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Optimization of release from magnetically controlled polymeric drug release devices
621
Optimization of release from magnetically controlled polymeric drug release devices Elazer R. Edelman* and Robert Lange? *Division of Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, MA 02139, USA, and Cardiovascular Division, Department of Internal Medicine, Brigham and Women’s Hospital and Harvard Medical Schools, Boston, MA 02115, USA; TDepartment of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Release rates from drug:polymer matrices embedded with small magnets increase in the presence of oscillating magnetic fields. Previous studies of these systems have defined those parameters that determine the extent of the increase in release, and implied that not only was the force generated within the matrix an important determinant of the extent of modulation but also that the greater the amount of matrix actually displaced, the greater the observed modulation. We investigated this possibility in the magnetic system and developed a model taking into account the intersection of the volume of a cylindrical polymer-drug magnet embedded matrix with an imaginary sphere representing the upper limit of matrix deformation by the magnet. The intersection correlated in a linear fashion with the increase in release (slope = 1.16 f 0.26, R = 0.664, P = 0.003, s.e.e. = 1.38). Magnet orientation alone was insufficient to explain the data. It appears that a modulated system is optimized when the modulating force overlaps precisely with the maximum amount of matrix drug that can be released. If the size of the matrix, position of the magnet, force generated on the matrix by the magnet, viscoelastic properties of the matrix, etc. are not matched then modulation is inefficient. These results should provide further insight into and a means of optimization for externally regulated controlled release systems. Keywords:
Controlled
release,
magnetic
fields,
drug
delivery,
sustained
release
Received 1 June 1992; revised 10 December 1992; accepted 16 December 1992
Increasingly, investigators and clinicians are concentrating on means of modulating the release of drugs from polymeric drug delivery systems’. Sustained and controlled release of compounds provide constant or continuously decreasing levels of drug which are often non-physiologic. Many diseases require only intermittent drug administration to deal with occasional exacerbation, or periodic administration to mimic normal diurnal variation in drug levels, e.g. insulin replacement in diabetes mellitus. We have developed and studied regulated release using magnetic fields. Small magnets are embedded within a drug-polymer matrix without affecting baseline release kinetics. When an oscillating external magnetic field is applied to the matrices, drug release is increased up to 30-fold’. Magnified videotaped images of areas of the matrix above the embedded magnets showed alternating compression and release of the material within a certain distance from the magnet’. The magnet’s motion followed the magnetic field: oscillations of the magnet were determined by the field frequency, and the extent of magnet motion was dictated by the magnetic field Correspondence
to Dr E.R. Edelman.
0 1993 Butterworth-Heinemann 0142-9612/93/060621-06
Ltd
amplitude. Controlled periodic mechanical deformation of the same matrices without magnets enhanced drug release in a similar fashion3, further supporting the hypothesis that the net effect involved translation of the magnet and displacement of the matrix. The area over which the mechanical displacement was applied was found to be an important determinant of the extent to which baseline release was increased. This stimulation of release from the matrix was termed modulation, and increased as the area over which the deformation was applied increased relative to the surface area of the polymer matrix face. A more complex relationship between the location of the centre of the applied deformation and the extent of release modulation was observed. Modulation increased as the deformation was applied at increasing radial distance from the centre of the polymer matrix face and then decreased as the deformation was applied closest to the border of the matrix face3. It was inferred from these data that the optimum configuration for a modulated release system required maximum overlap between the polymer:drug matrix and the volume over which the mechanical deformation could exert its effect. Deformation over a Biomaterials
1993, Vol. 14 No. 6
Modulated
622
large area would be transferred over a larger portion of the polymer matrix and induce a greater increase in release. As the area was shifted further from the centre of the polymer matrix face the overlap between the matrix and deformation influence decreased. We now examine whether these two observations, increasing modulation with increasing deformation area, and the correlation of the percentage of matrix capable of being pulsed with the extent to which release was stimulated above baseline, could be used to explain the extent of modulation observed when the magnetic system was used in practice.
METHODS
Matrix fabrication As detailed elsewhere’ ethylene-vinyl acetate copolymer (EVAc, 40% vinyl acetate), manufactured under the product name ELVAX-40P (DuPont Co., Wilmington, USA), was washed in distilled water and 95% alcohol to remove impurities and then dissolved in dichloromethane to form a 10% w/v solution, Bovine serum albumin (BSA, Sigma Chemical Co., St Louis, USA, molecular weight 88 800) was sieved to a particle size range of 150-180 pm and added to the EVAc solution (33% w/w]. The BSAEVAc mixture was poured into a cylindrical glass mould that rested on dry ice and had been precooled for 10 min. Nickel-coated samarium cobalt (SmCo,) magnets (Permag Northeast, Waltham, USA] were suspended over the hardening BSA-EVAc solution and dropped into the suspension after various times had elapsed. The different times between pouring and dropping left the magnet at different positions in the matrix after complete hardening. The SmCo, magnets were shaped spherically, cylindrically or toroidally. The spheres were 1.4 mm in diameter, weighed 10 mg each and were magnetized to approximately 100 G. The toroids and cylinders were 1.4 f 0.5 mm high and magnetized to 1100 G with pole vectors orthogonal to the end faces. The cylinders weighed 15 mg and had a diameter of 1.5 mm and the toroids weighed 80 mg and had an inner diameter of 1.5 mm and an outer diameter of 3.0 mm.
