Control of drug release from polymer matrices impregnated with magnetic beads —a proposed mechanism and model for enhanced release

Journal of Controlled Release. 1 (1984) 143-147 Elsevier Science Publishers B.V., Amsterdam --Printed

in The Netherlands

The need to regulate drug release rates in applications such m suppression of diabetic symptoms and birth control has previously led to the deuelopment of delivery systems containing small magnetic beads uniformly imbedded within drug-laden polymer matrices. An oscillating magnetic field imposed on such systems triggers a significant increase in release rate. A mechanism for enhanced release is proposed here, which draws upon the similarity between the observed increase in mass transfer by pulsation, e.g., promotion of axial diffusion in a cylinder with pulsed (but zero net) flow and enhanced drug release by the oscillating field. A mathematical model is derived based on this analogy. Its predictions ore consistent with general observations and provide correlations of release rates with the frequency and amplitude of the oscillatkg magnetic field and the intrinsic drug diffusivity.

The use of polymers to provide controlled, sustained delivery of drugs and other bioactive chemicals is an emerging technology with wide applications in clinical, pharrnaceutical, biological, agricultural, environmental and household uses. A large number of formulations and delivery devices has been advanced in recent years. Historical developments and current focuses of this field can be found in tke review by Langer [l]. Fn ad& tion to the often desirable near-constant, prolonged re!ease pattern, special applications, such as insulin release for diabetes and hormonal delivery for birth control, demand release rates that vary in a controlled fashion. Magnetically controlled systems have recently been developed to meet this requirement 12-41. These systems contain uniformly

dispersed small magnetic beads. Drug release in an aqueous medium is typical of diffusion controlled matrix systems. However, upon exposure to an oscillating external magnetic field, drug release attains a much higher rate (an enhancement of one order of magnitude is not uncommon). This enhancement phenomexx~ is reversible; upon removal of the external field the release rate drops to levels comparable to that prior to the imposition of the field. Detailed preparation procedures of these matrix delivery devices containing magnetic beads are reported in the literature (Z-41. These systems are typically fabrnxked using techniques developed forincolporatingmacromolecules into ethylene-vinyl acetate copolymers [5]. Briefly, the polymer and powdered drug are mixed in methylene chloride and then cast at a low temperature. Magnetic

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IMTRODUCTIOM

0 ,984 Elsevier Science Publishers

beads are then added to form a layered structure. The use of low temperature casting and drying prevents migration of the drug powder; a special procedure developed to embed the beads ensures distribution uniformity. Bovine serum albumin (BSA) and insulin represent the two most studied drugs to date delivered from such devices. A typical magnetic delivery system is a polymer matrix studded with uniformly distributed magnetic beads (-1 mm in diameter) and lumps of dispersed drug (-100-200 pm particles). Photo-micrographs of sectioned devices revealed an underlying network of pores with radii ranging from 1 pm to 5 (em. Tbe existence of this porous network is crucial to drug release; upon exposure of the device to an aqueous environment, the molecules are believed to diffuse from the reservoirs (undissolved lumps) through the pores (and their throats) filled with normal saline. Since the drug molecules are much smaller than the pore dimensions (BSA for example is an ellipsoid with axes of 140 by 40 A, which is usually described by a sphere of Stokes hydrodynamic radius 36 PI [6]), diffusion in the pores is essentially nnhindered by the presence of pore walls.

THEORETICAL

INTERPRETATION

A number of competing enhancement mechanisms can be hypothesized. However, comparison with currently available experimental evidence is sufficient to eliminate most in favor of one convincing mechanism, to be discussed in this paper. First, the increased release rate cannot be attributed to direct magnetic interactions of drug molecules with the external fieid, as a stationary field has no observable effect on the release kinetics. The mere presence of a magnetic field due to the imbedded beads alone exerts no influence on drug release either. The beads must be subjected to an alternating external field to induce enhancement. It is conceivable that the oscillating field causes the dispersed

