Vitamin D3 Visualizer

This Vitamin D3 Visualizer is a purely mathematical tool. The accuracy of the model depends on how the inputs are processed:

1. Daily Dosing (Highest Accuracy): The model for the daily base dose (≤ 25,000 IU) uses the Exponential-plus-Linear regression by Ekwaru et al. 2014 (Table 2), which provides the best fit to the study values (Ekwaru Table 4) across the validated data range up to 20,000 IU/day. It models how the level flattens over time and settles on a plateau.

2. Single Bolus (Good Accuracy): A single high dose (> 25,000 IU) is calculated using the Bateman model — calibrated against 9 clinical studies (e.g., Chen 2016, Rossini 2012). The short-term rise (peak) and slow decline are modeled accordingly.

3. Repeated Bolus Doses (Reasonable Approximation with Adaptive Damping): When high single doses are entered regularly (e.g. 50,000 IU weekly), the calculator uses an adaptive hybrid model: With each subsequent bolus within a 90-day window, the Bateman peak contribution is reduced and the corresponding dose fraction is transferred to the Ekwaru saturation model. This models biological adaptation (dominant mechanism: CYP24A1 upregulation). With weekly bolus dosing the system converges toward the Ekwaru steady state; with longer intervals (monthly) it settles slightly above. The damping factor (0.917) is fitted to the reference RCT Houghton 2016 (50,000 IU/week × 16 weeks → 61 ng/ml hit exactly). Validation across 5 repeat-bolus schedules: RMSE = 4.36 ng/ml across all 5; RMSE = 3.73 ng/ml restricted to the RCTs Cavalier+Houghton; Mean Δ ≈ −0.2 ng/ml (well centred). The remaining deviations — slight overshoot for monthly boluses (Cavalier pair +6 ng/ml) and undershoot for the Hashemipour cross-section (50k/mo) — reflect real study heterogeneity (compliance, cohort storage after ≥6 mo. history, sun exposure) and are not concealed by selective tuning. Direct comparison trials at equal cumulative dose (Cavalier 2018, Takács 2017, Ish-Shalom 2008) find no significant difference between daily and intermittent dosing — the predicted offset above in the model is a conservative approximation and lies clinically within measurement noise.

Fundamental Limitations: All values are population-level model calculations. Individual variability is substantial (genetic differences in CYP24A1, VDR polymorphisms, malabsorption, medications). The model cannot predict an individual's actual serum level.

BMI-dependent gain coefficient and range limits: The model uses a BMI-dependent saturation coefficient A(BMI) = 180.9 − 1.96 · BMI_eff, calibrated against Ekwaru Figure 3 / Table 4. Ekwaru Table 2 provides a global regression with constant A = 132.1; however, Ekwaru’s own Table 4 (recommendation table) shows systematically different saturation plateaus per BMI category. At normal weight (BMI 22) this gives A ≈ 138; at obesity (BMI 32.5) A ≈ 117 — biologically consistent with greater D3 sequestration in adipose tissue. The Y₀ term (baseline without supplementation) still follows Ekwaru Table 2 unchanged. BMI is internally clamped to [18.5 ; 35]: BMI_CAP = 35 (no Ekwaru data above this, extrapolation unreliable) and BMI_FLOOR = 18.5 (underweight cohort in Ekwaru: n=279, p=0.623, not significant). Validation against Ekwaru Table 4 (excl. underweight, 98.7% of cohort): Max|Δ| = 3.72 nmol/L, RMSE = 1.92 nmol/L. Laboratory testing is particularly advisable at BMI >35 and <18.5.

Region offset with dose-dependent damping: The regional offset reflects the population-averaged difference from the Ekwaru study cohort (Canada, approx. 68 nmol/L) — UV exposure as the main factor, alongside cultural, methodological and seasonal influences. Since cholecalciferol from sun and from supplements end up in the same 25(OH)D pool, the offset is damped with increasing supplement dose — strictly coupled to the Ekwaru saturation kinetics (factor B=0.1) and normalized exactly to zero at the dynamically calculated limit (X_CLIP). At 0 IU the offset applies in full (calibration of regional means is exactly preserved); at 2,000 IU still approx. 80%, at 10,000 IU about 31%, at 20,000 IU only 6%. This means two people from different regions will see their predicted levels converge at high supplement doses — physiologically correct, as the supplement then dominates over endogenous production.

4. Empirical Daily Processing Cap (Author's Concept): To realistically reflect toxicological risk and prevent mathematical distortions with extreme inputs, the tool uses a heuristic saturation limit of approx. 733 IU per kg of body weight. This constant is a specific concept of the author: It is derived from the clinical observation that chronic daily doses of approx. 50,000 IU overload the CYP24A1 degradation pathway in an average adult (70 kg). It serves the model as a mathematical safety anchor ("circuit breaker") to stabilize accuracy during massive overdoses.

Conclusion: The model provides population-level approximations. The best accuracy is achieved with continuous daily dosing. This tool does not replace laboratory diagnostics.

