Why distinguish blood from plasma?
Pharmacokinetic concentrations can be reported for plasma or for whole blood. These are different sample matrices, so a concentration measured in one is not automatically interchangeable with a concentration measured in the other. The blood-to-plasma concentration ratio summarizes their relationship for matched samples. In PBPK work, defining the ratio precisely helps ensure that a concentration, clearance, or model input is associated with the matrix it actually represents.
The ratio is a comparison of measured concentrations, not a binding constant and not, by itself, a measure of the concentration available to distribute or exert an effect. In particular, a ratio of total concentrations is not the same quantity as a ratio of unbound concentrations. Keeping those definitions separate is essential when interpreting data or converting between concentration measures.
Calculating the total-concentration ratio
“Matched” means that the blood and plasma concentrations refer to the same sampling time and the same relevant subject or experimental unit, with sample handling and measurement appropriate to the comparison. Pairing matters because concentrations can change over time. Dividing a blood concentration measured at one time by a plasma concentration measured at another time generally does not estimate the ratio for either time.
For example, if a paired whole-blood sample contains 6.0 mg/L and its plasma sample contains 4.0 mg/L, then \(R_{b:p}=6.0/4.0=1.50\). This says that the measured total concentration in blood is 1.50 times the measured total concentration in plasma for that pair. It does not say that the unbound concentration in blood is 1.50 times the unbound concentration in plasma.
Worked Example: A Single Paired Measurement
In a hypothetical experiment, matched blood and plasma samples collected at one sampling time have total concentrations of 8.4 mg/L and 6.0 mg/L, respectively. Calculate and interpret \(R_{b:p}\).
Check the inputs. Both values are total concentrations from matched samples, and both use mg/L. The ratio is therefore defined and the units cancel.
Calculation. $$ R_{b:p}=\frac{C_b}{C_p} =\frac{8.4\ \mathrm{mg/L}}{6.0\ \mathrm{mg/L}} =1.40. $$
Interpretation. For this hypothetical paired measurement, the total concentration in whole blood is 1.40 times the total concentration in plasma. The result is dimensionless. It is not an unbound concentration ratio or a statement about the concentration in a particular blood component.
A value greater than 1 means the measured total concentration is greater in blood than in plasma; a value less than 1 means it is lower in blood than in plasma; and a value of 1 means the two total concentrations are equal for the pair. These descriptions concern measured concentrations only. The ratio does not identify the mechanism underlying the difference.
Worked Example: Ratios Across Matched Sampling Times
In a hypothetical subject, paired total concentrations are measured at two sampling times. At the first time, \(C_b=3.6\) mg/L and \(C_p=4.5\) mg/L. At the second time, \(C_b=2.8\) mg/L and \(C_p=3.5\) mg/L. Calculate both ratios and compare them.
At the first time: $$ R_{b:p,1}=\frac{3.6\ \mathrm{mg/L}}{4.5\ \mathrm{mg/L}}=0.800. $$ At the second time: $$ R_{b:p,2}=\frac{2.8\ \mathrm{mg/L}}{3.5\ \mathrm{mg/L}}=0.800. $$
The total concentration is lower in blood than in plasma at both times, and the paired ratios are equal to 0.800. The equality does not mean that the concentrations themselves are equal: both concentrations fell between the two sampling times. Nor does equality at these two times establish that the ratio is constant at all times or concentrations; that would require more data and an assessment of variability.
Total and unbound concentration ratios
The definition above uses total concentrations. An unbound concentration ratio instead compares the unbound concentrations in the two matrices. If \(f_{u,b}\) and \(f_{u,p}\) denote the fractions unbound in whole blood and plasma, respectively, then the unbound concentrations are \(C_{u,b}=f_{u,b}C_b\) and \(C_{u,p}=f_{u,p}C_p\). Each fraction unbound is defined for its own matrix; it should not be assumed that the two fractions are equal.
The relation follows directly by substituting the definitions \(C_{u,b}=f_{u,b}C_b\) and \(C_{u,p}=f_{u,p}C_p\) into the unbound ratio, then grouping \(C_b/C_p\). It shows why the total ratio alone is insufficient to determine the unbound ratio: the fractions unbound in both matrices are also needed. If the fractions are equal, the two ratios are equal; without that equality, they generally differ.
Worked Example: Total and Unbound Ratios Are Not Interchangeable
For a hypothetical matched sample, suppose \(C_b=5.0\) mg/L and \(C_p=4.0\) mg/L. Suppose also that the fractions unbound are \(f_{u,b}=0.20\) and \(f_{u,p}=0.50\). Calculate the total and unbound ratios.
