Summary
Clinical Pharmacokinetics 9 (Suppl. I): 49-60 (1984) 0312-5963/84/0001-0049/$06.00/0 © ADIS Press Limited. All rights reserved.
Ultrafiltration vs Equilibrium Dialysis for Determination of Free Fraction
William F. Bowers, Scott Fulton and Judith Thompson Amicon Corporation, Danvers
The analytical basis of membrane separation in determining plasma free drug concentrations is developed from consideration of the generalised ideal mass action and conservation laws applied to thermodynamic states of differing component volumes. The intuitively surprising theoretical independence of free drug concentration with changing fractional volume of protein predicts the equivalence affinal free drug concentration after uniform pre-dilution with that after equilibrium dialysis against the same volume ofbuffer. Similarly. the ultra filtrate free concentration of drugs in ideal plasma binding equilibrium is theoretically constant. regardless of the extent of reduction in fractional volume of binding protein during filtration.
The pi(fa/ls in calculating free and bound fraction and concentration from equilibrium dialysis are reviewed and expressions presented to correct the major artefacts. The dilution behaviour of drugs is predicted from the normalised mass action model. Practical aspects of l'alidating ultrafiltration free drug levels using equilibrium dialysis are outlined.
Although membrane separation methods are widely employed for determining the biologically available fraction of drugs, hormones or other ligands which reversibly bind to plasma protein, the analytical foundation and consequences of the physical separation have not always been fully appreciated. A number of reviews have appeared dealing with methods for protein-ligand binding study (Bush and Alvin, 1973; Chignell, 1972; Craig, 1965; Greenberg, 1944; Kurz et aI., 1977; Steinhardt and Reynolds, 1969). It is our purpose to, firstly, consider the predictions of the ideal mass action law for equilibrium states reflecting the changed volume occupied by free drug and plasma protein which result from membrane separation. Secondly, detailed expressions are presented for consistent calculation of free fraction and concen-
tration from equilibrium dialysis data. Thirdly, the dilution behaviour of constant and variably bound drugs is illustrated, and related back to the prediction of the generalised mass law. Finally, a scheme for meaningful comparison of ultrafiltration and dialysis is presented in the context of validating routine clinical free drug assays based on ultrafiltration.
1. Ideal Binding Equilibrium: Effect of Change in Component Volume 1.1 General Description
In the simplest model for drug binding to plasma protein considered in this section, we postulate a single drug in 'ideal' equilibrium with a single plasma protein binding site, implying that molar
Ultrafiltration vs Equilibrium Dialysis
concentrations are essentially equivalent to thermodynamic activities. For protein, the ideal requires that affinity and total binding capacity stay constant as drug binds or protein concentration varies, excluding complications such as allosteric interaction or masking of the binding site caused by protein self-association. Where the ideal model applies, the effect of volume change on drug binding will be predictable from the laws of mass action and conservation of mass. Similarly, we initially postulate idealised semipermeable membrane separations without complications due to nonspecific adsorption, Donnan equilibria, hindered passage of free drug, or leakage of protein.
In starting plasma, the drug binding equilibrium is
Cu + Cpu = Cb (Eq. 1).
Free protein site concentration can be rewritten as
Cpu = Cp - Cb (Eq. 2)
and drug protein complex as
Cb=C-Cu (Eq. 3).
Writing the mass action law in terms of the association constant,
Cb K = (Eq.4)
Cu' Cpu
we can substitute equations 2 and 3 to obtain the familiar quadratic equation for starting plasma free drug concentration:
Cb K =
Cu' (Cp - Cb)
(C - Cu) (Eq. 5) =
Cu • (Cp - C + Cu)
K· Cu2 + (K • Cp - K • C + 1) • Cu - C = 0 (Eq. 6).
50
Given a volume of plasma, V, equation 6 defines an initial plasma equilibrium thermodynamic state.
To calculate the effect on free drug concentration of a change in volume occupied by drug and/ or protein in a new thermodynamic state i, we invoke conservation of mass about protein, equating initial and final amounts:
Cp ' V = CPi • Vdpi (Eq. 7)
CPi = Cp ' V/Vdpi (Eq. 8)
and conservation of mass about free and bound drug
(Eq, 9)
Substituting into equation 5:
K= C' V(Vdpi - CUi' Vdu;/Vdpi
CUi' (Cp ' V/Vdpi - C· V/Vdpi + CUi' Vdu;/Vdpi)
(Eq. 11).
