1. INTRODUCTION :
The recent studies exemplify a multifaceted approach in pharmaceutical sciences1, spanning green analytical techniques2,3,4,5, targeted phytotherapy6,7, autoimmune disease mechanisms8.9, and topical therapeutic formulations10. They highlight the progress and potential of integrating sustainable methods, natural compounds, and innovative delivery systems to address pressing clinical and cosmetic challenges.
Sunlight contains a broad spectrum of electromagnetic radiation, of which ultraviolet (UV) radiation poses the greatest risk to human skin.
Conventional SPF measurement primarily considers the UVB range (280–320 nm), responsible for sunburn. The UV-A (320–400 nm), UV-B (290–320 nm), UV-C (100–290 nm), and vacuo UV (10–100 nm) are traditional divisions of UV light. According to reports, erythema (also known as sunburn), accelerated skin aging, and the development of skin cancer are all negative consequences of UV-B radiation on human skin. Chemicals called sunscreens offer defense against the harmful effects of the sun, especially UV radiation. Numerous sunscreens can lessen the immunosuppressive and carcinogenic effects of sunshine, according to research conducted on animals.11 The skin possesses inherent capabilities to safeguard itself against UV rays, primarily through melanin. Sunlight not only stimulates the production of melanin, which functions as the skin's natural sunscreen, but also initiates hormonal protection and facilitates the synthesis of vitamin D, ultimately encouraging skin cell regeneration. However, it is important to note that shorter wavelengths and lower frequencies correspond to higher energy levels of light, which can lead to increased damage.12 Prolonged exposure to UV-C can damage the skin. Luckily, UV-C is entirely absorbed by atmospheric gases before it can reach the Earth's surface. In contrast, the longer wavelengths of UV-B and UV-A successfully penetrate the atmosphere.13,14,15 The compounds found in sunscreen absorb the majority of UV-B rays, stopping them from penetrating the skin, similar to how atmospheric molecules absorb UV-C rays and shield the Earth from them.
However, UVA rays (320–400nm) significantly contribute to skin aging and carcinogenesis. Traditional methods, such as the Mansur equation, do not account for the full UV spectrum, potentially underestimating the need for UVA protection16,17 The Mansur spectrophotometric method16, established in 1986, calculates the Sun Protection Factor (SPF) by measuring UVB absorbance and applying an erythemal effectiveness weighting function. While this method is widely accepted for in vitro SPF determination, it has notable limitations. Primarily, it focuses solely on UVB radiation, neglecting UVA rays that penetrate deeper into the skin and contribute significantly to photoaging and carcinogenesis. Additionally, the method employs uniform weighting functions, such as those developed by Sayre et al.,18 which do not account for regional variations in UV radiation intensity or differences in skin phototypes. Environmental factors like altitude, geographic location, and seasonal changes also influence UV exposure, yet the traditional model does not adjust for these variables, potentially leading to inaccurate assessments of sunscreen efficacy across diverse conditions.19
2. MATERIALS AND METHODS:
2.1 Materials:
Sunscreen samples are applied to a transparent substrate and allowed to dry. A spectrophotometer measures spectral transmittance from 290 to 400 nm. The new weighting function E_eff(λ) can be derived from updated erythemal action spectra and photoaging research. The integration can be computed numerically using trapezoidal or Simpson's rule.
2.2 Sample Preparation:
Based on solubility studies samples of concentration 10000 microgram per ml of were prepared in different solvents to determine the absorbance on UV spectrophotometer.
2.3 Determination of Absorbance:
The absorbance of different samples was determined on UV spectrophotometer at the various wavelengths 290, 295, 300, 305, 310, 315, 320.
2.4 Proposed SPF Formula:
To address these gaps, we introduce a new SPF equation:
……….………(1)
Where:
K = Calibration constant based on in vivo SPF benchmarks
λ₁, λ₂ = Spectral range (e.g., 290–400 nm)
E_eff(λ) = Combined weighting function reflecting erythema and photoaging
T(λ) = Transmittance of the sunscreen sample at wavelength λ
2.5 SPF in Space:
For extra-terrestrial environments, where solar radiation includes unfiltered UVC, the SPF formula is extended as:
………(2)
Where:
Espace(λ) = Modified action spectrum emphasizing UVC-induced DNA damage
Ks = Calibration constant based on extra-terrestrial UV flux
3. RESULT:
3.1 Deriving the SPF Equation:
1. Spectral Transmittance (T(λ)):
The transmittance T(λ) of the sunscreen sample represents the amount of UV radiation passing through the sunscreen layer at each wavelength. The sunscreen’s ability to block UV radiation is inversely proportional to its transmittance. For each wavelength λ, we can measure the amount of light that passes through the sunscreen and is incident on the skin.
2. Erythemal and Photoaging Effectiveness (Eeff(λ)):
The function Eeff(λ) represents the combined effectiveness of UV radiation in causing erythema (sunburn) and photoaging (skin aging). This function is derived from updated erythemal action spectra and photoaging research, combining the biological effects of both UVB and UVA radiation.
The weighting function is crucial because it assigns a biological relevance to each wavelength of UV radiation. For example, UVB radiation might be more erythemally effective, but UVA radiation is more deeply penetrating and associated with long-term skin damage.
The weighting function can be expressed as:
………..(3)
Where α is a constant reflecting the relative contribution of photoaging versus erythema.
3. Integration Across Wavelengths:
The integral of the weighting function Eeff(λ) multiplied by the sunscreen transmittance (1−T(λ)) over the spectral range of interest (290–400 nm or 200–400 nm for space conditions) yields the total protective effect of the sunscreen across the UV spectrum.
The SPF value is then calibrated against in vivo SPF benchmarks to ensure accuracy.18
3.2 Derivation:
a) Background: Traditional SPF Equation (Mansur Method)- The traditional SPF is calculated in vitro using the Mansur equation:
……………..(4)
Where:
CF is a correction factor
E(λ) is the erythemal effectiveness at wavelength λ
I(λ) is the solar spectral irradiance
Abs(λ) is the absorbance of the sunscreen at λ
b) Convert Absorbance to Transmittance:
Since:
…(5)
But instead of absorbance, we consider transmittance T(λ) directly. The quantity of light blocked is 1−T(λ) representing protection.
c) From Summation to Integration:
Replace the discrete summation with continuous integration over the extended UV range (290–400 nm):
…..(6)
Where:
K is a calibration constant (analogous to CF)
λ1=290 nm,λ2=400 nm
Eeff(λ) is a combined weighting function for erythema and photoaging
T(λ) is the measured transmittance of the sunscreen
d) Weighting Function Explanation:
Traditionally, E(λ) includes only erythemal weighting (e.g., Sayre et al., 1979). We now define:
…(7)
Where:
Eery(λ): erythemal action spectrum
Eage(λ): photoaging action spectrum (UVA emphasis)
w1,w2: user-defined weights (e.g., w1=0.7,w2=0.3w)
This makes the equation adaptable for various SPF considerations: skin cancer prevention, cosmetic protection, etc.
e) Extension for Space Environments:
In space, additional UV wavelengths (esp. UVC: 200–290 nm) are unfiltered. The SPF model becomes:
….….(8)
Where:
Espace(λ): custom weighting including UVC impact (e.g., DNA damage)
Ks: recalibrated constant for extraterrestrial UV flux
f) Final Derived Equation:
General Form:
……(9)
With:
Customizable spectral range [λ1,λ2]
Advanced weighting Eeff for erythema + aging
Physical transmittance T(λ)