First calculate the total-concentration ratio: $$ R_{b:p}=\frac{5.0\ \mathrm{mg/L}}{4.0\ \mathrm{mg/L}}=1.25. $$
The unbound concentrations are: $$ C_{u,b}=0.20(5.0\ \mathrm{mg/L})=1.0\ \mathrm{mg/L}, \qquad C_{u,p}=0.50(4.0\ \mathrm{mg/L})=2.0\ \mathrm{mg/L}. $$ Therefore: $$ R_{u,b:p}=\frac{1.0\ \mathrm{mg/L}}{2.0\ \mathrm{mg/L}}=0.500. $$ The relationship gives the same result: $$ R_{u,b:p}=1.25\left(\frac{0.20}{0.50}\right)=0.500. $$
In this hypothetical example, the total blood concentration is 1.25 times the total plasma concentration, while the unbound blood concentration is half the unbound plasma concentration. Reporting only “the blood-to-plasma ratio is 1.25” would be incomplete if the intended quantity were the unbound ratio.
Handling multiple pairs and reporting the result
With repeated paired observations, the calculation can be made for each pair. The summary should match the scientific question: the mean of individual ratios, the median and spread of those ratios, or a ratio of group-level mean concentrations are different summaries and need not agree. Do not silently replace one with another.
For example, the mean of paired ratios gives each pair equal weight. A ratio of mean concentrations, \(\bar{C}_b/\bar{C}_p\), instead compares the two group means and can give relatively greater influence to pairs with larger concentrations. State which summary was calculated and report the units of the underlying concentrations, the number of pairs, and the sampling conditions. The ratio itself has no units.
Before calculating or summarizing ratios, check the following:
- Confirm that the numerator is whole-blood concentration and the denominator is plasma concentration.
- Confirm that measurements are paired by subject or experimental unit and sampling time.
- Convert concentrations to the same units before division.
- Check whether values are total concentrations or unbound concentrations, and label the ratio accordingly.
- Document how below-quantification values and missing or unpaired samples were handled; do not treat an undefined or unreliable quotient as an ordinary measured ratio.
| Quantity | Definition | What it compares |
|---|---|---|
| Total blood-to-plasma ratio | \(C_b/C_p\) | Total concentration in whole blood versus total concentration in plasma |
| Unbound blood-to-plasma ratio | \(C_{u,b}/C_{u,p}\) | Unbound concentration in whole blood versus unbound concentration in plasma |
| Plasma fraction unbound | \(f_{u,p}=C_{u,p}/C_p\) | Unbound versus total concentration in plasma |
These measures answer different questions. A plasma concentration alone describes the plasma measurement, but does not give the corresponding whole-blood concentration unless an applicable blood-to-plasma ratio is available. A total blood-to-plasma ratio summarizes matrix concentrations, but does not replace either fraction unbound when the intended comparison is between unbound concentrations.
Common mistakes and limitations
- Reversing the ratio. Calculating \(C_p/C_b\) gives the plasma-to-blood ratio, the reciprocal of \(R_{b:p}\), not the defined blood-to-plasma ratio. Keep the matrix order in the subscript consistent with numerator and denominator.
- Using unmatched samples. Pairing a blood result from one time with a plasma result from another can confound a matrix comparison with a change in concentration over time. Use matched measurements or clearly identify why the comparison is not paired.
- Calling a total ratio an unbound ratio. The total ratio is \(C_b/C_p\); the unbound ratio also depends on \(f_{u,b}/f_{u,p}\). Do not infer one from the other without the required data.
- Ignoring units or matrix labels. A quotient is meaningful only when the concentration units are compatible and the samples are correctly identified. A ratio calculated with mismatched units can be numerically wrong even if the arithmetic is correct.
- Overgeneralizing a measured ratio. A ratio from one sample or condition does not establish that the ratio is constant across times, concentrations, subjects, or experimental conditions.
The ratio is a compact descriptive quantity, but it does not explain why blood and plasma concentrations differ, establish that the difference is constant, or by itself determine the unbound concentrations. Its interpretation is limited by the sampling design, analytical performance, and conditions under which the paired values were obtained. Mechanistic explanations require additional information rather than inference from the ratio alone.
Check Your Understanding
Use the definitions and show the calculation in each answer.
- A matched hypothetical pair has \(C_b=2.4\) mg/L and \(C_p=3.0\) mg/L. What is \(R_{b:p}\), and how should it be interpreted?
- For a matched pair, \(R_{b:p}=1.5\), \(f_{u,b}=0.10\), and \(f_{u,p}=0.30\). Calculate \(R_{u,b:p}\).
- Why is a blood concentration measured at 2 hours divided by a plasma concentration measured at 4 hours generally not a matched blood-to-plasma ratio?
- Suppose a researcher reports \(C_p/C_b=0.80\). What is \(R_{b:p}\), assuming the concentrations are positive and matched?
- Can \(R_{u,b:p}\) be determined from \(R_{b:p}\) alone? State the additional information needed.
Solutions. 1. \(R_{b:p}=2.4/3.0=0.800\), so the total concentration in blood is 0.800 times the total concentration in plasma for that pair. 2. \(R_{u,b:p}=1.5(0.10/0.30)=0.500\). 3. The concentrations are from different sampling times, so a change over time is mixed into the quotient; it does not isolate the relationship for a matched occasion. 4. The blood-to-plasma ratio is the reciprocal, \(R_{b:p}=1/0.80=1.25\). 5. No. The fractions unbound in blood and plasma are also needed, because \(R_{u,b:p}=R_{b:p}(f_{u,b}/f_{u,p})\).