Chapter 9
Diffusion and Dissolution
Diffusion is the migration of molecules from a region of high concentration to a region of lower concentration and is a result of the Brownian movement of the solute molecules. The phenomenon of diffusion can be observed if a crystal of copper sulphate is placed in a beaker of water. A saturated solution of copper sulphate forms around the crystal and the coloured zone gradually extends by diffusion until eventually there is a uniform concentration throughout. The migration of solute molecules in the absence of external forces such as movement of the solution by convection gradients is a measure of the escaping tendency of the solute to achieve an equilibrium state. A similar situation arises if a semipermeable membrane separates two solutions of unequal concentration, when the equilibrium is restored by the diffusion of the solvent molecules through the membrane, i.e. osmosis. Thus, osmosis is concerned with the escaping tendency of solvent molecules, and diffusion with the escaping tendency of the solute. The forces involved in the two processes are equal in magnitude but opposite in direction (Alexander & Johnson, 1949).
Fick’s Law of Diffusion
Fick’s First Law
By analogy with the processes involved in heat conduction, this law states that the amount of substance dm diffusing in the x direction in time dt across an area A is proportional to the concentration gradient dc/dx in the plane of the area:
(9.1)
The proportionality factor D is called the diffusion coefficient. (The negative sign denotes that diffusion takes place in the direction of decreasing concentration.) D is not strictly a constant, since it varies slightly with concentration but it can be regarded as a mean value for the concentration range covered. The dimensions of D are length2/time.
Fick’s Second Law
This is derived from the first law by eliminating the dependent variable m, and expresses the rate of change of concentration at any point:
(9.2)
Diffusion and Molecular Properties
The diffusion of colloidal particles is related to the frictional coefficient, of the particles by Einstein’s law of diffusion:
where k is the Boltzmann constant and T absolute temperature. For spherical particles the frictional coefficient is given by Stokes’ law:
where η is the viscosity of the medium and r the radius of the particle.
Therefore, for spherical particles:
(9.3)
where R is the gas constant and N the Avogadro number. The effect of temperature and viscosity on diffusion is apparent from this equation as D∝ (T/η) for a given solute. For nonspherical molecules the frictional coefficient increases with decreasing symmetry and with particle solvation, e.g. hydration.
Measurement of Diffusion
Porous disc method: A sintered glass disc separates the solvent and solution so that a concentration gradient occurs in the pores of the disc (Fig. 9.1). The liquid in the pores is immobilized and freed from the influence of external disturbance, so that the transport of solute through the pores is due solely to diffusion. Homogeneity of the separate phases is effected by slight convection currents, gentle stirring or rotation of the cell. For small concentration changes Fick’s first law can be applied:
(9.4)
where m is the amount of solute diffused, C1 and C2 are the concentrations of solute on either side of the disc at time t1 and t2, A is the cross section of the pores and L is the effective length of the pores. The quantities A and L are not directly measurable but the ratio A/L can be obtained by calibrating the cell with a solute of known D, e.g. KCI. The method is simple but has the following possible objections: (a) the calibration of the cell with very low molecular weight solutes may not be valid for high molecular weight solutes, especially if molecules of the latter are markedly asymmetric; and (b) entrapped air bubbles in the pores or adsorption of solute would invalidate the results.
Fig. 9.1 Porous disc apparatus.
Free Boundary Method. An initially sharp boundary is formed between the solvent and solution in a specially constructed diffusion cell. The diffusion is followed by measuring the concentration gradient along the cell by optical methods such as light refraction or light absorption. Very accurate temperature control is essential as convection gradients must be eliminated, since these would disturb the concentration gradient. The change of concentration gradient dc/dt at different times, t, is shown in Fig. 9.2. These curves take the shape of Gaussian distribution curves represented by the equation:
(9.5)
where C0 is the concentration of solute when t = 0. The diffusion coefficient of the sodium dodecylsulphate has been determined by this method (Brudney & Saunders, 1955).
Fig. 9.2 Concentration gradient at different times after formation of sharp boundary (t3 > t2 > t1).
