Ann. occup. Hyg., Vol. 47, No. 2, pp. 165-167, 2003
© 2003 British Occupational Hygiene Society
Published by Oxford University Press
Letters to the Editor |
Comment on Sartorelli et al. (1998): Invalid Calculation of Permeability Coefficients
Received 28 August 2002;
Sartorelli et al. (1998) have presented a regression purporting to describe the dermal permeability coefficient, kp, as a function of aqueous solubility and octanol–water partition coefficient for a selected group of compounds. The kp values on which this regression is based were obtained in vitro using monkey skin. Compounds were applied in a small amount of acetone (30 µl on 1.77 cm2). A similar set of experiments was described in another paper (Sartorelli et al., 1999), which compared dermal penetration of polycyclic aromatic hydrocarbons from acetone deposition and a lubricating oil.
The permeability coefficient for a chemical penetrating a membrane, kp, is defined as
kp = Jss/
C (1)
in which Jss, the steady-state flux, is expressed as mass of chemical penetrating per unit of area per unit of time and C, the steady-state concentration gradient between well-stirred external and internal phases (Cext – Kext/int·Cint) , is expressed as mass of chemical per volume of media. Consequently, kp has units of length per time, and is commonly reported in cm/h. Calculation is most convenient when it can be assumed that Cint 
0 and then that
kp Jss/Cext (2)
Traditionally, results of measurement of chemical penetration through skin have been reported as permeability coefficients calculated using equation (2). For a given chemical and external phase, kp will be independent of concentration as long as the skin is not damaged by the penetrating chemical or other external phase, Cext does not exceed the solubility limit Sext, and the chemical does not participate in reactions in the external phase (e.g. acid or base dissociations or association such as dimerization or micellization).
In the experiments described by Sartorelli et al. (1998, 1999), acetone would have evaporated rapidly. Consequently, the reported flux values, which were measured over several days, were from deposited pure compound, not from solution. In experiments such as these, calculating a kp is problematic for several reasons. First, the amount of chemical in the deposited film is often so small that it is depleted by absorption and steady state is never reached. However, this appears not to have been the case in Sartorelli et al.’s experiments. A second problem is that the deposited compound may not completely cover the exposed skin, resulting in a difference between the assumed and actual contact areas. In the Sartorelli et al. experiments the initial amount of chemical applied (M0) per area exposed (A) was too small to completely cover the skin surface. The largest value of M0/A was 125 µg/cm2, which would produce a film thickness of ~1.3 µm on a perfectly flat surface for a compound with density of ~1 g/cm3. Almost certainly this amount of material could not produce a confluent film on the highly uneven surface of skin. One should then expect that J, calculated using total rather than actual skin contact area, would increase with increasing M0/A (up to some point). (This phenomenon is commonly reported in the literature—see further discussion below.) The last problem is the specification of Cext. The original concentration in acetone is inappropriate because the acetone evaporates prior to the steady-state observation. An alternative, the concentration of the deposited pure compound (i.e. its density), is technically applicable, although not actually useful. Density is not related to thermodynamic activity and provides no real information on the driving force for dermal penetration.
Lacking an appropriate concentration term, Sartorelli et al. divided Jss by the initial surface loading as follows:
kSartorelli = Jss/(M0/A) (3)
in which the left-hand-side is actually a mass absorption rate constant with units of time–1. [Schuplein and Ross (1974) referred to this quantity as a transfer coefficient and labeled it kt.] If absorption was modeled as a constant fraction of initial mass:
(4)
the k in equation (4) would be equivalent to the quantity that Sartorelli et al. have labeled kp (and to Schuplein and Ross’s kt).
Therefore, the kp values reported with units of cm/h in Table 2 of Sartorelli et al. (1998) and in Table 3 of Sartorelli et al. (1999) are actually mass absorption rates with units of h–1. Specifically, we find that the quotient of flux and kp values presented in Table 3 of Sartorelli et al. (1999) are essentially the same as M0/A reported in the second column of Table 3. We made the same determination for Sartorelli et al. (1998), except that we had to estimate Jss from the data shown in their Fig. 2 since it was not reported explicitly. Sartorelli (personal communication) has subsequently confirmed this erroneous procedure. An earlier paper (Sartorelli et al., 1997) also reports kp as the quotient of absorption rate and ‘applied concentration’ without specifying units. We suspect that kp is also actually a mass absorption rate.