Disclaimer: This tool is provided "as is". Despite careful development, errors cannot be excluded — factual, computational, programming-related, or arising from advances in scientific knowledge. The operator assumes no liability for decisions made based on the results of this tool.

This tool is a purely academic visualization of the dose-response relationship described in the study by Ekwaru et al. (2014, PLOS ONE) between oral vitamin D supplementation and 25(OH)D serum levels. The displayed curves are model calculations at the population level — they show statistical averages, not individual predictions.

This tool is not a medical device, not a diagnostic instrument, and not a therapy recommendation. The underlying model calculations may contain errors, inaccuracies, or results that are entirely inapplicable to individuals. It must not be used as a basis for health decisions, diagnoses, or treatments. Always consult a physician or pharmacist before making any changes to supplementation, and have blood levels professionally tested in a laboratory. The operator assumes no liability for decisions made on the basis of this visualization.

Visualization Basis & Study

The visualization is based on the published study by Ekwaru et al. (2014, PLOS ONE). The study describes that the dose-response relationship between oral vitamin D supplementation and serum levels follows an exponential saturation curve (Exponential-plus-Linear regression, Ekwaru Table 2). It was also found that BMI (Body Mass Index) is a better predictor of 25(OH)D levels at the population level than absolute body weight. The time course is a pharmacokinetic approximation with a biological half-life of approximately 25 days.

Model used: Exponential-plus-Linear saturation model: Y = Y₀ + A(BMI) · (1 − e^−B·X_eff) + B_LIN · X_eff, with B = 0.1 and B_LIN = −1.1 (Ekwaru Table 2). The saturation coefficient A is BMI-dependent: A(BMI) = 180.9 − 1.96 · BMI_eff. At normal weight (BMI 22) this gives A ≈ 138; at obesity (BMI 32.5) A ≈ 117. Background: Ekwaru Table 2 provides a global regression with constant A = 132.1 across all BMI groups. However, Ekwaru’s own Figure 3 and Table 4 (recommendation table) present separate dose-response curves per BMI category with systematically different saturation plateaus — for obese individuals the plateau at high doses is substantially lower, biologically consistent with greater D3 sequestration in adipose tissue. Since this tool validates against Table 4, the gain coefficient A was fitted per BMI category and linearly interpolated (validation excl. underweight: Max|Δ| = 3.72 nmol/L, RMSE = 1.92 nmol/L). The BMI effect on Y₀ (baseline) still follows Ekwaru Table 2 unchanged (−1.5 nmol/L per BMI unit). Since the model has a BMI-dependent mathematical maximum, the tool calculates this peak (X_CLIP) dynamically and caps the calculation there. For higher doses, the bolus model takes over anyway (bolus threshold at 25,000 IU).

Averages, not individual predictions: The regression model shows the mean response per weight group in the study population. Individual levels in the study ranged from 10.1 to 394 nmol/L with supplementation doses from 0 to 55,000 IU/day. The scatter around the curve is substantial. Some people are "low responders" — due to genetic factors (VDR polymorphisms), malabsorption, or medications. Others are "high responders" (e.g., due to high VDR sensitivity) and achieve significantly higher levels at the same dose.

Dual-model architecture: The tool uses two pharmacokinetic models: (1) For daily base supplementation (up to 25,000 IU/day), the saturation model by Ekwaru et al. (2014) is used, which models the steady-state level achieved through regular intake over months. (2) For single doses above 25,000 IU (bolus), a Bateman pharmacokinetic model is employed, calibrated against 9 clinical studies (e.g., Chen 2016, Rossini 2012, Cipriani 2010). This models the actual curve of a single dose: rapid rise to peak, followed by exponential decline (elimination half-life approx. 25 days). Both models are combined via the superposition principle — the total level is the sum of the daily baseline and all active bolus curves. For repeated bolus doses, the tool applies adaptive damping: With each subsequent bolus within a 90-day window, the Bateman contribution is multiplied by a factor of 0.917 (gradual reduction), and the corresponding dose fraction is fed into the Ekwaru model as an equivalent daily dose — the cumulative transition follows α = 1 − 0.917ⁿ (n = number of prior boluses). This models the body's biological adaptation (dominant mechanism: CYP24A1 enzyme upregulation). With weekly bolus dosing, the system converges toward the Ekwaru steady state; with longer intervals (e.g. monthly) it settles slightly above. The damping factor (0.917) is fitted to the reference RCT Houghton 2016 (50,000 IU D3/week over 16 weeks → 61 ng/ml hit exactly; Cavalier 2018: 50,000 IU/month vs. 2,000 IU/day at equal AUC). For individuals with low body weight, even the daily dose may exceed the empirical daily processing cap (approx. 733 IU/kg, a heuristic estimate most plausibly constrained by hepatic 25-hydroxylase saturation); in this case, the excess is distributed as carry-over to subsequent days.

What the study shows: According to Ekwaru et al., at a supplementation of 10,000 IU/day, the modeled average value of all weight groups fell within the reference range of 75–150 nmol/L. The individual scatter in the study population was approximately ±50 nmol/L around the mean. The study further notes that in the examined population, calcium levels did not rise significantly with increasing vitamin D dose.