Magnet position The position of the magnets within the matrix and by inference their alignment with the external magnetic field were determined from radiographs of the matrices taken in three orthogonal directions. A standard clinical X-ray machine exposed the matrices to a 44 kV pulse of 120 mA for 33 ms. The position and orientation of the SmCo, magnets were determined from the radiographic images obtained from these exposures, A line was drawn through the true vertical of the matrix and was used as the axis of the matrix. Lines drawn along the true vertical and true horizontal of the magnet were used to define the magnet’s axes. The intersection of these lines was the centre of the magnet and the lateral displacement of the magnet centre from the matrix axis was used as the x-offset of the magnet. The y-offset was the distance between the magnet centre and the matrix bottom. The orientation of the magnet within the matrix was computed from the angle that the vertical axis of the magnet Biomaterials
1993, Vol. 14 NO. 8
release:
volume
model:
E.R. Edelman
and R. Langer
deviated from the vertical axis of the matrix. The cosine of this angle was one for a perfectly aligned magnet and zero for magnets completely misaligned.
Magnetic
modulation
of EVAc:BSA matrices
The magnetic field was generated by a plate demagnetizer (OS. Walker Co., Worcester, USA) capable of delivering a 80 Hz magnetic field at amplitudes varying from 0 to 900 G (peak to peak). When hydrated matrices were placed within the magnetic field BSA release increased instantly, as a function of field amplitude, for the duration of the field application. Release returned to baseline immediately after field withdrawal’. In all cases the kinetics of BSA release were monitored continuously and in real-time by means of a flow-through spectrophotometer’. Unless specified otherwise the matrices were subjected to 40 individual exposures of a 500 G, 60 HZ oscillating magnetic field for 20 min. A modulation index, termed ‘modulation’, was attained by dividing the peak absorbance by the average baseline absorbance observed before and after a magnetic field was applied.
Volume of magnetic
influence
Video recorded magnified images of magnet embedded matrices revealed that only matrix material within a given distance of the embedded magnets moved under deformation by the magnets’. This distance was dependent on characteristics of the matrix and magnet such that displacement was no longer observed at a distance equal to (2 X magnet mass X magnet pole strength magnetic field strength) polymer
material
modulus
X
of elasticity
This is not unexpected, as it is precisely the form that one would anticipate if one set the magnetic forces generated equal to the mechanical force as dictated for elastic material by Hooke’s law4. The matrix and magnet geometries were reconstructed on a digital computer. The volume of matrix that could be influenced by the magnet was determined from the intersection of the cylindrical matrices and an imaginary sphere with a radius equal to the limit of matrix displacement by the magnet (Figure 2). The origin of the sphere was the centre of the magnet. A random array of 10 000 points in and about the cylindrical matrix was computer generated. If the points fell within the intersection of the sphere and the matrix the points were added to a running tally. The total number of points in the tally represented the integrated intersecting volume. This number was normalized to the total number of points generated and was defined as the aligned volume. The aligned volume was then compared with the extent of modulation achieved for matrices made with toroid or cylindrical magnets.
Volume of influence:
empirical
data
To verify the model of modulation that incorporates a sphere of influence we examined modulation for: three different sized matrices embedded with one toroidal magnet; one-size matrix embedded with either a toroidal, cylindrical or spherical magnet; and one-size matrix
Modulated
623
release: volume model: E.R. Edelman and R. Langer
a
. .*.. .. .. .- --.-..
Figure 1 The two panels represent possible configurations of the relationship between the magnet and drug polymer matrix. a, In the ideal case the magnet is positioned so that it is located centrally within the cylinder and its effect matches the boundaries of the polymer matrix. b, If the magnet is positioned off centre then the overlap between matrix material and magnet effect is diminished. The points in the figure represent the computer generated random array of 10 000 points. A running tally was incremented if a point fell within the bounds of the cylindrical matrix and the sphere that represents the limit of the magnets effect in matrix material.
embedded with a cylindrical magnet after pre-release in saline for 72 h prior to any magnetic field exposure, or repeated exposure to magnetic fields prior to hydration. The first set of toroidal magnets were embedded within cylindrical BSA:EVAc matrices 6 mm high and 4.4,7 or 14 mm in diameter; five matrices per group. The use of different sized matrices for a given strength magnet was for examining whether changes in matrix size might dampen the modulatory effect as more of the matrix material falls outside the sphere of influence of the magnet. In another experiment matrices were embedded with magnets of different sizes but equivalent pole strength (toroids and cylinders, pole strength 1100 G), or equal sizes and different pole strengths (cylinders and spheres). This allowed us to examine the potential difference in modulation that might be observed with spheres of magnet influence of different sizes as calculated from the force equation noted above and verified by direct observation. Six matrices were fabricated with one of each magnet and exposed in mixed groups to 10 pulses of a 60 Hz, 500 G magnetic field for 20 min separated by 3-12 h periods of rest. The average and peak indices of modulation were calculated and compared for each group. A matrix was determined to have reached its peak response when the modulation index value rose to within 10% of the maximum observed modulation and was maintained within this range for four consecutive stimuli. The amount of drug released up until that point in time was computed as well. To determine whether the predominant determinant of release was the sphere of influence as opposed to mobilization of the embedded magnet with repeated exposure to the magnetic field, or changes in the morphology of the matrix with the progressive release of drug with time, matrices were released in saline before -magnetic stimulation, magnetic stimulation before release or simultaneous commencement of stimulation and release. Matrices embedded with a cylindrical magnet were subjected to 36 20 min pulses of 60 Hz fields before activated drug release after immersion in saline or after 72 h of prerelease. Five to six matrices were examined in each group at each time point.
