Specification24 July 202626 min

Design and scientific foundations of the Broncea algorithm

The full specification: ultraviolet dosimetry, vitamin D photobiology, systemic benefits and risks, and the mathematical model that combines them into a single score.

Abstract

The technical document behind Broncea's calculation engine. It covers UV dosimetry in standard units, the photobiology of vitamin D synthesis including the spectral correction of Young et al. (2021), a review of benefits and risks by level of evidence, and the complete parametrisation of the model — radiometric integration, individual erythemal threshold, saturating benefit functions and asymptotic penalty. Includes the traceability table mapping each mechanism to its primary literature, and all 73 cited sources.

1. Photobiology of sun exposure and dosimetry

Quantifying recommended exposure time requires abandoning the one-dimensional notion of "time in minutes" and moving to a rigorous model of ultraviolet dosimetry. The UV radiation reaching the Earth's surface is mostly UVA (315–400 nm) plus a smaller but biologically very active fraction of UVB (280–315 nm). The cutaneous response depends on the incident wavelength and on the genetic and phenotypic sensitivity of the individual.

To model exposure, the scientific community uses the Standard Erythema Dose (SED), an objective radiometric unit equal to 100 J/m² of UV radiation weighted by the McKinlay–Diffey erythemal action spectrum. The UV Index, the universal public-health metric, derives directly from that weighting: a UVI of 1.0 equals an effective irradiance of 25 mW/m².

1 h at UVI 1.0 = 25 mW/m² × 3,600 s = 90 J/m² = 0.9 SED

This yields the engine's operating constant: 0.015 SED per minute per point of UV index.

The physiological limit before acute damage is the Minimal Erythemal Dose (MED): the threshold energy, weighted by the action spectrum, required to induce perceptible redness with defined borders 24 hours after exposure. Where the SED is an absolute physical measure independent of the individual, the MED is a highly personalised biological variable.

UV index and solar geometry

Intensity is not constant during a session. It depends on the solar zenith angle, governed by latitude, season and hour. As the sun descends, the thickness of atmosphere and ozone the photons must cross increases sharply, preferentially attenuating UVB. At mid latitudes the UV index peaks at solar noon on the summer solstice, while in winter it can fall to levels where vitamin D synthesis is mathematically nil — the phenomenon known as "vitamin D winter".

Phototype and Individual Typology Angle (ITA)

The algorithm needs to categorise the user's susceptibility to erythema. Historically the Fitzpatrick scale (I–VI) has been used, originally designed to predict tolerance to PUVA phototherapy. That classification is inherently subjective, frequently confused with ethnic origin, and shows high inter-observer variability.

The state of the art in computational dermatology calls for a move to the Individual Typology Angle (ITA), an objective colorimetric metric based on the CIE-Lab colour space, computed from lightness L* and the yellow–blue axis b*:

ITA = arctan((L* − 50) / b*) × 180/π

ITA values map directly onto constitutive melanin concentration and set the individual's base MED.

ITA classification	Range (degrees)	Equivalent phototype	Base MED (SED)
Very light	> 55°	I	≈ 2.5
Light	41° to 55°	II	≈ 3.5
Intermediate	28° to 41°	III	≈ 5.5
Tan	10° to 28°	IV	≈ 7.8
Brown	−30° to 10°	V	≈ 12
Dark	≤ −30°	VI	≈ 15

The ITA ranges are the colorimetric standard. The intermediate MED values are not independent measurements: the model interpolates them between the two validated anchors (ITA 55° → 2.5 SED; ITA −30° → 15.0 SED).

Exposed body surface and age factors

The accumulation of systemic benefits, especially vitamin D endocrinology, is directly proportional to the amount of skin exposed. For anatomical modelling in adults the Wallace rule of nines is used, dividing the body into 9% regions (head, each arm) and 18% regions (anterior trunk, posterior trunk, each leg).

This rule introduces a critical bias in paediatric and obese populations. Infants have a much larger cephalic proportion — up to 19% under one year — and shorter lower limbs. The algorithm should adjust surface dynamically by age using the Lund-Browder tables. Age also determines the thickness of the stratum corneum and the viability of Langerhans cells, making children more susceptible to UV immunosuppression.

