Interpreting Total and Unbound Exposure in Organ Impairment

Why Total and Unbound Exposure Can Tell Different Stories

Organ impairment can alter both drug disposition and the fraction of drug bound to plasma proteins. In liver disease, for example, lower albumin concentration can increase the unbound fraction of some drugs; uremic substances can also affect binding. The total plasma concentration may then decrease while the unbound concentration stays similar or rises. A conclusion based on total exposure alone could therefore misrepresent the change in pharmacologically available drug.

The relevant comparison is not simply “total versus free.” Total exposure is useful for describing the amount measured in plasma and may be the exposure measure used to characterize safety or efficacy. Unbound plasma exposure is often more directly related to drug available for distribution, elimination, and target interaction. But unbound plasma concentration is not automatically the concentration at a tissue target, and neither measure is universally sufficient. Interpretation depends on the pharmacology, binding behavior, and whether the measurements and model represent the impairment state appropriately.

Definition: Let $C_{\mathrm{tot}}(t)$ be total plasma concentration at time $t$, including bound and unbound drug. Let $C_u(t)$ be unbound plasma concentration and $f_u(t)$ the unbound fraction. Under the usual equilibrium-binding description, $C_u(t)=f_u(t)C_{\mathrm{tot}}(t)$. Total AUC is the time integral of $C_{\mathrm{tot}}(t)$; unbound AUC is the time integral of $C_u(t)$. $C_{\max,\mathrm{tot}}$ and $C_{\max,u}$ are the maximum total and unbound concentrations over the specified observation interval.

For an impairment comparison, define an exposure ratio consistently as impaired-state exposure divided by reference-state exposure. A ratio above 1 indicates higher exposure in the impaired state; a ratio below 1 indicates lower exposure. Calculate separate ratios for total and unbound AUC, and, where peak exposure matters, for total and unbound peak concentration. State the units for the underlying exposures: for example, AUC in mg·h/L and concentration in mg/L. The ratios themselves are unitless.

From Binding Fraction to Unbound Exposure

The relationship between total and unbound AUC follows directly from the concentration relationship at each time. If $f_u$ is constant over the interval, it can be taken outside the integral. If it changes over time, it must remain inside the integral.

\mathrm{AUC}_u = \int_0^T C_u(t)\,dt = \int_0^T f_u(t)C_{\mathrm{tot}}(t)\,dt

\text{If } f_u(t)=f_u \text{ throughout } [0,T], \qquad \mathrm{AUC}_u=f_u\mathrm{AUC}_{\mathrm{tot}}.

This result assumes that the unbound fraction used is appropriate for the concentration range and biological matrix being considered. It does not assert that binding is unchanged between healthy and impaired states. In fact, the central issue here is often that the two states have different $f_u$ values. Nor does the formula imply that an unbound concentration is directly observed whenever total concentration is measured: estimating $C_u$ requires an appropriate binding measurement or a validated model.

Key result: When $f_u$ is constant within each state, the ratio of unbound AUCs is the total AUC ratio multiplied by the impaired-to-reference ratio of unbound fractions: $$ \frac{\mathrm{AUC}_{u,\mathrm{imp}}}{\mathrm{AUC}_{u,\mathrm{ref}}} = \frac{\mathrm{AUC}_{\mathrm{tot,imp}}}{\mathrm{AUC}_{\mathrm{tot,ref}}} \cdot \frac{f_{u,\mathrm{imp}}}{f_{u,\mathrm{ref}}}. $$

The same multiplication applies to peak concentrations only if $f_u$ is constant over the concentration-time profile in each state. More generally, $C_{\max,u}=\max_t\{f_u(t)C_{\mathrm{tot}}(t)\}$. The time of the unbound peak can differ from the time of the total peak. Thus, multiplying total $C_{\max}$ by an average or single-time binding fraction may give the wrong unbound $C_{\max}$.

Worked Comparisons

Worked Example: Total AUC Falls While Unbound AUC Rises

Suppose a hypothetical drug is administered under the same regimen in a reference group and an organ-impairment group. Within each group, assume $f_u$ is constant over the AUC interval. The reference group has total AUC $100$ mg·h/L and $f_u=0.010$. The impairment group has total AUC $60$ mg·h/L and $f_u=0.020$. Calculate and compare total and unbound AUC.

For the reference group:

\mathrm{AUC}_{u,\mathrm{ref}} = 0.010(100\ \mathrm{mg\cdot h/L}) = 1.00\ \mathrm{mg\cdot h/L}.