Multiplying through by V dpilV and rearranging gives:
K • Di • CUi2 + (K • Cp - K • C + D i) • CUi - C = 0 (Eq. 12).
Equation 12 is the generalised expression for free drug concentration in any state i of differing component volume, which may be evaluated by substitution of the dilution factor reflecting the new volume of distribution of free drug. Surprisingly, the free concentration of drug in state i given by equation 12 is independent of the protein volume of distribution in state i.
1.2 Uniform Dilution
After dilution, which we designate state 1, protein and free drug equilibrate to occupy the same increased volume, Vdp1 = VdUI' Substituting into equation 12:
Ultrafiltration vs Equilibrium Dialysis
K· DI • CUl 2 + (K· Cp - K· C + D I) • CUI - C = 0 (Eq. 13).
Since Dl is larger than 1, and all the other terms in equation 13 are the same as in equation 6, we see that CUI must be less than Cu. Equation 13 may be readily solved for the decreased postdilutional concentration of free drug.
1.3 Equilibrium Dialysis (Differential Dilution)
In equilibrium dialysis, which we designate state 2, the plasma retentate equilibrates across a semipermeable membrane with dialysate buffer. Protein osmotic pressure generally causes dialysis buffer to enter the retentate, while free drug diffuses into the dialysate buffer and comes to occupy the combined volume of the plasma and dialysate. As in state 1, we define a dilution factor for free drug as D2 = Vdu2/V and again substitute into equation 12 to obtain the equation of state 2:
K • D1 • CU12 + (K • Cp - K • C + D 2) • CU2 - C = 0 (Eq. 14).
Comparing the equations of states 1 (equation 13) and 2 (equation 14), we see that provided D, = D2, then CUl = CU2. Ideal uniform dilution and equilibrium dialysis against the same volume of buffer are thermodynamically equivalent states in terms of free drug concentration. If ideal protein binding is maintained, the mass law predicts that the free drug concentration after dilution depends only upon the free drug dilution factor, the total plasma concentrations of drug and protein, and the association constant, but is entirely independent of the protein dilution factor and resulting protein volume of distribution. Calculation of the diluted free concentration requires solution of equation 13 or 14, because free drug variation with dilution is non-linear and dependent on binding parameters.
The equivalence of uniform and differential dilution of free drug also provides an analogy for understanding the equilibrium basis of ideal ultrafiltration.
Glossary of Symbols"
C Plasma molar concentration of total drug
Cu Plasma molar concentration of unbound drug
Cb Plasma molar concentration of drug bound to a single site
51
Cp Plasma molar concentration of total protein binding Site
Cpu Plasma molar concentration of free protein binding site
K Equilibrium constant (L/mol)
V Volume of undiluted plasma
Vdp; Volume of distribution of protein (in vitro)
Vdu; Volume of distribution of unbound drug (in vitro)
D; Dilution factor for unbound drug (VdulfV)
CU2 Retentate concentration of unbound drug
C2 Relentate concentration of total drug
fu Plasma fraction of unbound drug (Cu/C)
fU2 Retentate fraction of unbound drug (Cu2lC2)
[DPMl Plasma concentration of tracer
[DPMol Dialysate concentration of tracer (no Donnan effect)
[DPMool Dialysate concentration of tracer (significant Donnan effect)
[DPMR] Retentate concentration of tracer (no osmotic dilution)
[DPMcb21 Retentate concentration of bound tracer (no osmotic dilution)
[DPMRO] Retentate concentration of osmotically diluted tracer
[DPMcu21 Retentate concentration of unbound tracer
EDR Effective Donnan ratio
Dp2 Dilution factor for retentate protein (Vdp2fV = Cp/CP2)
Subscript i Thermodynamic state after change in volume of distribution of unbound drug and/or protein
Subscript 1
Subscript 2
Subscript 3
Thermodynamic state after ideal uniform dilution
Thermodynamic state of plasma at dialysis equilibrium
Thermodynamic state after ideal ultrafiltration
• From the recently proposed general nomenclature for pharmacokinetics of Rowland and Tucker (1980).
