Erythrocyte uptake of drugs and its impact on volume of distribution (VD) determinations

In most volume of distribution (VD) determinations the drug partitioned in to erythrocytes (Cery) occupying 45% of blood volume is disregarded. The VD determinations can be erroneous on two accounts. The first is the indiscriminate reference to plasma (Cp) , whole blood (Cb) or serum (Cs) concentrations. The second is when Cery values are not considered in calculations. Isolated erythrocytes were incubated in plasma water (Cpw) represented by physiological saline drug solutions, the Cpw, Cery and Cb values were experimentally determined in vitro. Aberrations to the VD determinations are demonstrated using both theoretically and practically determined values of Cpw, Cery and Cb. Widely varying VD values 125 L to 2.55 L resulted when Cp data alone is used while the values differed marginally from 4.56 L to 5.53 L when Cb values were used for two setting using same amount of drug.


Introduction
The present study highlights the repercussions of indiscriminate use of drug blood concentration (C b ), plasma concentration (C p ) and serum concentration (C s ). A plasma determination is sometimes referred to as blood concentration. The erythrocyte partitioned drug has so far evaded receiving due recognition 1 . This identifies a fourth concentration parameter, which is the erythrocyte concentration of drugs (C ery ). This parameter is occasionally mentioned in the literature 2 . The C ery values are sometimes over five times higher than the C p values 3 . The results were treated to demonstrate variations in volume of distribution values with and without taking into account C rbc values. Similar variations were also demonstrated for situations where C b , C p or C s is used indiscriminately. The volume of distribution studies are understood with the aid of compartment models 5 .

Model theoretical V D calculations based on plasma (C p ), serum (C s ) or whole blood (C b ) concentrations:
The symbol C pw is for in vitro studies without using blood. The total blood volume of an adult is considered to be 4.5 L. Since 55 % by volume of blood constitute plasma, the volume of plasma approximates 2.5 L.
A 25 mg of a drug X was administered by IV bolus to a subject resulting in an immediate plasma concentration of (25 X 1000)/(2.5 X 1000)= 10 µg/ml, prior to drug partitioning. The figures 1a -e for 100 ml of blood depict the five situations required for the demonstration of model calculations. Lowering effects on drug concentrations C p and C ery due to 40% drug partitioning in to tissues are shown in Figure 1e.
The volumes of packed erythrocytes: plasma is 45: 55 and calculations must account for this numerical unevenness. Figure 1a shows a theoretical situation for a 100 ml blood sample immediately after a bolus injection of 25 mg of drug X before any partitioning. The blood and plasma are fully separated. This setup provides for an unaffected initial plasma drug concentration C p . Figure 1b shows the changes in Figure1a after the drug has partitioned in to erythrocytes. The concentration of the drug in erythrocytes (C ery ) and in plasma water (C p ) can be determined. Figure 1c shows a clear 100 ml plasma sample collected from supernatant after centrifugation, which had an initial drug concentration of 6µg/ ml as in Figure 1b. A fraction of drug is bound to plasma protein.
The separated serum now has a lower drug concentration of 4µg/ml. Here serum drug concentration C s can be determined. Figure 1d is similar to figure 1b but with lysed erythrocytes releasing the drug throughout the 100 ml sample. This gives the whole blood drug concentration C b calculated as follows.
Total drug in Figure 1b is calculated as follows. The amount of drug in plasma fraction = 6 µg/ml X 55 ml plasma = 330µg.The amount in erythrocyte fraction = 4.888 X 45 = 220 µg. Therefore the total drug in Figure 1d following erythrocyte lysis is 330 + 220 = 550 µg. The 550 µg quantity of the drug is distributed throughout the 100 ml sample. Therefore the resulting C b is 550µg/ 100 ml = 5.5µg/ml. Theoretical demonstration of anomalies of C P based V D determinations when C ery is neglected: An IV dose of 250 mg results in a 100 µg/ml (C P ) as explained earlier under subsection 'Model theoretical V D ……'.Take an extreme example where 98µg/ml of a drug has partitioned in to erythrocytes (C ery ) and only 2µg/ml is left in plasma (C P ) and also the reverse situation where 2µg/ml for C ery and 98µg/ml for C p . The V D calculations based on the above concentration values will be as follows.
The When considering 40% tissue drug diffusion, the values for plasma and erythrocytes can be expressed as C p ×0.6 (µg/ml) and C ery ×0.6 (µg/ml) respectively (Fig.1e).
Selected standard graphs for Doxycycline, Chloramphenicol and Rifampicin are shown in Figures 2, 3 and 4. Zones of inhibition for supernatant and erythrocytes following incubation in drug solutions are shown in Figure 5. Drug concentrations partitioned in to erythrocytes and remained in the supernatant are shown in Table 1.

