;ournalof controlled

release ELSEVIER Journal of Controlled Release 47 (1997) 13-20

Zero-order release of micro- and macromolecules from polymeric devices: the role of the burst effect

Balaji Narasimhan I '*, Robert Langer Department of Chemical Engineering, Massachusetts Institute of Technology, Building E25, Room 342, Cambridge, MA 02139, USA

Received I August 1996; revised 30 October 1996; accepted 21 November 1996

Abstract

A mathematical analysis is presented to elucidate the role of the burst effect in an essentially zero-order controlled release coated hemispherical polymeric device containing a single, small orifice in its center face. Asymptotic solutions of the model show that the burst effect is controlled by the solubility of the drug in the release medium and by the drug diffusion coefficient. The effect of the above mentioned parameters on the cumulative drug released from coated hemispherical devices was also studied. It was shown that as drug solubility increased, the drug released faster and the velocity of the interface between dissolved and dispersed drug is higher. The model solutions established that the burst behavior could be manipulated by using different initial drug distributions. Using the model, conditions under which the burst effect could be miniirnzed/maximized ~ere established. The model predictions were compared to experimental studies of sodium salicylate' relea~e from polyethylene hemispheres and bovine serum albumin release from ethylene-vinyl acetate copolymer hemispheres.

Keywords: Burst effect; Zero-order release; Macromolecular drugs; Drug solubility; Drug diffusion

1. Introduction

Numerous drug formulations are prepared by loading a drug in a dissolved or dispersed phase within a polymer matrix. When the polymer is placed in contact with a thermodynamically compatible liquid, the polymer begins to release its contents to the surrounding fluid and the drug diffuses through the polymer matrix. The release of the drug could be controlled by the diffusion of the drug, the penetra-

*Corresponding author. lpermanent Address: School of Chemical Engineering, Purdue

University, West Lafayette, IN 47907-1283, USA,

tion of the release medium or by relaxation of the polymer chains.

Such drug delivery systems have been widely used as controlled drug delivery devices [1-4]. Since the transport in these devices is usually in one dimen­sion, these designs have resulted in rectangular slabs. In such systems, the rate of release of the drug is inversely proportional to the square root of release time [5-7]. A variety of approaches have been proposed to obtain zero-order release from matrix devices. Among these are changing the matrix geometry [8-12], preparing polymer erosion-con­trolled devices [13-17], and polymer dissolution­controlled [18-20] systems.

These approaches though successful in obtaining

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14 B. Narasimhan, R. Langer / Journal of Controlled Release 47 (/997) 13-20

zero-order release, still failed to eliminate the burst effect, that is observed during the initial stages of the release [21,22]. Most drug release models fail to predict the initial burst [9]. In this contribD:.tion, a mathematical analysis is presented that quantitatively accounts for the burst effect. The geometry chosen was a partially coated polymeric hemisphere that was known to exhibit essentially zero-order release [10]. This particular geometry was chosen because the surface area to volume ratio for hemispheres is quite large, thus resulting in an enhanced burst effect.

2. 2. Mathematical analysis

An analysis is presented that describes the release of a drug from an inwardly releasing polymeric hemisphere. The release occurs only through a concave portion of the flat surface. All the other surfaces are laminated with an impermeable coating, and hence release is prevented. Fig. 1 shows a schematic of the hemispherical device.

The drug transport through the hemisphere is described using Fick's law as:

ac 1 a 2 ac - = --(r D-) at r2 ar ar

(1)

Here, c is the drug concentration (w/v) within the matrix at position r and at time t, and D is the drug diffusion coefficient (cm2 Is).

The initial and boundary conditions for the above equation are as follows:

t = 0 c = Co

Top View t = 0

oi ,....., , ,

Side View Cross Section

t.= 0

•

(2a)

Slice, Side View erOS5 Section at

time t 00

:-1

\--E....., I 'oi I I ...... I I

~ Fig. 1. Diagram of an inwardly releasing hemisphere; ai is the inner radius, ao is the outer radius, and R is the distance to the interface between the dissolved region (white) and the dispersed area (diagonal lines). Black represents laminated regions through which release cannot occur. Reproduced with permission.

where Co is the initial drug loading.

r = R

c = 0

c = C s

(2b)

(2c)

In the above equations, a j is the inner radius of the hemisphere and R is the radial coordinate of the interface between dissolved and dispersed drug within the matrix. c s is the solubility of the drug in the release medium. It is worthwhile to note that the concentration of drug in the dispersed matrix is always co' Also, as the drug diffuses into the surrounding medium, the interface R moves outward till it reaches the inner radius of the coating, ao'

Hence R is a function of time and the system becomes a moving boundary problem.

