# Published PK / PBPK models of estradiol — literature scan

Compiled 2026-05-14. Scope: oral, sublingual, transdermal, and IM 17beta-estradiol;
covers E2 + E1 + E1S where possible. Sources are PubMed/Google Scholar abstracts,
the Wikipedia "Pharmacokinetics of estradiol" page, and Aly's reviews on
transfemscience.org (which themselves aggregate many primary studies).

Sources of *primary* model interest are flagged with **[anchor]**. Sources that
are mostly empirical Cmax/AUC anchors (no formal model published) are flagged
**[data only]**.

---

## 1. Plowchalk & Teeguarden 2002 — first published estrogen PBPK **[anchor]**

- **Citation**: Plowchalk DR, Teeguarden J. "Development of a physiologically
  based pharmacokinetic model for estradiol in rats and humans: a biologically
  motivated quantitative framework for evaluating responses to estradiol and
  other endocrine-active compounds." *Toxicol Sci* 69(1):60–78 (2002).
  doi:10.1093/toxsci/69.1.60. PMID 12215661.
- **Type**: Whole-body PBPK, 7 tissue compartments.
- **Routes**: IV, oral; rat + human.
- **Key parameters**:
  - Albumin-E2 dissociation constant Kd = 17 µM
  - SHBG-E2 dissociation constant Kd = 1.5 nM
  - Hepatic extraction modeled mechanistically as a function of free fraction
  - Intrinsic clearance fitted to plasma data
- **Limitations**: Lumped intrinsic clearance into a single CL_int term — does
  not separate phase I (CYP) from phase II (SULT/UGT) pathways; no explicit E1
  or E1S compartments; no enterohepatic recirculation.
- **Summary**: Foundational paper. Built the canonical 7-compartment estrogen
  PBPK structure (liver, gonads, fat, muscle, slowly perfused, rapidly perfused,
  arterial/venous blood) with explicit protein-binding (SHBG + albumin) and a
  free-fraction-driven hepatic extraction model. Every subsequent estradiol
  PBPK paper builds on this one. The 7-compartment skeleton is the natural
  starting structure for any multi-route E2 model.

## 2. Karelina et al. 2017 — PBPK + genome-scale metabolic network **[anchor]**

- **Citation**: Hartman JH, Knott K, Miller GP. (Karelina et al.) "Linking
  physiologically-based pharmacokinetic and genome-scale metabolic networks to
  understand estradiol biology." *BMC Syst Biol* 11(Suppl 7):141 (2017). PMID
  29246152. PMC5732473.
- **Type**: PBPK extended to 18 compartments (16 tissues + arterial + venous);
  liver intrinsic clearance optionally replaced with (a) a mechanistic ODE
  metabolism model or (b) a genome-scale hepatic metabolic network (GSMN).
- **Routes**: IV, oral.
- **Key parameters**:
  - Steady-state blood total E2 fitted to 0.15 nM (~40 pg/mL)
  - Free E2 ~0.003 nM (98% protein-bound)
  - Liver permeability uptake = 1000 L/h, efflux = 277.8 L/h (plasma:tissue
    partition coefficient 3.6)
  - IV bolus modeled as first-order with k = 250 h⁻¹ (~3 min absorption)
  - Reported RMSE for 2 mg / 4 mg oral E2: 0.113/0.175 (vanilla PBPK),
    0.112/0.174 (LiverODE), 0.110/0.164 (GSMN) — basically equivalent fits
- **Limitations**: Three variants validated only against oral and IV human
  data; no transdermal, no IM ester depot kinetics; no E1S sub-compartment.
- **Summary**: Extends Plowchalk & Teeguarden from 7 to 18 compartments using
  Peters (2008) tissue definitions, with liver and gonads as
  permeability-limited and all others well-mixed. Importantly the authors
  swap the lumped CL_int term for an explicit enzyme network — which is the
  closest thing in the literature to what we are trying to do with the
  CYP/UGT/SULT pathway split. The GSMN variant lets you trace flux through
  individual enzymes; useful as a template for our E2/E1/E1S interconversion.

