Jeffrey L. Fox

General physical model for simultaneous diffusion and metabolism in biological membranes. The computational approach for the steady-state case

Abstract A computational approach has been presented for modeling simultaneous diffusion and metabolism in biological membranes. This approach has a virtually unlimited flexibility in the variety and complexity of metabolic schemes that can be modeled. Furthermore, non-uniform enzyme distributions, as well as composite membranes with any number of layers, can also be handled. Example calculations have been presented (using a real system currently being investigated in the authors laboratory) which show that the versatility of this approach is a necessity for the quantitative study of the system. Furthermore, the utility of this approach in guiding decisions as to what path to take in improving a prodrug for a given system is amply illustrated. It is expected that this physical modeling approach, when combined with techniques now being developed for determining the values of the various model parameters, will provide a very useful tool in the investigation and optimization of drug delivery systems.

A new two-site model for hydroxyapatite dissolution in acidic media

A physical model featuring two distinct types of dissolution sites for hydroxyapatite (HAP) crystals is presented. One of these sites (site No. 1) is associated with dissolution along c axis dislocations of HAP crystals and is the important site when dissolution occurs into partially saturated solutions. Site No. 2 is active only when dissolution occurs into nearly completely unsaturated solutions, and, because of its greater apparent rate constant, is the more important dissolution site under these conditions. In the physical model block dental enamel or a compressed HAP pellet is represented as a porous matrix of these HAP crystals with interstitial spaces which are permeated by the dissolution medium. The behavior of the model for various situations can be calculated by combining Ficks second law equation for diffusion with the kinetic equations for the behavior of the dissolution sites and solving the resulting boundary value problem. This model is capable of accounting for dissolution kinetics over a range of variation of experimental variables (degree of undersaturation, CaP ratio, and effective diffusion layer thickness). The model also correctly predicts the conditions necessary for zonal as opposed to surface dissolution: high partial saturation, a viscous dissolution medium, or the presence of a site No. 2 dissolution inhibitor. Electron microscopic studies of dissolution morphology at the single crystal level are also in full agreement with the model. Finally, an examination of the available data on enamel remineralization suggests that the holes formed as a result of site No. 1 dissolution are likely the primary sites for remineralization.

Theoretical model studies of intestinal drug absorption V. Non-steady-state fluid flow and absorption

Abstract A reasonably realistic physical model has been described for the simultaneous longitudinal spreading, fluid flow and absorption of drugs in solution under non-steady-state conditions m the small intestinal tract. Various input cases included first-order and zero-order stomach emptying and input from an infinite drug reservoir at constant infusion rate. The mathematical solutions were unique and rigorous. Theoretical simulations using reasonable physical parameter values illustrated the interrelationships of the longitudinal spreading diffusion coefficient, flow rate, apparent permeability coefficient and intestinal length on the change in concentration—distance profiles with time and the kinetics of appearance of unabsorbed drug at the end of the intestinal segment. The model is accessible to the design of intestinal absorption experiments and data interpretation on a quantitative mechanistic basis and also provides the way for studying intestinal absorption under more realistic situations.

A possible second site for hydroxyapatite dissolution in acidic media

Abstract Dissolution of human dental enamel and of synthetic hydroxyapatite pellets in completely unsaturated acetate buffer solutions was previously shown to follow a model in which a single dissolution site was employed. The present investigation reports similar studies carried out under the clinically more relevant conditions of dissolution into solutions partially saturated with respect to hydroxyapatite, and it is shown that under these conditions the dissolution kinetics may be described by a site which has properties different from the site responsible for dissolution into completely unsaturated solutions. The properties of this second site were consistent with experiments in which bulk solution conditions (degree of partial saturation, Ca P ratio) and effective diffusion layer thickness were varied. Thus, dissolution kinetics studies indicate that hydroxyapatite crystals have at least two different types of sites that are important in dissolution.

