Determination of the diffusion coefficient of IFN-α

The impact of compression force and time on the protein release kinetics can presumably be ascribed to alterations in the packing arrangement of drug, excipient, and matrix particles, which in turn influences the pore characteristics and consequently the drug release [112]. Tristearin, protein/HP-β-CD, and PEG particles can be expected to be packed more closely with increasing compression time and force. Thus, the implant porosity decreases, resulting in decreased drug release rates.

However, the fitting of Equation {9} based on Fick’s second law of diffusion to the experimental release data clearly showed that the underlying drug release mechanisms were not affected by the alteration in the manufacturing procedure (Figure 17). Irrespective of the applied compression force or time, systematic deviations between the theoretical data considering pure diffusion and the experimentally determined release values were observed. This means, that independent of the applied implant compression method the release of IFN-α from PEG-containing tristearin matrices was not purely governed by diffusion.

diffusion in gels or liquids several methods have been described in literature [252].

Dynamic Light Scattering was applied to investigate the diffusional behaviour of lysozyme [238] and bovine serum albumin [170] in the presence of various poly(ethylene glycols). Furthermore, Fluorescence Recovery after Photobleaching (FRAP) or the more elaborated Holographic Relaxation Spectroscopy (HRS) were used to evaluate the diffusion coefficient of macromolecules [173, 183].

Apart from the obvious need for advanced equipment and skills these methods impose some further restrictions. In HRS and FRAP the diffusant is tagged to a photochromic or photobleachable label, which in turn might affect the mobility [252].

Alternatively, the open-end capillary technique proposed by Anderson and Saddington provides a less laborious approach to determine the diffusion coefficient.

Here, the rate at which the solute diffuses out of the open end of a capillary into the acceptor medium is monitored under perfect sink conditions [5]. In addition to its simplicity the open-end capillary technique would provide the benefit that the conditions within the pores of the controlled release system can be simulated. As the liquid generated within the implant pores would presumably compromise IFN-α, HP-β-CD, and optionally PEG the capillaries were filled with these compounds dissolved in buffer medium. In contrast to the original experimental protocol, the acceptor medium did only contain phosphate buffer. This means that IFN-α, HP-β-CD, and PEG would diffuse out of the capillary simultaneously, which should provide additional information on the interdependency of excipient and protein liberation.

The experimental setup applied is illustrated in Figure 18. The capillaries with a diameter of 0.9 mm and a length of 3 cm were filled with IFN-α/HP-β-CD:PEG blends dissolved in isotonic phosphate buffer pH 7.4 to a final protein concentration of 2.5 mg/mL. The ratios of IFN-α/ HP-β-CD to PEG were chosen in analogy to the implant formulations. An IFN-α/HP-β-CD:PEG ratio of 1 to 1 dissolved within the capillary corresponds to an implant formulation with a preload of 10 % IFN-α/HP-β-CD co-lyophilisate and 10 % PEG. After filling, the capillaries were uprightly fixed in a beaker filled with the acceptor medium and tempered at 37 °C. The acceptor was stirred at 300 rpm.

Figure 18: Schematic presentation of the experimental setup used to determine the diffusion coefficient of IFN-α.

After predetermined points of time a capillary was removed and the remaining protein content within the capillary was determined. Figure 19 represents the declining protein concentrations within the capillary over time.

0 20 40 60 80 100

0 25 50 75 100

time, h relative IFN-α concentration within the capillary, %

Figure 19: Decrease of IFN-α concentration within the capillary.

The diffusion out of a capillary was measured according to the experimental setup shown in Figure 18.

Open symbols represent decay of IFN-α concentration in the absence and closed symbols in the presence of PEG (IFN-α/HP-β-CD:PEG blends 1:1) (average +/- SD; n = 3).

Clearly, no important differences between PEG-containing and PEG-free samples were found. However, the standard deviations were high and thus, the calculation of accurate diffusion coefficients was not possible. Presumably, the large deviations between the samples are due to the manual withdrawal of the capillaries, which might cause an uncontrollable convectional mass transfer out of the remaining capillaries.

Figure 20: Schematic presentation of the modified experimental setup used to determine the diffusion coefficient of IFN-α.

