Polychromatic-Light Irradiation Kinetics of Dacarbazine and Nifedipine. Application as New Reliable UVA-drug-actinometers.

30 The photokinetic behaviour of materials driven by polychromatic light is an area that 31 has not received a lot of attention in the literature. Most often, such photokinetic data 32 is treated by thermal kinetic models (i.e., the classical 0 th -, 1 st - or 2 nd -order equations). 33 Such models were not analytically derived from the rate-laws of the photodegradation 34 reactions. Polychromatic light kinetic modelling is hence of importance, as a means to 35 providing adequate toolkits and metrics. This paper aims at proposing two reliable 36 drug-actinometers useful for polychromatic UVA range. The general actinometric 37 methodology offered here is also useful for any drugs/materials obeying a primary 38 photoprocess where both reactant and photoproduct absorb the incident light, of the 39 𝐴𝐵 (1Φ) 𝜀 𝐵 ≠0 type. The present method has been consolidated by the  -order kinetics, 40 a mathematical model analytically derived from the photosystem’s rate-law. This 41 represents the first ever equation in the literature, to model polychromatic light of this 42 reactive system. This framework further demonstrated the lamp-specificity of 43 actinometers. Overall, Dacarbazine and Nifedipine photodegradations obeyed  -order 44 kinetics, and stand as effective actinometers that can be recommended for the ICH 45 Q1b photostability testing. 46 47 48 50


52
International Council on Harmonisation Q1b report [4] gives the procedures adopted 53 for stress testing and photostability of new drug substances and products. It is therein 54 recommended that photostability studies are conducted on the API both in its pure 55 chemical form, and in its final pharmaceutical formulation. These considerations 56 significantly contribute to the quality and safety of pharmaceuticals over their lifetime 57 from production to patient, including technical production, storage, manipulation, 58 administration and within the patient body [1][2][3][4][5]. Such photostability studies are also whether its data must be treated according to that methodology. 87 It has previously been shown [13] that the reaction kinetics of the primary 88 photoprocess whose photoproduct is transparent to the monochromatic irradiation 89 light, (1Φ) =0 , obeys the -order kinetics. Mathematically, the latter is defined by 90 a logarithmic function that carries an exponential term in its argument. The -order 91 kinetics defines a new reaction behaviour that is different from the ones undergone by 92 pure thermal reactions.

93
It was also acknowledged that when the photoproduct absorbs the excitation  The reduction of the light intensity, required for actinometric investigation, was 198 achieved by placing one or more copper grid-mesh tiles above the reactor (as light 199 intensity attenuating filters). to einstein/dm 3 /s as the unit required by photokinetics ( Fig.1).

214
Measurements involving wavelength have been performed at 1 nm steps.  A. This photochemical system has the label (1Φ) ≠0 .

248
The distinction between these two cases is relevant because their differential the optical path length of the collimated irradiation light inside the reactive medium.

282
The summation is carried out over the product of the photochemical quantum yield of and photoproduct (B). The total absorbance, in this case, is given by Where, ∆ ( ) takes the form The total absorbance, ∆ ( ) in Eq.2, should in practice have a numerical value 298 exceed, by far, unity when ∆ exceeds a few nanometers. Hence, if ∆ ( ) ≫ 1 then 299 10 − ∆ ( ) ≪ 1 and ∆ ( ), considering the mass balance, can be reduced to with 1 ∆ and 2 ∆ are both constants (expressed in M) for a given ∆ , and defined as By introducing Eq.4 in Eq.1, and rearranging the obtained rate-law to separate the 310 variables, we obtain Eq.7 can be solved by closed-form integration to yield the integrated rate-law (Eq.8).
The latter integrated rate-law (Eq.8) could be presented in much simpler form, The left-hand side term of the integrated rate-law (Eq.9), combines linear and 323 logarithmic terms has the dimension of a concentration (M).
and in its right-hand side term, has the dimension M s -1 , and is expressed as

The kinetic order of the polychromatic-light driven
The simple formulation of the integrated rate-law (Eq.9), with its coefficients 333 (Eqs.10 and 11), does not compare to any known integrated rate-laws proposed, to 334 date, in kinetics. The ( ) expression (Eq.10) is a mixture of a zeroth-order kinetics 335 (the linear section), and a first-order kinetics (the logarithmic section). Whereas, the 336 constant has a dimension of a zeroth-order reaction. Such a combination of kinetic 337 orders in one formula has never been observed before for a single reaction.

338
The dimension of can be thought as a strong argument to consider it as a  Accordingly, Eq.9 describes the particular kinetic behaviour of (1Φ) ≠0 345 photoreactions, and hence, defines a new reaction order: the -kinetic order.