Ultrafiltration vs Equilibrium Dialysis
1.4 Ultrafiltration(Differential Concentration)
In ultrafiltration, a pressure gradient forces plasma water containing free drug through a permselective membrane. The simplest model assumes complete selectivity of the membrane. The combined volume of ultrafiltrate plus retentate equals the (undiluted) initial plasma volume, so Vdu3 = V and D3 = I. Substituting into equation 12 for free drug concentration in the post-ultrafiltration thermodynamic state 3, comprising retentate plus ultrafiltrate,
K· Cul + (K· Cp - K· C + 1)· CU3 - C = 0 (Eq. 15).
Equations 6 for starting plasma and 15 for postultrafiltration equilibrium are, in fact, identical, predicting that ultra filtrate and retentate free drug concentration will be constant, regardless of the extent of ideal ultrafiltration and the degree of concentration of retained binding protein. Although the theoretical invariance of free ligand with changing protein volume of distribution was first stated in general form over 20 years ago (Gilbert and Jenkins, 1959) and later derived from different directions for ultrafiltration (Sophianopoulos et al., 1978; Whitlam and Brown, 1981), this point has escaped universal appreciation (e.g. Christensen et al., 1980; Jung et al., 1981; Paxton and Donald, 1980). Perhaps the most dramatic experimental demonstration of equilibrium ultrafiltration is the work of Paulus (1969), who found that aspartokinase substrate binding parameters obtained by ultrafiltration to apparent dryness and counting the fraction bound on the membrane agreed with results by an equilibrium gel filtration method.
An alternative intuitive explanation of the effect of component volume change can be found by reexamination of the mass law
Cb K = (Eq. 16).
Cu Cpu
Any dilutional change decreasing the concentration of free drug, Cu, will result in a dissociation
52
of Cb to Cpu; plus CUi, to maintain a constant value of K. Dissociation releases additional free drug, resulting in re-establishment of equilibrium at a new intermediate value of CUi and a new lower value of Cbi/CpUi.
In ideal ultrafiltration, however, free drug volume remains constant, while the concentrations of bound drug and free protein site increase at exactly the same rate as total protein. Thus, the retentate ratio Cbi/CpUi remains constant for any volume of ultrafiltrate, requiring no change in Cu to maintain K constant. Plasma free drug fraction is therefore theoretically obtainable directly from the ratio of ultrafiltrate free concentration to the total drug concentration in starting plasma.
1.5 Multiple Competing Ligands and Multiple Classes of Sites
The principles and predictions deloped for component volume effects on the free concentration of a single drug binding to a single non-interacting protein site are equally valid for the more general situation described, for example, by m classes of independent sites (k) in reversible equilibrium with n different competing drugs, metabolites or endogenous ligands (;) [Klotz and Hunston, i 975; Munson and Rodbard, 1980; Robbins and Johnson, 1979]. In this case, a set of simultaneous equations of state for the plasma concentration of each ligand can be written
"' ikK· JCu ,C = ,Cu + L: kCp· ------
k=1 n
I + L: ikK· JCu j=1
(Eq. 17).
Equation 17 is readily solved for the free and bound concentrations of each ligand using standard iterative numerical methods.
2. Determination 0/ Dialysable Plasma Free Drug 2.1 Dialysis Retentate Free Fraction
Although equilibrium dialysis is considered by many to be the preferred method for determining
Ultrafiltration vs Equilibrium Dialysis
drug-protein binding, the literature abounds with examples of incorrect calculation of dialysis data, and a number of critical papers have appeared dealing with various aspects of this thorny analytical problem (Behm and Wagner, 1979; Builder and Segel, 1978; Chadwick et aI., 1979; Kinget et aI., 1979; Kurz et aI., 1977; MacMahon et ai., 1984; McNamara and Bogardus, 1982; Nimmo et aI., 1977; Selikson et at, 1980; Smith and Jubiz, 1980; Steinhardt and Reynolds, 1969; Van der Giesen and Wilting, 1982). Common conceptual errors include failure to appreciate the dilutional shift in equilibrium caused by diffusion of free drug into the dialysate which increases the retentate bound fraction of variably bound drug, and failure to consistently define the post-dialysis equilibrium system with respect to free and total amounts of drug.
Practical problems often arise in dealing with significant Donnan effects, osmotic dilution of retentate, nonspecific adsorption of fee drug to the dialysis apparatus, binding of buffer ions, attainment of dialysis equilibrium, control of retentate pH, tracer impu.rity, and protein leakage into the dialysate.