Eq. (1) can be analytically solved by using the transformation u = cr. Eq. (1) becomes

(3)

Eq. (3) was solved using separation of variables after suitably modifying the initial and boundary con­ditions. Upon using u =cr in the solution of Eq. (3), the solution of Eq. (1) was obtained [23] as

c -Rcs(r - a)

r(R - a)

2 ~ [RC s COS(n7T) ] . n1T(r - a) + 1Tr n-::l n sm ( R - a

i )

n21T2Dt exp( )

(R - a)2

+ 4co i [ 1 ] (2n + 1)1T(r - a) 11' n=l 2n + 1 sin [ R - a

i ]

(2n + 1)2 1T2Dt exp(- (R _ a)2 ) (4)

The rate at which drug is inwardly released from the matrix, dQldt, is given as

(5)

From Eq. (4) and Eq. (5), we can write

B. Narasimhan. R. Langer I Journal of Controlled Release 47 (1997) 13-20 15

dQ

dt

(6)

The above equation describes the rate of release of drug as a function of time. R(t) is a function of time and this can be determined as follows: The total amount of drug ~nitially present, Mo, is given as

2 3 3 Mo = 37Tco(ao - a i ) (7)

At time t, the drug present in the device, M(t), is the sum of drug in the undissolved and the dissolved regions. This is given as

R

2 3 3 J[ 2 ] M(t) = 37TCo(a 0 - R ) + 27T r c(r,t) dr (8)

ai

Substituting Eq. (3) in Eq. (8),

2 3 3 2 3 M(t) = 37Tco(a· 0 - R ) + 3 7TC,R

x 2 2 4 3·'V 1 n 7T Dt)

+ -coR LJ 2" exp(- 2 ) 7T n~l n R

(9)

In the above equation, it has been assumed that R» a j • A total mass balance on the drug gives

Q(t) = Mo - M(t) (10)

where Q(t) is the mass of the drug released from the device at time t. Thus,

2 3 4 x 1 Q(t) = -37TCoR - -c R3 L - exp(

7To n~ln2

Differentiating the above equation with respect to time, an expression for dQ / dt can be obtained, which can then be equated to the r.h.s. of Eq. (6). Solving the resultant differential equation for R(t) and substituting it back in either Eq. (6) or Eq. (11) would yield the exact expression for Q(t).

Alternatively, a mass balance on the drug at the interface R can be written. This is given as

dR ac Co dt = (D a;:)r~R (12)

The initial condition for the above equation is that at t=O, R=a j •

In order to obtain insight into the mechanism, the asymptotic behavior of the above system of equa­tions was investigated. At steady state (t~CXl), Eq. (4) is transformed as

c = RcJr - a)

r(R - a) (13)

Consequently, the rate of drug release (Eq. (6)) is transformed as

dQ 27TDcsRai

dt R - a i

(14)

Differentiating Eq. (11) with respect to time after imposing a steady state condition,

dQ dt

(15)

Equating the r.h.s. of Eq. (14) and Eq. (15) we obtain

dR _ Dcsai 1

dt CO R(R - a) (16)

Eq. (16) is easily integrated to give

(17)

It is important to note that the same result could have been obtained by using Eq. (12) after applying the steady state condition. Similar results were obtained by Rhine et al. [9] using quasi-steady state analyses. At steady state, the dissolved drug interface has progressed far enough to assume that R» a j •

Imposing this condition on Eq. (14), it is evident that the rate of drug released is constant and is given by

(18)

Thus, the behavior of coated hemispherical drug delivery devices at long times is explained and expressions for both rate of drug release (Eq. (18))

16 B. Narasimhan, R. Langer / Journal of Controlled Release 47 (1997) 13-20

as well as the interface R as a function of time (Eq. (17» have been obtained. The next step is to explain the behavior of such systems at short times. This analysis should provide insight into the mechanism of the burst effect, which is observed during initial drug release and help in manipulating the extent of the effect to advantage.

