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A composite physical model involving the simultaneous receding boundary release of drug from a drug suspension–silicone polymer matrix system, diffusion across the aqueous layer, and passive transport across the vaginal membrane consisting of parallel lipoidal and aqueous pore pathways is described. Simulation studies with progesterone and hydrocortisone illustrate matrix release‐limiting, membrane absorption, and aqueous diffusion layer‐limiting cases when the cylindrical silicone delivery device is interfaced with the vaginal membrane of the rabbit.

The absorption of unbranched aliphatic alcohols in the rabbit vagina was studied using a perfusion method, and the absorption rates were found to be first order with respect to the drug concentration in the vagina from methanol to octanol. A physical model involving an aqueous diffusion layer in series with a membrane consisting of aqueous pores and lipoidal pathways was used for analyzing the data. The physically based parameters in the model were determined. An effective diffusion layer thickness (“unstirred layer”) of around 0.035cm was found. The increase in the permeability coefficient for the lipoidal pathway per methylene group was around 2.5 for this homologous series.

A model and explicit equations were developed to be used in the experimental design and data evaluation of situations where simultaneous metabolism and transport of drugs occur in the skin. By treating the skin as a two-ply laminate composed of the stratum corneum and the viable epidermis, which contains most of the catabolic enzymes that might render a drug inactive by metabolism, equations were developed permitting the in vitroassessment of factors that may affect topical bioavailability in vivo. Two situations were investigated. In the first, the drug was placed on the dermis side of the diffusion cell and did not penetrate the stratum corneum. In the second, the drug, placed on the epidermis side, penetrated the stratum corneum and then passed through the metabolizing epidermis. Expressions for determining the metabolic

This paper explores the physical model approach in studying the taste of drugs and assessing physical formulation factors for improving the undesirable taste of drugs. Various aspects of physiology relevant to the taste phenomenon have been reviewed to provide the biophysical basis for mathematical modeling. The model involves non-steady-state mass transport across the aqueous boundary layer and buildup of solute concentration at the essentially impermeable tongue surface. The theoretical predictions are consistent with experimental studies on the lag time to taste perception by the electrophysioiogical method and also with “instantaneous” psychophysical taste perception when solute concentrations much greater than the taste threshold are applied on the tongue. Within the framework of the non-steady-state model, novel experimental studies involving the use of a porous half-diffusion cell placed on the surface of an extended human tongue and the recording of the times for psychophysical taste response are proposed to quantify and provide mechanistic understanding of the taste of drugs and also physical formulation factors in overcoming undesirable taste properties.

A physical model including a diffusional layer in series with the membrane was developed for studying the possible differences between the pH at the membrane surface and that in the bulk solution. Both the membrane-secreted substances (acids and bases) and buffer constituents in the bulk solutions are assumed to contribute to the surface pH. Equations derived for this situation, together with experimental determinations of the acidic dissociation constant of the secreted material, the total secretion flux, the flux of total secreted acidic species, and the diffusional layer thickness, allow estimates to be made of the pH at the membrane surface. With the rabbit vagina, the membrane surface pH was close to that of the bulk solution in most cases. These results weresupported by the fact that the absorption of 1-alkanoic acids in pH 2.2phosphate buffers was relatively constant over the buffer concentrationrange of0.003–0.1Mphosphate.

The vaginal absorption of a homologous series of ionizable compounds, the 1-alkanoic acids, was studied using a perfusion method with a rib-cage cell surgically implanted in the rabbit vagina. The absorption rates of these compounds followed first-order kinetics. The physical model previously used for the 1-alkanols, but accounting for the pKa and pH effects in the present case, was employed in the analysis of the carboxylic acid data. The aqueous diffusion layer thickness was 0.031cm. The permeability coefficient for the lipoidal pathway increased 3.5-fold per methylene group. Both values agree reasonably well with those obtained in the alcohol study.

A physical model for the lyophilization kinetics of parenteral formulations is presented. Mathematical relationships are derived, which involve the simultaneous change in the receding boundary of the ice‐vapor interface with time as well as water vapor diffusion across the dry porous matrix and boundary layer. Heat from an external heat source is transferred across the frozen solution to the receding ice surface. The model predicts that the water lost and the receding boundary distance are linearly related to the square root of time when lyophilization is matrix controlled. The mathematical descriptions are predictive of the physicochemical and transport events and can lead to the design of quantitative experiments to relate theory to formulation design.