In the calculation scheme suggested here, loss of drug by nonspecific adsorption is explicitly accounted for by determining levels in both dialysate and retentate. For variably bound drugs the retentate free fraction so obtained will reflect the actual equilibrium total drug level in the retentate after loss of free drug to the dialysate and to nonspecific adsorption, if present. Free fraction of the variably bound drug in starting plasma must then be calculated from empirical binding parameters for the plasma sample obtained at varying total drug concentrations (e.g. Behm and Wagner, 1979; Monot et ai., 1983) or preferably at varying dialysate volumes to account for endogenous binding inhibitors or competing ligands in the plasma sample (Sjoholm et aI., 1976; Smith and Jubiz, 1980).
Significant overestimation in free fraction and concentration can result from even slight leakage of protein into the dialysate. For a 90% bound drug, 1 % leakage of binding protein will cause a 9% over-
53
estimate of free drug concentration. Absence of protein in the dialysate should be confirmed with a sensitive protein assay.
In general, there will be an increase in the volume of dialysis retentate due to influx of dialysate caused by the colloid osmotic pressure of plasma protein. Use of isotonic or higher concentrations of low molecular weight buffer does not entirely prevent this osmotic dilution, because buffer and salt ions freely equilibrate into the plasma compartment, and the osmotic pressure due to protein remains to be satisfied. In practice, retentate plasma volume increases until a hydraulic counterpressure in the retentate is achieved which offsets the colloid osmotic pressure. Variation in the internal volume of knotted dialysis tubing, or in the stretching of the dialysis membrane in multichamber devices, results in considerable variation in the final osmotic-hydraulic equilibrium retentate volume. Accurate and precise determination offree fraction by dialysis thus requires correction for this variable dilution of retentate as outlined below.
The Donnan distribution may cause significant error in determination of plasma binding of drugs which are weakly or moderately bound, because the dialysate concentration will not reflect the free concentration in plasma retentate (Keen, 1966). Use of swamping concentrations of electrolytes to diminish the Donnan distribution may cause artefacts due to competitive ion binding (Steinhardt and Reynolds, 1969; Van der Giesen and Wilting, 1982). It is possible to correct for significant Donnan distribution by calculating the effective Donnan ratio from drug ionisation and the distribution of a non-binding ion (Boyer et ai., 1947; Keen, 1966; Suter and Rosenbusch, 1977). Alternatively, if dialysis is performed under essentially physiological conditions, for example using a plasma ultrafiltrate as the dialysate (Van der Giesen and Wilting, 1982), it could be argued that the Donnan distribution in vitro will generally mimic that in vivo across the capillary wall, and the obtained free drug concentration will more closely reflect pharmacological availability than does the true plasma free concentration.
In the idealised case of negligible osmotic di-
Ultrafiltration vs Equilibrium Dialysis
lution or Donnan distribution, the retentate and dialysate free concentrations are equal, and the retentate free fraction is:
[DPMcu21 = ----------~----
[DPMcb2] + [DPMcU2]
[DPMo]
[DPMR]
2.1.1 Osmotic Dilution of RetentateNegligible Donnan Effect
(Eq. 18).
Given the difficulty of determining post-dialysis retentate volume, the most accurate method of correction is to calculate the retentate protein dilution, DP2, from the ratio of protein concentration measured in starting plasma to that in an aliquot of retentate. The total drug concentration in retentate diluted by dialysate containing free drug is:
1 [DPMRol = [DPMcb21' - + [DPMol (Eq. 19).
Dp2
Solving for bound concentration in undiluted retentate:
[DPMcb11 = {[DPMRol - [DPMolJ • DP2 (Eq. 20).
The free fraction normalised to undiluted retentate:
[DPMo] ~2 = ------------------------~~~~
{[DPMRO] - [DPMo]} • D p2 + [DPMo] (Eq. 21).
In the limit of no dilution, DP2 = 1 and equation 21 reduces to equation 18.
2.1.2 Donna"n Effect - Negligible Osmotic Dilution For ionised drugs with moderate free fraction,
retentate total concentration and free fraction will be different to that for a non-ionised drug of comparable binding affinity and total plasma level, because the Donnan distribution reciprocally alters the free concentration in retentate and dialysate, requiring different dialysis equilibria in each case to satisfy the mass action law. As discussed above
54
for osmotic dilution and adsorption, exact determination of the plasma free fraction of variably bound drugs subject to significant Donnan distribution requires calculation from empirical apparent binding parameters obtained at varying total drug levels.