RESULTS Matrix-magnet
geometry
When magnetic fields were applied to EVAc:BSA matrices of identical heights and three different radii embedded with a single toroidal SmCo, magnet a parabolic relationship with modulation was observed (Zrhle 1). Under these field and magnet-matrix conditions modulation peaked with a matrix 6.0 mm high and 7 mm in diameter. When the matrix was smaller or larger than this size modulation decreased substantially. As the force generated by a magnetic field on a magnetized particle is proportional to the vector dot product of the field strength and particle pole strength this force should depend on the cosine of the angle between these two vectors. If the extent of modulation followed force alone then one would observe that for the same field amplitude and pole strength the extent of modulation should depend upon the cosine of the angle alone. Thus, the modulation obtained after 10 different matrices were exposed to 40 field exposures was plotted against the cosine of the angle of magnet orientation within the polymer matrix. This was done for angle orientation in two orthogonal planes and then for the square root of the sum of squares of those values. In all cases there was no statistically significant correlation between observed modulation and the angle at which the magnet resided [Figure 2). Aligned volumes were determined for all matrices by computing the intersection of the spherical polymer matrix and a sphere about the embedded magnet whose
Table1 Extent of modulated BSA release from EVAc:BSA matrices of different sizes embedded with a 1100 G SmCo, magnet and exposed to 500 G, 60 Hz magnetic fields Matrix diameter (mm)
Modulation index
4.4 7.0 14.0
2.5 k 0.2 11.3 f 1.9 5.2 f 0.3
Biomaterials
1993, Vol. 14 No. 8
Modulated
624
l l .:
L
3*
0.80
0.85
0.95
0.90 Magnet
l
l
0
l
1.00
release:
volume
model:
E.R.
Edelman
and
R. Langer
was 27.6. In practice value.
no modulation
Timing of release
and field applications
exceeded
this ideal
As further verification of the existence of a sphere of magnet influence the maximization of modulation was found to be dependent upon the amount of drug released, not the number of previous stimuli or the time immersed in solution. When cylindrical matrices were embedded within the EVAc:BSA matrices, peak modulation was observed only after 40-469~ of the embedded drug had been released (Figure 4a).This occurred whether the matrices has been exposed to magnetic stimulation prior to the initiation of release, a period of release prior to stimulation, or whether the initiation of release coincided
orientation
Figure2 The extent of modulation obtained for EVAc matrices embedded with one SmCo, magnet and BSA (30% w/v) is plotted against the orientation of the magnet as determined from radiographs of the matrices. There is no statistically significant correlation between modulation and magnet orientation.
50
r
radius was equal to the maximum displacement obtainable for that matrix. A linear relationship was obtained as depicted in Figure3 (slope = 1.16 AI 0.26, R = 0.864, P < 0.003, s.e.e. = 1.38). The maximum overlap for the matrices and magnets used was 13.7 cm’. If the linear relationship described holds true this would imply that the maximum modulation obtainable from the matrices IMMED
pre-STIM
pre-RLS
50-
40 -
30 -
Sphere
4
6
10
8 Intersecting
12
volume
Figure3 Modulation obtained from 10 EVAc matrices embedded with one SmCo, magnet and BSA (30% w/v) is plotted against the intersecting volume. This volume was computed from the intersection of the volume of the cylindrical matrix and an imaginary sphere whose radius was determined by the maximum extent of magnet translation. As such this represents the volume of matrix capable of being pulsed. A linear relationship was obtained with a slope of 1.16 + 0.26 (R = 0.864, P < 0.003, s.e.e. = 1.379). Biomaterials 1993, Vol. 14 No. 8
of influence
(radius
mm)
Figure4 a, EVAc:BSA matrices embedded with a cylindrical SmCo, were exposed to a series of 20 min 60 Hz, 500 G oscillating magnetic fields immediately after immersion in saline and initiation of BSA release (IMMED), after 36 20 min pulses of the magnetic field (pre-STIM), or 72 h after immersion in saline (pre-RLS). In all cases 40-46% of the incorporated BSA had to be released before peak modulation was observed. b, The percentage of incorporated BSA released before peak modulation correlated precisely with the radius of the sphere of influence for three different matrix:magnet configurations subjected to magnetic field stimulation (slope = -9.8 + 0.9, R = 0.996, P = 0.028, s.e.e. = 1.48).
Modulated
release: volume
625
model: E.R. E&/man and R. Langer
with the first application of magnetic field stimulation. The amount of BSA released from the matrix before peak modulation was achieved correlated precisely with the radius of the spherical volume of influence (Figure 4b, slope = -9.6 + 0.7, R = 0.992, s.e.e. = 1.41,P < 0.001).
