3. DRUG RELEASE FROM MICROPARTICLES 29
3. DRUG RELEASE FROM MICROPARTICLES 30
time
0 5 10 15 20 25
C1
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
Figure 3.4: Time variant concentration profile ofC1.
time
0 5 10 15 20 25
C b
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Figure 3.5: Time variant concentration profile ofCb.
The results shown in Figs. 3.4 and 3.5 represent the respective time-dependent concentration profiles for free (C1) and bound (Cb) drug particles in the second phase of tissue transport, that is in the biolog- ical tissue. The characteristics of both the graphs are found to be quite similar as anticipated because in the second phase of the tissue, binding and unbinding processes take place simultaneously. If both the plots are observed minutely, one may notice thatCb attains its peak concentration afterwards in
3. DRUG RELEASE FROM MICROPARTICLES 31 comparison to that ofC1. This authenticates the validity of the model as it depicts graphically thatCb is formed fromC1and a minimum time is required for its formation.
0 2 4 6 8 10 12
time 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
C L-C 0
Figure 3.6: Time variant concentration deviation profile ofCL−C0.
The deviation of the drug concentration for solid and free drug (CL−C0) in the microparticular phase as well as that of bound and free drug (Cb−C1) in the tissue phase with time are plotted in Figs 3.6 and 3.7. The former deviation shows the process by means of which the solid loaded drug first unbinds to form free drug through dissociation and then it exhibits how some fraction of free drug binds again to form solid drug through association in the microparticle. The latter one shows that the free drug from the microparticle enters into the tissue through diffusion and after some time, a portion of it gets associated to form bound drug. This ongoing binding / unbinding process is well-established in Fig.
3.8, which emphasizes on the deviation towards the onset since it is not clearly visible from Fig. 3.7.
The influence of unbinding rate constant of drug (β0) on the solid loaded drug concentration in the microparticular phase is displayed in Fig. 3.9 over a stipulated period of time. It is observed that with decreasing binding rate, the solid drug concentrationCLincreases. This may be clearly understood if the internal process behind it is observed critically. First, solid drug solubilises to free drug and some portion of the free drug recrystallizes to form solid drug again. As, solubilisation process takes some time, before the next fraction of drug solubilises, some portion of recrystallized drug gets unbound due to its chemical property. Whenβ0decreases, certain bulge is noticed in the contour.
3. DRUG RELEASE FROM MICROPARTICLES 32
time
0 5 10 15 20 25
C b - C 1
-0.02 0 0.02 0.04 0.06 0.08 0.1 0.12
Figure 3.7: Time variant concentration deviation profile ofCb−C1.
time
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
C b - C 1
-0.02 0 0.02 0.04 0.06 0.08 0.1 0.12
Figure 3.8: Time variant concentration deviation profile ofCb−C1at the initial stage.
In order to understand the reason behind such behaviour, some factors must be considered. First, solubilisation is a comparatively slow process in comparison to dissociation / recrystallization phe- nomenon. Hence, before the next fraction of solid drug gets solubilised, recrystallization of free drug to solid drug occurs with very slow dissociation of solid drug (due to lowerβ0). The effect of bind-
3. DRUG RELEASE FROM MICROPARTICLES 33 ing rate constant of drug (δ0) on the drug concentrationCLin the microparticle over the entire period of time is depicted in Fig. 3.10. If the binding rate decreases, the solid bound drugCL decreases, which is indeed quite natural as it is just the reverse phenomenon with respect to the previous one (Fig.
3.9). In this figure also, certain bulge is observed for increased binding rate, which leads to increased recrystallization. Thus, this situation becomes similar to that for Fig. 3.9, which is already discussed.
time
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
C L
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
β0=6*10-5 β0=8*10-5 β0=10-4 β0=1.6*10-4
Figure 3.9: Time variant concentration profile ofCLat differentβ0.
Before discussing about the next two plots, Figs. 3.11 and 3.12, certain aspects of drug encapsulation in microparticle need to be considered. Solid loaded drug is dispersed in the microparticle in such a way that when transformation of solid drug to free drug occurs, solid and free phases of drug occurs in intermingled state throughout the microparticle. Thus, increased free drug concentration in comparison to that of solid drug leads to higher rate of diffusion due to less hindrance provided by the solid phase.
