Physiology Reference

Use this page when you need to explain what the SDK is actually simulating, what its numbers mean, and which quantities are physiological, measurement-related, or purely protective software limits.

Scope: - pre-clinical simulation and retrospective research only - not a treatment recommendation engine - not a medical device

The short version: - the SDK simulates glucose-insulin physiology - it can add CGM measurement behavior - it reports against clinical interpretation anchors - it enforces separate software safety rails

For live presentations, the same material is also available as: - research/eucys_pack/pdf/EUCYS_05_PHYSIOLOGY_REFERENCE_BROCHURE.pdf - research/eucys_pack/pdf/EUCYS_06_JURY_PHYSIOLOGY_BRIEF.pdf

Keeping those four ideas separate is important. A glucose target, a sensor plausibility bound, and a supervisor stop rule are all numbers in mg/dL, but they do not mean the same thing.

1. The Three Layers

Layer	What it represents	Main SDK components	Examples
Physiological state	What happens inside the virtual patient	CustomPatientModel, BergmanPatientModel, patient profiles, stress events	glucose, insulin action, carbs on board, exercise, dawn phenomenon
Measurement layer	What the virtual CGM reports to the algorithm	SensorModel, named sensor profiles	lag, noise, drift, dropout, compression lows
Interpretation and protection	How results are summarized or constrained	clinical metrics, realism checks, SafetyConfig, supervisor	TIR, hypo bands, maximum bolus, critical-stop logic

2. What The SDK Physiologically Represents

Concept	SDK representation	Why it matters
Blood glucose	current_glucose in mg/dL	Primary physiological state and report axis
Insulin exposure	insulin doses, insulin-on-board (IOB), insulin action curve	Separates delivered insulin from insulin that is still active
Carbohydrate exposure	meal events, delayed absorption, carbs-on-board (COB)	Prevents meals from becoming impossible instant spikes
Basal physiology	homeostatic drift toward a basal target	Prevents the simplified model from drifting endlessly without disturbances
Circadian variation	optional dawn phenomenon window; Hovorka-style runs gate the Fourier EGP oscillator behind dawn_phenomenon_strength	Lets early-morning glucose rise be represented explicitly without hidden always-on drift
Exercise	bounded event intensity from 0.0 to 1.0	Adds glucose-lowering stress independent of insulin dosing
Stress / illness physiology	stress events, stress hormones/pseudo-hormones in supported models	Lets glucose rise without a meal because of stress-mediated insulin resistance and increased endogenous glucose production
Hypoglycemia defense systems	experimental counterregulation, HAAF, glucagon, and renal-clearance layer	Makes explicit which rescue mechanisms are implemented experimentally and which assumptions still need calibration
Stem-cell / islet graft research	optional Bergman-mode graft mass state M_graft with glucose-responsive insulin secretion	Lets researchers explore simplified engraftment, placement-delay, and rejection hypotheses without claiming clinical transplant prediction
Meal mismatch	meal_mismatch_epsilon	Distinguishes announced carbohydrate from true carbohydrate exposure
Measurement imperfections	CGM lag, bias, random noise, drift, dropout, compression lows	Lets algorithms be tested against what a sensor would report, not only perfect latent glucose
Empirical residual variation	optional additive residual profile	Adds real-data-like day-scale irregularity on top of the mechanistic trajectory

3. Numbers That Matter Clinically

These are interpretation anchors, not automatic proof that a simulation is clinically valid.

Quantity	Number	Meaning
Target glucose range used for TIR	70-180 mg/dL	Standard CGM target band used in SDK reports
Level 1 hypoglycemia	54-69 mg/dL	Below range, but above the level-2 threshold
Level 2 hypoglycemia	<54 mg/dL	Clinically important low-glucose threshold
Common adult CGM target	>70% time in 70-180 mg/dL	Interpretation target for many nonpregnant adults using CGM
Common adult time-below-range target	<4% below 70 mg/dL	Interpretable as less than about 58 minutes per day
Common adult severe-low target	<1% below 54 mg/dL	Interpretable as less than about 15 minutes per day

The glucose bands and CGM targets above follow the international Time in Range consensus and the 2026 ADA Standards of Care. The SDK uses them for reporting language; it does not claim that a run meeting those numbers is automatically clinically proven. Evidence Base collects the full source legend.