DISCUSSION It appears that magnetically regulated drug release from polymer matrices is related to the movement of embedded magnets within the matrix. Magnified video taped images of areas of the matrix above the embedded magnets showed alternating compression and release of the material within a certain distance from the magnet’. Subsequent studies confirmed these findings and demonstrated that pulsatile deformations of the polymer matrices led to increased release above the haseline3. It would seem that whatever contributes to the movement of the magnet within the matrix contributes to the control of drug release. The force exerted on the magnet is related directly to the strength of the field and the magnetization of the magnet, and the number of movements of the magnet in the matrix in a given period of time increases with the field frequency. Thus, these factors should be expected to regulate magnetically stimulated release. The force that is exerted by an external magnetic field of strength 3 and gradient VB, on a magnet of magnetic moment iii, can be written as the vector dot product of iii and VB. The strength of the field generated by an electromagnet decreases linearly with distance from the electromagnet in the near field, the region in space adjacent to the surface of the electromagnet. In regions far from the magnet surface the field decreases as the square of the distance. These experiments were conducted within the near field, and the magnetic field at any point in space in this region can, therefore, be expressed as B = i,[B, - B,,z). As the gradient of a magnetic field uniform in all but the z direction can be simplified to VB = -i,B,, the force equation F = m - VB can be expressed as F = -mzBo. Since the component of the magnetic moment of the magnet in the direction of the field’s vector, m,, is strongest when the magnet is aligned with the field, the moment can be written as the product of a net magnetization, m, and the cosine of 8, the angle between the net direction of the field and the magnet’s pole vector. Thus, m, = m, cos 8 and the force generated by a magnetic field on a magnet can be written as F = -m,B,cos& If release modulation is determined by this force, the extent of modulation should increase in a linear fashion with the amplitude of the magnetic field, as well as the magnetization and orientation of the embedded magnet. While modulation indeed rose with increasing force of the applied magnetic field’* 5, the orientation of the magnet did not appear to be a primary determinant of modulation (Figure 2). A much stronger determinant was the amount of matrix being pulsed, i.e. how much of the matrix at any point of time was capable of responding to the magnetic stimulation. These data were verified in a variety of independent experiments. In the first case, an intermediate size matrix was the most efficiently modulated system. Matrices much smaller or much
larger were not modulated as well. Second, it appears that modulated release requires a period of ‘warm-up’ before which a less prominent effect is noted. This wannup is not determined by the number of pulsations of the magnet under the influence of the magnetic field but rather by a critical amount of matrix material that must be released. Once this level is reached the matrix responds most efficiently. Thus, it is probably not the case that the magnet is restrained within the polymer matrix and moves more freely once bonds are broken. Third, the threshold release level varies inversely with the area over which the embedded magnet can exert its influence. As this area expands the amount of matrix material that must be solubilized and released diminishes (Figure 4b). Thus, while motion of the magnet increases with force on the magnet, this effect seems to remain constant with time. Moreover, it appears to be of secondary importance to the amount of matrix that possesses solubilized drug capable of coming under the influence of the magnetic field and deformation of the embedded magnet. The ideal situation is where the bounds of the magnet deformation of the matrix correspond to the physical boundaries of the polymer:drug matrix, and where enough of the drug is in a soluble state capable of being released. Dry drug cannot be modulated as it cannot be released, just as drug that resides far beyond the volume of matrix that the magnet can deform cannot be modulated. This model of magnetic modulation of polymer matrix drug release incorporates the frequency and strength of the magnetic field, the pole strength of the magnet, its orientation within the field and position within the matrix. The model implies that a maximum amount of modulation should be achieved when the area of the matrix that moves with the magnet and the cylindrical volume of drug containing matrix overlap perfectly. In fact the radius of the overlap for the matrices tested in Figure 4b was 2.95 mm; 84.3% of the radius of the matrix that supplied the most efficient modulation. If magnetic modulated release is to be used the magnet field, embedded magnet, matrix and drug conditions should be configured to use only enough energy and materials to provide for this overlap.When the force generated by the coupling of the magnet and magnetic field is excessive or insufficient and is mismatched with the viscoelastic properties of the matrix resources are wasted and peak modulation will not be achieved. This might allow for custom design of pulsed delivery devices. We hope that analyses along these lines will shed further light on the mechanism of externally regulated controlled drug release and allow for optimization of such devices in practice.
ACKNOWLEDGEMENTS We thank Dr John Taylor for assistance with some of these experiments. This study was supported by a grant from the National Institute of Health, grant No. GM26698. Dr Edelman is currently supported by a PhysicianScientist Award from the National Institutes of Health (K12 AG00294). Biomaterials
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REFERENCES 1 2
3
Langer, R., New methods of drug delivery, Science 1990, 249,1527-1533 Edelman, E.R., Kost, J., Bobeck, H. and Langer, R., Regulation of drug release from polymer matrices by oscillating magnetic fields, Z, Biomed. Mater. Res. 1985, 19,67-63 Edelman, E.R., Fiorino, A., Godzinsky, A. and Langer, R., Mechanical deformation of polymer matrix controlled
4
5
volume
model: E.R. Edelman
and R. Langer
release devices modulates drug release,]. Biomed. Mater. Res. 1992, 26,1619-1631 McCarthy, M.J., Soong, D.S. and Edelman, E.R., Control of drug release from polymer matrices impregnated with magnetic beads - a proposed mechanism and model for enhanced release, I. Controlled Release 1964,1,143-147 Edelman, E.R., Brown, L., Taylor, J. and Langer, R., In vitro and in vivo kinetics of regulated drug release f:om polymer matrices by oscillating magnetic fields, J. Biomed. Mater. Res. 1987, 21, 339-353
Materials Research Society
Fall 1993
Meeting
Boston, Massachusetts, USA 29 November - 3 December 1993 This meeting will continue the Material Research Society’s tradition of offering a series of in-depth and interdisciplinary topical symposia. Each symposium will provide a forum for scientists and engineers to exchange information and ideas at the leading edge of materials research.
