Team:ETH Zurich/Modeling/SPF model

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Contents

Sun Protection Factor

Introduction

Sun Protection Factor (SPF) is a measure of the effectiveness of sunscreen. As an extremely simplified rule of thumb, the SPF gives you the time in minutes how much more time you can expose yourself to the sun. The higher the SPF, the better the protection against UV radiation. The measurement is tuned to represent the protection from sunburn, which is caused largely by UVB radiation. This is actually in conflict to the need for cancer prevention, because melanomas are thought to be caused by UVA and UVB radiation. However, to get an idea of the potential of E.colipse we used the wide-spread SPF. To learn more about the SPF, please read [http://en.wikipedia.org/wiki/Sun_protection_factor#Sun_Protection_Factor here].

Model

The formal definition of the SPF is the fraction of the weighted incoming radiation and the weighted transmitted radiation. Finally, this will yield the factor by which the total radiation is reduced.

ETH spf formula.png

E is the irradiaton, A is the weighting factor and MPF the monochromatic protection factor, i.e. the proportion by which the radiation is reduced for a specifc wavelength. The weighting factor A is the so called erythemal action spectrum [Vainio2001]. As mentioned it focuses on UVB radiation that causes sunburn.


Figure 1: Erythemal Action Spectrum. Approx. 99 % of the weight is assigned to UVB radiation, which causes sunburn.

As indicated by the formula above, the SPF is defined as a function of the transmittance at different wavelengths. Therefore we use the absorbance defined by the Lambert-Beer law using extinction coefficients and absorption spectra of PABA and E.coli colonies, the standard irradiation spectrum of the sun and varied the OD of our E.colis and the intracellular steady state PABA concentration. All parameters used can be found on our parameter page.

The figure below shows the absorption spectra of PABA [EC2006] and E.coli [Kiefer2010] , which are used for our SPF computation.

Figure 2: Absorption spectra of PABA and E.coli. The dangerous UVB radiation is filtered efficiently. However, the systems lacks UVA absorption capability.

Results

Figure 3 shows the SPF as function of intracellular pABA concentration and E.coli concentration. The layer of sunscreen is assumed to be 20 μm. This is an approximation of the standard application density (2 mg/cm²) used for the SPF.

Figure 3: Sun protection factor as function of pABA concentration and E.coli concentration.
Figure 4: Weighted irradiation. The data shown is the product of irradiation and erythemal action spectrum. The blue line indicates the radiation striking the layer of sunscreen. The dotted red line shows the remaining radiation after the layer. One can see the reduction of UVB radiation, but the UVA radiation remains hardly changed.


Discussion

The protective effect of our system is achieved by the absorption of PABA and E.coli. Due to the PABA our system efficiently reduces UVB radiation as shown in figure 4. However the lack of absorption in the UVA region poses problems. From the modeling perspective it is hard to achieve high SPF values, since large fractions of the UVA radiation remain hardly changed. In terms of health risk UVA is known to cause DNA damage, i.e. to contribute to and to initiate skin cancer.

Therefore further steps will include the incorporation of an UVA absorbing molecule, which can be produced by E.coli. Alternatively it would be possible to include such a molecule, with peak absorption between 330 and 360, in the medium (sunscreen lotion).


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