4. SDK Safety Rails Are A Different Kind Of Number

These values are deliberately conservative software controls. They protect simulations and supervisor behavior; they are not personalized clinical prescriptions.

Safety rail	SDK default	What it does
Hypoglycemia threshold	70 mg/dL	Marks low-glucose risk
Severe hypoglycemia threshold	54 mg/dL	Marks a more serious low-glucose state
Hyperglycemia threshold	250 mg/dL	Marks high-glucose risk for supervision
Critical termination rule	<40 mg/dL for 30 min	Stops a run after sustained extreme low glucose
Maximum bolus	5.0 U	Blocks a single excessive requested dose
Maximum insulin per hour	3.0 U	Limits recent cumulative delivery
Maximum insulin on board	4.0 U	Limits active insulin burden
Falling-trend stop	-2.0 mg/dL/min	Helps block dosing when glucose is falling quickly
Plausible sensor range	40-500 mg/dL	Broad fail-soft bound for incoming CGM-like readings
Maximum plausible CGM change	20 mg/dL per 5 min	Flags implausibly abrupt sensor movement

5. Patient Parameters

Parameter	Unit	Physiological meaning	Current validation range	Typical role in the SDK
initial_glucose	mg/dL	Starting glucose state	40-400	Sets the opening condition of a run
basal_insulin_rate	U/hour	Background insulin delivery	0.0-3.0	Basal exposure available to algorithms and reports
insulin_sensitivity / isf	mg/dL per U	How strongly 1 U of insulin lowers glucose	10-200	Converts insulin action into glucose effect
carb_factor / icr	g per U	Carbohydrate covered by 1 U of insulin	3-30	Couples announced meal size to bolus logic
glucose_decay_rate	per-minute coefficient	Homeostatic drift back toward a basal glucose target	0.0-0.2	Simplified stabilizing term, not a standalone clinical biomarker
glucose_absorption_rate	model gain	Strength of meal-to-glucose rise in the simplified model	0.0-0.2	Controls carbohydrate impact in the custom model
insulin_action_duration	min	Duration over which a dose remains active	60-720	Defines IOB decay and total insulin-action window
insulin_peak_time	min	Time of peak activity inside the dose-action curve	15-240, below duration	Shapes early versus late insulin effect
meal_mismatch_epsilon	ratio	true carbs / announced carbs	0.5-1.5	Models under- or over-estimation of meals
dawn_phenomenon_strength	mg/dL/hour	Extra early-morning rise or, in Hovorka-style mode, the scale of the dawn EGP oscillator	0-50	Adds explicit circadian disturbance
dawn_start_hour, dawn_end_hour	hour of day	Dawn-effect window	0-23, 0-24	Defines when dawn physiology is active
stem_cell_engraftment_percent	percent	Experimental functional beta-cell/islet graft fraction in Bergman mode	0+, usually 0-100 for demos	Scales glucose-responsive endogenous insulin secretion through M_graft
stem_cell_subq_fraction	ratio	Fraction of graft secretion routed through the subcutaneous insulin depot chain	0-1	Separates portal/direct appearance from delayed subcutaneous appearance
immune_rejection_rate	1/min	Exponential graft-mass decay coefficient	>=0	Simulates simplified loss of functional graft mass over time

One important reading tip: - glucose_decay_rate is a model coefficient, not a directly measured patient value. - insulin_sensitivity, ICR, basal rate, insulin duration, and starting glucose are the quantities that map most naturally to human-facing interpretation.

6. Built-In Starter Profiles

These are the CLI presets intended for first use and reproducible demos.

