High-density limit and inflation of matter.

We prove rigorously that for a nonvanishing probability of having electrons in matter, with Coulomb interactions, within a sphere of radius , the latter, necessarily, grows not any slower than for large , where denotes the number of electrons. Thus it is not surprising that matter occupies so large a volume.

Transdermal delivery of ketorolac tromethamine: permeation enhancement, device design, and pharmacokinetics in healthy humans.

Transdermal delivery of ketorolac tromethamine, a potent non-narcotic analgesic, through human skin in vitro and in vivo was investigated. In order to enhance and sustain the flux of ketorolac through human skin, various compositions of isopropyl alcohol (IPA), water, and isopropyl myristate (IPM) were evaluated. The solubility of ketorolac acid in an IPA/water binary vehicle mixture increased as the volume fraction of IPA increased from 0 to 90%. The solubility of ketorolac acid in an IPA/water/IPM (saturated) ternary vehicle mixture was practically the same as in the IPA/water binary vehicle mixture. The permeation of ketorolac acid through cadaver skin was evaluated using modified Franz diffusion cells. The skin flux increased as the IPA volume fraction was increased from 0 to 50% and then leveled off beyond 80% IPA loading. When IPM was added to the IPA/water binary vehicle mixture, a significant increase in the skin flux of ketorolac was observed. The skin flux decreased exponentially as the donor solution pH was raised from 3.5 to 7.0. The permeability of ketorolac through various membranes such as a microporous membrane and pressure-sensitive adhesive was evaluated. While a microporous membrane offered practically no diffusion resistance, the in vitro flux of ketorolac through cadaver skin decreased substantially upon lamination of pressure-sensitive adhesive onto a microporous membrane. Three liquid-reservoir type transdermal devices were fabricated using 6.5% ketorolac tromethamine gel, a microporous membrane, an adhesive membrane, and polyester backing film: TD-A (microporous membrane/acrylic adhesive), TD-B (microporous membrane/silicone adhesive), and TD-C (microporous membrane). The pharmacokinetics of ketorolac in 10 healthy humans following application of a transdermal device for 24 h was evaluated. The maximum plasma concentrations (Cmax) were 0.20, 0.18, and 0.82 microgram/mL for TD-A, TD-B, and TD-C, respectively. The total AUC values for the concentration-time curves were TD-C > TD-A > TD-B, and the terminal half-life ranged from 6.6 to 9.7 h.

Permeability of pure enantiomers of ketorolac through human cadaver skin.

The permeability of pure enantiomers of ketorolac acid, a potent non-narcotic analgesic, through human cadaver skin was evaluated. The melting temperature of each enantiomer was 20 degrees C higher than that of the racemic compound. As expected, the solubility of the racemic compound in water and isopropyl alcohol/water/isopropyl myristate (IPA/water/IPM, 50:50:1.5) was roughly 2 times higher than that of the enantiomers. The permeability of the enantiomers through poly(ethylenevinyl acetate) (EVA) synthetic membrane and human cadaver skin was determined with a side-by-side diffusion cell. The skin flux of the racemic compound was about 1.5 times higher than those of the enantiomers. On the other hand, no significant differences in the intrinsic permeability coefficient of the racemic compound and the enantiomers in the EVA membrane and human cadaver skin was observed. An excellent agreement between the predicted and experimental flux ratio of the racemic compound and enantiomer in the EVA membrane and cadaver skin was observed. The IPA/water/IPM (50:50:1.5) provided the highest in vitro skin flux of the S enantiomer among the three vehicle formulations studied. The skin flux of the active pure S enantiomer was ca. 34% higher than that of the impure S enantiomer in the racemic mixture. Furthermore, about 14% intersubject variability in the in vitro skin flux of the S enantiomer was observed. The required skin flux of the S enantiomer as calculated from the pharmacokinetic parameters was about 32 micrograms/cm2/h from a 25 cm2 transdermal patch, which was readily achievable from the IPA/water/IPM (50:50:1.5) ternary vehicle system.

Absorption of transdermally delivered ketorolac acid in humans.

Transdermal delivery of ketorolac acid, a potent analgesic, through human skin in vitro and in vivo was evaluated. The following three transdermal solutions were selected to study the in vitro skin permeation rate of ketorolac acid: formulation A, isopropyl alcohol: water: isopropyl myristate (IPA/water/IPM; 11:7:1); formulation B, ethanol: propylene glycol:isopropyl myristate (ET/PG/IPM; 11:7:2); and formulation C, IPM/capmul (glyceryl mono- and dicaprylate; Monoctanoin). The permeation of ketorolac acid through cadaver skin from a saturated drug solution was evaluated at 32 degrees C with a modified Franz diffusion cell. The in vitro skin fluxes were 180, 177, and 14 micrograms/cm2/h for formulations A, B, and C, respectively. The systemic bioavailability of ketorolac acid from three transdermal formulations was evaluated in nine healthy subjects in a randomized three-way crossover fashion. Hill Top chambers were used as prototype dermal delivery devices to load the drug solution. This procedure was followed by the immediate application of devices to human subjects for 24 h. Blood samples were collected at various time intervals up to 48 h, and the samples were assayed by HPLC. The basic pharmacokinetic parameters were derived from the drug plasma concentration versus time plot. The maximum drug plasma concentrations were 1.265, 0.696, and 0.092 micrograms/mL for formulations A, B, and C, respectively. Formulation A provided the highest in vitro and in vivo transdermal delivery rate among the three formulations studied. An excellent correlation between the in vitro steady-state skin flux and the area under the curve of in vivo plasma drug concentration versus time was observed for all the three formulations.