The influence of unbinding rate constant of drug (β0) on the free drug concentration in the micro- particular phase is displayed in Fig. 3.11 over a stipulated period of time. It is observed that with decreasing β0, the free drug concentrationC0 increases. In the event of smaller rate of dissociation (β0), both solid and free drugs are present in comparable amount in the system. So, the rate of diffusion of free drug lessens andC0 increases. The influence of binding rate constant (δ0) on the free drug concentration in the microparticle phase is presented in Fig. 3.12. With decreasing binding rate, the free drugC0decreases. The reason behind it is that recrystallization of free drug into bound drug lessens and maximum amount of free drug diffuses out of the microparticle. One may remark in this connection that, when the association rate is allowed to be minimum, most of the drug in the microparticle is in the form of free drug and consequently, the diffusion of the drug becomes maximum.
3. DRUG RELEASE FROM MICROPARTICLES 34
time
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
C L
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
δ0=6*10-5 δ0=10-4 δ0=1.3*10-4 δ0=1.6*10-4
Figure 3.10: Time variant concentration profile ofCLat differentδ0.
time
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
C 0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
β0=6*10-5 β0=10-4 β0=1.6*10-4
Figure 3.11: Time variant concentration profile ofC0at differentβ0.
3. DRUG RELEASE FROM MICROPARTICLES 35
time
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
C 0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
δ0=6*10-5 δ0=10-4 δ0=1.6*10-4
Figure 3.12: Time variant concentration profile ofC0at differentδ0.
time
0 2 4 6 8 10 12
C 1
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035
ka=7.5*10-5
ka=1.5*10-4 ka=3*10-4
Figure 3.13: Time variant concentration profile ofC1at differentka.
3. DRUG RELEASE FROM MICROPARTICLES 36
time
0 2 4 6 8 10 12
C 1
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035
kd=10-5
kd=2*10-5 kd=4*10-5
Figure 3.14: Time variant concentration profile ofC1at differentkd.
time
0 2 4 6 8 10 12
C b
-0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
ka=7.5*10-5 ka=1.5*10-4 ka=3*10-4
Figure 3.15: Time variant concentration profile ofCbat differentka.
3. DRUG RELEASE FROM MICROPARTICLES 37
time
0 2 4 6 8 10 12
C b
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
kd=10-5 kd=2*10-5 kd=4*10-5
Figure 3.16: Time variant concentration profile ofCbat differentkd.
The next couple of graphical representations (Figs. 3.13 and 3.14) reveal the time variant concentration profiles of free drug (C1) in the biological tissue for different values of association (ka) and dissociation (kd) rate constants. It must be kept in mind that when association rate constant gets increased, greater fraction of free drug (C1) gets transformed into bound drug (Cb) leading to higher concentration of bound drug and lower concentration of free drug. Since the dissociation rate constant is unaltered andCb concentration is higher, dissociation of bound drug leads to the formation of free drug. This re-transformation of free drug suffices the contour ofC1 to decline slowly. The present discussion is graphically illustrated in Fig. 3.13, which exhibits the influence of binding rate constant (ka) on the drug concentrationC1 in the tissue phase. The influence of unbinding rate constant (kd) on the free drug concentrationC1in the tissue is shown in Fig. 3.14. With decreasing unbinding rate constant,C1 decreases as lesser fraction of bound drug re-transforms back to free drug.
The slow degradation of C1 contours, which are having lower peaks, is due to the fact that flux of free drug (C1) into the biological tissue depends also on the concentration difference between those in microparticle and tissue respectively. Thus, whenC1contour peak is less, there is more influx of free drug into the tissue leading to its slow decline. On the other hand, for higherC1, there is less influx of free drug from the microparticle into the biological tissue. Hence, the correspondingC1 contour declines quickly.
The effects on theCbcontours due to the influence of the binding rate constant (ka), in the tissue phase, are shown in Fig. 3.15. It is an obvious observation that if the binding rate decreases thenCbdecreases.
On the other hand, in Fig. 3.16, the effects on theCbcontours due to the influence of the unbinding
rate constant (kd), in the tissue phase, are visualized. This is also quite obvious that with decreasing unbinding rate constant, the bound drug concentrationCbincreases. This is because as the dissociation phenomenon slows down, there is less re-transformation of bound drug back to free drug. Therefore, it may be inferred that with increasing binding rate constant and decreasing unbinding rate constant, the drug assimilation in the biological tissue takes prolonged time.
It is verified that the variation of concentration with space is meagre for all time compared to all other substantial variations shown and hence any discussion on this is considered insignificant.