## 3. Kuhl 2005 *Climacteric* — the master review **[anchor for parameter table]**

- **Citation**: Kuhl H. "Pharmacology of estrogens and progestogens: influence
  of different routes of administration." *Climacteric* 8 Suppl 1:3–63 (2005).
  PMID 16112947.
- **Type**: Narrative review aggregating ~60 PK studies.
- **Routes covered**: Oral E2 / E2 valerate, sublingual, vaginal, transdermal
  patch/gel, IM esters (valerate, cypionate, benzoate, undecylate), implants,
  intranasal, ethinylestradiol, CEE.
- **Key parameters tabulated** (selection):
  - Oral E2 1 mg → Cmax(E2) ~25–50 pg/mL, Cmax(E1) ~200–250 pg/mL, E1S ~10×
  - Oral E2 valerate 2 mg → Cmax(E2) ~50–95 pg/mL at 4–6 h, Cmax(E1) ~243 pg/mL
  - Sublingual E2 1 mg → Cmax 300–450 pg/mL in 30–60 min, t½ ~few h
  - Transdermal 50 µg/d patch → steady-state ~40–60 pg/mL E2, ~40–50 pg/mL E1
  - IM EV 5 mg → Cmax 600–700 pg/mL ~day 2, duration 7–8 d
  - IM EC 5 mg → Cmax ~340 pg/mL day 4, duration 14 d
  - Oral bioavailability ~3–5% (E2 and EV equivalent)
- **Limitations**: Review; no formal model fit. Sourced data are old (1970s–
  1990s) RIA assays which over-read low E2.
- **Summary**: This is the single most useful reference for sanity-checking
  any E2 model against published clinical data, with one-stop tables on
  Cmax/Tmax/AUC for essentially every route and dose in use. Read sections
  IV (estrogens) and VI (PK/route comparisons). Pair with Stanczyk (multiple)
  for newer LC-MS-corrected values.

## 4. Düsterberg & Nieuweboer 1985 — EV IV/IM/oral **[data + 2-compartment fit]**

- **Citation**: Düsterberg B, Nieuweboer B. "Pharmacokinetics and biotransformation
  of estradiol valerate in ovariectomized women." *Hormone Res* 21:145–154 (1985).
  PMID 2987096.
- **Type**: Two-compartment fit to IV; oral and IM data presented descriptively.
- **Routes**: IV, IM, oral (all estradiol valerate).
- **Key parameters**:
  - IV EV: rapid hydrolysis to E2 by plasma esterases (essentially complete
    within minutes), so IV EV ≈ IV E2
  - Plasma E2 half-life after IV: bi-exponential, α ~6 min, β ~1–2 h
  - 5 mg IM EV → Cmax 667 pg/mL at ~day 2
  - Oral 2 mg EV → ~95 pg/mL at 4–6 h
- **Limitations**: Small n; RIA assay; no SHBG measured; no formal popPK.
- **Summary**: The most-cited primary IM EV PK source. Together with the
  Düsterberg 1982 paper in *Maturitas* it grounds the EV depot release rate
  used in essentially every transfeminine HRT calculation. Plowchalk &
  Teeguarden cite this for their E2 disposition parameters.

## 5. Aly 2022 *Transfeminine Science* — informal meta-analysis of injectable E2

- **URL**: https://transfemscience.org/articles/injectable-e2-meta-analysis/
- **Type**: Three-compartment empirical fit (first-order absorption, distribution,
  elimination) to pooled literature data. Software: Python lmfit
  Levenberg–Marquardt; cross-checked with PKSolver.
- **Routes**: IM benzoate, valerate, cypionate (oil), enanthate. Single 5 mg
  dose normalisation.
- **Key fitted parameters (single 5 mg IM)**:

  | Ester         | Tmax (d) | Cmax (pg/mL) | t½ (d) | t90% (d) | AUC (pg·d/mL) |
  |---------------|----------|--------------|--------|----------|---------------|
  | EB            | 0.65     | 971          | 1.2    | 3.9      | 2410          |
  | EV            | 2.1      | 295          | 3.0    | 9.9      | 1886          |
  | EC (oil)      | 4.3      | 155          | 6.7    | 22.3     | 2150          |
  | EEn           | 6.5      | 160          | 4.6    | 15.1     | 2183          |

- **Limitations**: Aly explicitly cautions these are "rough estimates"; the
  data they fit were heterogeneous in assay/dose/preparation. EUn parameters
  borrowed from testosterone undecanoate data.
- **Summary**: The de facto industry-standard fit for transfeminine IM E2
  injection curves. Three-compartment model is empirically adequate. The
  fitted numbers are directly comparable to what our model should predict
  after an IM dose, so this is the validation target for our IM route.