Environmental factors, altitude and albedo

The algorithm must correct the global UV index returned by weather APIs for the local microclimate. Erythemal irradiance increases by roughly 6% to 10% per 1,000 m of altitude, through reduced atmospheric attenuation.

Albedo, the reflectivity of the underlying surface, amplifies the net dose received at non-zenithal geometries. Fresh snow can reflect up to 80% of incident radiation; beach sand between 15% and 20%; water between 5% and 10%.

Cloud cover is a treacherous variable: while dense formations attenuate strongly, cirrus or light haze can transmit up to 80% of erythemal radiation, leading people to prolong exposure under a false sense of thermal safety.

Photoprotection, sweat and reapplication

The Sun Protection Factor theoretically represents the dose multiplier required to induce erythema. A user with a MED of 3 SED using SPF 30 would hypothetically need 90 SED to burn. However, human behaviour invalidates the nominal efficacy.

In vivo laboratory testing uses a uniform application of 2 mg/cm². In practice users apply between 0.5 and 1.0 mg/cm², drastically reducing filtering capacity. An application at that density over an SPF 50 frequently results in an effective SPF closer to the square root of the nominal factor, around 7–10.

Protection also decays over time, and that decay accelerates exponentially with sweating — through raised skin temperature — and with immersion in water or abrasion from sand. The model must treat SPF not as a constant but as a decaying variable, with adaptive reapplication timers driven by user-declared events.

2. Photobiology of vitamin D

Cutaneous synthesis of cholecalciferol (vitamin D3) is the principal evolutionary route for maintaining bone mineral metabolism and multiple cell-signalling pathways. The process begins in the basal and spinous layers of the epidermis, where UVB radiation isomerises the B ring of 7-dehydrocholesterol to form previtamin D3, which then undergoes thermal isomerisation into vitamin D3.

The action spectrum and the Standard Vitamin D Dose (SDD)

For decades, predictive models used the CIE previtamin D3 action spectrum, based on ex vivo skin samples. Research led by Young et al. (PNAS, 2021) applied different spectra to healthy volunteers, quantifying the response of the serum biomarker 25-hydroxyvitamin D3, and found the original spectrum inaccurate: it required a 5 nm shift towards the blue.

To parametrise the algorithm, the Standard Vitamin D Dose (SDD) is used, defined as 100 J/m² of irradiance weighted by the corrected synthesis spectrum. The ratio between the erythemal and vitamin D spectra varies with zenith angle, but for moderate values it approaches:

SDD / SED ≈ 1.1

Under moderate to intense sunlight the skin accumulates effective metabolic dose faster than erythemal damage — which is what allows sufficiency to be reached before acute damage occurs. The rise in the serum biomarker is not linear but logarithmic in accumulated SDD.

Saturation, photodegradation and seasonal effects

Unlike oral administration, sun exposure has a built-in toxicity-limiting mechanism. Prolonged exposure of the same patch of skin, once a sub-erythemal level is reached, begins to photolytically cleave the newly formed previtamin D3 into biologically inactive compounds, predominantly tachysterol and lumisterol.

From an algorithmic standpoint this is decisive: exceeding the optimal exposure time — generally 15–30 minutes at a high UV index with sufficient surface — does not increase the endocrine vitamin D load, and increases only the risk of mutagenesis and photoaging.

Time requirements depend critically on melanin load, a potent broadband absorber. People with phototypes V and VI require three to six times the ambient dose to photoconvert equivalent amounts of 7-dehydrocholesterol compared with phototypes I and II. During winter at extreme latitudes the algorithm should report the ineffectiveness of exposure, marking the day as "vitamin D winter".

The consensus on photoprotection

A recurring public-health concern is the hypothesis that regular sunscreen use induces vitamin D deficiency by blocking UVB photons. After exhaustive reviews and consensus led by bodies such as the British Association of Dermatologists (Passeron et al., 2019), the verdict is conclusive: daily use of broad-spectrum sunscreen does not compromise serum vitamin D status in healthy populations.

