A rational way to develop approaches that will increase the stability of fast-degrading drugs in pharmaceutical dosage forms is by a thorough study of the factors that can affect such stability. In this section, the factors that can affect decomposition rates are discussed; it will be seen that, under certain conditions of pH, solvent, presence of additives, and so on, the stability of a drug may be drastically affected. Equations that may allow prediction of these effects on reaction rates are discussed. Although most of the emphasis is placed on decomposition in the aqueous phase, reflecting the large body of literature in this area, some discussion is included of studies of environmental factors influencing the decomposition of semisolid and solid dosage forms.
The pH of a drug solution may have a very dramatic effect on its stability. Depending on the reaction mechanism, a change of more than 10-fold in the rate constant may result from a shift of just 1 pH unit. When drugs are formulated in solution, it is essential to construct a pH versus rate profile, so that the optimum pH for stability can be located. Many pH versus rate profiles are documented in the literature, and they have a variety of shapes.
The study of the influence of pH on degradation rate is, however, complicated by the influence of the buffer components on the degradation rate. If the hydrolysis rate of the drug in a series of solutions buffered to the required pH is measured and the hydrolytic rate constant is then plotted as a function of pH, a pH-rate profile will be produced, but this will almost certainly be influenced by the buffers used to prepare the solutions, and it is probable that a different pH-rate profile would be obtained using a different buffer. Considering the simplest case of a nonionizable drug, it is necessary to consider not only the catalytic effect of hydrogen and hydroxyl ions, the so-called specific acid-base catalysis, but also the possible accelerating effect of the components of the buffer system, which is referred to as general acid-base catalysis. These two types of acid-base catalysis can be combined together in a general expression as follows.
kobs = k0 + [H+] + kOH- [OH-] + kHX[HX] + fc- [X-] (45)
In this equation, kobs is the experimentally determined hydrolytic rate constant, k0 is the uncatalyzed or solvent catalyzed rate constant, kH+ and kOH- are the specific acid- and base-catalysis rate constants, respectively, kHX and kX- are the general acid- and base-catalysis rate constants, respectively, and [HX] and [X-] denote the concentrations of protonated and unprotonated forms of the buffer. In a complete evaluation of the stability of the drug, the catalytic coefficients for specific acid and base catalysis and also the catalytic coefficients of possible buffers used in the formulation are determined.
By way of illustration we can consider a specific example of a stability study that has been reported for the antihypertensive vasodilating agent, ciclosidomine (62). Experiments carried out at constant temperature and constant ionic strength using a series of different buffers over the pH range 3 to 6 produced the graphs shown in Figure 3.
These plots show a marked effect of buffer concentration on the hydrolysis rate, particularly as the pH is increased from 3 to 4. The effect of the phosphate buffer on this system became less pronounced at higher pH and was found to have a negligible effect above pH 7.5. To remove the influence of the buffer, the reaction rate is measured at a
series of buffer concentrations at each pH and the data extrapolated back to zero concentration as shown in Figure 3. A buffer-independent pH-rate profile is then obtained by plotting these extrapolated rate constants as a function of pH.
A simple type of pH-rate profile reported for codeine sulfate (63) is illustrated in Figure 4. This drug is very stable in unbuffered solution over a wide pH range but degrades relatively rapidly in the presence of strong acids or bases. Since the influence of buffer components has been removed, the rate constants for specific acid and base catalysis can be calculated. Removing the terms for the effect of buffer from equation (45) gives kobs = k1 [H+]+k2 + ks[OH-] (46)
Consequently, a plot of measured rate constant kobs against the hydrogen ion concentration [H+] at low pH has a gradient equal to the rate constant for acid catalysis. Similarly, a plot of kobs against [OH-] at high pH gives the rate constant for base-catalyzed hydrolysis. For example, when k3[OH-] > k2 >> kj[H+], a log kobs versus pH profile such as the one depicted in Figure 5A may result. On the other hand, if kj[H+] and k3[OH-] are both much greater than k2, a log kobs versus pH profile may resemble the curve shown in Figure 5B. When kj[H+] > k2>> k3 [OH-], the log kobs versus pH profile will be a mirror image of Figure 5A, and when k2 >> kj[H+] + k3[OH-], the rate constant will be pH independent.
