How to Calculate Fraction Unbound in Blood
Use direct concentration data or protein-binding constants to estimate free drug exposure (fu) in plasma.
Expert Guide: How to Calculate Fraction Unbound in Blood
Fraction unbound in blood, often written as fu, is one of the most important pharmacokinetic parameters in clinical pharmacology, toxicology, and therapeutic drug monitoring. It tells you what portion of a drug in plasma is free (not protein-bound) and therefore immediately available to cross membranes, interact with receptors, be metabolized, and be cleared. If you only track total drug concentration and ignore fu, you can miss major shifts in pharmacologic effect, especially in critically ill patients, older adults, patients with liver disease, kidney disease, pregnancy, inflammation, or severe hypoalbuminemia.
In practical terms, total concentration is often what labs report first, but free concentration is usually what drives effect at the target site. That is why accurate fu calculation is essential for dose individualization. This guide explains the formulas, interpretation, common pitfalls, and real-world ranges so you can calculate fu correctly and use it in a clinical decision framework.
What Fraction Unbound Means
When a drug enters blood, a portion binds reversibly to plasma proteins such as albumin and alpha-1-acid glycoprotein (AAG). The rest remains unbound. The unbound fraction is defined as:
- fu = Cu / Ct where Cu is unbound concentration and Ct is total concentration.
- Fraction bound (fb) = Cb / Ct where Cb is bound concentration.
- fu + fb = 1.
If fu = 0.10, then 10% is free and 90% is bound. A small absolute change in fu can be clinically meaningful for highly bound drugs. For example, a rise from fu 0.01 to 0.02 doubles the free concentration at the same total level.
Core Equations You Should Know
- Direct concentration method: fu = Cu / Ct.
- Using bound concentration: fu = (Ct – Cb) / Ct.
- Single-site binding approximation: fu = 1 / (1 + Ka × P), where Ka is association constant and P is free protein concentration.
- Free concentration recovery: Cu = fu × Ct.
The first two are measurement-based and preferred when equilibrium dialysis, ultrafiltration, or validated free drug assays are available. The Ka model is useful when direct Cu is unavailable and a simplified protein-binding model is acceptable.
Step-by-Step: How to Calculate fu Correctly
- Collect concentration data from the same timepoint and matrix (usually plasma).
- Confirm units are aligned before calculation (for example, both Ct and Cu in mg/L).
- Choose the method:
- If Cu and Ct are available, use fu = Cu/Ct.
- If Cb and Ct are available, use fu = (Ct-Cb)/Ct.
- If only Ka and protein are available, estimate fu by 1/(1+Ka×P).
- Calculate percent unbound: fu × 100.
- Calculate free concentration if needed: Cu = fu × Ct.
- Interpret in patient context: albumin, AAG, renal/hepatic function, inflammation, competing drugs.
Worked Example 1: Direct Unbound Method
Suppose a patient has total concentration Ct = 20 mg/L and measured unbound concentration Cu = 2 mg/L.
- fu = Cu/Ct = 2/20 = 0.10
- Unbound percent = 10%
- Bound percent = 90%
Interpretation: although total concentration is 20 mg/L, only 2 mg/L is pharmacologically free at that sampling time.
Worked Example 2: Bound Concentration Method
If Ct = 15 mcg/mL and Cb = 12 mcg/mL:
- Cu = Ct – Cb = 3 mcg/mL
- fu = 3/15 = 0.20
- Unbound percent = 20%
This method is useful when a study reports bound amount directly or when binding partitioning is derived experimentally.
Worked Example 3: Ka and Protein Model
Assume Ka = 10,000 L/mol and protein concentration P = 0.0006 mol/L:
- fu = 1/(1 + 10,000 × 0.0006)
- fu = 1/(1 + 6) = 1/7 = 0.1429
- Unbound percent ≈ 14.29%
If Ct = 35 mg/L at the same point, estimated Cu = 0.1429 × 35 = 5.00 mg/L.
Typical Binding Statistics for Common Drugs
The table below summarizes commonly cited plasma protein binding ranges for selected drugs. These values vary by assay, concentration, and patient population, but they are useful anchor points for interpretation.
| Drug | Approximate Protein Binding | Approximate fu | Clinical Relevance |
|---|---|---|---|
| Warfarin | ~99% | ~0.01 | Very small fu changes can disproportionately increase anticoagulant effect. |
| Phenytoin | ~90% (lower in hypoalbuminemia/uremia) | ~0.10 (can rise) | Total levels may mislead; free phenytoin is often preferred in critical care. |
| Valproic acid | ~80% to 95% (concentration-dependent) | ~0.05 to 0.20+ | Nonlinear binding means fu rises as concentration increases. |
| Ceftriaxone | ~85% to 95% | ~0.05 to 0.15 | Binding can change in critical illness and low albumin states. |
| Digoxin | ~20% to 30% | ~0.70 to 0.80 | Higher free fraction means total and free concentrations are closer. |
| Lithium | Minimal binding | ~1.00 | Nearly all circulating drug is unbound. |
How Albumin Changes fu: Quantitative View
Albumin is a major binder for acidic and neutral drugs. When albumin falls, fu generally rises. The modeled values below use fu = 1/(1+KaP) with Ka fixed at 10,000 L/mol and albumin converted to mol/L (molecular weight approximately 66.5 kDa). This illustrates direction and magnitude of change.
| Albumin (g/dL) | Albumin (mol/L, approx.) | Modeled fu | Unbound Percent |
|---|---|---|---|
| 4.5 | 0.000677 | 0.1287 | 12.87% |
| 3.5 | 0.000526 | 0.1597 | 15.97% |
| 2.5 | 0.000376 | 0.2101 | 21.01% |
| 1.5 | 0.000226 | 0.3070 | 30.70% |
Clinical takeaway: as albumin declines, a drug with strong albumin affinity can show a substantial increase in free fraction even if total concentration appears unchanged.
Common Errors That Cause Wrong fu Estimates
- Unit mismatch: dividing mg/L by ng/mL without conversion creates major errors.
- Different sampling times: Ct and Cu must represent the same timepoint.
- Assuming constant binding: many drugs show concentration-dependent or saturable binding.
- Ignoring physiologic shifts: inflammation can raise AAG, while liver disease can lower albumin.
- Over-reliance on total concentration: especially risky for highly bound drugs.
How to Use fu in Clinical Decisions
fu is most useful when linked to drug effect, safety targets, and patient status. For a highly bound antiseizure drug, for example, a “therapeutic” total level may coexist with high free exposure if albumin is low. Conversely, elevated AAG in acute stress can lower free concentrations for basic drugs, sometimes reducing pharmacologic effect even when total levels look adequate.
In drug development, fu informs volume of distribution, clearance modeling, and PK/PD target translation. In bedside care, fu supports better interpretation of total assays, dose adjustments, and toxicity risk assessment.
Reliable Reference Sources
For foundational and clinical reference reading, review these authoritative resources:
- NIH NCBI (Bookshelf): Pharmacokinetics and related clinical principles
- MedlinePlus (.gov): Albumin blood test interpretation
- U.S. FDA (.gov): Clinical pharmacology framework in drug evaluation
Final Practical Summary
To calculate fraction unbound in blood, the most direct equation is fu = Cu/Ct. If bound concentration is known, use fu = (Ct-Cb)/Ct. If only protein-binding parameters are available, estimate with fu = 1/(1+KaP). Then always convert fu into clinically meaningful outputs: free concentration and unbound percentage. For highly protein-bound drugs, this step is not optional. It is often the difference between a correct interpretation and a dangerous one.