Preset	Initial glucose	Basal	ISF	ICR	Drift coefficient	Best use
stable-demo	130 mg/dL	0.2 U/h	40 mg/dL/U	15 g/U	0.001	smoke tests and teaching demos
stress-test	120 mg/dL	0.5 U/h	50 mg/dL/U	10 g/U	0.003	stronger disturbances and supervisor tests
endurance	140 mg/dL	0.0 U/h	20 mg/dL/U	25 g/U	0.0	long unattended software-endurance runs

7. Bundled Reference Patient Profiles

These profiles are shipped with the SDK for studies, demos, and physiological comparisons.

Profile	Initial glucose	Basal	ISF	ICR	Special physiology	Intended use
clinic_safe_baseline	140	0.50	50	10	none	calm benchmark baseline
clinic_safe_stress_meal	120	0.40	55	11	none	meal-stress benchmark
clinic_safe_hypo_prone	130	0.35	55	12	none	overnight hypo-risk challenge
clinic_safe_hyper_challenge	150	0.55	45	9	none	post-meal high-glucose challenge
clinic_safe_midnight	125	0.45	65	11	none	exercise-after-evening-meal challenge
clinic_safe_pizza	135	0.50	50	10	none	delayed-meal challenge
reference_free_living_t1d	151.7	0.50	50	10	Ohio-informed basal target 147, carb tail 270 min, meal mismatch 0.83	empirical free-living reference
reference_azt1d_t1d	135	0.50	50	10	dawn rise 4 mg/dL/h, meal mismatch 0.95	AZT1D-oriented reference
reference_hupa_ucm_t1d	130	0.50	50	10	dawn rise 8 mg/dL/h, meal mismatch 0.95	HUPA-UCM-oriented reference
default_patient	120	0.80	50	10	legacy simplified defaults	compatibility, not the best first demo choice
patient_559_config	130	0.90	45	12	slower drift, longer insulin action	alternate legacy virtual patient

Units: - glucose in mg/dL - basal in U/hour - ISF in mg/dL/U - ICR in g/U

Stem-Cell / Islet Graft Abstraction

The SDK contains a small Bergman-mode research extension for stem-cell or islet-graft hypotheses. It is deliberately simple:

\[ M_{graft}(0)=\frac{\text{engraftment percent}}{100} \]

\[ \frac{dM_{graft}}{dt}=-k_{reject}M_{graft} \]

\[ S_{graft}=\gamma M_{graft}\max(G-h,0) \]

The secretion term is split by placement:

\[ S_{plasma}=S_{graft}(1-f_{subq}), \quad S_{subq}=S_{graft}f_{subq} \]

S_plasma enters plasma insulin directly, while S_subq first enters the two-depot subcutaneous insulin absorption chain. This lets the simulator distinguish an immediate portal/direct abstraction from a delayed subcutaneous graft abstraction.

Important limitation: this is not a validated stem-cell therapy model. It does not simulate differentiation, vascularization, encapsulation, immune-cell populations, immunosuppressive drugs, or transplant eligibility. It is an educational algorithm-stress tool for asking "what if functional insulin secretion appeared, lagged, or decayed?"

Multi-Compartment Transplant Research Engine

For deeper experiments, iints.research.stem_cell_transplant adds a separate deterministic transplant engine. Unlike the minimal M_graft abstraction above, this runner tracks several graft-level states:

State	Meaning
immature_mass	cells that are present but not yet fully glucose-responsive
functional_mass	beta-like mass that can secrete insulin
vascularization	local blood-supply support for the graft
oxygenation	oxygen availability after vascularization, fibrosis, and graft demand
innate_inflammation	early inflammatory stress after implantation
adaptive_immunity	slower immune pressure against visible graft cells
fibrosis	encapsulation/scarring barrier that reduces diffusion and function
insulin_delay_pool_units	delayed insulin release pool for subcutaneous or encapsulated sites

The model uses placement presets:

Placement	Intended abstraction
portal	liver/portal-style graft with fast plasma insulin appearance but high early inflammatory exposure
subcutaneous	slower, initially oxygen-limited site with delayed insulin appearance
encapsulated	immune-shielded but diffusion/fibrosis-limited graft

The core update is still deliberately transparent:

\[ \frac{dV}{dt}=k_V(1-V)(1-0.75F)(1-0.35I_{innate}) \]

\[ O_{target}=\mathrm{clip}(0.10+0.90V-0.35F-0.10\max(0,M_{total}-1),0,1) \]

\[ \frac{dA}{dt}=k_A\,visibility\,M_{total}(1-S_{immuno})-k_{decay}A(0.3+S_{immuno}) \]

\[ M_{functional,t+1}=M_{functional}+M_{matured}-M_{death}-M_{dediff} \]

Insulin secretion is glucose-responsive:

\[ u_I = u_{max}M_{functional}O(1-0.55F)\sigma((G-G_{threshold})/slope) \]

The runner couples this graft output back into a Bergman virtual patient. Portal-style release is added to plasma insulin; delayed/subcutaneous release goes through the two-depot insulin absorption chain. This is much closer to a transplant stress simulator, but it remains pre-clinical research software, not a therapy predictor.

8. A Full Day That Actually Means Something

The current realistic day presets are intentionally not flat. They encode meals, delays, exercise, and a snack so that a glucose plot has a plausible daily story.

Preset event	Time	Value	Why it exists
breakfast	07:30	48 g carbs	first post-prandial excursion
lunch	12:15	62 g carbs	larger midday disturbance
exercise	12:45	intensity 0.35 for 30 min	glucose-lowering counterpressure after lunch
dinner	18:00	74 g carbs	largest daily meal challenge
snack	21:30	18 g carbs	small late-day excursion

The free_living_t1d preset uses a related but slightly lighter pattern:

Event	Time	True carbs / intensity	Reported carbs	Duration
breakfast	08:00	42 g	39.9 g	40 min
lunch	12:00	59 g	57.8 g	50 min
exercise	16:30	intensity 0.1	n/a	35 min
dinner	18:00	68 g	66.6 g	60 min
snack	21:30	12 g	12 g	40 min

That second table matters because it shows a realistic research distinction: - true carbs affect physiology - reported carbs are what the algorithm believes

9. Scenario Event Semantics

Event type	Main fields	Physiological meaning
meal	value, optional reported_value, absorption_delay_minutes, duration	Real carbohydrate intake with optional annotation error and delayed absorption
missed_meal	value	Carb exposure not properly announced to the controller
exercise	value from 0.0 to 1.0, duration	Increased glucose use / falling-glucose challenge
exercise_end	none required	Explicitly ends an exercise phase
sensor_error	value	Measurement disturbance, not true physiology
ratio_change	isf, icr, basal_rate, dia_minutes	Time-varying therapy ratios, useful for sensitivity studies

10. Sensor Profiles

The algorithm normally sees CGM-like readings, not necessarily the latent glucose state.

Sensor profile	Noise SD	Blood-to-ISF lag	ISF tau	Noise memory	Dropout probability	Drift cap	Compression low behavior
ideal	0 mg/dL	0 min	5 min	none	0	0 mg/dL	none
clinical_cgm	5 mg/dL	5 min	10 min	AR(1) colored noise	0	0 mg/dL	none
free_living_cgm	8 mg/dL	10 min	10 min	long-memory approximation, H=0.75	0.004	18 mg/dL	occasional 10-26 mg/dL lows
compression_prone	8.5 mg/dL	12 min	12 min	long-memory approximation, H=0.78	0.003	20 mg/dL	stronger 18-42 mg/dL compression lows

The purpose of these profiles is not to declare one CGM brand "correct." They provide repeatable measurement stress levels for algorithms and supervisor logic. The long-memory sensor mode is a compact multi-scale AR approximation inspired by fractional-noise theory; it is not an exact vendor CGM model or exact fBM sampler.