In vivo Remineralization Using a Sustained Topical Fluoride Delivery System

The efficacy of a new remineralization system was determined in vivo by maintaining a low concentration of approximately 1 ppm fluoride for 48 hrs against a demineralized human tooth. Human subjects were selected who wore removable partial dentures containing two or more of the demineralized teeth with film system. The findings indicate levels of fluoride uptake to 500 ppm at 50 micron depths in experimental sites.

Transmission electron microscopic confirmation of the morphological predictions of the two-site model for hydroxyapatite dissolution

Hydroxyapatite (HAP) crystals were dissolved under two types of solution conditions designed to produce contrasting dissolution morphologies according to the recently proposed two-site model for HAP dissolution [Fox, J. L., Higuchi, W. I., Fawzi, M. B., and Wu, M. S., J. Colloid Interface Sci., 67, 312 (1978)]. In accordance with this model, dissolution into partially saturated buffers proceeded via formation of holes in the crystals, while dissolution of comparable amounts of material into completely unsaturated buffers showed no such holes. These results show that the two dissolution sites inferred from dissolution kinetics experiments are, in fact, physically distinct sites and that dissolution from site No. 1 results in hole formation. The physical location of site No. 2 is not yet certain.

Dissolution rate of apatite powders in acidic fluoride solutions and the relationship to hydroxyapatite disk and bovine enamel behavior

Abstract The dissolution kinetics of synthetic hydroxyapatite (HAP) and carbonate-containing HAP powders have been studied in fluoride-containing acetate buffer solutions partially saturated with respect to HAP ( K FAP = 10 −115 to 10 −123 ). The experimental results indicate that in the case of HAP powders the dissolution rates become very slow when the K FAP values of the dissolution medium are larger than 10 −119 . For the carbonate-containing apatites, however, there is a significant dissolution in the region 10 −115 ≥ K FAP ≥ 10 −119 which is in the region of physiological and therapeutic significance. The present results with the HAP powder together with HAP pellet data show that the dissolution of HAP pellets in the region 10 −114 > K FAP > 10 −119 results from an extended transient period rising from sustained deposition of F − on the surface and at intermediate depths in the ‘lesion’. Similar effects have also been observed with bovine teeth dissolution in acidic F − solutions.

A New Acid Abrasion Procedure for Studying F Profiles in Demineralized/Remineralized Bovine Tooth Enamel

Remineralization patterns and F profiles in remineralized bovine enamel subjected to prior demineralization have been studied using a new acid-abrasion procedure. These data were then compared to thos

Novel topical fluoride-delivery system for remineralization of dental enamel: optimization studies

Abstract Further studies have been conducted on a calcium fluoride delivery system with a view to optimizing its ability to remineralize dental enamel. The influence of particle size and load of calcium fluoride used, as well as treatment time, was evaluated in vitro on prior demineralized bovine enamel. Initial studies with the original singlemembrane system did not allow an unambiguous interpretation of efficacy, due to persistent interference from calcium fluoride particles. To overcome this problem, the system was modified to include a second membrane as protection for the enamel surface. This double-membrane system revealed a marked particle size and load effect on fluoride delivery. The performance of a high load of small size calcium fluoride particles was significantly better than previous results obtained with the system and approached the most effective remineralizing conditions established with solution fluoride.

Application of effect-compartment model to bumetanide-indomethacin interaction in dogs

Analyses of bumetanides dose-response relationship have been complicated by the hysteresis observed between the drugs urinary excretion rate and its sodium excretion. This apparent time lag reflects the disequilibrium between the urine concentration and effect compartment (biophase) which occurs during the early distribution phase. In the present article, an expanded pharmaco-dynamic model has been introduced in which the hypothetical effect compartment is linked, by a first-order process (Kue),to the urine compartment. Drug dissipation from the effect compartment occurs by means of the first-order rate constant, Keo.This representation accommodates bumetanides luminal site of action in the kidney tubule as well as the drugs temporal component. Application of this model to the bumetanide-indomethacin interaction in dogs is examined.