Unbound Drug Filtration Across the Glomerulus

From Plasma Concentration to Filtered Drug Amount

Glomerular filtration is a route by which drug leaves the plasma and enters the tubular fluid. Its rate depends on how much drug is available in the plasma water, how much fluid the kidneys filter, and how readily the drug crosses the glomerular filtration barrier. These quantities must be kept distinct: the plasma concentration reported for a drug is often total concentration, whereas filtration is driven by unbound drug.

The calculation below isolates filtration. It does not, by itself, describe what happens to drug after it enters the tubule. Tubular reabsorption or secretion can alter the amount ultimately excreted in urine, so filtration flux should not be equated with net urinary excretion unless those other processes are absent.

This definition of \(\theta_g\) is relative to unbound plasma concentration. If a data source instead defines a sieving ratio relative to total plasma concentration, that ratio already incorporates the effect of protein binding; multiplying it by \(f_{u,p}\) again would count binding twice. Always check the denominator used for the reported coefficient.

Deriving Filtration Flux and Clearance

Filtration flux is the amount of drug entering the filtrate per unit time. By definition, each unit volume of filtrate contains drug at concentration \(C_{\mathrm{filtrate}}=\theta_g C_{u,p}\). Multiplying this concentration by the volume of filtrate produced per unit time gives the amount filtered per unit time.

The units verify the result: volume per time multiplied by amount per volume gives amount per time. For example, if GFR is in L/min and concentration is in mg/L, \(\dot A_{\mathrm{fil}}\) is in mg/min. Clearance is the flux divided by the concentration used as its reference. Thus, filtration clearance referenced to total plasma concentration is \(\dot A_{\mathrm{fil}}/C_p\), whereas filtration clearance referenced to unbound plasma concentration is \(\dot A_{\mathrm{fil}}/C_{u,p}\).

Both quantities have units of volume per time, but they answer different questions. \(CL_{\mathrm{fil},p}\) is the filtration flux expressed relative to total plasma concentration; \(CL_{\mathrm{fil},u}\) expresses the same flux relative to unbound plasma concentration. When binding is negligible, \(f_{u,p}\) is near 1 and the two clearances are similar. When binding is substantial, total-plasma-referenced filtration clearance is reduced in proportion to \(f_{u,p}\), provided the sieving coefficient is defined as above.

Worked Calculations

Interpreting the Calculation and Checking It

The expression for filtration flux is a direct consequence of a volume rate multiplied by a concentration. Its simple form is useful in a PBPK model because it makes the dependencies explicit: at fixed GFR and \(\theta_g\), doubling \(C_{u,p}\) doubles filtration flux; at fixed concentrations and \(\theta_g\), doubling GFR doubles it. These proportionalities follow from the equation and apply only while the relevant parameters remain unchanged.

A practical calculation should pass several checks. First, concentration in filtrate must be \(\theta_g C_{u,p}\) under the convention used here. Second, the GFR and concentration units must cancel to amount per time. Third, the calculated filtration clearance should equal flux divided by the concentration named in its subscript. For \(0\leq f_{u,p}\leq1\) and \(0\leq\theta_g\leq1\), the model implies \(CL_{\mathrm{fil},p}\leq\mathrm{GFR}\) and \(CL_{\mathrm{fil},u}\leq\mathrm{GFR}\). A result exceeding GFR under these definitions signals a unit, definition, or calculation problem.

Filtration is only one term in renal drug handling. The earlier material on renal drug mass balance distinguishes filtration from the net balance that determines urinary drug recovery. If observed renal clearance differs from the filtration-only prediction, that difference does not by itself identify a mechanism. Check the concentration basis, binding measurement, GFR, sieving-coefficient definition, and units first. If these are appropriate, processes beyond filtration or a mismatch between the model assumptions and the physiological state may contribute. The filtration equation alone cannot separate those possibilities.

A second common error is to call \(\mathrm{GFR}\) the filtration clearance for every drug. That is only the unbound-referenced clearance when \(\theta_g=1\); the clearance referenced to total plasma concentration is \(\mathrm{GFR}\,f_{u,p}\theta_g\). A third error is to apply \(f_{u,p}\) when the provided sieving ratio is already defined relative to total plasma concentration. Establishing the coefficient's definition prevents this double adjustment.