In real-world scenarios, failures in application density and film homogeneity allow a sub-erythemal fraction of UVB to reach the basal layers, sufficient to maintain endocrine homeostasis over time while severely inhibiting acute mutational risk.

The algorithm must not zero the vitamin D counter when the user applies sunscreen, only reduce its rate of accumulation.

3. Systemic benefits of solar radiation

Strong evidence

Modulation of all-cause mortality. The longitudinal MISS study (Melanoma in Southern Sweden), led by Lindqvist, prospectively followed nearly 30,000 women for 20 years. It found that active avoidance of sun exposure is a risk factor for all-cause mortality comparable to smoking, carrying a 2.0-fold higher risk than the highest-exposure groups. Women who were regularly exposed showed markedly lower incidence of cardiovascular disease and thromboembolism, far outweighing the risk associated with skin cancer.
Circadian regulation and sleep quality. Visible radiation, particularly blue wavelengths (450–490 nm), is captured by intrinsically photosensitive retinal ganglion cells expressing melanopsin. The signal travels to the suprachiasmatic nucleus of the hypothalamus, the central pacemaker. Morning outdoor exposure — 10,000 to 100,000 lux, against 300–500 lux indoors — synchronises the clock, suppresses residual melatonin and advances the onset of night-time sleep.
Endocrine homeostasis. Intestinal calcium absorption, keratinocyte differentiation and reduction of pro-inflammatory cytokines.

Moderate evidence

Vasodilation and blood-pressure reduction via nitric oxide. Controlled trials such as those by Opländer and colleagues showed that UVA radiation — excluding UVB — produces an immediate systemic drop in blood pressure and increases blood flow. The mechanism is photodecomposition of epidermal stores of S-nitrosothiols and nitrites, releasing bioactive nitric oxide into the bloodstream. It occurs at normal biological doses, equivalent to about 30 minutes of summer sun.
Mood, endorphins and serotonin. UV light induces cleavage of proopiomelanocortin in epidermal cells, generating melanocyte-stimulating hormone and beta-endorphins. This pathway provides endogenous analgesia and is linked to improvements in emotional wellbeing, partly explaining the resolution of seasonal affective disorder and a degree of physiological "addiction" to the sun.

Emerging or contested evidence

Systemic immunomodulation in autoimmune disease. Suppression of the adaptive immune response may have beneficial roles in reducing flare-ups of certain disorders, though this requires further confirmation on cytokine profiles.
Infrared photobiomodulation (IR-A). Infrared-A radiation penetrates deep into the dermis, affects mitochondrial cytochromes and stimulates oxidative-stress adaptation responses that may pre-condition cells against imminent UVB damage.

4. Photobiological risks and pathophysiology

Photobiology strictly separates acute effects — temporally tied to overexposure and dominated by UVB — from chronic cumulative effects, deeply influenced by UVA penetration into the dermal matrix.

Acute risks

Erythema and sunburn. In response to direct photochemical DNA damage, the dermal endothelium increases permeability, inducing oedema and acute sterile inflammation mediated by histamine, prostaglandins, tumour necrosis factor and reactive oxygen species. Excess energy triggers keratinocyte apoptosis, forming what are clinically called sunburn cells. Combined with raised body temperature from infrared radiation, the effect is synergistically harmful.
Photo-induced immunosuppression. UV radiation paralyses the skin's immune system, creating a tolerogenic environment that lets tumour neoantigens evade detection. In vivo action-spectrum studies (Damian et al., BJD 2011) showed that immunosuppressive efficacy has a secondary critical peak at 370 nm, already within UVA. Since UVA makes up the vast majority of solar photons at ground level and is poorly filtered by some sunscreens, it is the largest contributor to immunosuppression from routine exposure.
Ocular phototoxicity. Can cause photokeratitis, cortical cataracts and long-term macular damage. ICNIRP occupational guidelines set restrictive daily limits for ocular exposure weighted by the actinic spectrum.