Regional Baselines

The Canadian study population (Ekwaru 2014, 53° N) serves as the reference (approx. 68 nmol/L). All other regions are calibrated as offsets relative to this: South Asia/India (approx. 33 nmol/L — urban Delhi median: ~19 nmol/L, rural: ~40 nmol/L; tool value weighted toward urban) · Middle East (approx. 42 nmol/L — MENA meta-analysis: pooled mean 46 nmol/L (95% CI 40–52); UAE mean ~50 nmol/L, Saudi women often <30 nmol/L; conservative value due to strong sex- and culture-based dispersion) · Germany (approx. 50 nmol/L — DEGS1, Rabenberg 2018 VDSP/LC-MS-MS-standardised, n=6995: 49.5 nmol/L; the original CLIA mean of 45.6 nmol/L (Rabenberg 2015) was found to be systematically underestimated after VDSP standardisation) · Poland (approx. 50 nmol/L — Płudowski/Hilger 2014, n=5775: 18.0 ng/ml = 45 nmol/L (late winter/spring); annual mean ~50 nmol/L after summer correction) · Mediterranean (approx. 50 nmol/L — sun paradox: cultural sun avoidance; Greece ~63, southern Spain/postmenopausal Athens cohort considerably lower; Italy/Spain adults ~50–60 nmol/L) · USA North/Midwest (approx. 65 nmol/L — NHANES 2017–2018, US total median 68.7 nmol/L) · USA South (approx. 70 nmol/L — NHANES, South higher than North due to stronger UV exposure) · East Asia/China (approx. 46 nmol/L — meta-analysis 2021, 105 studies, n=234,519: 44.3 nmol/L) · Scandinavia (approx. 58 nmol/L — regional mean; Finland post-fortification 65 nmol/L, Norway/Sweden lower; FINRISK 2002 pre-fortification: 45–48 nmol/L) · Australia (approx. 65 nmol/L — Australian Health Survey 2011–2013, n=5,034, nationally representative: winter/spring 55–60, summer/autumn 70–75 nmol/L; high UV exposure offset by strong sun protection campaigns) · Equator/East Africa (approx. 115 nmol/L — Luxwolda et al. 2012: Maasai 119, Hadza 109 nmol/L, traditionally living population). The offset is gradually reduced to zero as the supplement dose increases — at very high daily doses (from approx. 25,000 IU), the supplement fully dominates and regional differences disappear. This models the physiological effect that oral vitamin D increasingly substitutes endogenous production from sunlight (saturation of the total system).

Note on dropdown values: The nmol/L values shown are epidemiological population averages. The actual baseline modelled at 0 IU is calculated from individual parameters (age, BMI, biological sex) and naturally deviates from these static averages.

Selection „Start 25(OH)D = Base” in the baseline dropdown (default): The model treats the entered starting value as the personal baseline (sun/diet) instead of the regional population average. The drift anchor is set so that at 0 IU the steady state matches the starting value exactly; at daily dose > 0 the dose-dependent saturation gain is added on top. Useful for users who know their current lab value — the trajectory is then not artificially pulled toward the regional average. Alternatively, a region can be selected from the dropdown.

📄 Scientific Publications (10 Studies)

Base Saturation Model (Daily Dosing)

Ekwaru JP et al. (2014): PLOS ONE — doi:10.1371/journal.pone.0111265

Bateman Pharmacokinetics (Bolus Calibration >25,000 IU)

50,000 IU: Armas LAG et al. (2004), JCEM — doi:10.1210/jc.2004-0360

70,000 IU: Roth et al. (2012), Nutr J — doi:10.1186/1475-2891-11-114

100,000 IU: Ilahi M et al. (2008), AJCN — doi:10.1093/ajcn/87.3.688

150,000 IU: Meekins ME et al. (2014), EJCN — doi:10.1038/ejcn.2013.278

250,000 IU: Kearns MD et al. (2015), EJCN — doi:10.1038/ejcn.2014.209

300,000 IU: Chen PZ et al. (2016), APS — doi:10.1038/aps.2016.82

500,000 IU: Sanders et al. (2010), JAMA — doi:10.1001/jama.2010.594

600,000 IU: Cipriani C et al. (2010), JCEM — doi:10.1210/jc.2010-0502

100k, 300k, 600k IU: Rossini M et al. (2012), CTI — doi:10.1007/s00223-012-9637-y

Repeat-Bolus Validation (adaptive damping)

Cavalier E et al. (2018): Nutrients — PMC6024703

Takács I et al. (2017): Endocrine — doi:10.1007/s12020-016-1137-9

Ish-Shalom S et al. (2008): JCEM — doi:10.1210/jc.2008-0241

Houghton LA et al. (2016): J Steroid Biochem Mol Biol — PMC4724876 (RCT, older subjects without sun exposure, 16 wk, 50k IU/wk D3 → 61 ng/ml)

Hashemipour S et al. (2022): Br J Clin Pharmacol — doi:10.1111/bcp.15186 (cross-sectional, endocrinology-clinic cohort with ≥6–12 mo. prior supplementation)