beads to rotate (and perhaps even translate slightly) in the matrix, thus straining the matrix, compressing and expanding the channels, and altering the integrity of the matrix. Formerly unconnected channels may become continuous via creation of additional pores, and the n&work is made more permeable. However, the hypothesis of induced permanent damage cannot explain the reversibility of the release enhancement phenomenon. When the external field is turned off, the newly created channels are expected to continue facilitating mass transport, contrary to the experimental observation that the drug release rate reverts to the original level. We suggest that the major observed effect stems from the alternate compression and expansion deformation suffered by the pores as a result of the nearby rotating and oscillating beads, consistent with the above hypothesis. However, no permanent damage needs to be sustained by the polymer matrix. The contracting and dilating channels cause the fluid within to underao a oulsatile flow. Although no net conve&ive &ion in either direction along the tube axis is induced, the oscillation alone is able to greatly improve diffusive mass transfer. The use of pulsatile flow to enhance mass transfer is a well-known phenomenon in chemical engineering literature. Lemlich and Levy reported the effect of vibrating horizontal cylinders in increasing sublimation to room air [8]. Krasuk and Smith investigated mass transfer from the wall to a fluid in pulsed flow in a circular tube [9]. A number of other studies have been devoted to the effect of pulsation in increasing mass transfer rates in liquid--liquid extraction columns [lo- -12] ( and in solid-fluid transfer in packed towers [13]. Harris and Gore” [14] advanced a theory for the rate of mass transfer through a long tube connecting the reservoirs of constant concentration with oscillating flow in the tube. The oscillation is imagined to be driven by a piston with reciprocating displacement. The increase in transfer relative to that due

146

to molecular diffusion alone is given as a function of three dimensionless groups: an oscillating Reynolds number, wa2/v (where w is the frequency of pulsation, a is the cylinder radius, and v is the fluid kinematic an amplitude parameter, A/a viscosity), (where A is the amplitude of piston displacement), and the Schmidt number, SC = u/D (where D is the diffusivity of the diffusing species in the fluid filling the cylinder). The magnetically controlled drug delivery process is remarkably similar to the ideal axial diffusion in a cylinder with pulsed flow. Since the beads are uniformly distributed, their rotation and translation caused by the external field are expected to deform most of the channels. The deformation affects nearby channels to the greatest extent, with its influence decreasing gradually in reaching more remote ones. This oscillatory deformation sets up a pulsatile flow pattern within the pores, wbicb perturbs the steady axial concentration gradient of the drug. This perturbation leads to a higher “effective gradient” and consequently enhanced mass transfer. We will assume the instantaneous volumetric flow rate, 9, through any cross.section of the tube to be given by: 7 = ‘/aAwnax (c+“~ + .Ciwf)

(1)

The radial profile of the axial velocity, w, also fluctuates periodically, and is given by w = wA[l - Jo(arla)lJoWleiwt

f-

[4 - ~,(~wJ0b)l wA[l - Ja(a’r/a)/Jo(cu’)]e-‘W’ 14 - SJ,(ol’)/a’J&‘)]

(2)

where (Y = (-iwazjv)“z, CC’ = (iwaz/u)“*, and Jn is the Bessel function of the first kind of order n. The unsteady diffusion equation in terms of the local drug concentration, c, becomes

ac

W~C ,+-=D

a2

a% ar

-2

+--+-

1 ac

as2

r ar

a9

(3)

With the proper boundary conditions of no ma.ss flux through the tube wall and fixed time averages at the ends of the tube (governed by the reservoir concentration and external fluid condition surrounding the device) eqns. (2) and (3) can be solved 1141 to yield the final result:

where Q is the time-averaged release rate with the imposed pulsation, Q. is the background release rate in the absence of pulsation, and p = (-i&/D)“2.

