Steady-state dialysis

A number of experimental methods are used to determine the amount of bound drug and/or free drug in a mixture, including equilibrium dialysis, steady-state dialysis, ultrafiltration, and size exclusion chromatography. Each of the methods is described briefly here. 

FIGURE 3.32 Steady-state dialysis method for analysis of drug—protein binding. 

The data analysis of the steady-state dialysis method is given by ... 

Steady-state dialysis - The equihbrium dialysis technique is accelerated by having buffer flow at a constant rate on one side of the semi-permeable membrane and by stirring both sides in order to minimize the concentration gradients [36]. Diafiltration - A type of dialysis equihbrium in which pressure is used to force the ligand-containing solution from one chamber into the protein-containing chamber [37]. 

The method tenned "recycling gel partition" by Ford and Winzor (ref. 35) is similar to the batch method, but it has the advantage of permitting convenient binding determinations for an entire series of different ligand concentrations in a way related to the steady-state dialysis method of Colowick and Womack (ref. 36). The partition equilibriun... 

Solute flux within a pore can be modeled as the sum of hindered convection and hindered diffusion [Deen, AIChE33,1409 (1987)]. Diffusive transport is seen in dialysis and system start-up but is negligible for commercially practical operation. The steady-state solute convective flux in the pore is J, = KJc = where c is the radially... 

Partial) dialysis in flow analysis. The sample solution flows along one side of the membrane, while the analyser solution passing (often in counter-current) on the other side takes up the diffused components from the sample. A dynamic equilibrium is reached (under steady-state conditions) in the leaving analyser solution, which is then analysed and from the result of which the analyte content can be derived via calibration with standard solutions treated in exactly the same way. This is a common procedure, e.g., in Technicon AutoAnalyzers, and has also been applied in haemoanalysis by Ammann et al.154 as described above. 

Graph used to calculate the point of no net flux for dopamine (DA). Using regression analysis, the extracellular concentration of DA is estimated via the difference method [the DA concentration in the perfusate minus the concentration of DA in the dialysate] plotted against the DA concentration in the perfusate. Values above the zero on the y-axis indicate diffusion to the brain, whereas values below the zero indicate diffusion from the brain. The zero point on the y-axis represents a steady state, at which no net flux of DA occurs across the dialysis membrane and represents the extracellular concentration of DA on the x-axis. Figure from Parsons, L.H., Justice, J.B., Jr. (1994). Quantitative approaches to in vivo brain microdialysis. Crit Rev Neurobiol. 8(3) 189-220... 

According to the Michaelis-Menten equation, the rate of the reaction depends on the activity of the enzyme, enzyme concentration, and upon several other factors such as the pH, the temperature, availability of cofactors, activators and/or inhibitors, and the concentration of the substrate (analyte). Moreover, the reaction rate depends on the thickness of the slice of tissue or crude extract, and on the size of the dialysis membrane, when used. By contrast, the steady-state potential obtained is dependent only on the substrate concentration and the temperature. 

Calibration is necessary to allow correlation between collected dialysis concentrations to external sample concentrations surrounding the microdialysis probe. Extraction efficiency (EE) is used to relate the dialysis concentration to the sample concentration. The steady-state EE equation is shown in equation (6.1), where Coutiet is the analyte concentration exiting the microdialysis probe, Ci iet is the analyte concentration entering the microdialysis probe, CtiSSue> is the analyte tissue concentration far away from the probe, Qd is the perfusion fluid flow rate and Rd, Rm, Re, and Rt are a series of mass transport resistances for the dialysate, membrane, external... 

In general, the volume of distribution of the central compartment (Vc), in which peptides and proteins initially distribute after an IVadministration, is typically equal to or slightly larger than the plasma volume of 3-8 L (approximate body water volumes for a 70-kg person interstitial 12 L, intracellular 27 L, intravascular 3 L). Furthermore, the steady-state volume of distribution (Vss) is usually no more than twice the initial volume of distribution, or approximately 14-20 L [13, 37, 43]. This distribution pattern has been described for the somatostatin analogue octreotide (Vc 5.2-10.2 L Vss 18-30 L), and t-PA analogue tenecteplase (Vc 4.2-6.3 L Vss 6.1-9.9 L) [52]. Epoetin-a also has a volume of distribution estimated to be close to the plasma volume at 0.0558 L/kg after an IVadministration to healthy volunteers [53]. Similarly, Vss for darbepoetin-a has been reported as 0.0621 L/kg after an IV administration in patients undergoing dialysis [54], and distribution of thrombopoie-tin has also been reported to be limited to the plasma volume (-3 L) [55]. 

Most membrane operations indicated in Table I are run as continuous steady state processes with a feed, permeate, and retentate stream (see Fig. 1). For example, in dialysis, a feed stream comprising blood with urea and other metabolic by-products passes across the upstream face of a membrane while an electrolyte solution without these by-products passes across the lower face of the membrane. A flux of by-products (A) occurs into the downstream where it is taken away as a permeate and the purified blood leaves as nonpermeate. 

Li et al. [37-39] described the use of the bacterial species Bacillus subtilis and Bacillus licheniformis entrapped between a polycarbonate membrane and a Teflon-covered DO probe. The differences between the steady-state signals before and after exposure to the test samples were used as a measure of the sample BOD levels. Riedel et al. [32-33] described the use of the yeast Trichosporon cutaneum, or both T. cutaneum and B. subtilis, sandwiched between a dialysis membrane and a polyethylene-covered DO probe. In these cases, the sensor response times were speeded up by measuring the initial rates of change of the signals. In this way, measurements could be made within 30 s rather than within 15-20 min for the steady-state approach [33]. 