For the impairment group:

\mathrm{AUC}_{u,\mathrm{imp}} = 0.020(60\ \mathrm{mg\cdot h/L}) = 1.20\ \mathrm{mg\cdot h/L}.

The total AUC ratio is $60/100=0.600$. The unbound AUC ratio is $1.20/1.00=1.20$. Therefore, total AUC is 40% lower, while unbound AUC is 20% higher. The ratio identity gives the same answer: $0.600(0.020/0.010)=1.20$. If the corresponding total peak concentrations were 10 mg/L and 6 mg/L, their unbound peaks would be $0.010(10)=0.100$ mg/L and $0.020(6)=0.120$ mg/L, respectively, provided binding is constant over each profile. In this hypothetical comparison, the total measures alone would give the opposite directional impression from the unbound measures.

Worked Example: Calculating Both Exposure Ratios

Consider another hypothetical drug with reference total AUC $80$ mg·h/L and $f_u=0.020$, and impaired-state total AUC $44$ mg·h/L and $f_u=0.050$. The total peak concentrations are 8.0 mg/L and 4.4 mg/L, respectively. Assume each state’s unbound fraction is constant over time. Calculate the four exposure ratios.

The reference unbound AUC is $80(0.020)=1.60$ mg·h/L, and the impaired-state unbound AUC is $44(0.050)=2.20$ mg·h/L. Thus:

R_{\mathrm{AUC,tot}}=\frac{44}{80}=0.550, \qquad R_{\mathrm{AUC},u}=\frac{2.20}{1.60}=1.375.

For peak concentration, the reference unbound peak is $8.0(0.020)=0.160$ mg/L, and the impaired-state unbound peak is $4.4(0.050)=0.220$ mg/L. Therefore:

R_{C_{\max,\mathrm{tot}}}=\frac{4.4}{8.0}=0.550, \qquad R_{C_{\max,u}}=\frac{0.220}{0.160}=1.375.

Total AUC and total peak are each 45% lower in the impaired state, whereas the unbound AUC and peak are 37.5% higher. These results do not by themselves establish a change in clinical effect or toxicity. They show that the exposure conclusion depends on which exposure measure is connected to the relevant pharmacological endpoint.

Worked Example: A Changing Unbound Fraction Shifts the Unbound Peak

Suppose a hypothetical impaired-state profile is sampled at 0, 2, 4, and 8 hours. Total concentrations are 0, 8, 6, and 2 mg/L, respectively. Measured unbound fractions at those times are 0.020, 0.020, 0.040, and 0.040. Estimate AUCs by the trapezoidal rule and identify each peak among the sampled times.

Multiplying total concentration by the unbound fraction at each time gives unbound concentrations $0$, $0.160$, $0.240$, and $0.080$ mg/L. For total AUC, the trapezoidal contributions are $2(0+8)/2=8$, $2(8+6)/2=14$, and $4(6+2)/2=16$ mg·h/L. Hence $\mathrm{AUC}_{\mathrm{tot}}=8+14+16=38$ mg·h/L.

For unbound AUC, the contributions are $2(0+0.160)/2=0.160$, $2(0.160+0.240)/2=0.400$, and $4(0.240+0.080)/2=0.640$ mg·h/L. Thus $\mathrm{AUC}_u=0.160+0.400+0.640=1.20$ mg·h/L. The sampled total peak is 8 mg/L at 2 hours, but the sampled unbound peak is 0.240 mg/L at 4 hours. Multiplying the total peak by the unbound fraction at 2 hours would give $8(0.020)=0.160$ mg/L, not the unbound peak. The peak time changed because the unbound fraction increased later in the profile.

Assumptions, Diagnostics, and Interpretation

The calculations above are interpretable only when the underlying quantities are comparable. Total and unbound concentrations should refer to the same drug species, plasma matrix, dosing condition, and observation interval. If active metabolites contribute materially to pharmacology, parent-drug exposure alone may not characterize total pharmacological activity. A comparison should also distinguish plasma from whole-blood concentrations: a plasma $f_u$ cannot simply be applied to a whole-blood concentration.

For a constant-$f_u$ calculation, binding should be sufficiently stable over the profile and within the relevant concentration range. If binding is saturable, concentration-dependent, or altered over time by disease-related factors, use time- and concentration-appropriate $f_u(t)$ values or a binding model rather than one scalar fraction. Rapid equilibrium is generally presumed when relating instantaneous total and unbound concentrations; if binding is not at equilibrium on the timescale of interest, the simple relationship may not describe the profile.

