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Sensitivity-driven Personalization of a Glucoregulatory Model for Digital Twin Therapeutics in Type 1 Diabetes

Clara Escorihuela-Altaba, Vihangkumar V. Naik, Eleonora Manzoni, Jose Garcia-Tirado

arXiv:2609.31259v1eess.SYcs.SY

TL;DR

Individual glucose modeling requires reliable parameter identification, yet parameter influence in dynamic physiological systems varies over time and with input conditions. This study extends time-series Sobol sensitivity analysis across participants and conditions, reporting a consistent influential subset and lower prediction error with individualized parameters.

  • Problem

    In dynamic physiological systems, parameter relevance varies over time and with input conditions, so a single-condition sensitivity ranking may miss important influences.

    Source: §2.2 · p. 4

  • Method

    The study combines parameter ranks across dynamic conditions into a global ranking and uses the influential subset for individualized HGM identification.

    Source: §2.4 · p. 5, §5 · p. 14

  • Results

    Approximately 60% reductions in RMSEav and RMSENP H at 15-, 30-, and 60-minute PHs were reported for individually identified LES parameters versus population parameters in both modes.

    Source: §4 · p. 12

  • Takeaways & Limitations

    A consistent influential parameter subset can simplify identification by avoiding computationally intensive global sensitivity analysis for every new individual.

    Source: §4 · p. 11, §5 · p. 14

    Structural and practical identifiability were not explicitly assessed, and Sobol assumes independent parameters despite possible HGM correlations that can hinder unique estimation.

    Source: §4 · p. 11

Abstract

from arXiv · show

Digital twins are increasingly used in diabetes research, but reproducing individual glucose dynamics requires accurate identification of glucoregulatory model parameters. Traditional sensitivity analysis can identify influential parameters, yet a ranking based on limited conditions may miss parameters that matter during specific disturbances or for particular individuals. We therefore examine both the magnitude and timing of parameter influence across dynamic input-output conditions and assess whether a common ranking holds across participants. We analyze the Hovorka glucoregulatory model using data from 192 participants receiving automated insulin delivery therapy in the Type 1 Diabetes and Exercise Initiative dataset. We extend Sobol sensitivity analysis to time series and rank parameter influence under four conditions: full-day profiles, isolated meal disturbances, insulin bolus injections, and postprandial responses. We combine the condition-specific results into a global ranking and use it to select parameters for participant-specific identification. Compared with population parameters, identification restricted to the sensitivity-derived subset reduces the root mean square error of 60-minute glucose predictions by 60%, to approximately 31 mg/dL. These findings suggest that a global ranking can capture parameter influence across individuals and dynamic conditions. By narrowing the parameters requiring identification, this approach reduces computational cost and could accelerate the development of personalized diabetes digital twins.

1 Introduction

The introduction motivates personalized glucose modeling by noting that daily-life variability challenges current AID performance and that individual models depend on reliable parameter identification. It presents sensitivity analysis across dynamic conditions as a way to select parameters for participant-specific modeling.

1 Introduction

  • AID performance is better overnight than during variable daytime conditions involving meals and physical activity.Personalization is presented as a route toward addressing individual differences in daily-life therapy needs.Source: §1 · p. 1
  • A medical digital twin is a measurement-informed virtual representation that supports monitoring, simulation, prediction, or therapeutic decisions.Its computational model may be data-driven, physiological, or hybrid.Source: §1 · p. 2
  • Forecasting uses known current states and unknown future inputs, whereas intervention-informed prediction prescribes future inputs such as meals, insulin, or activity.The paper distinguishes these as two operational modes of the same individualized model.Source: §1 · p. 2
  • Parameter identification is challenged by limited data, parameter correlations, and identifiability issues, while parameter relevance in dynamic systems varies over time and with inputs.The introduction identifies global sensitivity analysis as a way to prioritize influential parameters for estimation.Source: §1 · p. 2
  • The earlier time-series Sobol ranking study used only one simulated and one real individual, limiting assessment of inter-subject variability and generality.This work extends that methodology to a large T1DEXI cohort to establish a population-level HGM ranking and prioritize parameters for subject-specific identification.Source: §1 · p. 2

2 Methods

The methods combine time-varying Sobol sensitivity analysis across multiple glucose–insulin conditions with a participant-specific parameter-identification and prediction-evaluation procedure.

2.1 Hovorka glucoregulatory model for type 1 diabetes

  • The HGM represents carbohydrate digestion and absorption, subcutaneous insulin absorption, and glucose-insulin regulation in response to physiology, meals, and insulin therapy.The model output is measured bloodstream glucose; the paper refers readers to its appendix and Table 1 for model equations and state, input, and parameter details.Source: §2.1 · p. 2

2.2 Sobol sensitivity analysis

  • Dynamic Sobol indices address time-varying output variance and condition-dependent parameter influence by evaluating the model across the input-output sequence.The method produces temporal first- and total-order indices; weighted indices are averaged to quantify parameter influence across the sequence.Source: §2.2 · p. 4

2.3 The T1DEXI adult cohort dataset

  • The analysis includes 192 adults receiving closed-loop therapy, with seven days for identification and three for validation.A one-day identification-data window is used for participant-specific sensitivity analysis; inclusion required at least 10 consecutive days meeting missing-data criteria.Source: §2.3 · p. 4

2.4 Global parameter ranking

  • Four rankings cover all-day data, meals without boluses, isolated boluses, and postprandial responses, then are combined using equally weighted condition ranks.Event-specific sensitivity is calculated in a 20-minute window centered on each event; the all-day ranking uses average first-order indices across participants.Source: §2.4 · p. 5

2.5 Parameter identification

  • For each participant, parameters are identified in global-rank order by nonlinear least squares minimizing average RMSE across prediction windows.The procedure stops when average RMSE plateaus; identification uses the intervention-informed mode with future inputs assumed available.Source: §2.5 · pp. 5–6

2.6 Model performance analysis

  • Performance is assessed at 15-, 30-, and 60-minute horizons in intervention-informed and forecasting modes.Intervention-informed predictions use true future insulin and meal inputs; forecasting assumes no future bolus or carbohydrate inputs and holds basal delivery constant.Source: §2.6 · p. 6

3 Results

Parameter rankings are consistent as participants are added, but relative influence changes across dynamic conditions. The global ranking guides participant-specific identification, whose predictive gains diminish after adding τS.