In brain research, microdialysis sampling employing a miniaturized dialysis unit (probe) containing a dialysis membrane of a few millimeters length has become popular. The probe is implanted into the tissue or organ of the test animal and is infused with an isotonic solution (typically at 0.5-25 L/min). A steady-state osmotic flux across the membrane removes molecules with a mass below the cutoff of the membrane from the extracellular matrix. Microdialysis yields relatively clean samples of volumes in the range 20-100 jU-L. However, the recovery of neuropeptides can be as low as 0.5-15%, leading to a low neuropeptide concentration in the samples [5,6]. 

Antibodies raised to the transition state analogue (Fig. 7.3) will bind to the transition state of the hydrolysis reaction, lowering the activation energy and therefore catalyzing the reaction. These antibodies were trapped at the surface of a pH electrode using a dialysis membrane [Fig. 7.4(a)]. The reaction (Eq. 7.17) produces a change in local pH at the surface of the electrode, since acetic acid is one of the products. The measured pH therefore decreases as the phenyl acetate concentration increases in the external solution, since the steady-state concentration of acetic acid in the reaction layer increases [Fig. 7.4(b)]. 

Most problems with this procedure have involved tracer impurities and the separation of bound and free labeled fractions. Several separation techniques have been used, including equilibrium dialysis, membrane ultrafiltration, and steady-state gel filtration. Their deficiencies include a requirement for a large sample volume, the need for complicated correction of sample volume changes that occur during the separation, and difficulties of collecting and measuring radioactivity in numerous fractions of each sample. Equilibrium dialysis has been used most often in the past, but serious errors often arise from the sample dilution required by this method. Symmetrical dialysis of undiluted samples is reported to be less susceptible to tracer contamination and dilution effects. Ultrafiltration also appears to overcome these problems and to obviate errors caused by dilution. 

AC will decrease with time in the case of a batch dialysis cell, which is not at steady state. If the same type of membrane were run in a continuous process where the flow of the solution is countercurrent to the solvent flow direction, AC would be constant. In most applications, many of the cells are pressed together to make a stack, and all the cells are run in parallel. 

The key to economic cell production is rapid growth to cell densities like those in the rumen, namely 1010 or 1011 cells/ml. Acidic end-products are used to feed a methane generator, so that most of the carbon is recovered in a useful form. An unusual feature of this process is that rapid ultrafiltration rather than slow dialysis can be used to feed the methane fermentor. Insoluble substrates such as starch, hemicellulose or cellulose are retained within the rumen fermentor by appropriate membranes. The rapid interchange of soluble acids between the two fermentors allows only a low steady-state concentration to develop in the rumen fermentor because conversion to methane proceeds simultaneously in the second fermentor. 

Interesting peculiarities of mass transfer processes are observed in fine membranes permeable to ions but impermeable to colloidal particles (semipermeable membranes, e.g. collodium film). If such a membrane separates colloidal system or polyelectrolyte solution from pure dispersion medium, some ions pass through the membrane into the dispersion medium. Under the steady-state conditions the so-called Donnan equilibrium is established. By repeatedly replacing the dispersion medium behind the membrane, one can remove electrolytes from a disperse system. This method of purifying disperse systems and polymer solutions from dissolved electrolytes is referred to as the dialysis. 

Daptomycin is poorly absorbed orally and should only be administered intravenously. Direct toxicity to muscle precludes inttamuscular injection. The steady-state peak serum concentration following intravenous administration of 4 mg/kg in healthy volunteers is approximately 58 pg/mL. Daptomycin displays linear pharmacokinetics at doses up to 8 mg/kg. It is reversibly bound to albumin protein binding is 92%. The serum half-life is 8 to 9 hours in normal subjects, permitting once-daily dosing. Approximately 80% of the administered dose is recovered in urine a small amount is excreted in feces. Dosage adjustment is required for creatinine clearance below 30 mL/minute this is accomplished by administering the recommended dose every 48 hours. For hemodialysis patients, the dose should be administered immediately after dialysis. 

In 1993, a report, which helped to understand that conundrum of the KJratio to the high efficacy seen in vivo, was published. Researchers at Ciba-Geigy in Switzerland demonstrated that finasteride is a slow-onset inhibitor of type 2 5AR. However, the rate of inhibition is very slow such that steady-state rates are not reached until 30 min in the presence of 10 nmol 1 finasteride. For finasteride concentrations greater than 10 nmol 1, all progress curves displayed a plateau suggesting complete saturation of the ET complex. Attempts were made to determine a dissociation constant however, the ET complex could not be reactivated after 12 h of dialysis suggesting irreversible inhibition by covalent modification. The authors calculated a revised upper limit of 1 nmol 1 for the value of finasteride, which is more consistent with the clinical results. 

Another example deals with amino acid analysis using immobilized specific microorganisms in combination with selective electrodes (35). Thus, glutamine could be analyzed by an electrode consisting of a potentiometric ammonia gas sensor and a layer of the bacterium Sarcina flava (American type culture collection 147) trapped in the volume between a NHo-permeable membrane on the surface of the electrode and a dialysis membrane in contact with the surrounding solution (Fig. 10). Using this electrode, steady state potentials were reached within 5 minutes. 

FIG. 14 Dependence of the steady-state limiting current 4 on the concentration of o-glucose Cs h was measured at 0.5 V versus Ag/AgCl with film-coated glucose oxidase (180 rg)-BQ (30%)-carbon paste electrodes at a film thickness of (a) 50 /xm (nitrocellulose film), (b) 50 fim (dialysis membrane), and (c) 100 fjm (dialysis membrane). (From Ref. 33.)... 

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