Diffusion through gels: The rate of diffusion of low molecular weight solutes through dilute aqueous gels of gelatin and agar is nearly the same as in water alone, provided that chemical interaction and adsorption effects are absent. This is not surprising when one considers that a semisolid gel of agar could contain as much as 99% water. This water, immobilized by the network structure of the gel, is a continuous phase through which solute can diffuse. As the concentration of gelling substance is increased, the pore size of the gel decreases and the rate of diffusion will fall rapidly when the pore size is comparable with the size of the diffusing molecule. In addition to this sieve-like action of the gel, other factors such as the viscosity of the liquid within the pores will affect the diffusion rate. If the mesh possesses ionizable groups of opposite charge to that of the diffusing particle, adsorption or ion exchange reactions may occur. Agar is an acidic polysaccharide which forms a gel with water at concentrations as low as 0.5%. One-half ester sulphate is present in about 8–50 galactose units giving rise to a negatively charged mesh on ionization of the −O−SO3H groups. These anionic groups will interact with cations such as the basic dyes and quaternary ammonium compounds and retard their diffusion. This can be overcome to some extent by the inclusion of suitable electrolytes in the gel to decrease the ionization of the diffusing molecules. In the case of diffusion through aqueous gelatin gels, the pH of the gel will influence the ionization of the −NH2 and −COOH groups. On the acid side, the isoelectric point, the gel will be positively charged, while on the alkaline side it will be negatively charged (see p. 96).
Let us now consider the diffusion of neutral particles. Fig. 9.3 represents a cylinder of gel in contact with a solution of concentration C0. Assuming that the solution is homogeneous and of constant concentration, the relationship between the diffusion coefficient and the concentration of the solute C at a distance x from the gel/solution boundary is given by:
which may be written with logarithms to the base 10 as:
(9.6)
Fig. 9.3 Diffusion of solute from solution into gel.
Thus a plot of x2 against (should be a straight line with a slope of 2.301 × 4D(log C0 − C) enabling D to be calculated.
Cooper and Woodman (1946) found this equation to apply to the diffusion of crystal violet in agar gels. Sodium chloride was included in the gel to repress the ionization of the dye. The migration of the dye could be followed visually and the coloured edge was matched with a tube containing 1:5,00,000 crystal violet (C = 2 × 10−6).
An alternative method of determining D in gels is to dissolve the solute in the gel and follow the rate of diffusion into water in contact with the gel. Nixon et al. (1967) studied the rate of diffusion of methylene blue from gelatin-glycerin gels using this method.
Cup plate methods of assay of antibiotics are dependent on diffusion through agar gels previously seeded with a test organism. After incubation, the organisms fail to grow where the antibiotic has reached a sufficiently high concentration so that the zone of inhibition can be correlated with antibiotic potency.
Diffusion Through Membranes
Membranes have already been mentioned in connection with dialysis (p. 91) which enables small molecules to be separated from macromolecules. All membranes have a gel-like structure and although the ‘pore size’ is referred to it should be noted that the pores are not uniform channels but are tortuous, resulting from the random network structure of the gel. The pore size will be affected by the liquid content of the gel, and swelling will result in an increased pore size. Artificial membranes can be prepared from regenerated cellulose (Cellophane), cellulose acetate, etc. (Alexander & Johnson, 1949). Natural membranes are usually quite thin, frequently only 10nm or so in thickness. The permeability of these plays an important part in the rate of absorption of a drug which has to pass through cell membranes to reach its site of action. Permeability can sometimes be explained on the basis of physicochemical mechanisms (passive transport) but it cannot explain the transport of solutes against a concentration gradient which is mediated through enzymatic action (active transport). This chapter will be concerned only with passive transport and will attempt to indicate the physicochemical principles that can assist in correlating drug properties with permeability. For instance the relatively rapid passage of a low molecular weight solute across a membrane could be depicted by Fick’s first law, although the situation would be complicated for low transport rates by the osmotic flow of water in the opposite direction. Some saline cathartics exert their action in this way by causing an influx of water into the gastrointestinal tract.
The rate of absorption of orally administered weakly acidic and weakly basic drugs is of particular interest (Brodie, 1964). Their absorption can be explained by passive diffusion of the unionized molecular species through the lipoidal membrane of the gastrointestinal tract. The unionized species are generally lipid soluble in contrast to the ionized species that are insoluble in lipid but soluble in water. The proportion of ionized-unionized molecules will thus control the solubility in the lipid and can be estimated from a knowledge of the pKa of the drug and the pH of the environment (see p. 17).