For short times (t-70), the concentration profile of the drug is given as

Rcs(r - a) r(R - a) c

2 ~ [RC,COS(n7T) ] . n7T(r - a) + - L.J sm( R _ )

1Tr n~l n ai

4co ~ [ 1 J. (2n + l)1T(r - a) + - L.J 2n + 1 sm[ R - a ]

1T n= 1 1

(19)

Using Eq. (12), the temporal evolution of the interface R can be obtained as

dR Dcsai 4Dco c- = -o dt R(R - a

i R - ai

(20)

Eq. (20) can be integrated from t=O to t(R=O to a) to obtain

~t = 0.5(~r + (~) - 1.5

c, (R) + 0.25-'- In -Co a i

(21)

Since this analysis is being performed for short times, it is assumed that the RI a j -1. Hence approxi­mations can be made for the squared and the logarithmic terms in Eq. (21).Thus, we can write

(li) = 1 + __ 16_D_t_ a i a~(6 + B)

Here B is given by cJco'

(22)

The rate of drug release is obtained similar to the procedure discussed for the steady state asymptote by performing a mass balance on the drug. The final expression for the rate of drug release is

dQ dt

(23)

Substituting Eq. (22) in Eq. (23), we obtain

dQ 3 2 dt = 21Tcoai k(1 + kt) (24)

Here, k is given as

16D k = ----

a~(6 + B) (25)

Upon integrating Eq. (24), the amount of drug released as a function of time can be obtained. From Eq. (24), we observe that for the drug release rate to be independent of time, kt« 1.0. This reduces Eq. (24) to

(26)

The values of the fraction of drug released can be obtained by normalizing Q(t) with respect to Mo' the initial drug loading.

3. Results and discussion

An estimate for the burst time can be obtained using the above analysis as

€ t =-

k (27)

where E« 1.0. It is easily inferred from Eq. (25) and Eq. (27) that the period of burst can be con­trolled by the parameters Band D. For small values of B, the burst time is small. In other words, for drugs that are poorly soluble in the release medium, the burst time is small. Comparing the rates of drug release during the burst effect (Eq. (26» and the steady state (Eq. (18», we observe that

[dQldt], -> 0

[dQldt], -> ~

16

B(6 + B) (28)

From the above equation, it can be concluded that the burst effect is significant for systems where B-O(1).

Summarizing, we observe that for drugs that are highly soluble in the release medium, the burst time is very long. Conversely, for drugs that are poorly soluble in the release medium, the burst time is

B. Narasimhan. R. Langer / Journal of Controlled Release 47 (1997) 13-20 17

shorter. Another important parameter in the above analyses is D, the drug diffusion coefficient. As D increases, the burst duration decreases (Eq. (25) and Eq. (27)). This is to be expected because even if the drug is highly soluble in the release medium, its size is large enough to prevent it from diffusing out of the polymer matrix. Also, the ratio between the amounts of drug released during and after the burst period is independent of the drug diffusion coefficient. This is expected because the amount of drug released during the burst is strictly a function of how soluble the drug is in the release medium. On the other hand, diffusional limitations of the drug could cause it to release after a long burst period. This also makes this approach suitable for studying release of very slow­ing releasing macromolecules like proteins and pep­tides. It is also worthwhile to note that the release is linear with time during the burst period before settling to a lower release rate (which is also linear) for longer times. The behavior for intermediate times is determined by the exact solution of the system equations presented.

Simulations were performed to analyze the points presented above. Fig. 2a shows the effect of the drug solubility on the drug release. It is observed that as drug solubility decreases, the amount of drug re­leased also decreases. In addition, the time for which the burst effect persists also decreases (see Fig. 2b, which is a magnified plot of the region in Fig. 2a for the first 6 h of release). Also, after the burst period is over, lesser drug is released during the same time

0.9

0.8

1°·7 CD 0.6 a: co ~O.5 '0

" iDA LL. 0.3

0.2

0.1

- - 8=0.05

8 = 0.35 -8=0.55

~~-7--~--~~--~'0~-'~2--~'4~~'~6--~'8--~2o nme(days)

"C

when the drug solubility is lower. This is true because the drug solubility is a thermodynamic constraint, which cannot be violated at any point in the release process.