Chronic and cumulative risks

Keratinocyte cancers. Chronic, inadvertent exposure causes mutations through failures in nucleotide excision repair after the formation of cyclobutane pyrimidine dimers induced by UVB. Mechanistic research also uncovered "dark CPDs" induced by UVA, which disrupt antioxidant mechanisms and induce chemical DNA bridges even hours after exposure ends.
Malignant melanoma. Unlike squamous cell carcinoma, which depends on chronic exposure, melanoma correlates with episodes of acute high-intensity damage. Severe blistering burns during childhood or adolescence sharply raise the risk of malignant melanocyte transformation. IARC Monograph 100D classifies UV radiation as a Group 1 human carcinogen.
Photoaging. UVA penetrating to the dermis induces reactive oxygen species and activates matrix metalloproteinases, enzymes that selectively destroy type I and III collagen fibres, resulting in elastosis and premature skin laxity.

5. Architecture of the score

The product's objective is the integral, minute-by-minute computation of a health score. Unlike models that merely suggest "spending minutes in the sun", it must behave as a dose–response integration engine. Four architectural criteria:

01Multiple biological pathways. Exposure simultaneously promotes vitamin D synthesis — driven by accumulated dose across the body surface — and nitric oxide mobilisation — driven by incidental UVA. Both must contribute to the daily marker.
02Dynamic spectral sensitivity. The UV index changes constantly with solar geometry and cloud cover at the geolocated position.
03Intelligent sunscreen management. Probabilistic reduction of erythemal impact based on temporal SPF degradation, sweat level and water events, without zeroing the vitamin D gain, in line with dermatological consensus.
04Asymptotic damage penalty. The algorithm rewards time in the sun, but triggers a collapse in the score and warns forcefully when accumulated energy crosses the critical erythemal line.

6. Mathematical model and parametrisation

A. Physical dose: radiometric integration

At each interval the UV index is captured and converted into instantaneous erythemal irradiance. Accumulated erythemal dose is its integral, corrected for ground albedo and for the real transmission of the sunscreen:

D_er(t) = ∫₀ᵗ 0.015 · UVI(τ) · a · T_SPF(τ) dτ [SED]

Albedo factor (a). A fixed environmental multiplier by surface: grass 1.05; water 1.10; dry sand 1.15; snow 1.80.

Sunscreen transmissivity. Rather than assuming the theoretical transmissivity of the label, the algorithm implements an effective SPF approximated by the square root of the nominal, modelling the standard sub-optimal application. The shield also suffers exponential degradation:

SPF_eff(t) = √SPF_nominal · e^(−t/τ)

τ is the degradation constant, which shortens sharply if the user reports heavy sweating or swimming. Reapplication resets the integral.

By clinical design — the Passeron consensus — the factor applied to the parallel vitamin D accumulation is not evaluated the same way as for erythema, but allows a static residual factor of UVB photons that continue to slowly support bone metabolism without burning the skin.

B. Individual risk

From the colorimetric or declared value, the constitutive MED is obtained, modelled by interpolation within the validated range (ITA 55° → 2.5 SED; ITA −30° → 15.0 SED). The inflammatory stress factor is then the ratio of accumulated dose to personal threshold:

R(t) = D_er(t) / MED(ITA)

As R approaches 1, warning signals begin.

C. Biological benefit functions

Two independent subsystems are parametrised.

1. Vitamin D score. Uses the exposed body surface, determined from the user's clothing selection and the Lund-Browder constants for children or the rule of nines for adults. The vitamin D dose comes from an empirical regression on the UV index. The endocrine gain curve has a photolytic saturation ceiling, modelled as an inverted logarithmic decay function, so it does not grow without bound.

2. Vascular and circadian score. Driven by uptake of the UVA spectrum and mobilisation of endogenous nitric oxide. Since photodecomposition requires energy but saturates quickly, it accumulates linearly up to a ceiling.

D. Final score

The score is a convex combination of the benefits, truncated by a penalty function in case of dermatological negligence:

Score = [ w₁ · S_vitD + w₂ · S_NO ] · P_erythema (w₁ = 0.65 · w₂ = 0.35)

Penalty function. A sharp fall is wanted as the MED is approached. An inverted sigmoid serves that purpose, with its inflection point at 85% of the individual MED.

