Why Maternal Binding and Hemodilution Need Separate Accounting
Across gestation, plasma volume expands, hematocrit often falls, and concentrations of binding proteins can change. These changes matter because a measured total plasma concentration is not the same quantity as the unbound concentration in plasma. The whole-blood concentration is different again: it depends on both the plasma concentration and the amount of drug partitioning into red blood cells.
For many drugs, unbound maternal plasma concentration is the relevant maternal concentration to consider when describing passive transfer at the maternal side of the placenta. This does not by itself determine placental passage or fetal exposure: those also depend on properties of the placenta and the drug. Here the task is narrower: calculate maternal concentration quantities consistently, and understand how gestational changes in binding and blood composition affect them.
A reduction in binding protein can increase \(f_{u,p}\), but it does not automatically increase \(C_{u,p}\). If total plasma concentration is also changing, the unbound concentration depends on the product \(f_{u,p}C_{p,\mathrm{tot}}\). Likewise, a decline in total concentration does not establish that unbound concentration has declined. Calculate the quantities rather than inferring one from another.
Binding and the Unbound Concentration
A useful simplified model assumes reversible binding to one class of sites, with negligible site occupancy. If \(P\) is the concentration of available binding sites and \(K_a\) is an association constant, the unbound fraction is approximated by \(1/(1+K_aP)\). This approximation assumes binding is at equilibrium, binding is linear over the concentration range of interest, and other influences on binding are not changing. It is a calculation model, not a universal description of maternal binding.
The approximation shows why protein concentration and unbound fraction are not proportional in general. If protein concentration changes by a given percentage, the resulting change in \(f_{u,p}\) depends on the starting value of \(K_aP\). In practice, albumin and alpha-1-acid glycoprotein can change differently, and affinity can also be affected by competing ligands, pH, or other physiological conditions. A single-protein approximation should therefore be identified explicitly when used.
Worked Example: Estimating a Binding Change as Protein Concentration Falls
Suppose a hypothetical drug has an unbound fraction of 0.0500 at a binding-protein concentration of 40 g/L. For illustration, assume the low-occupancy model applies, the effective association constant is unchanged, and this protein is the only relevant binding protein. Estimate the unbound fraction at 30 g/L. Then compare unbound concentrations if total plasma concentration changes from 10.0 mg/L to 8.00 mg/L.
At 40 g/L, the model implies \(1/f_{u,p}=1+K_aP\). Thus \(K_aP=1/0.0500-1=19.0\). With protein concentration reduced to 30 g/L, the product becomes \(19.0(30/40)=14.25\). Therefore:
Initially, \(C_{u,p}=0.0500(10.0\ \mathrm{mg/L})=0.500\ \mathrm{mg/L}\). At the lower protein concentration, \(C_{u,p}=0.06557(8.00\ \mathrm{mg/L})=0.5246\ \mathrm{mg/L}\). Total plasma concentration fell by 20%, but the estimated unbound plasma concentration rose by about 4.92%. The conclusion follows from the stated binding approximation and the supplied total concentrations; it is not a general prediction that lower protein always increases unbound concentration.
Hemodilution Is a Concentration Effect, Not a Binding Equation
Hemodilution refers here to an increase in plasma volume relative to blood cells, commonly reflected in a lower hematocrit. Plasma-volume expansion can lower a concentration when the amount of drug in the relevant distribution space does not increase in proportion. It does not, by itself, specify what happens to binding or to the unbound concentration. Those require additional information about protein concentration, drug amount, distribution, and the timing of measurement.
A deliberately simple accounting example makes the distinction clear. Suppose, at a particular instant, 30.0 mg of drug is confined to the maternal plasma compartment. This is a hypothetical compartment calculation, not a complete maternal PBPK model. If plasma volume is 3.00 L, plasma concentration is 10.0 mg/L. If plasma volume expands to 3.90 L while the amount remains 30.0 mg and no other processes act, concentration becomes \(30.0/3.90=7.69\) mg/L. The amount is unchanged; the concentration is lower because it is distributed in a larger volume.
Worked Example: Combining Plasma Expansion and a Binding Change
Continue the simplified compartment calculation, and suppose the unbound fraction changes from 0.0500 to 0.0656 as in the preceding example. Assume the drug amount remains 30.0 mg in plasma, plasma volume expands from 3.00 L to 3.90 L, and the calculated unbound fraction applies at each time. Find total and unbound plasma concentrations before and after expansion.