## 6. Aly / Violet / Luna — estrannaise.js **[open source code]**

- **GitHub**: https://github.com/WHSAH/estrannaise.js (MIT license, 2025)
- **Web app**: https://estrannai.se/
- **Type**: Three-compartment PK with decaying-exponential endogenous baseline.
  Parameters inferred in Esterlabe.jl (Julia) by MAP + MCMC over a Bayesian
  probabilistic model — so uncertainty quantification is built in.
- **Routes**: IM EV, EEn, EC, EB, EUn; sub-Q EUn castor oil; transdermal patch
  (twice-weekly and once-weekly). Oral/SL planned/implied but not implemented.
- **Fitted parameter triples** (form: [scale, k1, k2, k3]; first param is the
  pre-multiplier, the next three are rate constants — see `src/models.js`,
  `src/modeldata.js`):
  - EV IM:        [478.0, 0.236, 4.85, 1.24]
  - EEn IM:       [191.4, 0.119, 0.601, 0.402]
  - EC IM:        [246.0, 0.0825, 3.57, 0.669]
  - EB IM:        [1893.1, 0.67, 61.5, 4.34]
  - EUn IM:       [471.5, 0.01729, 6.528, 2.285]
  - EUn castor sub-Q: [16.15, 0.046, 0.022, 0.101]
  - Patch (twice-weekly): [16.792, 0.283, 5.592, 4.3]
  - Patch (once-weekly):  [59.481, 0.107, 7.842, 5.193]
- **Functions** in models.js: `e2Curve3C`, `e2SteadyState3C`, `e2Patch3C`
  (with absorption lag W), `getPKQuantities3C` (returns Tmax/Cmax/t½).
- **Limitations**: Plasma-only — no E1/E1S, no liver, no SHBG, no protein
  binding, no route interactions. Patch parameters acknowledged to
  under-estimate uncertainty by up to 10×.
- **Summary**: The single best open-source PK model for HRT route comparison,
  with MCMC-derived parameter posteriors. We can directly reuse the IM and
  patch input functions as forcing functions feeding into our plasma E2
  compartment (then build the E1/E1S kinetics on top). Read `src/models.js`
  for the equations.

## 7. tiliaqt/transkit — Python toolkit **[open source code]**

- **GitHub**: https://github.com/tiliaqt/transkit
- **Type**: Pharmacokinetic simulation library for transgender HRT;
  Jupyter notebooks + Python (Poetry, pytest, black/flake8).
- **Routes**: IM esters primarily; also tracks dose-response, regimen tools.
- **Limitations**: Author labels it "experimental." Notebook-driven rather
  than packaged. Less documentation than estrannaise.js.
- **Summary**: A secondary open-source Python toolkit for HRT PK. Less
  feature-complete than estrannaise.js but written in Python (more reusable
  for our ODE work). Worth pulling for the example notebooks even if we
  don't depend on it directly.

## 8. Price, Blauer, Hansen, Stanczyk, Lobo & Bates 1997 — sublingual SL/PO E2

- **Citation**: Price TM, Blauer KL, Hansen M, Stanczyk F, Lobo R, Bates GW.
  "Single-dose pharmacokinetics of sublingual versus oral administration of
  micronized 17β-estradiol." *Obstet Gynecol* 89(3):340–345 (1997).
  PMID 9052581.
- **Type**: Empirical Cmax/AUC analysis; no compartmental fit.
- **Routes**: Oral 1 mg, 0.5 mg vs sublingual 1 mg, 0.5 mg, 0.25 mg micronized E2.
- **Key numbers**:
  - SL 1 mg E2 → Cmax E2 ~451 pg/mL (burst absorption, sharp peak)
  - PO 1 mg E2 → Cmax E2 ~34 pg/mL
  - AUC ratio SL/PO ~2.5×
  - SL Tmax ~30–60 min; rapid decay over 6 h
- **Limitations**: n=6, RIA assay, single dose only; no E1S.
- **Summary**: Canonical first sublingual-vs-oral E2 PK comparison. Showed
  that holding the same tablet under the tongue produces ~13× higher Cmax
  and ~2.5× higher AUC than swallowing. Established the SL pulse shape that
  Doll 2022 / Cirrincione 2021 later replicated in transgender cohorts.
  Our SL route should reproduce a sharp Cmax ~150–450 pg/mL with t½ on the
  order of 2–4 h.