A simple model representing the gastrointestinal fluid, the gastrointestinal membrane, and blood as separate compartments is represented in Fig. 9.4. The aqueous phases A (pH 2.0) and C (pH 7.4) represent the alimentary tract and blood compartments, respectively. B is the immiscible lipid phase. The driving force, which transports drug from A across the two interfaces will depend on the partition coefficients between A/B and B/C which will be controlled by the pKa and pH. The ratio of concentration of the drug in the two compartments A and C at equilibrium is given by:
Fig. 9.4 Partition model of acidic drug. A. Aqueous phase, pH 2; B. Organic phase; C. Aqueous phase, pH 7.4 HX, unionized acid; H+ X−, ionized acid.
Perrin (1967), using a partitioned cell, studied the rates of transfer of salicylic acid (pKa 2.96) and amidopyrine (pKa 5.1) between aqueous buffers (pH 2 and pH 7.4) and an insoluble organic solvent as an in vitro model for a lipoidal membrane. Assuming that the rate of transport followed first order reaction kinetics, the theoretical rates could be correlated with experimental results.
Diffusion of Drugs from Dosage Forms
Sustained release of drugs from tablets has been obtained by incorporating the drug in an insoluble matrix such as plastic resin, wax and fatty alcohol. When brought into contact with the gastrointestinal fluid the drug particles will be slowly leached out as the fluid penetrates the pores of the tablet. Diffusion of the solute through the liquid-filled tortuous paths will play a significant part provided that the tablet retains its framework during the process. Higuchi (1963) suggested that the rate of release of drug from one surface of an insoluble matrix would be governed by the relationhip:
(9.7)
where Q is the amount of drug released per unit area at time t, D is the diffusion coefficient, ɛ is the porosity of the matrix, Cs is the solubility of the drug, τ is the tortuosity of the matrix and A is the concentration of the drug in the tablet. Desai et al. (1965), discussed the applicability of this equation to the rate of release of sodium salicylate from plastic matrices.
Theories of Dissolution
There are three theories reported in the literature to explain the process of dissociation, viz. (1) the film theory, (2) the surface renewal or penetration theory and (3) the limited salvation theory.
Film Theory
When a particle is immersed in liquid (Fig. 9.5), it begins to dissolve and immediately be surrounded by a stagnant film of solvent whose thickness will depend on the agitation conditions the particle is subjected to. It is known as diffusion layer. A concentration gradient will occur, equivalent to Cs-Cb, where Cb is the concentration of drug in the bulk solution and hence at the end of the boundary layer. Cs is the concentration of drugs in diffusion layer or saturated layer or saturated solubility.
Fig. 9.5 Diffusion layer model. The figure shows the concentration gradient within a film adjacent to a dissolving particle.
Assuming that the steady state exists, Fick’s first law of diffusion may be used to describe the transport.
(9.8)
where J is the diffusion current; D is the diffusion coefficient; and δc/δx is the concentration gradient. This is considered constant as depicted by the linear relationship shown in Fig. 9.5, and clearly δc/δx is equivalent to the slope of the line [(Cs-Cb)/h]. If the dissolved mass is equivalent to m, the volume of the dissolution medium is V and the surface area of the dissolving solid is S, Eq. 9.8 may be rearranged as Eq. 9.9.
(9.9)
This in turn may be rearranged to:
(9.10)
where k is the dissolution rate constant.
Eq. 9.10 may be integrated and subjected to boundary conditions. For situation where Cb
Cs, that is, sink condition, Eq. 9.10 simplifies to Eq. 9.11:
Cs, that is, sink condition, Eq. 9.10 simplifies to Eq. 9.11:
(9.11)
In the above equations, it is assumed that S remains constant during dissolution. However, this is not true for dissolving particles. Consequently, the method involving constant surface area discs is frequently used to determine dissolution rates to avoid changes in surface area.
