.

Calculate and inspect FF.
Evaluate \(\mathrm{GFR}/\mathrm{RPF}\). Investigate an implausible result rather than treating a broad reference orientation as a rigid pass-or-fail rule.

Calculate drug filtration separately.
Use absolute GFR, unbound plasma concentration, and any specified sieving coefficient, keeping concentration and flow volume units consistent.

Check Your Understanding

Answer each question, then compare with the brief solutions below.

A hypothetical model specifies GFR of 150 mL/min and RPF of 120 mL/min for the same kidney and time. What is FF, and what should be checked?
RBF is 900 mL/min and Hct is 0.40. Calculate RPF.
Why is an indexed GFR not directly interchangeable with an absolute RPF in the FF equation?
With GFR \(=90\ \mathrm{mL/min}\), \(f_{u,p}=0.10\), and \(C_p=4.0\ \mathrm{mg/L}\), what is the filtered mass rate under the freely filterable assumption?

Solutions. 1. \(\mathrm{FF}=150/120=1.25\). The stated GFR exceeds the paired plasma delivery, so verify units, indexing, subject, condition, and the flow measurements before using the pair. 2. \(\mathrm{RPF}=900(1-0.40)=540\ \mathrm{mL/min}\). 3. Indexed GFR is reported per 1.73 m², whereas absolute RPF is volume per time; de-index GFR for the individual before forming the ratio. 4. First, \(f_{u,p}C_p=0.10(4.0)=0.40\ \mathrm{mg/L}\). Then \(90\ \mathrm{mL/min}=0.090\ \mathrm{L/min}\), so the filtered rate is \(0.090(0.40)=0.0360\ \mathrm{mg/min}\).