Before expansion, \(C_{p,\mathrm{tot}}=30.0\ \mathrm{mg}/3.00\ \mathrm{L}=10.0\ \mathrm{mg/L}\), giving \(C_{u,p}=0.0500(10.0)=0.500\ \mathrm{mg/L}\). After expansion, \(C_{p,\mathrm{tot}}=30.0/3.90=7.692\ \mathrm{mg/L}\). The unbound concentration is \(0.0656(7.692)=0.5046\ \mathrm{mg/L}\).
In this constructed example, total concentration falls by 23.08%, while unbound concentration is almost unchanged, increasing by about 0.92%. The result combines two specified effects: dilution of the same amount into a larger plasma volume and a rise in unbound fraction. In a real maternal system, drug exchanges with tissues, is eliminated, and may enter or leave plasma; a one-compartment fixed-amount calculation cannot substitute for those processes.
When interpreting observations, distinguish a concentration measured at a clinical sampling time from a calculation that holds drug amount constant. Concentrations can also change because of dose timing, clearance, distribution, or adherence. The earlier material on pregnancy-specific changes in drug clearance concerns one of those additional processes; the binding calculation does not remove its influence.
Hematocrit and the Blood-to-Plasma Ratio
To convert between plasma and whole-blood concentration, define hematocrit \(H\) as the fraction of blood volume occupied by red blood cells. Let \(C_{\mathrm{RBC}}\) be drug concentration in red blood cells, and define \(K_{\mathrm{RBC},p}=C_{\mathrm{RBC}}/C_{p,\mathrm{tot}}\). Assume plasma and red-cell concentrations refer to the same sample at equilibrium, and that blood volume is represented by plasma and red-cell fractions. The whole-blood concentration is the volume-weighted sum:
Substituting \(C_{\mathrm{RBC}}=K_{\mathrm{RBC},p}C_{p,\mathrm{tot}}\) and dividing by \(C_{p,\mathrm{tot}}\) gives the blood-to-plasma relationship:
This derivation shows why hematocrit alone does not determine \(R_b\): the result also depends on red-cell partitioning. If \(K_{\mathrm{RBC},p}=1\), then \(R_b=1\) for any hematocrit under these assumptions. If drug concentration is lower in cells than plasma, a falling hematocrit moves \(R_b\) closer to 1; if cell concentration is higher, the direction is reversed.
Worked Example: Converting Whole-Blood Concentration to Unbound Plasma Concentration
A hypothetical maternal sample has \(C_b=4.20\ \mathrm{mg/L}\), \(H=0.300\), and \(K_{\mathrm{RBC},p}=1.40\). Assume the ratio is measured for this sample at equilibrium and applies to total concentrations. If the plasma unbound fraction is 0.0800, calculate \(R_b\), total plasma concentration, and unbound plasma concentration.
First, \(R_b=(1-0.300)+(0.300)(1.40)=0.700+0.420=1.12\). Since \(R_b=C_b/C_{p,\mathrm{tot}}\), total plasma concentration is \(C_{p,\mathrm{tot}}=4.20/1.12=3.750\ \mathrm{mg/L}\). Therefore \(C_{u,p}=0.0800(3.750)=0.300\ \mathrm{mg/L}\).
The whole-blood result is higher than the total plasma result because the assumed red-cell concentration exceeds the plasma concentration. Using 4.20 mg/L directly as the plasma concentration would instead give \(0.336\ \mathrm{mg/L}\) unbound, an overestimate under these stated conditions.
Putting Gestational Changes Together
A consistent comparison across gestation requires specifying which quantities are measured and which are assumed. The following hypothetical comparison holds the red-cell partition coefficient constant, while total plasma concentration, unbound fraction, and hematocrit change. It illustrates that total plasma, unbound plasma, and whole blood can move by different amounts and even in different directions.