Overall, the resistance to mass transfer away from the surface of a dissolving substance is a function of the ratio of the diffusion coefficient and the diffusion layer thickness. Dissolution is the balance between molecules leaving and re-entering the solid surface, and it depends upon the concentration of the solute in the vicinity of the dissolving surface. In turn, the diffusion rate and convictive transport in the dissolution medium will vary with the geometry of the experimental set-up. It is important to calculate dissolution rate at the time of the transfer of substances from the solid surface in contact with the liquid phase next to the solid. Such a condition can be obtained using an eccentrically placed constant surface area disc mounted on a horizontal rotating support and was used to calculate intrinsic dissolution rate. These were defined as the maximum mass transfer from the solid to liquid phase. The data were extrapolated to infinite speed of revolution at an infinite distance from the centre of revolution to obviate the effect of dissolution layer thickness on dissolution rates.
Constant surface area discs have been used in the development of a convective diffusional model for describing dissolution. Since diffusion cannot be considered as the sole contributor to dissolution, convection – caused by agitation – must be a driving factor for dissolution. This treatment leads to the development of a model that accounts for mass transport of the solute by fluid flow as well as diffusion. Eq. 9.12 describes the kinetics of such a model for one face of a circular tablet.
(9.12)
where R is the dissolution rate of a fluid having a shear rate of α at the interface, D is the diffusivity, and r is the radius of the exposed circular surface. Wurster and Taylor considered that Eq. 9.13 predicts the influence of agitation on the dissolution rate constant K.
(9.13)
where N is the agitation rate. The exponent b approximates unity for diffusion-controlled system but exceeds unity when dissolution occurs under turbulent conditions. Although the hydrodynamic layer is important, turbulence at a depression in a dissolving solid surface is an important factor that may increase the dissolution rate. Disc porosity in excess of 20% increases the dissolution rate from compressed disc owing to the increase of surface area at the surface.
Much of the above, by examining dissolution at the start of the process or from disc of constant surface area, has neglected the fact that particle size decreases during dissolution. Data treatment accounting for the change in dissolution rate of monodisperse powders whose surface areas decrease during dissolution are usually based on the cube root law of Hixson and Crowell, as shown in Eq. 9.14.
(9.14)
where W0 represents the original mass of the drug, W is the amount remaining at time t, and K is the dissolution rate constant. A typical plot is indicated in Fig. 9.6. The dissolution kinetics is representative of solid surface area that changed predictably with the mass transfer into solution. Its derivation assumed that (1) dissolution takes place normal to the surface of the dissolving solid, (2) agitation effects are uniform across the surface, (3) no stagnation of liquid in any region within the volume of the solid takes place and (4) the solid particles remain intact. The treatment has been extended to nonsink condition.
Fig. 9.6 Dissolution data of a hypothetical solid plotted as cumulative amount released (right axis) and after cube-root-law data treatment (left axis).
Surface Renewal Theory
Danckwerts disapproved the existence of a stagnant layer by assuming that turbulence extended to the surface and that there was no laminar boundary layer. It was proposed that surface is continuously being replaced with fresh liquid, such that the drug concentration at the surface interface does not reach Cs but a lower limiting value Ci. Thus, the surface is continuously replaced with fresh liquid. Macroscopic pockets of the fresh solvent reach the solid-liquid interface by eddy diffusion in a random manner. During residence at the interface, the pockets of fresh solvent (Fig. 9.7). Thus, the surface renewal process may be related to the solute transport rate and hence dissolution. Such a hypothesis may be supported by the fact that molecules must solvate before they are capable of dissolving. The model proposed is shown in Eq. 9.15.
(9.15)
Fig. 9.7 Schematic representation of the surface renewal theory of dissolution.
Limited Salvation Theory
The film theory and each of the surface-renewal theories assumes that solid-solution equilibrium exists at the solid-liquid interface and mass transfer is the slow step of the dissolution process, thereby controlling dissolution. An intermediate concentration, which is less than saturation (less than Cs), may exist at the interface results salvation is a function of solubility rather than diffusion. The salvation mechanism role as deduced from dissolution studies cannot be underestimated. The stagnant film theory assumes that a linear concentration gradient exists throughout the layer, that steady state exists, and that D is independent of concentration. From Fick’s second law of diffusion, steady state implies that the amount of solute entering and leaving a plane at distance x from the surface is the same, as shown in Eq. 9.16.