The potentially significant consequence of Sartorelli et al.’s misrepresentation of their results is that readers will use the data in those papers inappropriately to estimate chemical fluxes. The regression equation provided by Sartorelli et al. (1998) describes a mass absorption rate, not kp. It is defined as follows:
kSartorelli = 0.01498 + 0.00109 Sw – 0.00113 ln Kow (5)
in which Sw is the solubility limit in water in units of g/l and Kow is the octanol–water partition coefficient. Estimation of Jss in a manner consistent with Sartorelli et al.’s derivation requires that values generated from equation (5) be multiplied by initial surface loading, M0/A, rather than Cext as would normally be expected. Unfortunately, there is already at least one published example in which flux has been erroneously calculated by multiplying the quantity described by Sartorelli et al.’s regression by Cext (Semple et al., 2001). That product would have units of mass/volume/time rather than mass/area/time and cannot be flux.
It is clear that the Sartorelli et al. regression cannot be used to predict a permeability coefficient. A second question is whether it might still be used to predict a mass absorption rate. Perhaps because Sartorelli et al. (1999) confused their result with kp, they did not question the assumption implicit in equation (5) that their k depends on properties of the chemical alone (Sw and Kow). For equation (5) to be valid in this second sense, the mass absorption rate must be independent of surface loading. Unless the ratio of flux to loading is constant over a large range of loading, equation (5) could only be applicable at the specific surface loadings used experimentally. However, experimental studies that have examined the relationship between J and M0/A for solvent deposited solids have found that mass absorption rates often decrease at sub-linear rates with increasing M0/A until a critical value of M0/A (representing effectively complete coverage) is reached (Akhter and Barry, 1985; Wester and Maibach, 1999; Reddy, 2000; Zendzian, 2000). Above that point, fractional absorption would be expected to decrease linearly (vary inversely) with M0/A. Generalization of equation (5) also presumes that the thermodynamic activity of two compounds in the surface of the skin is the same if their surface loading is the same. For this to be true, two conditions must be met. First, the actual skin contact area must be the same for the same surface loading. Second, the ratio of the concentration of the compound in the outermost skin relative to its solubility in that skin must be the same for both compounds. While it is difficult to assess the likelihood that the latter requirement will be met, it is likely that contact area will be different for compounds with different density. For example, the fraction of surface area covered by 100 µg/cm2 would probably be larger for naphthalene (
= 0.997 g/cm3) than for lindane (1.87 g/cm3). General applicability of equation (5) is therefore very unlikely even if the units of the result are expressed correctly.
REFERENCES
Akhter SA, Barry BW. (1985) Absorption through human skin of ibuprofen and flurbiprofen: effect of dose variation, deposited drug films, occlusion and the penetration enhancer N-methyl-2-pyrrolidone. J Pharm Pharmacol; 37: 27–37.[Web of Science][Medline]
Reddy MB. (2000) Examining issues in percutaneous transport using mathematical models. Ph.D. thesis, Golden, CO: Colorado School of Mines,.
Sartorelli P, Aprea C, Bussani R, Novelli MT, Orsi D, Sciarra G. (1997) In vitro percutaneous penetration of methyl-parathion from a commercial formulation through the human skin. Occup Environ Med; 54: 524–5.
Sartorelli P, Aprea C, Cenni A et al. (1998) Prediction of percutaneous absorption from physicochemical data: a model based on data of in vitro experiments. Ann Occup Hyg; 42: 267–76.
Sartorelli P, Cenni A, Matteucci G, Montomoli L, Novelli MT, Palmi S. (1999) Dermal exposure assessment of polycyclic aromatic hydrocarbons: in vitro percutaneous penetration from lubricating oil. Int Arch Occup Environ Health; 72: 528–32.[CrossRef][Web of Science][Medline]
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Wester R, Maibach, HI. (1999) Interrelationships in the dose response of percutaneous absorption. In Bronaugh RL, Maibach HI, editors. Percutaneous absorption, 3rd edn. Drugs and the pharmaceutical sciences, vol. 97. New York: Marcel Dekker. pp. 297–313.
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