The kinetics of uptake and release of desmosterol, cholesterol, and β‐sitosterol by Burkitt lymphoma cells at 26°, pH 7.3, and isoosmotic conditions were quantitatively and mechanistically interpreted. The data are in agreement with the model involving the passive transport of the unbound sterol across the ratedetermining plasma membrane, with rapid distribution within the heterogeneous cell interiro. Effective permeability (Pe) and partition (Ke) coefficients of the sterols were inversely proportional to the serum concentration in the external media due to sterol‐serum binding. These results are consistent with the mechanism in which only the unbound solute in the external solution participates in the membrance transport process. At al serum levels, Peand Keincreased with increasing sterol polarity: desmosterol > cholesterol > β‐sitosterol.

General physical models are derived for the diffusional transport of drugs across membranes of mammalian cells in culture suspension. These models represent different sets of possible physical processes taking place during the transport of a drug molecule. Once the diffusing species reaches the cell barrier, it may gain entrance to the cell kinetically by one of the principal quasisteady‐state mechanisms, all of which assume the cell membrane to be an integral part of the total barrier.

Mass transport studies with three cardiac glycosides in the Burkitt lymphoma cell system have provided significant examples of the factorization and quantification of the influences of serum‐drug binding, membrane‐drug binding, cell interior binding, and intrinsic membrane permeability upon the uptake and release kinetics of drugs in living cell systems. All of the data from the glycosides are in agreement with the general physical model involving the rapid equilibration of the solute within the cell after permeation through the rate‐determining plasma membrane barrier. The transport of digitoxin was influenced by membrane and serum binding and that of digoxin was influenced by membrane binding. There was no binding of ouabain to the plasma membrane and serum. The variables in the uptake and release kinetic studies at pH 7.3 included the use of viable and heat‐inactivated cells, fetal bovine serum levels, and temperature.

In situabsorption studies with dinoprost in the rat jejunum were carried out using a modified Doluisio technique. The absorption rate was first order. There was a sigmoidal decrease in the rate with increasing buffer pH (from 3.5 to 9.5), which strongly indicated the partitioning of weak acid species into the lipoidal membrane. An asymptotic minimum rate was attained from buffer pH 7.5 to 9.5, operationally indicative of transport of anions across aqueous pores. The importance of the aqueous diffusion layer on the mucosal side of the membrane was evident; rates at pH 3.5 and 4.5 were faster at high agitation hydrodynamics in the lumen solution. Preliminary studies showed that there was no metabolism in the lumenal solution and that metabolism occurred within the membrane. The transport mechanism involved simultaneous passive diffusion and bioconversion in the membrane because (a) a 1.5 × 104-fold range in dinoprost concentration (0.014–210 μM) showed no saturable carrier-mediated tendency on the rate, (b) iodoacetic acid and indomethacin did not inhibit the absorption rate, and (c) the shape of the absorption-pH profiles was suggestive of passive diffusion. The prostaglandin did not have apparent adverse membrane and vascular effects under the conditions employed. The quantification and factorization of the physically meaningful transport parameters were accomplished using the physical model previously described. The permeability coefficients of the aqueous diffusion layer for the oscillation and static hydrodynamic situations were 0.8 × 10−4and 1.7 × 10−4cm/s, respectively. The effective transport-bioconversion permeability coefficients of the membrane were 2.57 × 10−4cm/s at buffer pH 3.5 and 1.46 × 10−4cm/s at pH 4.5; the effective permeability coefficient of the aqueous pores was 1.5 × 10−5cm/s. Depending upon the buffer pH, 3.5 or 4.5, and the two hydrodynamic situations, the total transport rate was 45–76% aqueous diffusion controlled.

In situabsorption studies with dinoprostone in the rat jejunum were carried out to provide a quantitative mechanistic insight of the absorption process. The variables included buffer pH (3.5–9.5), buffer capacity, hydrodynamics in the lumen, and concentration. The disappearance kinetics from the lumen was first order. The rate decreased with increasing pH in a sigmoidal manner and reached a minimum at about pH 9. These results indicate the effects of the partitioning of nondissociated species in the lipoidal membrane and transport across aqueous pores. The rate was higher with the higher degree of agitation of the lumenal solution. Between two hydrodynamic situations, the differences in the rates were large at pH 4.5 where the transport was largely aqueous diffusion controlled and then tended to become smaller with increasing pH where the transport became effectively membrane controlled. The 15-oxo- and 13,14-dihydro-15-oxo metabolites of dinoprostone were found. The physical model was applied to quantify the permeability coefficients of the aqueous diffusion layer and the aqueous pores of the membrane and the effective membrane transport-bioconversion permeability coefficient at various pH values. The overall absorption process of dinoprostone was similar to that of the less lipophilic dinoprost reported earlier and also more rapid. Hence, baseline absorption studies were completed with two major reference prostaglandins from which estimations of intestinal absorption can be made for their analogues and derivatives.