(9.16)
Since the function SD(δc/δx) is a constant (and may be taken to be -α), it follows that dC/dx = −α/SD, and Eq. 9.17 applies.
(9.17)
where the boundary condition that concentration is equal to saturation at the solid interface (C = A at x = 0) has been imposed. Since the concentration at x = h is Cb, Eq. 9.18 follows:
(9.18)
(9.19)
Design of Dissolution Apparatus
The ideal features of a dissolution apparatus are as follows:
1. The fabrication, dimensions and positioning of all components must be precisely specified and reproducible, run to run.
2. The apparatus must be simply designed, easy to operate and useable under a variety of conditions.
3. The apparatus must be sensitive enough to reveal process changes and formulation differences but still yield repeatable results under identical conditions.
4. In most cases, the apparatus should permit a controlled but variable intensity of mild, uniform, nonturbulent liquid agitation. Uniform flow is essential because changes in hydrodynamic flow will modify dissolution.
5. Nearly perfect sink conditions should be maintained.
6. The apparatus should provide an easy means of introducing the dosage form into the dissolution medium and holding it, once immersed, in a regular and reliable fashion.
7. The apparatus should provide minimum mechanical abrasion to the dosage form (with exceptions) during the test period to avoid disruption of the microenvironment surrounding the dissolving form.
8. Evaporation of the solvent medium must be eliminated and the medium must be maintained at a fixed temperature within a specified narrow range. Most apparati are thermostatically controlled at around 37°C.
9. Samples should be easily withdrawn for automatic or manual analysis without interrupting the flow characteristics of the liquid. In the latter case, efficient filtering should be achieved.
10. The apparatus should be capable of allowing the evaluation of disintegrating, nondisintegrating, dense or floating tablets or capsules and finely powdered drugs.
11. The apparatus should allow good interlaboratory agreement.
There are two principal types of apparatus design.
One is based on the limited volume that is constrained to the size of the container used. The second type uses a continuous flow cell to house the dosage form and permits constant replenishment of the dissolution fluids.
Compendial Procedures
The general principle of dissolution tests is that the powder or solid dosage form is tested under uniform agitation, which is accomplished by either passing the medium over the sample or by rotating the sample in the medium. Two general methods are currently included in the USP XXVIII and the British Pharmacopoeia (BP) 2004 to measure dissolution from immediate-release oral tablets and capsules, while there are several variants used in the testing or modified-release oral-dosage forms and other, nonoral types of dosage form.
Basket Apparatus (USP Apparatus 1)
The basket method was first described in 1968 by Pernarowski et al. A container, the basket, constrained the enclosed tablet or capsule, allowed or fluid change and could be used either in continuous flow or in restricted volume modes. This gradually evolved to the USP XXVIII and BP 2004 Apparatus 1 – the Rotating Basket Apparatus (Fig. 9.8). The dimensions are taken from the USP XXVIII, although those given in the BP 2004 are similar. The apparatus consists of a motor, a metallic drive shaft, a cylindrical basket and a covered vessel made of glass or other inert transparent material. The latter should be made of materials that do not sorb or react with the sample tested. The contents are held at 37 ± 0.5oC. There should be no significant motion, agitation or vibration caused by anything other than the smoothly rotating stirring element. The vessel is cylindrical with a hemispherical bottom and sides that are flanged at the top. It is 160–175mm high and has an inside diameter of 98–106mm, and a nominal capacity of 1000mL. A fitted cover may be used to retard evaporation but should provide sufficient openings to allow ready insertion of a thermometer and allow withdrawal of samples for analysis.
Fig. 9.8 The basket-stirring element of USP 28 (Apparatus 1).
The shaft is so positioned that its axis is no more than 2mm at any point from the vertical axis of the vessel and should rotate smoothly, without significant wobble. The shaft rotation speed should be maintained within ±4% of the rate specified in the individual monograph. The shaft has a vent and three spring clips or other suitable means to fit the basket into position. Each should be fabricated of stainless steel, type 316 or equivalent. Welded seam and stainless steel cloth (40mesh or 425mm) is used, unless an alternative is specified. A 2.5mm thick gold coating on the basket may be used for acidic media. For testing, a dosage unit is placed in a dry basket at the beginning of each test. The distance between the inside bottom of the vessel and the basket is 25 ± 2mm. Although the basket apparatus in the USP XXVIII and BP 2004 are similar and have a common design, considerable changes have taken place since basket apparati were first included in official monographs.