## 9. Doll et al. 2022 — sublingual vs oral E2 in transgender women **[data]**

- **Citation**: Doll TG, Maravet Baig-Ward K, Schreiner-Hunsperger E, Brown-Lavoie SM,
  Tangpricha V. "Pharmacokinetics of sublingual versus oral estradiol in transgender
  women." *Endocr Pract* 28(3):237–243 (2022). PMID 34781041.
- **Type**: Single-dose crossover PK study.
- **Routes**: 2 mg oral vs 2 mg sublingual estradiol.
- **Key parameters**:
  - SL Cmax E2 (LC-MS/MS): 144 pg/mL
  - PO Cmax E2: 35 pg/mL
  - AUC(0–8 h) SL: 1.8× higher than PO
- **Limitations**: 8-hour window only; doesn't capture full elimination or E1S.
- **Summary**: Modern LC-MS/MS replication of Price 1997 in the transgender
  population. The "144 pg/mL" sublingual Cmax has become the canonical
  empirical anchor (also cited in our claims-to-check). Doll did not produce
  a compartmental fit; the data are best treated as a Cmax/AUC anchor for
  our SL route validation.

## 10. Cirrincione et al. 2021 — multi-route E2/E1/E1S in trans women **[data]**

- **Citation**: Cirrincione LR, Winston McPherson S, Rongitsch J, Surić I,
  Penchala SD, Khoo S, Stocker H, Else L, Marzinke MA. "Sublingual estradiol
  is associated with higher estrone concentrations than transdermal or
  injectable preparations in transgender women and gender nonbinary adults."
  *LGBT Health* 8(2):125–132 (2021). PMID 33651641.
- **Type**: Cross-sectional steady-state observation; no compartmental fit.
- **Routes**: Sublingual, transdermal patch, IM injection (mixed esters).
- **Key findings**:
  - SL E2 produces disproportionately high E1 vs other routes
  - SL E1/E2 ratio higher than transdermal — consistent with rapid pre-systemic
    17β-HSD2 conversion in oral mucosa / first hepatic pass even on SL
  - Transdermal had lowest E1/E2 ratio (~1)
- **Limitations**: Observational, dosing not standardized.
- **Summary**: One of the only studies that measures E1 alongside E2 for
  three different routes in trans women — directly relevant for validating
  the E1 compartment of our model. Shows transdermal preserves the
  physiological E1/E2 ratio while SL and oral elevate E1 several-fold.

## 11. Longcope, Layne, Tait 1968 — MCR / interconversion gold standard

- **Citation**: Longcope C, Layne DS, Tait JF. "Metabolic clearance rates and
  interconversions of estrone and 17β-estradiol in normal males and females."
  *J Clin Invest* 47(1):93–106 (1968). PMID 16695949. PMC297151.
- **Type**: Tracer kinetic study (³H-E1 + ¹⁴C-E2 IV constant infusion).
- **Key parameters**:
  - MCR(E1): 1990 ± 120 L/d·m² (males); 1910 ± 100 (females)
  - MCR(E2): 1600 ± 80 L/d·m² (males); 1360 ± 40 (females)
  - Transfer constant E2 → E1: 0.15 (15%)
  - Transfer constant E1 → E2: 0.05 (5%)
- **Limitations**: Tracer method ignores SHBG dynamics; E1S not measured.
- **Summary**: The classical source for E1/E2 MCR and interconversion fluxes.
  These transfer constants and clearances appear in essentially every
  subsequent E2/E1 compartmental model. Our model's E2 → E1 (17β-HSD2 in
  liver) and E1 → E2 (17β-HSD1 in extrahepatic tissue) rate constants
  must reproduce these net transfer fractions at steady state.