In order to improve accuracy an alternative experimental setup was established (Figure 20). Each capillary was now fixed at the bottom of a separate vial. After filling the capillary the vial was carefully charged with the acceptor medium. The prepared vials were incubated at 37 °C and 40 rpm. At predetermined time points the acceptor medium was removed with a pipette. Then the content of the thin glass capillary was transferred to determine the remaining protein concentration.

0 20 40 60 80 100

0 100 200 300

time, h relative IFN-α concentration within the capillary, %

Figure 21: Decrease of IFN-α concentration within the capillary.

The diffusion out of a capillary was measured according to the experimental setup shown in Figure 20.

Open symbols represent decay of IFN-α concentration in the absence and closed symbols in the presence of PEG (IFN-α/HP-β-CD:PEG blends 1:1 „, IFN-α/HP-β-CD:PEG blends 1:2 S) (average +/- SD; n = 3).

In Figure 21 the obtained concentration profiles are presented. In accordance with the first experimental setup no significant differences between PEG-containing and

PEG-free samples were observed. Furthermore, the deviations between three independent vials were lower than those found with the first approach (compare Figure 19 and 21).

Based on the experimental determined protein liberation data the diffusion coefficients of IFN-α in the presence and in the absence of PEG were evaluated by fitting an analytical solution of Fick´s second law (see Chapter III.2.16).

As the protein release could only occur via the capillaries´ openings, the mathematical analysis could be restricted to one dimension with the following equation [5]:

⎟⎟⎠

⎜⎜ ⎞

⎝

⎛ ⋅ ⋅

⋅ π

⋅ +

− ⋅ π ⋅

⋅ +

− ⋅

=

∑

∞ =

t L D

4 ) 1 n 2 exp ( )

1 n 2 ( 1 8 M

M

2 2 2

0

n 2 2

t

{Repetition of equation 13}

where Mt and M∞ represent the absolute cumulative amounts of IFN-α released at time t, and infinite time, respectively; L denotes the length of the capillary.

Table 5 summarises the calculated protein diffusivities of IFN-α. It should be mentioned that the modification of the original capillary technique might account for an apparent increase in the diffusion coefficients. As only the liquid within the capillaries contains HP-β-CD and optionally PEG there might be an osmotic driven water influx. This effect would contribute the diffusion release of IFN-α resulting in diffusion coefficients higher than those which would be obtained with the original method proposed by Anderson and Saddington [5]. However, the obtained values are in good agreement with literature data reported for proteins with a comparable molecular weight. For instance, for lysozyme, a 14.4 kDa protein, diffusion coefficients between 0.8-1.3 x 10^-6cm²/s were reported [83]. Furthermore, comparing the diffusion coefficients obtained in PEG-free and in PEG-containing medium it can be concluded that the presence of different amounts of PEG did not substantially alter the mobility of IFN-α in the release medium.

Therefore, it can be summarised that the presence of PEG within the water-filled pores of the implants did not affect the mobility of dissolved IFN-α during the release from tristearin implants. As explained above, a time-dependent alteration of protein diffusivity in such a context would mainly arise from the effects of PEG on the viscosity of the buffer media.

Table 5: Diffusion coefficients of IFN-α within phosphate-buffer filled capillaries comprising various amounts of PEG.

The diffusion coefficients were determined by fitting Equation {13} to the release data shown in Figure 21.

IFN-α/HP-β-CD:PEG ratio D, x 10^-6 cm²/s

1:0 1.8 1:1 1.8 1:2 1.7

However, the drug diffusivity within a controlled release device is not only a function of the composition of the liquid within the pores. In addition, the characteristics of the generated pores might be even more important for the diffusivity of the drug (see Chapter I.5).

It has to be taken into account that the continuously leaching out of the protein itself and of the incorporated hydrophilic excipients (HP-β-CD and PEG) progressively increases the porosity of the implants. Such a time-dependent increase in porosity might enhance the diffusivities during release. However, the mathematical solution of Fick´s second law of diffusion used to analyse the release data assumed constant diffusion coefficients over the entire release period. This means, a possible explanation for the observed deviations between the calculated release curves and the experimental obtained protein liberation might be a time-dependent increase in the protein mobility due to an increase in matrix porosity.

In order to evaluate if such a scenario is of relevance, the release of PEG and HP-β-CD was monitored simultaneously to the protein delivery. If a time-dependent increase in diffusivity by changes of the pore structure is of importance, systematic deviations between the mathematical predicted release data and the experimentally obtained data should be observed also for HP-β-CD and PEG.