A method for evaluating the passive permeability and single-step metabolism of drugs in suspension cultures of mammalian cells was formulated assuming linear kinetics. It was assumed that the metabolizing enzymes are driven by endogenous substrates present in steady-state quantities. The presence of the drug in radiolabeled tracer quantities was assumed to cause only a small perturbation from the endogenous steady-state operating point. The time course solutions for the drug and its metabolite are given in terms of macroscopic constants, and their physical interpretations are given in terms of metabolic and transport parameters.

Earlier reports from these laboratories described a procedure for determining vaginal drug absorption in the rabbit based upon a perfusion system, and data on the vaginal absorption of the straight-chain aliphatic alcohols and carboxylic acids were given. These studies have been extended to the rhesus monkey. Rib-cage-type cells were designed for intravaginal insertion through the vulval orifice and to fit the specific dimensions of the monkey vagina. The general design of the cell was similar to that used in the rabbit vaginal absorption studies. The perfusion system was checked by using 3H-polyethylene glycol 4000, and no significant leaks from the cell were found. The absorption of the alcohols followed first-order kinetics. The computed apparent permeability coefficients for the alcohols were of comparable magnitude to those previously reported for the rabbit vaginal membrane.

A general physical model is described for the simultaneous active and passive transport of conjugated and unconjugated bile acids from nonmicellar solutions in the ileum. It reduces to the passive absorption mechanism in the duodenum and jejunum. The model provides the basis for the experimental design of in situ studies and the quantification of physically meaningful and experimentally accessible transport parameters and of the effect of functional groups on bile acids. The interaction and factorization of (a) the permeability of the stagnant water layer, the lipoidal and aqueous channel pathway of the membrane according to the diffusion mechanisms, (b) the permeability of the membrane according to the active mechanism, (c) the bile acid concentration dependence, and (d) the pH and pKa are mathematically explicit. Theoretical computations indicated that the stagnant water layer may be the rate-determining barrier. A model is described for the first-pass absorption of bile acids from dilute solutions in the small intestine.

The predictive value of a recently developed physical model was tested in the topical treatment of cutaneous infections caused by herpes simplex virus type 1 in hairless mice with two ester prodrugs of 9-β-D-arabinofuranosyladenine (ara-A) (1). The tests were conducted with 2′,3′-di-O-acetyl-ara-A (4) and 5′-O-valeryl-ara-A (3) topically applied with and without 15% 1-dodecylazacycloheptan-2-one (2) (Azone), a percutaneous penetration enhancer. In addition to the in vivo studies, in vitro diffusion cell experiments with excised, full-thickness skin from hairless mice were conducted to determine the penetration enhancement effects of 2. As previously observed, 2was able to induce remarkably large (100- to 1000-fold) flux enhancements in these in vitro experiments. Consistent with predictions based on the physical model studies, formulations of 3and 4without 2had little or no influence on the pathogenesis of the herpes simplex virus type 1 infections; when 2was present in the formulations, both 3and 4had dramatic therapeutic effects consistent with the predictions made with the physical model. Prodrug 4with 2was especially efficacious in the prevention of virus-induced lesions and in the survival of all animals. Similar results were obtained with acyclovir plus 2in this model system.

The simultaneous chemical equilibria and mass transfer of basic and acidic drugs through a two-phase compartment model were theoretically investigated. The model consisted of a well-stirred bulk aqueous phase, an aqueous diffusion layer, and a lipid barrier for perfect and imperfect sink cases. The nonsteady and quasi-steady-state changes in the concentration-distance distributions in the lipid phase were studied. The rate of change of the total drug concentration in the bulk aqueous phase was described in the general form of a first-order equation useful for the evaluation of experiments. A limiting steady-state relationship involving the transport rate with the partition coefficient, pH at the aqueous-lipid interface, dissociation constant of the drug, aqueous and lipid diffusion coefficients, and thickness of the diffusion layer was derived. Increasing the agitation rate in the aqueous phase markedly affects the pH profiles for the rate of transport. The pH-partition theory is shown to be a limiting case of the more general approach presented.