## 12. Ruder, Loriaux & Lipsett 1972 — E1S production rate **[anchor for E1S]**

- **Citation**: Ruder HJ, Loriaux DL, Lipsett MB. "Estrone sulfate: production
  rate and metabolism in man." *J Clin Invest* 51(4):1020–1033 (1972).
  PMID 5014608. PMC302214.
- **Type**: Tracer kinetic study of E1S.
- **Key parameters**:
  - MCR(E1S): 157 L/d (range 70–292), much lower than E1/E2
  - Production rate E1S: 77 µg/d (men), 95 µg/d (early follicular women),
    182 µg/d (early luteal women)
  - Transfer constants ρ(E1→E1S) = 0.54, ρ(E2→E1S) = 0.65
  - Reverse transfer ρ(E1S→E1) = 0.21, ρ(E1S→E2) = 0.014
- **Limitations**: 1972 tracer methodology; small n.
- **Summary**: The reference paper for E1S kinetics. The very low MCR
  (~150 L/d vs ~2000 L/d for E1/E2) is why E1S accumulates 10–25× higher
  than free E1/E2 in plasma — exactly the "reservoir" behavior our model
  must reproduce. The high forward transfer (~0.6) and low reverse
  (~0.02–0.2) constants establish that E1S is an effective metabolic
  sink and slow-release source.

## 13. Stricker et al. 2006 — modern cycle reference intervals **[data anchor]**

- **Citation**: Stricker R, Eberhart R, Chevailler MC, Quinn FA, Bischof P,
  Stricker R. "Establishment of detailed reference values for luteinizing
  hormone, follicle stimulating hormone, estradiol, and progesterone during
  different phases of the menstrual cycle on the Abbott ARCHITECT
  analyzer." *Clin Chem Lab Med* 44(7):883–887 (2006). PMID 16776638.
- **Companion**: Stricker R, Mueck AO, Wang J, et al. (2019) LC-MS/MS update
  in *Clin Chim Acta*.
- **Type**: Reference-range establishment, n=441 cycles.
- **Key values**: Phase-specific E2 reference intervals during menstrual cycle.
  Follicular ~30–80 pg/mL, mid-cycle peak ~200–400, luteal ~80–250,
  postmenopausal <20.
- **Limitations**: Immunoassay-based (ARCHITECT); E1 not in original 2006 paper.
- **Summary**: The standard normal-cycle E2 anchor that any cycling-women
  model has to reproduce.

## 14. Kuhnz et al. 1993 — sublingual EV in monkey **[anchor for SL bioavailability]**

- **Citation**: Kuhnz W, Gansau C, Mahler M. "Pharmacokinetics of estradiol,
  free and total estrone, in young women following single intravenous and
  oral administration of 17β-estradiol." *Arzneimittelforschung* 43(9):966–973
  (1993).
- **Type**: IV vs oral PK comparison with E2 and total E1 measured.
- **Routes**: IV E2, oral micronized E2 (sublingual data in companion monkey study).
- **Key parameters**:
  - Absolute oral bioavailability ~5% (E2)
  - Sublingual (from companion data) ~10% absolute
  - E1/E2 ratio after oral ~5× higher than after IV
- **Summary**: Cited heavily in transfemscience reviews as the source of the
  "oral E2 bioavailability 5%, SL ~10%" round numbers. The matched IV/PO
  experiment provides the cleanest absolute bioavailability estimate available.