11. Model Families

Model	Main internal states	Strength	Best use
CustomPatientModel	glucose, IOB, COB, active insulin doses, active carb intakes, exercise state	fast, transparent, easy to stress-test	quick demos, regression tests, safety sweeps
BergmanPatientModel	plasma glucose G, remote insulin action X, plasma insulin I, stomach glucose, gut glucose	more mechanistic ODE structure with gut compartments	physiology-focused studies
HovorkaPatientModel	19-state experimental ODE: glucose compartments, gut absorption, subcutaneous insulin/glucagon depots, plasma hormones, insulin action, HAAF memory, GLUT4 exercise state	richer compartmental ODE-style physiology with exposed internal states	research simulations that need active insulin, glucagon, insulin effect, exercise, stress, and hypoglycemia-defense assumptions
EmpiricalResidualModel	additive day-scale residual template	adds real-data-like irregularity to an otherwise clean trajectory	realism studies and synthetic-mirror work

Bergman defaults

Parameter	Default	Meaning
p1	0.028 1/min	insulin-independent glucose uptake
p2	0.025 1/min	decay of remote insulin action
p3	5.0e-6 (mU/L)^-1 min^-2	insulin-action gain
Gb	120 mg/dL	basal glucose
n	0.23 1/min	insulin degradation
Ib	7 mU/L	basal plasma insulin
tau_meal	40 min	gastric-emptying time constant
k_abs	0.05 1/min	intestinal absorption rate
f_bio	0.90	absorbed fraction
gamma	0.0	endogenous insulin secretion gain; defaulted to zero for T1D mode

The ODE structure is inspired by the Bergman minimal-model tradition and meal-compartment work such as Dalla Man et al.; the SDK still remains a research simulator rather than a clinical digital twin.

Hovorka-style model notes

The experimental Hovorka-style model is intended for research runs that need clearer separation between delivered insulin, subcutaneous insulin absorption, plasma insulin, delayed insulin action, exogenous glucagon, exercise-driven GLUT4/NIMGU, and hypoglycemia-defense assumptions. It is useful for AI and MPC experiments because the controller can inspect internal state variables instead of treating glucose as the only signal.

Molecular context, not simulator state

The images below explain which proteins motivate two model abstractions. The ODE state does not contain atomic coordinates, and the AlphaFold models do not calculate glucose transport or hormone response.

GLUT4 · SLC2A4 · P14672Structural context for the bounded exercise-driven muscle-uptake term. The prediction does not model membrane translocation, transport rate, or exercise physiology.

Glucagon receptor · GCGR · P47871Structural context for glucagon-mediated liver rescue assumptions. The prediction contains no ligand, G protein, membrane, or hepatic glucose-production dynamics.

See Digital Twin Biology for the pLDDT key, model provenance, PAE workflow, and interpretation limits.

Current experimental extensions: - GLP-1-style gastric-emptying feedback slows meal appearance when intestinal glucose is high. - GLUT4/NIMGU exercise state increases non-insulin-mediated muscle glucose uptake during exercise. - Dawn/circadian EGP uses a bounded Fourier-series modifier, but only when dawn_phenomenon_strength is enabled. - HAAF and counterregulation expose repeated-low memory and blunted rescue behavior for research discussions. - Renal glucose clearance uses a smooth threshold/splay-style curve instead of a hard cutoff.

Important boundary: - the implementation is for simulation research and education - parameters are not personalized clinical estimates - stress and exercise modifiers are intentionally explicit so assumptions can be audited

12. Real-Data Physiology Calibration

The SDK now includes a calibration-audit step for processed real CGM datasets such as OhioT1DM. This does not identify a clinical digital twin. It measures empirical glucose-shape features and turns them into conservative simulator parameter hints.