Symposium S Biomolecular materials by design This symposium will address 1) the design and synthesis of biomolecular materials from simple polymers to complex macromolecular assemblies, and 2) potential applications from passive structural components to “smart materials”. Symposium organizers: Hagan Bayley, David Kaplan and Manuel Navia
Symposium T Biomaterials for drug and cell delivery This symposium will focus on the development of novel biomaterials and the improved understanding and utilization of existing biomaterials for the controlled release of drugs, growth factors, and other bioactive molecules to specific tissues. In addition, emphasis will be given to biomaterials for use in tissue engineering. Symposium organizers: Antonios G. Mikos, H. Bernstein, Regina Murphy
Biomaterials
1993, Vol. 14 No. 8
Optimization of release from magnetically controlled polymeric drug release devices Elazer R. Edelman* and Robert Lange? *Division of Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, MA 02139, USA, and Cardiovascular Division, Department of Internal Medicine, Brigham and Women’s Hospital and Harvard Medical Schools, Boston, MA 02115, USA; TDepartment of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Release rates from drug:polymer matrices embedded with small magnets increase in the presence of oscillating magnetic fields. Previous studies of these systems have defined those parameters that determine the extent of the increase in release, and implied that not only was the force generated within the matrix an important determinant of the extent of modulation but also that the greater the amount of matrix actually displaced, the greater the observed modulation. We investigated this possibility in the magnetic system and developed a model taking into account the intersection of the volume of a cylindrical polymer-drug magnet embedded matrix with an imaginary sphere representing the upper limit of matrix deformation by the magnet. The intersection correlated in a linear fashion with the increase in release (slope = 1.16 f 0.26, R = 0.664, P = 0.003, s.e.e. = 1.38). Magnet orientation alone was insufficient to explain the data. It appears that a modulated system is optimized when the modulating force overlaps precisely with the maximum amount of matrix drug that can be released. If the size of the matrix, position of the magnet, force generated on the matrix by the magnet, viscoelastic properties of the matrix, etc. are not matched then modulation is inefficient. These results should provide further insight into and a means of optimization for externally regulated controlled release systems. Keywords:
Controlled
release,
magnetic
fields,
drug
delivery,
sustained
release
Received 1 June 1992; revised 10 December 1992; accepted 16 December 1992
Increasingly, investigators and clinicians are concentrating on means of modulating the release of drugs from polymeric drug delivery systems’. Sustained and controlled release of compounds provide constant or continuously decreasing levels of drug which are often non-physiologic. Many diseases require only intermittent drug administration to deal with occasional exacerbation, or periodic administration to mimic normal diurnal variation in drug levels, e.g. insulin replacement in diabetes mellitus. We have developed and studied regulated release using magnetic fields. Small magnets are embedded within a drug-polymer matrix without affecting baseline release kinetics. When an oscillating external magnetic field is applied to the matrices, drug release is increased up to 30-fold’. Magnified videotaped images of areas of the matrix above the embedded magnets showed alternating compression and release of the material within a certain distance from the magnet’. The magnet’s motion followed the magnetic field: oscillations of the magnet were determined by the field frequency, and the extent of magnet motion was dictated by the magnetic field Correspondence
to Dr E.R. Edelman.
0 1993 Butterworth-Heinemann 0142-9612/93/060621-06
Ltd
amplitude. Controlled periodic mechanical deformation of the same matrices without magnets enhanced drug release in a similar fashion3, further supporting the hypothesis that the net effect involved translation of the magnet and displacement of the matrix. The area over which the mechanical displacement was applied was found to be an important determinant of the extent to which baseline release was increased. This stimulation of release from the matrix was termed modulation, and increased as the area over which the deformation was applied increased relative to the surface area of the polymer matrix face. A more complex relationship between the location of the centre of the applied deformation and the extent of release modulation was observed. Modulation increased as the deformation was applied at increasing radial distance from the centre of the polymer matrix face and then decreased as the deformation was applied closest to the border of the matrix face3. It was inferred from these data that the optimum configuration for a modulated release system required maximum overlap between the polymer:drug matrix and the volume over which the mechanical deformation could exert its effect. Deformation over a Biomaterials
1993, Vol. 14 No. 6
Modulated
622
large area would be transferred over a larger portion of the polymer matrix and induce a greater increase in release. As the area was shifted further from the centre of the polymer matrix face the overlap between the matrix and deformation influence decreased. We now examine whether these two observations, increasing modulation with increasing deformation area, and the correlation of the percentage of matrix capable of being pulsed with the extent to which release was stimulated above baseline, could be used to explain the extent of modulation observed when the magnetic system was used in practice.
METHODS
Matrix fabrication As detailed elsewhere’ ethylene-vinyl acetate copolymer (EVAc, 40% vinyl acetate), manufactured under the product name ELVAX-40P (DuPont Co., Wilmington, USA), was washed in distilled water and 95% alcohol to remove impurities and then dissolved in dichloromethane to form a 10% w/v solution, Bovine serum albumin (BSA, Sigma Chemical Co., St Louis, USA, molecular weight 88 800) was sieved to a particle size range of 150-180 pm and added to the EVAc solution (33% w/w]. The BSAEVAc mixture was poured into a cylindrical glass mould that rested on dry ice and had been precooled for 10 min. Nickel-coated samarium cobalt (SmCo,) magnets (Permag Northeast, Waltham, USA] were suspended over the hardening BSA-EVAc solution and dropped into the suspension after various times had elapsed. The different times between pouring and dropping left the magnet at different positions in the matrix after complete hardening. The SmCo, magnets were shaped spherically, cylindrically or toroidally. The spheres were 1.4 mm in diameter, weighed 10 mg each and were magnetized to approximately 100 G. The toroids and cylinders were 1.4 f 0.5 mm high and magnetized to 1100 G with pole vectors orthogonal to the end faces. The cylinders weighed 15 mg and had a diameter of 1.5 mm and the toroids weighed 80 mg and had an inner diameter of 1.5 mm and an outer diameter of 3.0 mm.