The free fraction reflecting the post-dialysis retentate level of ionised drug is obtained using the corrected dialysate concentration:
[DPMcu21 = [DPMool • EDR (Eq. 22)
[DPMooJ • EDR =
[DPMRI (Eq. 23).
2.1.3 Donnan Efj'ecl and Osmotic Dilution Combining equations 21 and 22
[DPMool • EDR fUl = --------------------------------
{[DPMRol - [DPMool • EDRJ ' Dp2 + [DPMool • EDR
(Eq. 24).
2.2 Dialysis Retentate Total Drug Concentration
As in section 2.1, in the idealised case of negligible osmotic dilution, the post-dialysis retentate total concentration is obtained from the drug and tracer levels in starting plasma
[DPMR] . c [DPM]
(Eq. 25).
Equation 25 reflects the actual total drug in the dialysed plasma, incorporating the effects of diffusion of free drug into the dialysate chamber, as well as significant nonspecific binding loss and Donnan effects, if present.
2.2.1 Osmotic Dilution of Retentate From equation 24, total concentration normal
ised to undiluted retentate is:
{[OPMROj - [DPMDDj' EDR} • D p, + [OPMooj' EOR C,= 'C
[DPM)
(Eq. 26).
Ultrafiltration vs Equilibrium Dialysis
If Donnan distribution is negligible, equation 26 is used with EDR set equal to 1.
2.3 Dialysis Retentate Free Drug Concentration
Post-dialysis free drug concentration is subject only to correction for the Donnan effect, if present:
[DPMDDl • EDR
[DPMl
[DPMDl
[DPM] ·c
·C
(Eq. 27).
3. Free Drug Variation with Dilution 3.1 Model Systems
By way of illustration, the effect of ideal uniform dilution and equilibrium dialysis on the free concentration and fraction of phenytoin is simulated in figure 1, using equation 12 and reported values for phenytoin-albumin apparent binding parameters (LeComte et ai., 1979). As seen in figure la, the predicted plasma phenytoin free fraction on the ordinate varies inversely with protein concentration, but is invariant with plasma total drug concentration over a range exceeding that seen clinically. Similarly, the predicted dialysis retentate free fraction, fU2' is constant with decreasing total retentate drug concentration caused by increasing dialysate volume dilution of free drug, represented by movement to the right along the solid lines. This again is consistent with the well-known independence of phenytoin free fraction with variation of total drug concentration within the therapeutic range (LeComte et ai., 1979; Lunde et ai., 1970; Porter and Layzer, 1975). Conversely, the ideal mass law model predicts that fu 1, the uniformly diluted phenytoin free fraction, will increase nearly proportionally with dilution in the therapeutic range, represented by movement to the right along the broken lines in figure lao This free fraction is equivalent to that obtained in equilibrium dialysis referred to total moles of drug in dialysate plus re-
55
tentate (Oppenheimer and Surks, 1964; Vlahos et ai., 1982). The predicted behaviour offu1 with uniform dilution is also in good agreemept with observed behaviour of this drug (Lunde et ai., 1970). The variation of free drug concentration with di-
O.B - - - fU1
--1"2
0.6
Cp (mmOI~) __ c: 0.4 0 ---'fi
2.5 ~ " ~ 0.2 u. 5
a
O.B
c: 0
~ 0.6
" u c: 8 " ~ 0.4
CUi '0
" CU ~ E C; 0 ... -C-z 0.2
b 0.8
0.-1
-
Phenytoin
/' /
/
Unbound solute
0.6 0.4
/ I / I
/ I // I
/ I // ,I
/
/' /'
/ /
0.2
Fig. 1. Dilution effect on plasma free phenytoin (after LeComte et aI., 1979). Simulations using equation 12 with K = 745 L/mol, n = 8 and albumin concentrations of 4.35g/100ml (Cp = 5 mmol/ L) or 2.18g/100ml (Cp = 2.5 mmol/L). Identical results obtained with total plasma drug concentrations from 0.5 to 25 I'g/ml (C = 2 to 100 I'mol/L). [0; = dilution factor for unbound drug.] (a) Effect of increasing dialysate volume on retentate free fraction, assuming retentate volume normalised to starting plasma volume according to equation 21. Also, effect of increasing buffer volume in uniform dilution on diluted free fraction assuming ideal mass law behaviour, or the equivalent dialysis free fraction referred to total drug in dialysate plus retentate. (b) Effect of dilution on free concentration compared with starting plasma.