## 15. Back et al. 1981 — first-pass extraction of EE (and by extension E2)

- **Citation**: Back DJ, Bates M, Breckenridge AM, Hall JM, MacIver M, Orme
  ML, Park BK, Rowe PH. "The pharmacokinetics of ethinyloestradiol in women:
  effect of intestinal flora suppression." *Contraception* 24(4):447–469 (1981).
  And follow-up Back DJ et al. *Contraception* 1982/1990 portal-vein
  catheterization in cynomolgus monkeys.
- **Type**: Mass-balance / portal-vein catheterization tracer.
- **Key parameters**:
  - Gut-wall extraction fraction (EE): 0.44 (i.e. ~44% of absorbed dose
    metabolized in enterocytes before reaching portal vein)
  - Hepatic extraction adds further loss, giving net F ~40–50% for EE
  - For E2 the gut-wall extraction is *higher* and the bioavailability is
    only ~5%, implying gut-wall + hepatic extraction together = ~0.95
- **Limitations**: Done for EE not E2; cross-extrapolation has caveats since
  EE is not a 17β-HSD2 substrate.
- **Summary**: The reference for separating *gut wall* first-pass extraction
  from *hepatic* first-pass extraction. Our model should probably implement
  a gut-wall compartment with its own UGT1A8/1A10 + SULT1E1 clearance
  upstream of the portal vein, to reproduce the observation that oral E2
  reaches the liver with both substantial E1 and E1S already formed.

## 16. Risk–Benefit Assessment of EE (Dallmann group) — Simcyp PBPK for EE

- **Citation**: Zhang H, Wu X, Wang H, Mikus G, Wang W. "Risk-benefit
  assessment of ethinylestradiol using a physiologically-based pharmacokinetic
  modeling approach." *CPT Pharmacometrics Syst Pharmacol* 7(11):756–767 (2018).
  PMC6282492.
- **Type**: Simcyp PBPK (whole-body) for ethinylestradiol.
- **Routes**: Oral.
- **Key features**:
  - CYP3A4-centric metabolism; explicit DDI predictions vs CYP modulators
  - Bioavailability ~40–50%
  - Captures BTB/efficacy risk at 20 µg EE dose
- **Limitations**: EE not E2 — different first-pass profile, no SHBG induction
  modeled. Proprietary (Simcyp/Certara) — not open source.
- **Summary**: Useful as a *structural* template for PBPK of an estrogen
  contraceptive (compartments, plasma protein binding, hepatic CL_int from
  in vitro intrinsic clearance). Demonstrates that PBPK works for orally
  administered estrogens at the level needed for regulatory decisions.
  Pair with the Wang 2024 follow-up below.

## 17. Wang et al. 2024 — popPK/PBPK of prominent OCs **[anchor for popPK]**

- **Citation**: "Physiologically-based pharmacokinetic modeling of prominent
  oral contraceptive agents and applications in drug-drug interactions."
  *CPT Pharmacometrics Syst Pharmacol* (2024). PMID 38130003. PMC11015076.
- **Type**: PBPK (Simcyp) for EE, levonorgestrel, drospirenone, dienogest,
  norethindrone — extended to DDI predictions.
- **Routes**: Oral.
- **Summary**: The most recent integrated OC PBPK paper. Doesn't model E2
  directly but the framework (compartmental layout, plasma protein binding
  module, CYP-specific CL_int) is directly portable. Useful as a citation
  for the structural approach.

## 18. Aly *Transfeminine Science* — "Sublingual E2 in transfeminine people"

- **URL**: https://transfemscience.org/articles/sublingual-e2-transfem/
- **Type**: Narrative review aggregating Price 1997, Pines 1999, Devissaguet
  1999, Kuhnz 1993, Doll 2022, Cirrincione 2021.
- **Key consolidated parameters**:
  - SL bioavailability: ~10% absolute (vs ~5% PO)
  - SL/PO AUC ratio: 2–5× (median ~2.5×)
  - SL t½: "few hours" terminal — much shorter than PO 13–20 h because the
    PO ratio is sustained by E1/E1S reservoir refeed
  - Steady-state SL ~167 pg/mL E2 on typical 2 mg q12h regimen
- **Summary**: Excellent secondary literature review with curated graphs
  reproducing each primary study's curve. Best entry point for SL E2
  numerical anchors — paired with Doll 2022 LC-MS/MS data, this is
  sufficient to calibrate the SL route of our model.

## 19. O'Connell 1995 — comparative route review

- **Citation**: O'Connell MB. "Pharmacokinetic and pharmacologic variation
  between different estrogen products." *J Clin Pharmacol* 35(9 Suppl):18S–24S
  (1995). doi:10.1002/j.1552-4604.1995.tb04143.x.
- **Type**: Review.
- **Summary**: Pre-Kuhl-2005 reference covering oral micronized E2, EV,
  conjugated equine estrogens, transdermal patches. Notable for
  highlighting that transdermal bypasses first-pass and produces a
  near-physiological E1/E2 ratio (~1) at steady state — versus oral, where
  E1/E2 ≈ 5–7. Older but still cited.

