A DETERMINATION OF THE EFFECTIVE SURFACE AREA OF A SUBCUTANEOUSLY IMPLANTED SUSPENSION

The effective surf ace area of a parenteral drug in suspension, that which is exposed to body fluids a~ the injection site, is a major determinant of its in vivo absorption rate. Precise methods o f determining the effective surface area without disturbing the in vivo system have not been developed . A method to estimate the effective surf ace area of a subcutane ously injected suspension based on the urinary excretion of drug from solid disk implants of known surface area is presented. Standard curves for the mean surf ace area of from two to four subcutaneously implanted cylindrical disks of pure sulfadiazine versus cumulat ive urinary sulf adiazine excretion to 48 hours were developed for three test animals . By applying the urinary excretion data obtained following the subcutaneous injection of an aqueous suspension of sulfadiazine to the appropriate standard curve for area, a preliminary estimate of the apparent or effective in vivo surface area for the suspension formu lation was obtained. Improvements i n the experimental methodology which would control certain biopharmaceutical factors related to parenteral drug ab sorption from subcutaneous sites, and increase the statistical significance of the surf ace area estimate are suggested.

use of solid implants is not without disadvantage , however. A surgical proce dure is required for dosage administration or removal, which is usually less convenient to the physician and patient than an injection at the same site (1). Cosmetically, the suspension is unnoticed, whereas the solid dose form would be more likely to be noticed and would therefore be less acceptable. Parenteral dose forms are thus usually designed as suspensions rather than implants when prolonged action is desired.
The purpose of this project was to develop a preliminary method of determining the apparent or effective surface area of a subcutaneously injected suspension in vivo.
While there is presently no published method to determine the effective surface area of a parenteral drug in suspension at the site of injection, the mathematical relationships (i.e., models, equations, rate constants and analog computer techniques) dealing with the absorption of certain solid implanted drugs of known geometric design have been investigated by . The application of certa in specifically related principles deriv ed from i( ' ,. ! these studies applied to systems of pure · drug in aqueous suspension would be an extension of the class ical work on the physical and biological properties of injectable procaine penicillin G sus pe n s i ons published by Ober et al . (7) in 1958.
The accepted assumptions unde rlying th e processes involved ·with drug absorption from the implantati on site are: 1) that the absorption rate is in part proportional to the effective solid surface area expos e d to the surrounding tissues and in part due to the intri nsi c physical properties of the drug, i.e., solubility, pKa , diffusion layer pH and diffusion coefficient (2)(3)(4), 2) tha~ th e absorption or disappe ar ance of drug fro m a soli d implant or parenteral depot mimics a zero-order p roc ess which is dissolution rat e limited, ( i.e ., wh e~e the ratedetermining step is the dissolution of drug from the so~id form) (8,9); 3) that the effective or apparent surface area of a depot whose geonetry is ill-defined is le ss than the total true surf ace area of all the particles making up the sus pensi on as compared to the . a re a of all the partic les as measured in vitro by gas adsorption techniques ( lO) ;and 4) that the amount of drug and metabolite excreted over time, in this case of sulfadiazine and its acetylated metabolite, is directly proport i onal to the amount absorbed ( 11 ).
2 ( ( If a drug is formulated into a compr essed pellet of known geometric shape and dimension, which can be implanted and then removed before it is compl etely absorbe d , the absorption rate can be estimated if certain quantitative information ( e .g., changes in pellet dimensions with respect to time ) is known. Accordingly, for a disk shaped implant , the weight, W, at any time follo wing implantation (t) is (3): Where~= the apparent density, D 0 is the initial diameter of the disk, H 0 its initial height and k the ab--1 sorption constant having units of length X time .
The area, A, of a disk at any time after implantation is ( 12): In bo th these equations it is assumed that the shape of the i mplant is not distorted during the implant ation 0 0 time, and that D and H are both~ kt.
The absorption constant, k, for a geometrically defined drug in pellet form at a particular absorption site in a given animal species can be determined using equation In this study, an in vivo system of implanted drug in aqueous suspension was studied in order to develop a correlation between a physical property (effectiv e surface area) and its biological parameter unchanged sulfadiazine and its metabolites ~e~e ~easu red according to a colorimetric assay proc edure deve:oped by Bratton and Marshall (13 ).