346
As a characterisation of -order kinetics, let us look at some of its properties.  10 − (0) ) is equal to unity when ∆ (0) ≫ 1.
Finally, it is important to underline that the It was also demonstrated that the quantum yields of their respective 400 phototransformations were wavelength-dependent following sigmoid trends (the 401 highest values of the quantum yield were situated towards the higher wavelengths).

402
The quantum yield values of DBZ and NIF over ∆ will be used for our investigation of 403 the polychromatic light irradiation of these drugs.   drugs' photodegradation with no measurable presence of by-products (Fig.2). Little respectively. Notice that the former values for the spectra of DBZ show that ∑ 441 (i.e., of DBZ-PP) is much smaller than that of DBZ. This is not the case for NIF whose 442 total absorption coefficient is practically the same as that of its photoproduct (less than 443 0.9% difference, which was also later confirmed from their calibration graphs, Table   444 1). This means that in both cases a calibration graph of the reactant is sufficient for our 445 study. The increasing quantum yields with wavelength (Fig.3) indicate that both drugs are

475
The experimental data from these traces, of both drugs, were well described by 476 the -order kinetic model (Eq.9), with (t) values obtained for different concentrations, 477 evolve according to linear relationships with photoreaction time (Fig.4). The -order kinetic formulae (Eqs.9-11) allowed the determination of the individual 524 -order overall rate-constants ( ) and initial velocities ( 0 ) for each kinetic trace 525 recorded for NIF and DBZ. An excellent correlation (less than 5% error) was found 526 between these experimental values and the ones independently calculated using (∆) r 0 exp. , (▲) r 0 cld.

(b) NIF
to -order kinetics (Eq.9) and the experimental , values corresponding to each 559 individual total light intensity 0, ∆ , , were determined.

560
A perfectly linear relationships linked variations of the overall rate-constant and the 561 total light intensity for both investigated drugs with relatively high (r > 0.99) correlation 562 coefficients of the lines, with intercepts close to zero (Fig.7). The experimentally 563 constructed graphs in Fig.7 conform well to the principle predicting an increasing 564 photoreactivity with light intensity as expected for (see above point (vi)). Nonetheless, 565 such a correlation might come as a surprise, because such a linear trend is not obvious 566 from the formula of (Eq.11, which explicitly depends on individual 0 ). In fact, since 567 Eq.11 predicts that a specific value of , will correspond to a given irradiation with 568 total 0, ∆ , , Eq.11 can be re-written for that purpose, as linear relation of , and 0, According to Eq.15, the gradients of the lines in Fig.7, represent the coefficients 576 , #4 and , #4 of the drugs for the employed Lamp #4. The fact that , #4 is 577 almost 6.5-fold higher than , #4 (respectively, 1365 and 211 M -1 s, Fig.7), clearly 578 indicates that NIF photodegradation under Lamp #4 is faster than that of DBZ. Also,  Now, in terms of using these drugs as actinometers, the following procedure 614 can be adopted. This actinometric method is developed here for DBZ and NIF but can presented above (Fig.7). The detailed procedure can be performed according to the following chart.     changing species that are irradiated with the same lamp (Fig.7), or changing lamp 703 profiles for the same species (Fig.8) (Fig.8).

717
The above discussion confirms the validity of -order equations but does not tell 718 whether the NIF-actinometer is universal. For this let us consider the scenario where 719 NIF-actinometery was developed on a particular lamp (let it be Lamp #4 with , #4 720 its constant, Table 2) and the test lamp could be any of the set (Lamp #1 to #4).

721
Obviously, if the test lamp is #4 then there are no issues and the unknown intensity 722 could be worked out as described in the above procedure (act-10).

723
More interestingly, is the case when the test lamp is different from #4 (let it be

756
Our experimental results for NIF and DBZ actinometries confirm that can be 757 proposed as reliable actinometers for the UVA range of polychromatic light sources, 758 and alternatives to the ICH Q1b actinometer. NIF and/or DBZ actinometry will provide 759 reliable and more accurate measurements for pharmaceutical photostability studies.

760
The low concentrations needed for such actinometry reduces considerably the cost of 761 these methods. They also open a venue to recruiting more (1 ) ≠0 drug-762 actinometers to allow widening the spectral range covered.

763
The -order kinetics is proven to be the best way available today to describe

764
(1 ) ≠0 reactions when exposed to polychromatic light. In this context, the 765 classical kinetic (0 th -, 1 st -and 2 nd -) orders become, de facto, invalid for this type of 766 reactions and undoubtedly lead to incorrect results and conclusions.

767
A new perspective in photokinetics and actinometer emerges from the present 768 study, that is, rate-laws, integrated rate-laws are both mechanism and light condition 769 specific which leads actinometry to being both lamp profile and actinometer, specific.