Ultrafiltration vs Equilibrium Dialysis
lution for the 2 albumin total site concentrations of figure la is simulated in figure 1 b, expressed in normalised form as a fraction of the plasma free concentration. As drug binding increases with increasing protein concentration, 'buffering' ofthe free concentration to dilution increases and the free concentration curve shows greater departure from the limiting linear dilution behaviour of a nonbound solute (indicated by the dotted line).
The dilution behaviour of disopyramide, which exhibits variable binding in the therapeutic range, is in contrast to that of phenytoin. Scatchard analysis of plasma disopyramide binding indicates the presence of at least 1 high affinity, low capacity class of binding sites, as well as at least 1 lower affinity, less saturable class of site (Hinderling et aI., 1974). The 2-site apparent binding parameters of Hinderling and co-workers obtained with pooled plasma were used with equations 8 and 10 substituted into equation 17 to predict the behaviour of disopyramide (fig. 2). The intermediate pair of curves in figure 2a, which roughly correspond to the therapeutic range for disopyramide, show the significant variability of disopyramide retentate free fraction with dilution, emphasising the need for empirical model-fitting and back-calculation to accurately determine the plasma free traction from dialysis data for variably bound drugs. Figure 2b shows that free disopyramide concentration variation with dilution over the entire concentration range studied by Hinderling et al. (1974) is more nearly linear than that seen for phenytoin, reflecting the lower degree of plasma binding of this drug.
3.2 Normalised Binding Model
The constant or variable behaviour with varying total concentration of the free fraction of any drug can be more easily understood in terms of a normalised form of the mass action law (Rosner, 1975). This is obtained by rearranging equation 6 in terms of the bound drug fraction rather than the free drug concentration:
(Cb/C)' - ! I + C,,/C • [I + (1/C p • K)ll • Cb/C + Cp/C = 0
(Eq. 28).
56
For a single drug binding to a single class of site,
fu = 1 - CblC (Eq. 29)
and the behaviour of the free fraction for that interaction can be predicted from the ratio CplC and the product Cp ' K, (fig. 3). Uniform dilution can be visualised as vertical movement along a line
0.8
c: :8 g 0.6 Q) g 8 '" ~ 0.4 Cu, "0
'" c;u ~ ~ C,
Unbound solute z 0.2
-C-
b 08 0.6 0.4 0.2
D-' ,
Fig. 2. Simulations for the effect of dilution on free disopyramide (after Hinderling et aI., 1974). ,K = 1 X 106 L/mol; ,Cp = 1.6 I-'mol/L; 2K = 8.44 x 103 L/mol; 2Cp = 22.5 Ilmol/L. (a) Effect of increasing dilution on retentate free fraction. (b) Effect of dilution on normalised free concentration.
Ultrafiltration vs Equilibrium Dialysis
parallel to the ordinate, since the ratio Cp/C remains constant while Cp' K decreases. For all plasma free fractions less than unity, uniform dilution will thus cause a dramatic increase in the free fraction. Conversely, the differential dilution of free drug only in equilibrium dialysis, with the free fraction being defined in terms of the unchanged volume of retentate only, can be viewed as movement to the right along a given function line, where the value of Cp • K remains constant while Cp/C increases as total drug, C, decreases due to the loss of free drug into the dialysate. In this case the retentate free fraction will decrease as the
~ ~r-. 1.0
0.8 \1 \~
0.6
0.4
c: ofl g Q)
~ 0.2 u.
57
site to total drug ratio increases up to a limiting value for Cp/C of about 20 for systems with Cp • K products of up to about 100. For very high affinity or high capacity systems with Cp' K products well over 100, the limiting value for the free fraction will be reached at 0 for any value of Cp/C greater than I.
Looking back at the model systems in section 3.1, for phenytoin, Cp ' K is in the range 1.8 to 3.8, and Cp/C is greater than 25 for any value of plasma total phenytoin (C) up to 0.1 mmol/L (25 ~g/ml), approaching the upper limit of clinical practice. Referring to figure 3, the normalised model cor-
Cp·K
r-t-. 0.1
\
~ fU2 (0) -r ~r
~ 10' ~
-3 -2 -1 o 2 3 4
log (Cp/C)
Fig. 3. Variation of free drug fraction with Cp • K and CplC (after Rosner, 1975).