Since the ab s orntio~ ra~e of the implan ts is assume d to be propor tiona l to ...... \....  The sulf adiazine powder used to prepare the solid disks was also used without modification · to prepare the aqueous suspension for subcutaneous implantation. An independen t microscopic analysis was performed to determine the average particle surface area and specific sur- 8 ( the incision was teased apart to provide from two to four site s for the implantation of the disks as appropriate.
Following this, the disks were implanted in two, three, or four corner sites, the implantation time was noted, an d the incision wa s closed by suturing .
After the 48 ho u rs urine sample collection, the animal was reanesthetized, the sutures were cut and the disks were located manually and removed by palpation without the aid of forceps.  (   Tables I and II give the measured he ight, diameter and weight of each of the sulf adiazine disks before and after implantation. From these data, t he volume, area, and density were calculated . These values are also ineluded in Tables I and II.   Tables III, IV (14 ) , Ballard (2 ,15 ) , and Ritschel ( 16) . The evaluation of parenteral suspended or solid implanted dose formulation s depends in part upon the de t ermination of the surface area of the solid particles of the depo t exposed to the surrounding tissue and fluids once the suspension vehicle has migrated from the injection site ( 15 ). The influence of crystalline particle size o n surf ace area and on drug absorption was demonstrated in 1 9 55 by Foglia ( 1 7) . He showed that by increasing the surface area of parahydroxypropiophenone ( PHP) through a particle size reduction from 10 , 000~3 to 2000 ~3 , pharmac o logical activity could be produced in rats in parenteral do ses of 0. 05 rag where no activity was demonstrated in doses as high as 120 mg using the larger particle size .
In 1958, Ober and co-workers (7) (Tables VI-VIII). 29 ( rats A, B and C are generally similar to those previously reported in studies (2,5) utilizing a siffi ilar experimental design.
As a first approximation, the mean absorption rate of a subcutaneous i mplant at any time is considered to be proportional to the surf ace area exposed to body fluids at the implantation site (2). When the in vivo absorption rate of sulf adiazine from implanted disks is approximated by urinary excretion of sulfadiazine and its metabolite unexpected variations in the results may occur. These may depend partly upon the influence of certain biopharmaceutical and physiological factors inherent to the model and partly to the experimental design.
The pH of body fluids (i.e., urine and plasma ) is known to affect the excretion rate and plas ma half-lives of drugs which are weak acids and bases. Sulfadiazine, an organic weak acid, has a pKa' of 6.28 at 28 c 0 (12).
According to the pH partition hypothesis (19) of incomplete voiding is lesse ned somewhat when data are collected over long time intervals (6). Also, in this experiment, water was continuously available to the animals.
Baldridge ( 18)   animals . Total urinary sulf adiazine excretion was followed to assess the absorption rates of the sulfonamide from subcutaneous tissue.
2. Standard curves for mean disk surface area versus cumulative sulfadiazine excretion to 48 hours were prepared.
A quantity of sulfadaizine in aqueous suspension was then injected subcutaneously and its cumulative urinary total sulfadiazine excretion to 48 hours used to obtain a prelimin a ry estimate from the standard curve of the effective in vivo surf ace area of the injected suspension in the test animal observed .
3. The reliability of the proposed method to accurately estimate the effective mean suspension surf ace area cannot be established from the present data.
However, the validity of the data could be increased by modifying the experimental method to: 1) decrease the influence of the many physiochemical factors which combine to influence the rates of drug absorption and excretion, and 2 ) increase the statistical significance of the data obtained. Direct visual microscopic analysis of the dry powder in Cargille immersion oil revealed needle-shaped crystals uniform in size with an occasional large particle. One hundred particles were selected at random and their lengths and widths determined. It was assumed that the height of each crystal was equal to its width . The powder density 3 was estimated by pycnome ter to be 1.43 gm/cm A summary of the properties of the sulf adiazine powder based upon the analysis of 100 randomly selected particles is as follows: ·