Magnet position The position of the magnets within the matrix and by inference their alignment with the external magnetic field were determined from radiographs of the matrices taken in three orthogonal directions. A standard clinical X-ray machine exposed the matrices to a 44 kV pulse of 120 mA for 33 ms. The position and orientation of the SmCo, magnets were determined from the radiographic images obtained from these exposures, A line was drawn through the true vertical of the matrix and was used as the axis of the matrix. Lines drawn along the true vertical and true horizontal of the magnet were used to define the magnet’s axes. The intersection of these lines was the centre of the magnet and the lateral displacement of the magnet centre from the matrix axis was used as the x-offset of the magnet. The y-offset was the distance between the magnet centre and the matrix bottom. The orientation of the magnet within the matrix was computed from the angle that the vertical axis of the magnet Biomaterials
1993, Vol. 14 NO. 8
release:
volume
model:
E.R. Edelman
and R. Langer
deviated from the vertical axis of the matrix. The cosine of this angle was one for a perfectly aligned magnet and zero for magnets completely misaligned.
Magnetic
modulation
of EVAc:BSA matrices
The magnetic field was generated by a plate demagnetizer (OS. Walker Co., Worcester, USA) capable of delivering a 80 Hz magnetic field at amplitudes varying from 0 to 900 G (peak to peak). When hydrated matrices were placed within the magnetic field BSA release increased instantly, as a function of field amplitude, for the duration of the field application. Release returned to baseline immediately after field withdrawal’. In all cases the kinetics of BSA release were monitored continuously and in real-time by means of a flow-through spectrophotometer’. Unless specified otherwise the matrices were subjected to 40 individual exposures of a 500 G, 60 HZ oscillating magnetic field for 20 min. A modulation index, termed ‘modulation’, was attained by dividing the peak absorbance by the average baseline absorbance observed before and after a magnetic field was applied.
Volume of magnetic
influence
Video recorded magnified images of magnet embedded matrices revealed that only matrix material within a given distance of the embedded magnets moved under deformation by the magnets’. This distance was dependent on characteristics of the matrix and magnet such that displacement was no longer observed at a distance equal to (2 X magnet mass X magnet pole strength magnetic field strength) polymer
material
modulus
X
of elasticity
This is not unexpected, as it is precisely the form that one would anticipate if one set the magnetic forces generated equal to the mechanical force as dictated for elastic material by Hooke’s law4. The matrix and magnet geometries were reconstructed on a digital computer. The volume of matrix that could be influenced by the magnet was determined from the intersection of the cylindrical matrices and an imaginary sphere with a radius equal to the limit of matrix displacement by the magnet (Figure 2). The origin of the sphere was the centre of the magnet. A random array of 10 000 points in and about the cylindrical matrix was computer generated. If the points fell within the intersection of the sphere and the matrix the points were added to a running tally. The total number of points in the tally represented the integrated intersecting volume. This number was normalized to the total number of points generated and was defined as the aligned volume. The aligned volume was then compared with the extent of modulation achieved for matrices made with toroid or cylindrical magnets.
Volume of influence:
empirical
data
To verify the model of modulation that incorporates a sphere of influence we examined modulation for: three different sized matrices embedded with one toroidal magnet; one-size matrix embedded with either a toroidal, cylindrical or spherical magnet; and one-size matrix
Modulated
623
release: volume model: E.R. Edelman and R. Langer
a
. .*.. .. .. .- --.-..
Figure 1 The two panels represent possible configurations of the relationship between the magnet and drug polymer matrix. a, In the ideal case the magnet is positioned so that it is located centrally within the cylinder and its effect matches the boundaries of the polymer matrix. b, If the magnet is positioned off centre then the overlap between matrix material and magnet effect is diminished. The points in the figure represent the computer generated random array of 10 000 points. A running tally was incremented if a point fell within the bounds of the cylindrical matrix and the sphere that represents the limit of the magnets effect in matrix material.
embedded with a cylindrical magnet after pre-release in saline for 72 h prior to any magnetic field exposure, or repeated exposure to magnetic fields prior to hydration. The first set of toroidal magnets were embedded within cylindrical BSA:EVAc matrices 6 mm high and 4.4,7 or 14 mm in diameter; five matrices per group. The use of different sized matrices for a given strength magnet was for examining whether changes in matrix size might dampen the modulatory effect as more of the matrix material falls outside the sphere of influence of the magnet. In another experiment matrices were embedded with magnets of different sizes but equivalent pole strength (toroids and cylinders, pole strength 1100 G), or equal sizes and different pole strengths (cylinders and spheres). This allowed us to examine the potential difference in modulation that might be observed with spheres of magnet influence of different sizes as calculated from the force equation noted above and verified by direct observation. Six matrices were fabricated with one of each magnet and exposed in mixed groups to 10 pulses of a 60 Hz, 500 G magnetic field for 20 min separated by 3-12 h periods of rest. The average and peak indices of modulation were calculated and compared for each group. A matrix was determined to have reached its peak response when the modulation index value rose to within 10% of the maximum observed modulation and was maintained within this range for four consecutive stimuli. The amount of drug released up until that point in time was computed as well. To determine whether the predominant determinant of release was the sphere of influence as opposed to mobilization of the embedded magnet with repeated exposure to the magnetic field, or changes in the morphology of the matrix with the progressive release of drug with time, matrices were released in saline before -magnetic stimulation, magnetic stimulation before release or simultaneous commencement of stimulation and release. Matrices embedded with a cylindrical magnet were subjected to 36 20 min pulses of 60 Hz fields before activated drug release after immersion in saline or after 72 h of prerelease. Five to six matrices were examined in each group at each time point.