Example:

iints research physiology-calibrate \
  --real-data data_packs/public/ohio_t1dm_full/processed/ohio_train.csv \
  --output-json results/physiology_calibration/ohio_report.json \
  --output-profile results/physiology_calibration/ohio_profile_hints.yaml

The report computes: - dataset-level mean, CV, time-in-range, hypo/high percentages, and rate-of-change tails - post-meal peak timing and peak amplitude when carbohydrate events are available - exercise-response summaries when exercise/activity flags are available - dawn rise estimates from overnight versus early-morning CGM medians

The generated profile hints include: - initial_glucose - basal_glucose_target - carb_absorption_duration_minutes - glucose_absorption_rate - max_glucose_rate_mgdl_per_min - dawn_phenomenon_strength

Interpretation rule: - use the hints as starting points for simulator presets - validate the resulting simulator runs with realism checks and AGP/report outputs - do not present the hints as individualized clinical parameters

Current OhioT1DM aggregate calibration run:

Split	Rows	Subjects	Mean glucose	TIR 70-180	Median post-meal peak	Raw hint summary
train	153,055	12	159.174 mg/dL	63.916%	110.0 min	initial 151.2, basal target 147.0, carb duration 331.5 min
test	35,925	12	161.584 mg/dL	63.468%	97.5 min	initial 153.233, basal target 148.0, carb duration 272.0 min
all	188,980	12	159.632 mg/dL	63.831%	110.0 min	initial 151.733, basal target 148.2, carb duration 323.0 min

The public reference_free_living_t1d profile uses a gate-compatible calibration compromise: it adopts the Ohio train basal target (147.0 mg/dL) while keeping carbohydrate absorption at 270.0 min because the raw train duration hint (331.5 min) made the current preset realism gate fail on baseline/free-living regression tests. This is intentional: real-data hints must pass simulator realism checks before becoming defaults.

13. Experimental Or Not Fully Calibrated Yet

Not fully represented	Current SDK handling
endogenous glucagon and epinephrine counterregulation	implemented experimentally in the Hovorka-style model; current runs should not be interpreted as calibrated hormone assays
HAAF and hypo-awareness memory	implemented as an experimental bounded memory state; not a clinically validated predictor of awareness or severe-hypoglycemia risk
exogenous glucagon PK/PD for dual-hormone pumps	implemented as an experimental Hovorka-style depot/plasma/effect layer with simulator safety caps; not emergency-dose guidance
illness, infection, menstrual cycle, steroid exposure	approximated through scenario disturbances and stress events; not a complete endocrine illness model
fat/protein mixed-meal kinetics	approximated with delayed meal profiles such as pizza_paradox
GLP-1 / incretin physiology	represented as a bounded meal-emptying modifier, not a personalized incretin hormone assay
circadian endocrine rhythms	represented as an optional dawn EGP oscillator, not a full cortisol/growth-hormone model
exercise GLUT4 translocation	represented as a bounded NIMGU state, not a calibrated muscle-biopsy model
renal glucose losses	implemented as a smooth threshold/splay-style clearance term; not a personalized renal function model
individualized pharmacokinetics for every insulin formulation	represented through configurable duration/peak parameters, not full formulation-specific PK for every commercial insulin
long-horizon adaptation in real patients	studied through scenarios and residuals, not a personalized adaptive physiological twin

14. Hypoglycemia Science Layer

The experimental hypoglycemia layer is organized around four explicit pillars. This is important because a simulator that only models carbohydrates and insulin can look plausible while still missing the body's rescue systems.

Pillar	Model idea	Status	Main source anchors
Endogenous counterregulation	Low glucose and fast downward trends drive rescue states that raise endogenous glucose production and reduce effective insulin sensitivity	experimental	gerich_1979_counterregulation, cryer_2013_haaf_mechanisms
HAAF memory	Recent time-below-range increases a slow memory state that blunts later rescue response	experimental	cryer_2013_haaf_mechanisms, cryer_2013_haaf_diabetes
Exogenous glucagon PK/PD	Dual-hormone research separates delivered glucagon, subcutaneous depot, plasma appearance, and delayed glucose effect	experimental	lv_2013_exogenous_glucagon_pk, haidar_2013_insulin_glucagon_pk, haidar_2013_dual_hormone_ap
Renal glucose clearance	Hyperglycemic renal loss is represented as a smooth threshold/splay-style curve instead of an abrupt cutoff	experimental	hummel_2018_renal_glucose_handling, defronzo_2013_renal_reabsorption_splay

For the full explanation and equations, see Hypoglycemia Science Model.