| Time point | \(C_{p,\mathrm{tot}}\) (mg/L) | \(f_{u,p}\) | \(H\) | \(K_{\mathrm{RBC},p}\) | \(C_{u,p}\) (mg/L) | \(R_b\) | \(C_b\) (mg/L) |
|---|---|---|---|---|---|---|---|
| Reference | 8.00 | 0.100 | 0.400 | 0.500 | 0.800 | 0.800 | 6.40 |
| Later gestation | 6.00 | 0.160 | 0.320 | 0.500 | 0.960 | 0.840 | 5.04 |
For the reference time point, \(C_{u,p}=0.100(8.00)=0.800\ \mathrm{mg/L}\), \(R_b=0.600+(0.400)(0.500)=0.800\), and \(C_b=0.800(8.00)=6.40\ \mathrm{mg/L}\). Later, \(C_{u,p}=0.160(6.00)=0.960\ \mathrm{mg/L}\), \(R_b=0.680+(0.320)(0.500)=0.840\), and \(C_b=0.840(6.00)=5.04\ \mathrm{mg/L}\). Thus total plasma concentration decreases by 25%, unbound plasma concentration increases by 20%, and whole-blood concentration decreases by 21.25%. Under these assumptions, the increase in \(R_b\) reflects the lower hematocrit when red-cell concentration is below plasma concentration.
For a maternal concentration considered at the blood-facing side of the placenta, \(C_{u,p}\) is often a more informative input than total plasma concentration when transfer is driven by unbound drug. Whole-blood measurements can be used to recover plasma quantities only when the matrix conversion is supported by an appropriate \(R_b\), and unbound concentration still requires \(f_{u,p}\). This tutorial does not specify a placental transfer model.
Diagnostics, Alternatives, and Limitations
Before using these calculations, check that concentration units match, binding fractions lie between 0 and 1, hematocrit is entered as a fraction rather than a percentage, and \(R_b\) is formed from concentrations in the same sample. The equations also assume compatible sampling times: a binding fraction from one gestational time point should not be applied uncritically to a total concentration from another. If an inferred \(R_b\) is implausible or inconsistent with paired measurements, investigate matrix handling, assay methods, hematocrit, and whether red-cell partitioning varies with concentration or gestation.
A common mistake is to treat a lower total plasma concentration as evidence of lower unbound concentration, or to use whole-blood concentration as if it were plasma concentration. The correction is to calculate \(C_{u,p}=f_{u,p}C_{p,\mathrm{tot}}\) and, when starting with whole blood, first convert using \(C_{p,\mathrm{tot}}=C_b/R_b\). Another mistake is to attribute all gestational concentration change to hemodilution. A volume expansion calculation isolates dilution only when the amount and all other relevant processes are held fixed; clinical concentration changes generally do not satisfy that condition.
When available, measured unbound fractions and paired blood and plasma concentrations can avoid relying on a simplified binding or red-cell model. Model-based prediction may be necessary when measurements are unavailable, but it should represent the relevant binding proteins and their gestational changes as well as the drug's concentration range. Either approach has limitations: measurements can be sensitive to sample handling and assay conditions, while predictions depend on uncertain parameters and assumptions such as equilibrium and linearity. Report the assumptions and retain the matrix, gestational time point, and units alongside each concentration.
Check Your Understanding
For each question, try the calculation before reading the solution.
- A hypothetical drug has \(C_{p,\mathrm{tot}}=5.00\ \mathrm{mg/L}\) and \(f_{u,p}=0.120\). What is \(C_{u,p}\)?
- At two gestational time points, total plasma concentrations are 9.00 and 7.00 mg/L, while unbound fractions are 0.0400 and 0.0600. Does unbound concentration rise or fall, and by how much?
- If \(H=0.350\) and \(K_{\mathrm{RBC},p}=0.800\), calculate \(R_b\). If total plasma concentration is 2.50 mg/L, calculate whole-blood concentration.
- Why is a fixed-amount plasma-volume calculation not sufficient to predict a clinical unbound concentration during pregnancy?
Solutions. 1. \(C_{u,p}=0.120(5.00)=0.600\ \mathrm{mg/L}\). 2. Initially \(C_{u,p}=0.0400(9.00)=0.360\ \mathrm{mg/L}\); later it is \(0.0600(7.00)=0.420\ \mathrm{mg/L}\), an increase of \(0.0600\ \mathrm{mg/L}\), or 16.7%. 3. \(R_b=0.650+(0.350)(0.800)=0.930\); hence \(C_b=0.930(2.50)=2.325\ \mathrm{mg/L}\). 4. It holds the amount in plasma fixed and omits exchange with tissues, elimination, dosing, and other changes. A clinical unbound concentration also depends on the total plasma concentration and unbound fraction at the sampling time.