RESULTS Matrix-magnet
geometry
When magnetic fields were applied to EVAc:BSA matrices of identical heights and three different radii embedded with a single toroidal SmCo, magnet a parabolic relationship with modulation was observed (Zrhle 1). Under these field and magnet-matrix conditions modulation peaked with a matrix 6.0 mm high and 7 mm in diameter. When the matrix was smaller or larger than this size modulation decreased substantially. As the force generated by a magnetic field on a magnetized particle is proportional to the vector dot product of the field strength and particle pole strength this force should depend on the cosine of the angle between these two vectors. If the extent of modulation followed force alone then one would observe that for the same field amplitude and pole strength the extent of modulation should depend upon the cosine of the angle alone. Thus, the modulation obtained after 10 different matrices were exposed to 40 field exposures was plotted against the cosine of the angle of magnet orientation within the polymer matrix. This was done for angle orientation in two orthogonal planes and then for the square root of the sum of squares of those values. In all cases there was no statistically significant correlation between observed modulation and the angle at which the magnet resided [Figure 2). Aligned volumes were determined for all matrices by computing the intersection of the spherical polymer matrix and a sphere about the embedded magnet whose
Table1 Extent of modulated BSA release from EVAc:BSA matrices of different sizes embedded with a 1100 G SmCo, magnet and exposed to 500 G, 60 Hz magnetic fields Matrix diameter (mm)
Modulation index
4.4 7.0 14.0
2.5 k 0.2 11.3 f 1.9 5.2 f 0.3
Biomaterials
1993, Vol. 14 No. 8
Modulated
624
l l .:
L
3*
0.80
0.85
0.95
0.90 Magnet
l
l
0
l
1.00
release:
volume
model:
E.R.
Edelman
and
R. Langer
was 27.6. In practice value.
no modulation
Timing of release
and field applications
exceeded
this ideal
As further verification of the existence of a sphere of magnet influence the maximization of modulation was found to be dependent upon the amount of drug released, not the number of previous stimuli or the time immersed in solution. When cylindrical matrices were embedded within the EVAc:BSA matrices, peak modulation was observed only after 40-469~ of the embedded drug had been released (Figure 4a).This occurred whether the matrices has been exposed to magnetic stimulation prior to the initiation of release, a period of release prior to stimulation, or whether the initiation of release coincided
orientation
Figure2 The extent of modulation obtained for EVAc matrices embedded with one SmCo, magnet and BSA (30% w/v) is plotted against the orientation of the magnet as determined from radiographs of the matrices. There is no statistically significant correlation between modulation and magnet orientation.
50
r
radius was equal to the maximum displacement obtainable for that matrix. A linear relationship was obtained as depicted in Figure3 (slope = 1.16 AI 0.26, R = 0.864, P < 0.003, s.e.e. = 1.38). The maximum overlap for the matrices and magnets used was 13.7 cm’. If the linear relationship described holds true this would imply that the maximum modulation obtainable from the matrices IMMED
pre-STIM
pre-RLS
50-
40 -
30 -
Sphere
4
6
10
8 Intersecting
12
volume
Figure3 Modulation obtained from 10 EVAc matrices embedded with one SmCo, magnet and BSA (30% w/v) is plotted against the intersecting volume. This volume was computed from the intersection of the volume of the cylindrical matrix and an imaginary sphere whose radius was determined by the maximum extent of magnet translation. As such this represents the volume of matrix capable of being pulsed. A linear relationship was obtained with a slope of 1.16 + 0.26 (R = 0.864, P < 0.003, s.e.e. = 1.379). Biomaterials 1993, Vol. 14 No. 8
of influence
(radius
mm)
Figure4 a, EVAc:BSA matrices embedded with a cylindrical SmCo, were exposed to a series of 20 min 60 Hz, 500 G oscillating magnetic fields immediately after immersion in saline and initiation of BSA release (IMMED), after 36 20 min pulses of the magnetic field (pre-STIM), or 72 h after immersion in saline (pre-RLS). In all cases 40-46% of the incorporated BSA had to be released before peak modulation was observed. b, The percentage of incorporated BSA released before peak modulation correlated precisely with the radius of the sphere of influence for three different matrix:magnet configurations subjected to magnetic field stimulation (slope = -9.8 + 0.9, R = 0.996, P = 0.028, s.e.e. = 1.48).
Modulated
release: volume
625
model: E.R. E&/man and R. Langer
with the first application of magnetic field stimulation. The amount of BSA released from the matrix before peak modulation was achieved correlated precisely with the radius of the spherical volume of influence (Figure 4b, slope = -9.6 + 0.7, R = 0.992, s.e.e. = 1.41,P < 0.001).