15. How To Use This In A Presentation

For a doctor: - start with the glucose bands, hypo thresholds, and what the patient model includes - then show that measurement imperfections and supervisor limits are separate layers

For an engineer: - start with the patient-parameter table and model-family table - then show that the same physiology can be replayed under different sensor and algorithm conditions

For EUCYS: - say that the SDK is not only "drawing glucose curves" - say that it exposes the assumptions behind the curves: patient ratios, meals, exercise, sensor behavior, and safety rails - use the day table and patient-profile table as concrete evidence that the simulator is parameterized, inspectable, and reproducible

16. Source Trail

Use these pages together: - Evidence Base for the literature legend - Scientific Workflow for study design - Study Analysis for outcome interpretation - API Reference for implementation symbols

Key external anchors used by this page: - ADA Professional Practice Committee, Glycemic Goals, Hypoglycemia, and Hyperglycemic Crises: Standards of Care in Diabetes-2026. - Battelino et al., Clinical Targets for Continuous Glucose Monitoring Data Interpretation. - Bergman et al., Quantitative estimation of insulin sensitivity. - Hovorka et al., Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes. - Dalla Man et al., Meal simulation model of the glucose-insulin system. - Gerich et al., Hormonal mechanisms of recovery from insulin-induced hypoglycemia in man. - Cryer, Mechanisms of Hypoglycemia-Associated Autonomic Failure in Diabetes. - Lv et al., Pharmacokinetics modeling of exogenous glucagon in type 1 diabetes mellitus patients. - Hummel et al., Physiology of renal glucose handling via SGLT1, SGLT2 and GLUT2. - Riddell et al., Exercise management in type 1 diabetes: a consensus statement. - Mandelbrot and Van Ness, Fractional Brownian Motions, Fractional Noises and Applications. - Campbell et al., Pathogenesis of the Dawn Phenomenon in Patients with Insulin-Dependent Diabetes Mellitus. - Richter and Hargreaves, Exercise, GLUT4, and skeletal muscle glucose uptake. - Naslund et al., GLP-1 slows solid gastric emptying and inhibits insulin, glucagon, and PYY release in humans.

Mathematical Appendix: Tissue-Specific Resistance

To isolate molecular receptor affinity, peripheral resistance, and hepatic resistance, the Hovorka-style insulin action gains are scaled deterministically before ODE integration. The molecular scalar (\(A_{scalar}\)) applies to the receptor/action channels globally, while the GTEx-inspired muscle and liver scalars (\(M_{scalar}\) and \(L_{scalar}\)) separate peripheral glucose disposal from hepatic EGP suppression. This ensures mathematical stability at \(t=0\) while enabling dynamic stressor testing:

\[k_{b1} = S_{IT} \cdot k_{a1} \cdot Sens_{overall} \cdot A_{scalar}$$ $$k_{b2} = S_{ID} \cdot k_{a2} \cdot Sens_{overall} \cdot A_{scalar} \cdot M_{scalar}$$ $$k_{b3} = S_{IE} \cdot k_{a3} \cdot Sens_{overall} \cdot A_{scalar} \cdot L_{scalar}\]

This formulation allows the simulator to trigger global INSR-style resistance (driven by \(A_{scalar}\)), fasting hyperglycemia (driven by a reduction in \(L_{scalar}\)), or post-prandial absorption failures (driven by a reduction in \(M_{scalar}\)), forcing candidate algorithms to handle distinct physiological phenotypes.