Ultrafiltration vs Equilibrium Dialysis
rectly predicts the constancy of the phenytoin free drug fraction with dialysate dilution or total plasma concentration. Similarly, the disopyramide system at the low end of the therapeutic total plasma drug concentration scale has 1 interaction with a Cp • K of 1.6 and CplC of 0.2 and a second site class with a Cp ' K of 0.19 and a CplC of 2.8. While binding to both classes of sites will vary with total drug level according to figure 3, clearly the former low capacity, high affinity interaction is nearly saturated in starting plasma, and this site will cause a significant decrease in free fraction with increasing dialysate volume, moving to the right down the steeply descending portion of the binding curve for this site.
4. Validation 0/ Ultrajiltrate Free Drug Level 4.1 Donnan Distribution
The presence of a Donnan distribution of micro-ions in ultrafiltration of protein solutions has been clearly documented (Boyer et aI., 1947; Greenberg and Greenberg, 1931-1932; Greenberg and Gunther, 1929-1930). The comments in section 2.1 on the Donnan distribution in dialysis apply equally to ultrafiltration. Greenberg and Gunther found identical 10% elevations in the chloride content of serum ultrafiltrates and dialysates. Furthermore, Greenberg and Greenberg found remarkably constant ion levels in increasing ultrafiltrate volumes from alkali caseinate solutions, in contrast to prediction, given the increase in retentate protein concentration which should amplify the Donnan distribution. While the constancy of ultrafiltrate ion concentration with increasing filtrate volume remains unexplained, ultrafiltration is nevertheless capable of giving free values for plasma ionised drugs which are equivalent to dialysis and similarly correctable by the effective Donnan ratio, if desired.
4.2 Membrane Permselectivity
Requirements for protein retention in ultrafiltration are comparable to those discussed for di-
58
alysis in section 2.1. Furthermore, the kinetic nature of ultrafiltration imposes requirements that the membrane pores be large enough to minimise the 'sieve' effect caused by preferential passage of plasma water vs free drug. Use of dialysis tubing for ultrafiltration can cause significant sieve errors depending on drug molecular weight (KUTZ et aI., 1977). Recently available ultrafiltration membranes offer significantly improved selectivity.
4.3 Free Drug Recovery From Plasma
In general, the most definitive protocol for ultrafiltration device validation is the sequential method (after Kurz et aI., 1977). In this scheme, patient plasma samples containing drug are first dialysed to equilibrium and the post-dialysis retentate free fractions calculated as described in section 2.1. The fraction thus obtained reflects nonspecific loss of drug to the dialysis system, if any, and the altered post-dialysis retentate free fraction of drugs exhibiting concentration-dependent binding or competitive binding with endogenous ligands. The dialysis plasma retentate is then ultrafiltered, and the free fraction calculated from the ultrafiltrate concentration over the dialysis retentate conceniration. Constant ultrafiltrate free fraction, with increasing filtrate volume (identical to the prior dialysis retentate free fraction) confirms negligible nonspecific loss of free drug to the ultrafiltration device, apparent ideal behaviour of drug binding during filtration, and negligible sieve effect in the presence of polarised retained plasma protein. Protein leakage into dialysate and filtrate should also be routinely monitored by protein assay in device validation studies.
Acknowledgements
We thank Peter Todd and Rudy Haschemeyer (Cornell University, Medical College) for developing the nonlinear least-squares program used for simulation of dilution effects in specific site multiple equilibria. We also thank David Kabakoff, Kaye Chegwidden, Maureen Cronin, Jane Ruppel, Anna Jaklitsch, Michael Wandell, and our many other colleagues at Syva Corporation for stimulating discussions and encouragement in the distillation of these comments.
Ultrafiltration vs Equilibrium Dialysis
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Ultrafiltration vs Equilibrium Dialysis
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Suter, P. and Rosenbusch, J,P.: Determination of the Donnan effect in equilibrium dialysis and a simple method for its correction. Analytical Biochemistry 82: 109-114 (1977).
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Whitlam, J.B. and Brown, K.F.: Ultrafiltration in serum protein binding determinations. Journal of Pharmaceutical Sciences 70: 146-150 (1981).
Authors' address: Dr William F. Bowers, Amicon Corporation, 17 Cherry Hill Drive, Danvers, Massachusetts 01983 (USA).