The USP XVIII described a cylindrical vessel with a slightly concave bottom. The vessel was 16cm high and has 10cm internal diameter with a nominal capacity of 1000mL. No precise specifications were given for the concave bottom, and differences in tolerances supplied by different manufacturers were common. Flask shape had affected the hydrodynamics of systems and consequently it was considered better to have flasks of uniform hemispherical shape. The flat-bottomed flask described in the BP 1980 alleviated the problems of manufacturing tolerances in vessel shape. Irrespective of apparatus design, there are still several potential problems. The wire basket corrodes following exposure to acidic media, the basket method gives poor reproducibility due to inhomogeneity of the agitation conditions produced by the rotating basket, and clogging of the basket can occur due to adhering substances. Additionally, particles can fall from the rotating basket and sink to the bottom of the flask where they will not be subjected to the same agitation as that inside the basket. Finally, there is the possibility of dissolution being accelerated by abrasion of the dosage form’s surface as it rubs against the basket mesh—the so-called cheese grater effect.
Paddle Apparatus (USP Apparatus 2)
An apparatus described by Levy and Hayes may be considered the forerunner of the beaker method. It consisted of a 400-mL beaker and a three-blade, centrally placed polyethylene stirrer (5cm diameter) rotated at 59rpm in 250mL of dissolution fluid (0.1N HCl). The tablet was placed down the side of the beaker and samples were removed periodically. In Apparatus 2, (Fig. 9.9) the paddle apparatus method, a paddle replaces the basket as the source of agitation. As with the basket apparatus, the shaft should position no more than 2mm at any point from the vertical axis of the vessel and rotate without significant wobble. The specifications of the shaft are given in Fig. 9.9. A distance of 25 ± 2mm between the blade and the inside bottom of the vessel is maintained during the test. The metallic blade and shaft comprise a single entity that may be coated with a suitable inert coating to prevent corrosion. The dosage form is allowed to sink to the bottom of the flask before rotation of the blade commences.
Fig. 9.9 The paddle-stirring element of USP XXVIII (Apparatus 2).
In the case of hard-gelatin capsules and other floating dosage forms, a ‘sinker’ is required to weight the sample down until it disintegrates and releases its contents at the bottom of the vessel. The sinker has to hold the capsule in a reproducible and stable position directly below the paddle, but it needs to be constructed in such a fashion that it does not significantly affect hydrodynamic flow within the vessel, nor should it appreciably reduce the surface area of the capsule available to the dissolution medium. Two designs have predominated, the three-fingered clip and the helical spring. The former comprises a small circular disc with three short, parallel rods sticking out from it, into which the capsule is wedged. The device is typically plastic but the disc contains metal, which gives it the necessary weight to fall to the bottom of the vessel. The latter is a stainless steel or plastic-coated stainless steel helix (coil, spring) down the middle of which is inserted the capsule. However, with this design, as the thickness of the wire used and the number of turns in the spring increase, the available surface area of the capsule decreases, leading to a concomitant decrease in the observed rate of dissolution.
The USP allows for ‘a small, loose piece of nonreactive material such as not more than a few turns of wire helix…’ while the Japanese Pharmacopoeia (JP) actually prescribes a specific sinker (Fig. 9.10).
Fig. 9.10 Typical sinker designs: (A) three-pronged sinker; (B) JP basket sinker; (C) Helical-spring sinker.
Reciprocating Cylinder Apparatus (USP Apparatus 3)
An apparatus comprising vertically reciprocating tubes sealed with mesh discs at each end to restrain the dosage form is official in USP XXVIII as the reciprocating cylinder apparatus. This has been commercially developed as the Bio-Dis apparatus®, which allows tubes containing the sample to be plunged up and down in a small vessel containing the dissolution medium (Fig. 9.11). It has been designed to allow the tubes to be dipped sequentially in up to six different media vessels, using programmes that vary the speed and duration of immersion. It allows automated testing for up to 6 days and the manufacturers advocate its use in the testing of extended-release dosage forms. It became official in USP XXII as Apparatus 3 and is prescribed for the testing of extended-release articles. However, there is some evidence that samples tested using this apparatus tend to yield higher values of amount released than might be found using alternative procedures.