7. History and traceability

The database should record an exhaustive session payload, serving both user experience and eventual medical feedback:

01Accumulated UV dose in total daily SED, in physical units: shows the real impact on skin stress.
02Mean and maximum UV, contextualising how aggressive the sun was that day.
03Effective exposure: average percentage of the body exposed across the session history.
04Estimated benefit: accumulated representation of the health acquired.
05Photoprotection events: timestamp of each application and reapplication.
06Cumulative damage meter: a monthly background counter warning of long-term risk — photoaging and carcinogenesis — if weeks show excessive incidental doses, even without erythemal peaks.

8. Recommendation logic

The algorithm acts as a preventive agent through a notification manager driven by the numerical resolution of the model:

Morning notification (circadian). If low-intensity daylight is detected within two hours of waking: brief exposure now synchronises the circadian clock and improves night-time sleep, with no appreciable cutaneous risk.
Early photoprotection warning. When the dose crosses a prudent threshold with no active declared SPF: the optimal benefit point is close; applying protection now slows premature ageing.
Benefit saturation alert. When the target is reached: continuing will no longer add endocrine benefit and will increase epidermal risk.
Dynamic reapplication alarm. When elapsed time plus the swimming or sweat multiplier reaches the breakdown of the protective shield.
Acute danger alert. When the radiometric dose approaches the individual genetic limit and erythema is imminent.

9. Validation and level of evidence

Designing public-health algorithms requires transparent scrutiny against international guidance. Every formula is traceable to reviews with a high level of evidence:

Mechanism	Level of evidence	Primary literature
SED and SDD dosimetric weighting and the UV index	Strong — ISO/CIE international standards and the World Meteorological Organization	CIE 209:2014; McKinlay–Diffey spectrum
Daily photoprotection does not inhibit vitamin D synthesis in real conditions	Strong — expert panel and systematic reviews (British Association of Dermatologists)	Passeron et al., BJD 2019, and multiple meta-analyses
Moderate sun exposure reduces cardiovascular and all-cause mortality	Moderate-strong — prospective study over 20+ years in 30,000 participants	MISS study, Lindqvist, Karolinska Institute
5 nm shift in the in vivo vitamin D synthesis spectrum	Strong — in vivo spectroscopy superseding earlier ex vivo spectra	Young et al., PNAS 2021
Endogenous blood-pressure reduction through UVA nitric oxide mobilisation	Moderate — controlled clinical trials on immediate vascular responses	Opländer et al., Circulation Research 2009
Immunosuppression driven principally by long-wavelength UVA	Moderate-strong — in vivo human hypersensitivity model	Damian et al., BJD 2011
Objective phototyping via the ITA metric in CIE-Lab space	Strong — de facto standard in dermatological colorimetric research	Chardon et al.
The full UV spectrum is a Group 1 human carcinogen	Strong — International Agency for Research on Cancer and WHO	IARC Monograph 100D

10. Conclusions and implementation

For deployment to a general audience, the system integrates these operational steps:

01Baseline sensory intake. Onboarding discards the subjective questionnaires of the classic Fitzpatrick method in favour of a tone calibration, which fixes the intrinsic constant of the system of equations with a reasonable safety margin.
02Dynamic integration and on-device computation. The phone computes the integral equation in the background from the UV index returned by weather services, corrected for solar geometry, cloud cover and the state of the sunscreen.
03Resolving public ambiguity. The socially hardest link in preventive sun medicine is the tension between sunscreen phobia and irrational sun phobia. Where doubt exists, the algorithm categorically follows contemporary research: it does not zero vitamin D synthesis when sunscreen is used, affirming that filters are the priority in melanoma prevention while sub-clinical endocrine benefits continue to accumulate.
04Extensibility. The logic is parametrised. If future trials define precise multipliers for oral photoprotective ingredients currently under discussion, the structural equation absorbs the update as a new internal protective coefficient.

By combining global guidance with advanced physiological metrics, the system moves beyond a simple timer to become a tool that makes daily interaction with the solar environment intelligent, biologically productive and safe.