The present study was part of a long-range attempt to describe quantitatively the coalescence or flocculation behavior of emulsions. Several baseline experiments of emulsion coalescence kinetics were conducted with stress placed on the elimination of possible artifact effects. Dibutyl phthalate, dioctyl phthalate, ditolyl, and “Unity Oil” were chosen as the oil phases in this investigation. Dilute emulsions of the oils in varying concentrations of sodium lauryl sulfate solutions were prepared ultrasonically, and the changes in the particle number and size distribution with time were studied in electrolyte solutions. The data obtained were treated by plotting the reciprocal of the cumulative number of particles greater than a specified size versustime. A theoretical analysis involving the consideration of finite emulsion droplet-size distributions showed that this method of data treatment is valid for the experimental systems in this study. For rapid reaction systems, the slopes of these Smoluchowski-type plots were directly related to the Smoluchowski rate constant. Rapid reaction conditions were found when the surfactant concentration was sufficiently low or when the electrolyte concentration was sufficiently high. The possible influences of wall effects, oil volatility, oil solubility, creaming (or sedimentation), shear, and mixing effects upon the rate constants were investigated. In the cases of ditolyl and the phthalates, it was found that these influences were negligible or could be eliminated by modifying the techniques involved in the procedure. In studies over a 10-fold range of oil concentration, 100-fold range of surfactant concentration, and a 6-fold range of electrolyte concentration, a maximum rate constant for coalescence of 4.0 × 10-12cm.3/sec. (±5%) was observed. Interestingly, this maximum rate constant is about 70% of the theoretical Smoluchowski rate constant.

Using the Haydon-Taylor model in which the surfactant head groups are situated at some distance from the oil surface, the interaction energy of electrostatic repulsion (VR) between oil droplets in dilute electrolyte solutions is derived for the two cases: constant-surface potential and constant-surface charge. For comparison, the repulsive energy is also derived for the constant-surface charge case without the effect of this adsorbed layer model. The Haydon-Taylor model accounts for the penetrability of the electrolyte and dielectric constant in the adsorbed surfactant layer of varying thickness, the degree of surface coverage, particle-size effect, ionic strength, and the dielectric constant in the bulk solution. In the constant-potential case, the resulting VRequation is identical to the classical Derjaguin, Landau, Verwey, and Overbeek (DLVO) one. Computations show that as flat plates and spheres approach each other, VR(constant-surface charge with impenetrable adsorbed layer) > VR(constant-surface charge with penetrable adsorbed layer) > VR(constant-surface potential). Because of the possible 50- to 100-fold difference in magnitude between them, proper choice of the model is important when considering application of the theory to the rigorous kinetic treatment of the coalescence of o/w emulsions and flocculation of suspensions.

Based on first principles of diffusion, equations were derived to predict transport rates of micelle-solubilized drug from its aqueous environment to an oil phase. The basic equations also take into account the possible effects of an electrical barrier between the micelle and the charged oil-water interface. These processes may be considered as being analogous to absorption of water insoluble-bile soluble drugs, and may be used to evaluate the mechanism of transport in such situations. The physical model includes the effects of the free drug-solubilized drug equilibrium, the diffusion coefficients of both free and solubilized drug, ionic strength of the aqueous medium, and the micelle size. A novel experimental approach based on the use of emulsion droplets as the “sink” is described.

The diffusional transport of drugs across a membrane under the influence of hydrostatic (or osmotic) flow is described. The physical model consists of a bulk aqueous phase with a diffusion layer followed by a heterogeneous (lipid/aqueous) compartment and a perfect sink. The steady-state rate of change of the total drug concentration in the bulk aqueous phase is in the general form of a first-order equation useful for the evaluation of experiments. Computations are made for different cases in simulation of the in situabsorption of drugs in animals when the tonicity of the drug solution is varied. Several limiting models are mathematically deduced from the more general approach.

The studies of Beckett and Moffat on the human buccal absorption of p-n-alkyl phenylacetic, p-halogen phenylacetic, and toluic acids at various buffer pH's were analyzed quantitatively by the physical model approach using a two-phase compartmental diffusion model. Nonlinear regression analysis was used to obtain self-consistent estimates of relevant transport parameters such as the permeabilities of the aqueous diffusion layer and lipoidal membrane and the pKa. Good agreement of the absorption rate-buffer pH profiles between the experimental results and theory was found. The incremental partition constant of the lipoidal biophase for a methylene group with the p-alkyl phenylacetic acid series was found to be 2.22, in agreement with 2.33 obtained previously for the n-alkanoic acids. Halogen substituent constants on the para-position of phenylacetic acid and position constants of a methyl group on the para-, meta-, and ortho-positions of benzoic acid relative to aqueous-buccal membrane partitioning were also determined. After comparing these constants with those in the literature, it appears that the rate-determining environment in the lipoidal buccal membrane has a polarity like isobutanol.

Following the guidelines provided by the physical models derived earlier, sensitive experimental techniques and procedures were developed. Baselines for solute transport studies were established from experiments on the uptake of cholesterol−11C by Burkitt lymphoma cells in culture suspension at pH 7.3 under iso‐osmotic conditions. The experimental data were evaluated by the model involving the rapid equilibration of the solute in the cell interior after permeation through the plasma membrane. The time‐dependent predictions of this model agreed well with the data. Effective permeability and partition coefficients were calculated and found to be inversely proportional to the serum level used. These results are in agreement with the mechanism by which only the unbound cholesterol in the external solution participates in the membrane transport process.