The temporal evolution of the normalized dis­solved drug/dispersed drug interface, R/ a j is pre­sented in Fig. 3a. Again, as drug solubility decreases, the velocity of the interface decreases. To ascertain the effect of the duration of the burst on R/a j , the behavior for the first 10 h is depicted in Fig. 3b. The duration of the burst is shortest when drug solubility is the least. Also, the slope of the curve beyond the burst period increases as the drug solubility in­creases.

The effect of the drug diffusion coefficient, D, on release kinetics is shown in Fig. 4. As D increases, the total amount of drug released increases. Due to diffusional limitations, the duration of the burst decreases as the diffusion coefficient increases. It is also evident that the amount of drug released during the burst period is independent of the diffusion coefficient. This is to be expected as the diffusion coefficient is a transport parameter and is indepen­dent of the thermodynamics of the system.

Finally, Fig. 5 presents the dependence of the burst time on drug solubility. The behavior is linear (Eq. (27)) as expected. It is interesting to note the presence of an intercept on the time axis in this plot. This indicates that the burst effect would be present even if the drug was negligibly soluble in the release medium. This is attributed to the uniform drug

0.045,----~----~----~----~--------~

0.04

0.035

m 0.03

~ ';0.025 2 o '0 0.02 §

] 0.Q15

0.01

0.005

-8=0.55

8 = 0.35 - - B = 0.05

°0~--~----~----~3~--~----~----~

Time (hours)

Fig. 2. Effect of drug solubility on drug release kinetics. (a) The parameters used are: D = 1.5 X IO -6 em' / s, a, = 0.09 cm, ao = 0.60 cm; and ,·(b) effect of drug solubiliiy on the burst time. The values of the parameters are the same as in Fig. 2a.

18 B. Narasimhan. R. Langer I Journal of Controlled Release 47 (/997) /3-20

5.5

t 5

C

- - 6=0.05 ,g 3 C>

6 = 0.35 ~ -6=0.55 " ~ 2.5

1 z 2

10L---~'0----~20----~30-----~~--~5~0----~60·

(a) Tim. (hours)

,.

5 Time (hours)

- 8=0.55

B = 0.35

- - 6=0.05

10

Fig. 3. Effect of drug solubility on the temporal evolution of the normalized interface between dissolved drug and dispersed drug, Ria;. (a) The values of the parameters used are the same as in Fig. 2a; and (b) effect of burst time on Ria;.

distribution (which is an implicit assumption in this whole analysis) in the device, which exhibits an initial release. It appears therefore that different initial drug distributions could be effectively utilized to manipulate the burst behavior depending on the application, even in cases when the solubility of the drug is not a factor. The importance of the initial drug distribution in manipulating the release be­havior of drugs has been discussed by Lee [24].

4. Experimental verification

Experimental verification of the drug release

0.8,---~--~--~--~~--~--~--~~-----;

0.7

0.6

* 10.5 II' C>

50.4

"0 0

:§ 0.3

£ 0.2

0.1

0 0

, , ,

D = 4e-OB

- - D=2e-07

-D=le-06

10 12 14 16 18 20 Time (days)

Fig. 4. Effect of drug diffusion coefficient, D, on the drug release kinetics. The parameters used are: B = 0.25, a; = 0.09 cm, ao = 0.60 cm.

model presented in the previous section has been attempted by comparing the predictions with differ­ent systems. Two separate systems were considered and the experimental drug release profiles were compared with the model predictions.