Fig. 9.11 The reciprocating cylinder apparatus of USP XXVIII (Apparatus 3).
Flow-Through Cell Apparatus (USP Apparatus 4)
Limited-volume apparati with a finite volume of dissolution fluid suffer from the problem that they operate under nonsink conditions, which results in limitations when poorly soluble drugs are considered.
A flow-through system and reservoir may be used to provide sink conditions by continually removing solvent and replacing it with fresh solvent. Alternatively, continuous recirculation may be used when sink conditions are not required. The drawbacks of non-flow-through apparatus include (1) lack of flexibility, (2) lack of homogeneity, (3) the establishment of concentration gradients, (4) their semiquantitative agitation, (5) the obscuring of details of the dissolution processes and (6) their variable shear.
Consequently, the flow-through apparatus has been developed, which features a dissolution cell of low volume (often <30mL) and a reservoir to provide fresh solvent. This is official in USP XXVIII as USP Apparatus 4 (Fig. 9.12) where it is prescribed for testing extended-release articles.
Fig. 9.12 Schematic diagram of a flow-through dissolution cell.
The basic components are reservoir, pump, heat exchanger, column (cell), tablet support, filter system, and analytical method. The systems enable solvent to be taken from a suitable reservoir and passed straight through the apparatus containing the dosage form to be either assayed and removed (effluent system) or recirculated (recycling system). The design of the pump to remove the solvent from the reservoir is crucial to the results obtained from such systems. The pump used may be either a displacement (oscillating or peristaltic) or a momentum (centrifugal) type. However, peristaltic pumps may create oscillations that might result in faster dissolution rates than might otherwise have occurred.
Dissolution is affected by factors such as the volumetric flow rate, the cross-sectional area of the cell, the initial drug quantity, liquid velocity and drug concentration. The maintenance of a controlled flow is crucial to column methods and can be influenced by the inlet system. Laminar flow of solvent through the cell is achieved by placing glass beads at the bottom of the cell to facilitate similar disintegration of all surfaces of the sample. It is common to place the tablets on such supports, but attrition (by glass beads) may encourage breakdown of the dosage form thereby increasing dissolution rates. Tablet support and consistent positioning in the liquid flow are prerequisites for consistent results. Consequently, attempts have been made to embed the tablet in glass wool or glass beads. Laminar flow conditions are typically used for tablets, hard-gelatin capsules, powders and granules. Suppositories and soft-gelatin capsules are placed in the cell without beads for turbulent flow. Nicolaides, Hempenstall and Reppas have reported differences in the dissolution rate of a poorly soluble drug, tiaglitazone, from an immediate-release (IR) tablet formulation based on the presence or absence of a tablet holder and/or beads in the flow-through cell.
Flow-through facilities can be constructed from cylindrical chromatographic columns with flow rates as low as 1mL/min. Ascending flow minimizes the problems associated with air bubbles and allows laminar flow of the solvent and ascending columns are the most common types of flow-through apparatus. The columns may be short with tapered inlet and outlet sections but generally are long sections of straight-sided tubing to provide hydrodynamic stability to the liquid flow. The material under test is placed in the vertically mounted dissolution cell, which permits solvent at 37 ± 0.5°C to be pumped in from the bottom.
The cell type selected is dependent on the dosage form being tested. Standard cells used for tablets and capsules have an internal diameter of 12mm but may show a higher dissolution rate when compared to 26mm cells due to higher flow velocity. For testing powders and granules, a modified cell containing two screen plates is used where the sample is placed between the screen plates. The suppository cell is designed for use with suppositories and soft gelatin capsules. Fats and gels used in these dosage forms are separated in this type of cell so as not to block the filters. The cell for implants has a 1mL volume due to the low flow rates (e.g. 5mL/h) required for testing this dosage form in a test that may continue over several weeks.
The flow rate of the dissolution medium through the cell must be specified for each product. The USP recommends a flow rate between 4 and 16mL/min with an allowance of ±5%. Manual operation and sampling for this type of test can be tedious and the system can be automated to control the pump, heat exchanger and test procedure, and deliver samples to a fraction collector. The system can be programmed to switch between different media at predetermined time points to allow pH changes during the test.