RESULTS AND DISCUSSION To provide realistic descrip,rons of our systems, we must first determine the parameters in eqn. (4). The density and viscosity of normal saline solution are reported [15] to be 1.00287 g/cm3 and 1.10 X 1O‘3 Pa s. The diffusion coefficients of BSA and insulin in water are estimated to be 6.1 X 10“ cm2/s, and 7.3 X lo-’ cm2/s, respectively [lS]. These values give a Schmidt number of 1.65 X lo4 for these diffusing macromolecules (BSA and insulin), in distinct contrast to those characteristic of small molecules with a diffusion coefficient on the order of 10m6 cm*/s and a Schmidt number in the neighborhood of 10). Figure 1 shows curves calculated using eqn. (4) for the three cases, BSA. insulin and a tvnical .smaR molecule. As is evident in this-&figure, the msgnctic modulation method is particularly effective for macromolecule release; a much higher frequency must be employed for small drug

0.8

beads distorts nearby pores. We assume such distortion is felt for all pores within a distance L. The extent of distortion is then related to the Young’s modulus of the matrix, E, which is measured [17] to be on the order of lo7 N/m2 at the temperature of interest. The shear modulus, G, is l/3 the Young’s modulus. To a first order of approximation, we have: Tangential force on the bead surface in the direction of surface displacement due to bead rotation or translation

0.6

0.4

0.2

0

10-q

10-S

10-I

Fig. 1. Fractional enhancement of drug release rate as a function of oscillating Reynolds number cab culated by the made, for systems with different Schmidt numbers.

molecules to achieve comparable enhancement. This is consistent with the much shortened time scale of small molecule diffusion, which dictates an increased frequency to produce appreciable effects. Direct comparison of predicted cmes shown in Fig. 1 with experimental data is only possible if A and a are known (or rather, the ratio of them is determined). In this regard, approximation must be made, since the theory assumes a uniform cylindrical cross-section, while in reality the pores have dimensions varying over a fairly wide range. We will assume that the non-uniform, polydisperse porous network is represented by a uniform collection of channels with a constant radius in the neighborhood of 3 pm. The strategy invoked to estimate the effective amplitude of volumetric flowrate fluctuation relies on knowledge of the external magnetic field strength, the permanent dipole moment of the imbedded magnetic beads, the bead volume, and the elastic modulus of the polymeric matrix. In the most recent exp:perimcnts documented elsea%xe [17], a field strength of 1600 gauss was used, corresponding to a dipole moment of 2.058 X 10.” A m*. The torque, 7, on the

$------$

7

bead radius

GX

surfaceareaX

G X (head radius)2 X $-

E=

(5)

where E is the shear strain sustained by the matrix between beads. A reasonable estimate of L is the average inter-bead distance. With the above cited values, and the known bead radius and inter-bead distance, the calculated equivalent piston displacement, A, is 2.06 X 10y5 m. This gives a value of 6.4 for the dimensionless amplitude parameter, A/a. As will be shown later, optimal fitting of release data on BSA 1171 requires this dibxensionless parameter to be 5.2. We consider this minor difference inconsequential, as the estimated value of 6.4 is based on several properties only approximately known. Table 1 summarizes some data [17] on BSA enhanced release from ethylene---jhyi acetate copolymer and our model predictions. The model adequately describes the obzerved trend of increasing release rate with increasing frequency, and predicts the correct magnitude of release enhancement. In conclusion, preliminary evidence sup. ports the general validity of the model proposed here. It can thus be used to provide a preliminary estimate of the optimal matrix mechanical and morphological properties, bead dimension and distribution, and msg. netic field strength and frequency, in order to achieve a desired degree of modulation for a dn.g with known diffusivity.

TABLE

1

Comparison of model predictions and experimental data (17, of BSA release modulated by 3x1 external magnetic field Fractional

w

E:.&, 31.42

(5 4)

41.47 (6.67 H,) 59.69 (8.5 H,) 69.11(11 H,) ‘With

increase in release rate

Model prediction’

2.14 * 0.21

1.67

2.93 f 0.45 4.77 * 0.28 5.62 i 0.55

2.18 4.78 5.81

Ala= 5.2.

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’ MR.Levy,