Results
Calculations for percentage difference of V D values based on C Pw , C ery and C B given by the third dilution for chloramphenicol, 109.3µg /ml (Table 1)

Discussion
On an average adult blood volume of 4.5 L the erythrocytes occupy 45% equivalent to 2.0 L. The drug in erythrocytes is not represented in the formula D B = V D . C P.
Most studies avoid C b determinations due to the presence of hemaglobin from lysed erythrocytes. The regular formula for volume of distribution determinations should be V D = D B /C b . This formula is mainly applicable for an IV administered drug that follows one compartment model. Drug partitioned into erythrocytes practically acts like a portion that has been spilt out of the compartment model studies. In this event all the determinations that follow are flawed.
There is a problem with protein binding C protein (Fig.1c). In the case of the anticoagulant warfarin, protein binding is as much as 99% of the drug. The V D values using C P yield unrealistic results unless the analytical procedure extracts the bound drug as well. The degree of saturation of binding sites, the intensity of binding forces, type of bonds, functional groups of amino acids involved, types of plasma proteins involved, the polarity of extracting solvent system can all affect the extraction of the drug from the protein complex as against the free drug.
Equations A and B show that although the same amount of drug remains within the vascular system a drastic difference of over 40 times in the V D values when C P values are used in the calculations. Equations C and D show that results from C b values will remain nearly equal with only about 10% difference. Under C and D, the C ery fraction which has not diffused in to tissues is accounted reflecting the amount of drug held within the vascular system.
For all intent V D informs us how the drug is distributed in the body. Accordingly, a drug that accumulates in tissues draw most of the drug out of vascular system leading to a low C P and a large V D as per formula V D = D B / C b . Both the fractions of drug represented in plasma C P and in erythrocytes C rbc are intravascular based. These two fractions do not account for the drug distributed in to tissues which the V D intends to reflect. Now a low C P and a large V D as described above will still appear to hold good even when C rbc is five times the C P as in the case of chloroquine infected with Plasmodia. It is a distortion of the real situation with respect to biopharmaceutical interpretation of disposition of a drug. There is not so much drug in tissues as it appears. In such a situation the use of whole blood drug concentration C b which is a larger value than C P will better reflect a comparatively lower V D as most of the drug is accumulated in the erythrocytes.
The accurate formula for volume of distribution determinations should be V D =D B / C b in which C b accounts for drug in plasma, plasma protein bound drug and the drug in erythrocytes 7 . In other words all of C P, C protein and C rbc should be lumped together using the weighted average as their volumes are not equal.

Conclusion
The amount of drug partitioned in to erythrocytes and remained in plasma varied between large percentages as indicated in Table 1. There appear to be an increasing trend in the erythrocyte partitioning when the concentration of the drug was increased.
Chloramphenicol, Rifampicin and Oxytetracycline shows significant amount of erythrocyte partitioning. It indicates a potentially deleterious effect on volume of distribution determinations if C ery values are ignored. When C b values are used no such differences occur as demonstrated by equations C and D. The determination of volume of distribution using only the plasma drug concentration could be misleading. The erythrocyte partitioning should to be taken into consideration to arrive at C b for realistic V D determinations.