Hsieh et al. [10] discussed the development and design of drug-loaded hemispheric polymeric de­vices, laminated with an impermeable coating, ex­cept for an exposed cavity in the center face. Hemispheric devices for low molecular weight drugs were prepared by heating and compressing poly­ethylene and sodium salicylate, which was used as the model drug, in a brass mold. Similar systems for high molecular weight drugs were prepared by dissolving ethylene-vinyl acetate (EVAc) copolymer

0.9

0.8

0.7

0.6

!:II 0.5

0.4

0.3

0.2

0.1

0 19 19,5 20 20.5 21 21.5 22 22.5

Time (hours)

Fig. 5. Drug solubility as a function of burst time. The parameters used are: D=1.5xlO-6 cm 2 /s, a; =0.09 cm, e=O.OI.

B. Narasimhan, R. Langer I Journal of Controlled Release 47 (1997) 13-20 19

in methylene chloride and adding bovine serum albumin (BSA), which was then placed in a hemis­pheric mold at - 80°C, followed by a two-step coating and drying procedure at - 20°C and 20o~. Both systems contained cavities in the center face of the hemisphere and the remainder of the matrices were coated with impermeable materials. The frac­tion of drug released was measured using a spectro­photometric assay [10].

Fig. 6a presents data of the fraction of sodium salicylate released as a function of time at 37°C. The same figure shows predictions of the fractions re­leased using Eq. (18) and Eq. (26). Here, D was calculated using a free volume approach as 1.26 X 10-6 cm2 Is for sodium salicylate [25], a i and ao were taken as 0.1 cm and 0.5 cm as per the dimensions used by Hsieh et al. [10]. The model predictions agree with the experimental data within experimental error. It should be noted that this is an independent prediction of the data and not a fitting.

Hsieh et al. [10] also studied the release of BSA from EVAc hemispheres. The fraction of BSA re­leased a function of time is shown in Fig. 6b. The parameters used in the prediction in this case are: D = 7.5 X 10 - 8 cm 2 I s, calculated as before using a free volume approach [25], ai = 0.09 cm, ao = 0.65 cm. The agreement is good, thus validating the use of the model to analyze the release of macromole­cules from such hemispherical devices. The calcula-

.., " In .. " a; a: 0.8

~ >-.~ 0.6 iii til

E " 0.4 'ij 0 til

'0 0.2

" 0

~ !!! IL

5 10 15 20

(a) Time (days)

tion of the burst time (Eq. (27» shows that the burst period for this case is very small compared to the total time of release (approximately 70 days). Also, from Fig. 5, for B=0.35 and D=7.5XIO- 8 cm2/~, the burst time is about 6 days which is still small compared to the time of release. Hence, even though both equations were used, the change in slope is not very obvious because of the big differences in the times for which they were used.

5. Conclusions

A mathematical analysis has been developed to quantitatively describe the role of the burst effect during essentially zero-order drug release from coated hemispherical polymeric devices. Asymptotic solutions of the model equations provided insight into the mechanism of the burst effect. It was shown the burst effect is controlled by the drug solubility in the release medium as well as by the drug diffusion coefficient in the polymer. The model predictions were verified with available experimental data on micro- as well as macromolecular drug release from coated hemispherical polymeric matrices and the agreement was found to be good. The analysis has shown that by changing parameters such as the drug solubility and drug diffusion coefficient, the burst

0.7

.., 0.6

" til .. 0.5 " a;

a: c( 0.4 til III

'0 0.3

" 0 0.2 :;::;

u !!! IL 0.1

(b) Time (days)

Fig. 6. (a) Fraction of sodium salicylate released as a function of time from coated polyethylene hemispheres. Data of Hsieh et al. [10]. The parameters used are: D= 1.26 X 10- 6 cm2 /s, a, =0.l0 em, ao =0.50 em, B =0.25. Standard error of the mean of the release at each time point was 4%. The open circles represent experimental data while the line represents model predictions. (b) Fraction of BSA released as a function of time from coated EVAc hemispheres. Data of Hsieh et al. [10]. The parameters used are: D = 7.50 X 10 -8 cm'l s, a, = 0.09 em, ao = 0.65 em, B = 0.35. Standard error of the mean of the release at each time point was 12%. The open circles represent experimental data while the line represents model predictions.

20 B. Narasimhan, R. Langer I Journal oj Controlled Release 47 (1997) 13-20

effect could be manipulated to advantage, thus paving the way towards improved design and de­velopment of sustained zero-order release systems.

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