Further advantages of the flow through method include (1) selection of laminar or turbulent solvent flow conditions; (2) simple manipulation of medium pH to match physiological conditions; and (3) application to a wide range of dosage forms, e.g. tablets, hard and soft gelatin capsules, powders, granules, implants, and suppositories.
While the applicability of the flow-through apparatus to biorelevant dissolution tests still requires further investigation and optimization, an in vitro–in vivo correlation (IVIVC) has been reported with this apparatus using physiologically relevant flow rates and media.
Paddle-Over-Disk Apparatus (USP Apparatus 5)
This uses the paddle apparatus (USP 2) with the sample, usually a transdermal delivery system, being attached to a stainless steel disk, which is then placed on the bottom of the vessel, directly under the paddle.
Cylinder Apparatus (USP Apparatus 6)
This is a modification of the basket apparatus (USP Apparatus 1) with the basket being replaced by a stainless steel cylinder. The sample is again usually a transdermal delivery system attached to the outside of the cylinder.
Reciprocating Holder Apparatus (USP Apparatus 7)
There are several variants to this apparatus, which is based on a sample holder that oscillates up and down in the medium vessel. The sample holder may take the form of a disc, cylinder or a spring on the end of a stainless steel or acrylic rod, or it may simply be the rod alone. The sample is attached to the outside of the sample holder either by virtue of being self-adhesive (e.g. transdermal delivery system) or is glued in place using a suitable adhesive. This apparatus may be used for transdermal products, coated-drug delivery systems or other suitable products (e.g. osmotic pump devices). It is prescribed for the drug-release testing of pseudoephedrine hydrochloride extended-release tablets USP where the tablets are enclosed in a 5×5cm2 wrap of nylon, which is then attached to the rod.
Intrinsic Dissolution Method (USP)
Two variations of the IDR apparatus exist—the rotating disc apparatus (Wood Apparatus, Fig. 9.13) and the stationary disc apparatus (Fig. 9.14). Both types of apparatus employ a compacted pellet of pure drug produced by compressing an aliquot of powder in a stainless steel punch and die. The die is mounted onto a smooth polished-base plate and the punch is driven into the die using a hydraulic press. The USP states a compression dwell time of 1min at the minimum compression force required to form a nondisintegrating compacted pellet. Thebase plate is then detached to expose a smooth and constant pellet surface at the face of the die and it is this pellet surface that is subjected to the dissolution test. In the rotating disc apparatus, the die is then inverted and screwed onto a customized shaft on a dissolution tester, which is then lowered into the dissolution medium until the face pellet is 3.8cm from the bottom of the vessel. The shaft is then rotated in the same way as USP Apparatus 1 and 2. In the stationary disc apparatus, the die containing compressed pellet is placed face up into a flat-bottomed dissolution vessel prefilled with the appropriate volume of dissolution medium. The medium is stirred by means of a rotating paddle (e.g. USP Apparatus 2) positioned 6mm above the pellet surface.
Fig. 9.13 Schematic of rotating disk intrinsic dissolution rate apparatus (Wood apparatus).
Fig. 9.14 Schematic of a stationary disc intrinsic dissolution rate apparatus.
Disadvantages of the rotating disk apparatus include the risk of air bubbles forming on the surface of the pellet, which could affect the dissolution rate and heat loss of approximately ±2oC through the shafts when the dies are first lowered into the dissolution medium. Using the stationary disc apparatus significantly reduces the formation of air bubbles, while heat losses are eliminated since the dies are totally submerged in the dissolution medium.
The IDR is calculated by plotting the cumulative amount of substance dissolved per unit area of the exposed pellet surface against time until 10% of the drug pellet has dissolved. Linear regression should be applied to data points up to this point and the slope of the regression line gives the IDR of the substance under test in mg/min/cm2. However, this compendia calculation may prove difficult to apply to poorly soluble compounds where 10% dissolution may not be achieved. In these instances, it may be practical to use an analytical method with sufficiently high sensitivity to be able to plot 6–8 data points before 10% dissolution and apply linear region.
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