DISCUSSION It appears that magnetically regulated drug release from polymer matrices is related to the movement of embedded magnets within the matrix. Magnified video taped images of areas of the matrix above the embedded magnets showed alternating compression and release of the material within a certain distance from the magnet’. Subsequent studies confirmed these findings and demonstrated that pulsatile deformations of the polymer matrices led to increased release above the haseline3. It would seem that whatever contributes to the movement of the magnet within the matrix contributes to the control of drug release. The force exerted on the magnet is related directly to the strength of the field and the magnetization of the magnet, and the number of movements of the magnet in the matrix in a given period of time increases with the field frequency. Thus, these factors should be expected to regulate magnetically stimulated release. The force that is exerted by an external magnetic field of strength 3 and gradient VB, on a magnet of magnetic moment iii, can be written as the vector dot product of iii and VB. The strength of the field generated by an electromagnet decreases linearly with distance from the electromagnet in the near field, the region in space adjacent to the surface of the electromagnet. In regions far from the magnet surface the field decreases as the square of the distance. These experiments were conducted within the near field, and the magnetic field at any point in space in this region can, therefore, be expressed as B = i,[B, - B,,z). As the gradient of a magnetic field uniform in all but the z direction can be simplified to VB = -i,B,, the force equation F = m - VB can be expressed as F = -mzBo. Since the component of the magnetic moment of the magnet in the direction of the field’s vector, m,, is strongest when the magnet is aligned with the field, the moment can be written as the product of a net magnetization, m, and the cosine of 8, the angle between the net direction of the field and the magnet’s pole vector. Thus, m, = m, cos 8 and the force generated by a magnetic field on a magnet can be written as F = -m,B,cos& If release modulation is determined by this force, the extent of modulation should increase in a linear fashion with the amplitude of the magnetic field, as well as the magnetization and orientation of the embedded magnet. While modulation indeed rose with increasing force of the applied magnetic field’* 5, the orientation of the magnet did not appear to be a primary determinant of modulation (Figure 2). A much stronger determinant was the amount of matrix being pulsed, i.e. how much of the matrix at any point of time was capable of responding to the magnetic stimulation. These data were verified in a variety of independent experiments. In the first case, an intermediate size matrix was the most efficiently modulated system. Matrices much smaller or much
larger were not modulated as well. Second, it appears that modulated release requires a period of ‘warm-up’ before which a less prominent effect is noted. This wannup is not determined by the number of pulsations of the magnet under the influence of the magnetic field but rather by a critical amount of matrix material that must be released. Once this level is reached the matrix responds most efficiently. Thus, it is probably not the case that the magnet is restrained within the polymer matrix and moves more freely once bonds are broken. Third, the threshold release level varies inversely with the area over which the embedded magnet can exert its influence. As this area expands the amount of matrix material that must be solubilized and released diminishes (Figure 4b). Thus, while motion of the magnet increases with force on the magnet, this effect seems to remain constant with time. Moreover, it appears to be of secondary importance to the amount of matrix that possesses solubilized drug capable of coming under the influence of the magnetic field and deformation of the embedded magnet. The ideal situation is where the bounds of the magnet deformation of the matrix correspond to the physical boundaries of the polymer:drug matrix, and where enough of the drug is in a soluble state capable of being released. Dry drug cannot be modulated as it cannot be released, just as drug that resides far beyond the volume of matrix that the magnet can deform cannot be modulated. This model of magnetic modulation of polymer matrix drug release incorporates the frequency and strength of the magnetic field, the pole strength of the magnet, its orientation within the field and position within the matrix. The model implies that a maximum amount of modulation should be achieved when the area of the matrix that moves with the magnet and the cylindrical volume of drug containing matrix overlap perfectly. In fact the radius of the overlap for the matrices tested in Figure 4b was 2.95 mm; 84.3% of the radius of the matrix that supplied the most efficient modulation. If magnetic modulated release is to be used the magnet field, embedded magnet, matrix and drug conditions should be configured to use only enough energy and materials to provide for this overlap.When the force generated by the coupling of the magnet and magnetic field is excessive or insufficient and is mismatched with the viscoelastic properties of the matrix resources are wasted and peak modulation will not be achieved. This might allow for custom design of pulsed delivery devices. We hope that analyses along these lines will shed further light on the mechanism of externally regulated controlled drug release and allow for optimization of such devices in practice.
ACKNOWLEDGEMENTS We thank Dr John Taylor for assistance with some of these experiments. This study was supported by a grant from the National Institute of Health, grant No. GM26698. Dr Edelman is currently supported by a PhysicianScientist Award from the National Institutes of Health (K12 AG00294). Biomaterials
1993, Vol. 14 No. 8
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Modulated
release:
REFERENCES 1 2
3
Langer, R., New methods of drug delivery, Science 1990, 249,1527-1533 Edelman, E.R., Kost, J., Bobeck, H. and Langer, R., Regulation of drug release from polymer matrices by oscillating magnetic fields, Z, Biomed. Mater. Res. 1985, 19,67-63 Edelman, E.R., Fiorino, A., Godzinsky, A. and Langer, R., Mechanical deformation of polymer matrix controlled
4
5
volume
model: E.R. Edelman
and R. Langer
release devices modulates drug release,]. Biomed. Mater. Res. 1992, 26,1619-1631 McCarthy, M.J., Soong, D.S. and Edelman, E.R., Control of drug release from polymer matrices impregnated with magnetic beads - a proposed mechanism and model for enhanced release, I. Controlled Release 1964,1,143-147 Edelman, E.R., Brown, L., Taylor, J. and Langer, R., In vitro and in vivo kinetics of regulated drug release f:om polymer matrices by oscillating magnetic fields, J. Biomed. Mater. Res. 1987, 21, 339-353
Materials Research Society
Fall 1993
Meeting
Boston, Massachusetts, USA 29 November - 3 December 1993 This meeting will continue the Material Research Society’s tradition of offering a series of in-depth and interdisciplinary topical symposia. Each symposium will provide a forum for scientists and engineers to exchange information and ideas at the leading edge of materials research.
Symposium S Biomolecular materials by design This symposium will address 1) the design and synthesis of biomolecular materials from simple polymers to complex macromolecular assemblies, and 2) potential applications from passive structural components to “smart materials”. Symposium organizers: Hagan Bayley, David Kaplan and Manuel Navia
Symposium T Biomaterials for drug and cell delivery This symposium will focus on the development of novel biomaterials and the improved understanding and utilization of existing biomaterials for the controlled release of drugs, growth factors, and other bioactive molecules to specific tissues. In addition, emphasis will be given to biomaterials for use in tissue engineering. Symposium organizers: Antonios G. Mikos, H. Bernstein, Regina Murphy
Biomaterials
1993, Vol. 14 No. 8