Permeability of ketorolac acid and its ester analogs (prodrug) through human cadaver skin.

The in vitro skin permeabilities of ketorolac acid (KA), a potent nonsteroidal analgesic, and its two ester analogs as prodrug through human cadaver skin were investigated. The two esters of KA, namely, the ethyl ester (KEE) and [(N,N-dimethylamino)carbonyl]methyl ester (KDAE), were selected. The melting temperature of the two esters was significantly lower than that of ketorolac free acid. The partition coefficients (KO/W) were 600, 3541, and 124 for KA, KEE, and KDAE, respectively. The enzymatic hydrolysis of KEE and KDAE by human pooled serum at 37 degrees C was investigated. The esters were hydrolyzed to KA by the serum esterases; the metabolic rate constants were 0.0418 and 0.0148 min-1 for KDAE and KEE, respectively. The serum half-life of KDAE was about 3 times shorter than KEE. When split-thickness cadaver skin was incubated with ester solution at 32 degrees C, the enzymatic hydrolysis of these esters was observed. The metabolic rate in the skin, however, was significantly lower than in the human pooled serum. The skin permeations of KA, KEE, and KDAE through heat-separated epidermis from propylene glycol (PG), PG/glyceryl monocaprylate (GMC) (9:1), and PG/Azone (19:1) vehicle mixtures were evaluated using modified Franz flow-through diffusion cells. The skin fluxes of KA, KEE, and KDAE from PG/GMC (9:1) were 50 +/- 10, 15 +/- 4, and 57 +/- 6 micrograms/cm2/h, respectively. KA was detected in the receiver compartment, albeit to a lesser extent. In conclusion, KDAE appeared to be a better ester prodrug than KEE because it exhibited relatively higher skin flux and faster enzymatic hydrolysis by human serum to liberate the parent drug.

Micellar solubilization of timobesone acetate in aqueous and aqueous propylene glycol solutions of nonionic surfactants.

The micellar solubilization of timobesone acetate, a novel topical corticosteroid, was studied in aqueous and aqueous propylene glycol solutions of 1 to 5% nonionic surfactants at 25 degrees C. The surfactants used were polyoxyethylene (POE) sorbitan monofatty acid esters (polysorbates), fatty acid esters (Myrj), and fatty alcohol ethers (Brij), as well as sucrose monolaurate (Crodesta SL40). The increase in the solubility of timobesone acetate in the micellar solutions was dependent on the type and concentration of surfactant. The solubilizing capacity of the surfactant micelles and the distribution coefficient of timobesone acetate in aqueous micellar solutions were found (1) to increase with increasing length of the hydrophobic fatty acid group; (2) to increase according to the structure of the hydrophilic group in the order of POE sorbitan ester, sucrose ester, POE ester, and POE ether; (3) to be unaffected by the increase in POE chain length; and (4) to tend to decrease in surfactant containing unsaturated fatty acid groups. In aqueous propylene glycol solution, the solubilizing capacity increased slightly, i.e., up to 1.5-fold in 50% propylene glycol solution, for the ester-type surfactants (polysorbates and Myrj). But this increase was not observed in the ether-type surfactant (Brij) solution. The distribution coefficient decreased logarithmically with increasing concentrations of propylene glycol in the solution. This was caused by the logarithmic increase in the timobesone acetate solubility in the bulk phase, while the solubility in the micellar phase was practically unchanged. The results support the equilibrium distribution model of micellar solubilization.

Release of lonapalene from two-phase emulsion-type ointment systems.

The in vitro release of lonapalene, a novel nonsteroidal antipsoriatic agent, was studied from two-phase emulsion-type ointment systems into a perfect sink of propylene carbonate at 32 degrees C. Lonapalene was completely solubilized in the ointments consisting of an internal phase of propylene carbonate (PC)-propylene glycol (PG) mixture dispersed within an external phase of a petrolatum base. The PC:PG ratio was varied to investigate separately the effects of (1) the initial concentration of lonapalene, (2) its saturation level, and (3) the volume fraction of the internal phase. The release profile consisted of an initial release rate which was higher than the ensuing diffusion-controlled release rate. The initial rate was attributed to the release of lonapalene from the surface globules of internal phase directly into the sink. Both rates increased with increasing lonapalene initial concentration in the ointment. For ointment systems in which the saturation level of lonapalene was kept constant, neither release rate was affected by the increasing volume fraction of the internal phase up to 12%. Further increase in this volume fraction to 25% afforded a significantly higher initial rate, while the diffusion-controlled rate was unchanged. However, an increase in the volume fraction of the internal phase with a concomitant decrease in the saturation level of lonapalene in the ointment resulted in a decrease in the initial rates and, to a lesser degree, the diffusion-controlled release rates. The diffusion coefficient in the external phase, calculated from the effective diffusion coefficient, was (2.68 +/- 0.24) X 10(-9) cm2/sec.