The degradation of codeine is particularly susceptible to the effect of buffers; for example, the hydrolysis rate in 0.05 M phosphate buffer at pH 7 is almost 20 times faster than in unbuffered solution at this pH. In phosphate buffers of neutral pH, the major buffer species are H2PO- and HPO2-, either of which may act as a catalyst for codeine
degradation. Values of the catalytic coefficients of these two species may be determined from the experimental data in the following way. In neutral pH solutions, the observed rate constant, kobs, is given by kobs = k2 + kH2PO4- [H2PO4 ] + Vo2- [HPO4~ ] (47)
where kH2PO4 and kHPO24 are the rate constants for catalysis by H2PO4 and HPO44 ions, respectively, and BT is 4the total concentration of phosphate buffer. The terms for specific acid and base catalysis have little effect at this pH and need not be considered in this treatment.
From equation (48), a plot of kobs against BT will have an intercept, k2, and a gradient k'. To find values for the two catalytic coefficients, the equation is rearranged into the following linear form k0
A second plot of the apparent rate constant k against the fraction of the acid buffer component present, that is, [H2PO-/BT] will have an intercept at [H2PO-/BT] = 0 equal to kHPO2—. Furthermore, the k value at [H2PO-/BT] = 1 is the other catalytic coefficient kH2PO-.
The relationship between the ability of a buffer component to catalyze hydrolysis, denoted by the catalytic coefficient, k, and its dissociation constant, K, may be expressed by the Bronsted catalysis law as kA = aKa for a weak acid and kB
bK^B for a weak base
where a, b, a, and b are the constants characteristic of the reaction, the solvent, and the temperature (64,65). a and b are positive and vary between 0 and 1.
Because codeine has a pKa of 8.2 at 25°C, its ionization state will change over the pH range 6 to 10, with potential implications for its stability. With this particular drug there are no appreciable stability problems associated with changes in its ionization, but this is not the case with many drugs, and complex pH-rate profiles are often produced because of the differing susceptibility of the unionized and ionized forms of the drug molecule to hydrolysis. In such cases, a detailed analysis of the reaction of each of the molecular species of the drug with hydrogen ion, water, and hydroxide ion as a function of pH allows the rationalization of the pH versus rate profile. When the drug is either monoacidic or monobasic, an equation similar to equation (46) can be written. Here, however, three kinetic terms are written for the acidic form of the drug, HA, and three terms for the basic form, A (electronic charges on HA and A are not designated here because either HA or A can be charged):
kofa = kl [H+]/ha + kfHA + ks[OH-l/HA + k4[H+]/A + / + k6[OH-]/A
where and fha
Again, equation (52) can be analyzed by considering each individual term as a function of pH. Since the magnitudes of both fHA and fA are dependent on the relative magnitudes of Ka and H+, the kinetic terms can be evaluated under three conditions: (i) when [H+] >> Ka, (ii) when [H+] = Ka, and (iii) when [H+] << Ka (Table 3). The log kobs versus pH profile for each kinetic term is shown in Figure 6, using a hypothetical pKa of 6 and the condition that kH+ = 107, k2 = k3 = k4 = 107, k5 = k6 = 1. The profiles in Figure 6 show one break each in the lines, with a change of slope of 1 unit at the breaks. It is also seen that term (B) is equivalent to term (D) and that term (C) is equivalent to term (E), as far as
Table 3 Kinetic Expressions for Each Term in Equation (52)
Logarithm of kinetic term When [H+] >> Ka When [H+] = Ka When Ka >> [H+]
log ^[H+1/Ha log k2fHA log fe,[OH-]/HA log k4[H+^A log k/A log k6[OH-^A
log k3Kw + pH log kAKa log k5Ka + pH log k6KwKa + 2 pH
og IKT og k4Ka og I
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