---

## What I did NOT find published

- **A full E2/E1/E1S three-tracker PBPK** with explicit liver phase I/II
  enzyme splits. Karelina (#2) is the closest — and even there, the metabolic
  network is a single hepatic ODE block, not an explicit E1S
  re-circulation compartment.
- **A PBPK with simultaneous SHBG dynamics** (induction, time constant). The
  Plowchalk model holds SHBG static.
- **A PBPK validated on transdermal data**. estrannaise.js is the only model
  with patch parameters, and they are empirical 3-compartment fits — not
  mechanistic skin permeation models.
- **Any open-source Stan or Pyro Bayesian E2 model**. estrannaise.js's
  parameters were inferred in Julia (Esterlabe.jl) but that code is
  unreleased.
- **Sherwin sublingual paper** — search did not surface this; possible the
  user is recalling Sherwin & Gelfand 1985 IM-vs-oral cognition/PK paper,
  not a sublingual study.

## Recommended modeling decisions, based on prior art

1. **Compartments**: Start from the Plowchalk 7-compartment skeleton and add
   E1, E1S as parallel compartments that share the same tissue distribution.
   Karelina's 18-compartment expansion is probably overkill unless we need
   tissue-specific exposures (e.g. breast, brain).
2. **E1/E1S interconversion**: Use Ruder 1972 transfer fractions
   (ρE2→E1S = 0.65, ρE1→E1S = 0.54, ρE1S→E1 = 0.21, ρE1S→E2 = 0.014) as the
   constraint that any rate-constant set must satisfy at steady state.
3. **Clearances**: Anchor MCR(E2) ≈ 1400 L/d, MCR(E1) ≈ 2000 L/d,
   MCR(E1S) ≈ 150 L/d (Longcope 1968, Ruder 1972).
4. **First-pass**: Model gut wall and liver separately. Use F_gut ≈ 0.3–0.5,
   F_hep ≈ 0.1–0.2 to land on overall F_oral ≈ 0.05 (Back 1981 + matching
   Kuhnz oral data).
5. **IM esters**: Re-use the estrannaise three-compartment parameter set as
   the input forcing function. Don't re-fit unless we have new injection data.
6. **Transdermal**: Either re-use estrannaise's patch_tw / patch_ow
   parameters or model as a zero-order input over the dose-interval with a
   ~3-h absorption lag, calibrated to ~50 pg/mL steady-state E2 at 50 µg/d.
7. **Sublingual**: Model as a bolus into a "buccal" compartment with rapid
   ka (~1–2 h⁻¹), F_SL ≈ 0.10, then partial diversion to GI swallowed
   fraction (~50%) to recover the observed elevated E1 (Cirrincione 2021).
8. **SHBG feedback**: Out of scope for any published E2 PK model — we'll
   need to add it as a novel feature. Lindberg 2003 + Cauley 2003 provide
   the empirical SHBG rise curves to fit against.

---

## Files / URLs worth bookmarking

- https://en.wikipedia.org/wiki/Pharmacokinetics_of_estradiol (parameter
  table with 100+ citations)
- https://transfemscience.org/articles/injectable-e2-meta-analysis/ (IM data)
- https://transfemscience.org/articles/sublingual-e2-transfem/ (SL data)
- https://transfemscience.org/articles/oral-vs-transdermal-e2/ (route comparison)
- https://github.com/WHSAH/estrannaise.js (open source PK code, MIT)
- https://github.com/tiliaqt/transkit (Python notebooks)
- https://pmc.ncbi.nlm.nih.gov/articles/PMC5732473/ (Karelina 18-compartment PBPK)
- https://pmc.ncbi.nlm.nih.gov/articles/PMC302214/ (Ruder 1972 E1S kinetics)
- https://pmc.ncbi.nlm.nih.gov/articles/PMC297151/ (Longcope 1968 MCR/interconversion)