Useful checks include plotting $C_{\mathrm{tot}}(t)$, $f_u(t)$, and their product, $C_u(t)$, on the same time grid; checking units and whether $0\leq f_u\leq1$; and verifying that integrated unbound concentrations agree with the reported unbound AUC. A suspicious result can arise from mixing binding fractions measured in different matrices, using one time-point fraction for a changing profile, or applying a fraction measured after sample dilution without accounting for the effect of dilution on binding. Very low unbound concentrations may also be close to an assay’s quantification limit, making an apparent change in $f_u$ or $C_u$ unreliable.

Approach	What it describes well	Main caution
Total exposure	Measured or modeled total plasma concentration; relevant when the endpoint or monitoring practice is empirically linked to total concentration.	May change because binding changes, even when unbound exposure changes little or in the opposite direction.
Unbound exposure	Unbound plasma concentration and its time course; often more directly related to target access and some clearance processes.	Requires appropriate binding data or a validated binding model, and may not equal tissue or target-site exposure.
Joint interpretation	Shows whether binding and disposition changes lead to different total and unbound conclusions.	Does not by itself identify the clinical consequence; the pharmacological endpoint and relevant exposure measure still need justification.

The choice between total and unbound exposure should follow the mechanism being interpreted. Unbound concentration is often a useful measure because unbound drug can cross membranes and interact with targets, but transporters, tissue partitioning, local binding, and barriers can make plasma unbound concentration an imperfect proxy for target-site concentration. Conversely, a validated therapeutic range or exposure-response relationship may be defined using total plasma concentrations. In those settings, replacing total exposure with unbound exposure without re-establishing the relationship can be misleading.

Nor does a binding change alone determine how systemic exposure must respond. Hepatic delivery, intrinsic metabolic capacity, renal elimination, and other processes can change at the same time as binding. The PBPK interpretation should therefore distinguish the modeled or measured concentration change from the proposed mechanism that produced it. An increased $f_u$ is not, by itself, proof that unbound AUC rises: total concentrations and clearance may also change.

Common Pitfall and Practical Use

A frequent error is to conclude, “Total AUC fell, so pharmacological exposure fell.” That conclusion assumes total and unbound exposure move together. The first worked example shows why that assumption can fail: a lower total AUC accompanied a higher unbound AUC. The correction is to report both measures when binding changes plausibly, calculate their ratios separately, and explain which measure is relevant to the pharmacological question. Avoid the opposite overstatement as well: a higher unbound plasma AUC does not prove greater target-site exposure or a particular clinical outcome.

A second error is to multiply total $C_{\max}$ by a single $f_u$ when the fraction varies over time. The peak of a product is not generally the product of the peak and a selected fraction. Calculate the unbound concentration profile first and then find its maximum. This is especially important when concentration-dependent binding or changing disease-related binding conditions can shift the time of the unbound peak.

The practical interpretation is strongest when the exposure metric, binding assumptions, and pharmacology are stated together. Report the impaired-to-reference total and unbound AUC ratios, and the corresponding peak ratios when peak exposure is relevant. Include the units of AUC and concentration, describe how $f_u$ was obtained, and indicate whether the unbound peak was calculated pointwise. Treat disagreement between total and unbound measures as a mechanistic clue to investigate, not as a calculation error to resolve by choosing whichever measure supports a preferred conclusion.

Check Your Understanding

Answer each question, then compare your reasoning with the solutions below.

A reference group has total AUC 50 mg·h/L and $f_u=0.040$. An impaired group has total AUC 40 mg·h/L and $f_u=0.060$, constant within each group. What are the two unbound AUCs and their impaired-to-reference ratio?
Why can total $C_{\max}$ multiplied by an average $f_u$ fail to give unbound $C_{\max}$?
What is one reason that unbound plasma exposure may not equal exposure at the pharmacological target?
A total AUC ratio is 0.70 and the ratio of impaired-to-reference unbound fractions is 1.50. Find the unbound AUC ratio, assuming constant $f_u$ within each state.

Solutions. (1) The reference unbound AUC is $50(0.040)=2.00$ mg·h/L; the impaired unbound AUC is $40(0.060)=2.40$ mg·h/L. The ratio is $2.40/2.00=1.20$, a 20% increase. (2) If $f_u$ varies over time, the maximum of $f_u(t)C_{\mathrm{tot}}(t)$ need not occur when total concentration is maximal, and an average fraction need not equal the fraction at the unbound peak. (3) Tissue transport, local binding, barriers, or tissue partitioning can separate plasma unbound concentration from target-site concentration. (4) The unbound AUC ratio is $0.70(1.50)=1.05$, or 5% higher in the impaired state.