Vitamin D3 Visualizer

📊 Notes on Model AccuracyThis 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 (0.93) was calibrated against clinical data (Houghton 2016: 50,000 IU/week × 16 weeks → 61 ng/ml; Cavalier 2018: 50,000 IU/month vs. 2,000 IU/day at equal AUC; Hashemipour 2022: repeat-bolus cross-section). Validation across 5 repeat-bolus schedules: RMSE = 3.90 ng/ml. 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 (Germany −22 nmol/L from RKI data, equator +47 nmol/L from Luxwolda 2012) reflects endogenous vitamin D production from sun exposure. Since cholecalciferol from sun and from supplements share the same saturation curve in the body, the offset is damped with increasing supplement dose — strictly coupled to the enzymatic Ekwaru saturation (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 against Luxwolda/RKI 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 & IMPORTANT NOTICEThis 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 reduced by 20% and the corresponding dose fraction is fed into the Ekwaru model as an equivalent daily dose. 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 was calibrated against clinical data (50,000 IU D3/week over 8–16 weeks). 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. 38 nmol/L — UAE mean: ~50, Saudi women often <30 nmol/L; strong sex-based spread) · Germany (approx. 46 nmol/L — DEGS1, RKI 2008–2011, n=6995: 45.6 nmol/L annual mean) · Poland (approx. 50 nmol/L — annual mean; Płudowski/Ducki 2016 measures late-winter trough ~45 nmol/L, summer up to ~55 nmol/L) · Mediterranean (approx. 50 nmol/L — sun paradox: cultural sun avoidance; Greece ~63, southern Spain/postmenopausal Athens cohort considerably lower) · USA North/Midwest (approx. 62 nmol/L — NHANES) · USA South (approx. 54 nmol/L) · East Asia/China (approx. 46 nmol/L) · Scandinavia (approx. 58 nmol/L — NNR 2023 post-fortification Norway/Finland; 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.

📄 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)