3.1 Global parameter ranking

  • VI and ke rank highest overall, while their importance decreases postprandially as VG, τD, and τS become more relevant.Source: §3.1 · p. 8
  • Rankings remain consistent as participants are added, with Kendall’s W and p-values indicating strong concordance from the earliest participants onward.Figure 4 presents concordance and p-values as participants are added one at a time.Source: §3.1 · p. 8, Figure 4 · p. 8
  • A majority-vote strategy combines results across dynamic conditions and 30 participants into one global parameter ranking.Source: §3.1 · p. 8

3.2 Parameter identification and model performance analysis

  • Parameters are added to identification sequentially in global-rank order until average RMSE reaches a plateau; performance is assessed all day and in two-hour windows around major disturbances.The disturbance windows cover meal-only, bolus-injection, and postprandial events.Source: §3.2 · p. 8
  • Beyond τS, further additions yield only marginal population-level gains, though within-participant tests detect consistent reductions; progressively larger subsets improve more participants’ RMSEN60, with τD important in “all events.”The reported marginal-gain pattern also appears in the “all events” case.Source: §3.2 · pp. 9–10
  • Intervention-informed and forecasting examples show remarkably similar prediction accuracy, differing most when meal or bolus information falls within the prediction horizon.The examples cover two participants over a validation day.Source: §3.2 · p. 10

4 Discussion

The sensitivity rankings were broadly consistent across participants, but parameter influence varied with dynamic conditions. Individual identification improved glucose-prediction errors, while identifiability and evaluation caveats constrain what that improvement establishes.

4 Discussion

  • VI and ke ranked in the top two across cohorts and dynamic conditions; τS and τD became more influential during postprandial responses.The relative importance of remaining parameters varied by condition, supporting sensitivity analysis across long sequences with diverse inputs.Source: §4 · p. 11
  • Stable, significant Kendall’s W values as cohort size increased indicate similar participant sensitivity patterns, allowing a common influential subset while retaining individual parameter identification.A common subset can substantially reduce identification computation time given the high cost of sensitivity analysis.Source: §4 · p. 11
  • Structural and practical identifiability were not assessed, and VI, ke, VG, and SI2 estimates often reached admissible bounds, suggesting local identifiability limits or parameter compensation.Sobol analysis assumes statistically independent inputs, although some HGM parameters may be correlated.Source: §4 · p. 11, Figure 11 · p. 14
  • The sensitivity-analysis framework can extend to other HGM variants and compartmental physiological models, including models expanded to represent exercise dynamics.The baseline model does not explicitly represent physical activity, although T1DEXI contains physical-activity information.Source: §4 · p. 12
  • Approximately 60% reductions in RMSEav and RMSENP H at PHs of 15, 30 and 60 min were observed with individually identified LES parameters versus population-based parameters in both prediction modes.The reductions were reported across both intervention-informed and forecasting modes.Source: §4 · p. 12
  • Prediction errors were higher for all events than all day, and informed predictions were not significantly better than forecasting predictions under the reported conditions.Meal and bolus reports may not align with CGM dynamics; rapid, nonlinear meal and insulin responses make event conditions especially challenging.Source: §4 · p. 12, Figure 9 · p. 12
  • The 60-minute horizon was chosen as a clinically relevant short-term compromise, and sensitivity-index magnitudes depend partly on user-selected parameter sampling bounds and input scaling.The ranking method is not inherently limited to 60 minutes and can be extended to longer windows.Source: §4 · pp. 11, 13
  • RMSE measures prediction against clinical observations but does not fully validate a physiological digital twin; counterfactual or therapy-planning use may need plausibility and intervention-consistency criteria.The appropriate validation metrics, fitting approach, and forecasting method depend on the intended application.Source: §4 · p. 13

5 Conclusion

This study derives a global HGM parameter ranking from diverse dynamic conditions and participant data, then uses it to prioritize parameters for individual identification. The resulting models improve prediction relative to population parameters and perform similarly in intervention-informed and forecasting modes.

5 Conclusion

  • The global HGM ranking accounts for inter-subject variability and diverse real-life conditions, avoiding computationally intensive global sensitivity analysis for every new individual.The study assessed parameter influence by both magnitude and temporal relevance across individuals.Source: §5 · p. 14
  • Accurate identification was achieved with a small subset of the most influential parameters, while additional parameters provided only marginal prediction-accuracy improvements.Source: §5 · p. 14
  • Identified models achieved nearly identical glucose-prediction performance in intervention-informed and forecasting modes, including when future meal and insulin information was unavailable.The authors state that this supports applicability to real-world forecasting and decision-support systems.Source: §5 · p. 15
  • The proposed sensitivity analysis is applicable beyond the HGM to compartmental physiological models for prioritizing parameters during identification.Source: §5 · p. 15

Ethics statement

The study did not involve human participants or animals.

Ethics statement

  • Ethical approval and informed consent were not required because the study involved no human participants or animals.Source: Ethics statement · p. 15

Funding statement

The authors report that the study received no external funding.

Funding statement

A Hovorka glucoregulatory model

The HGM is described as a model with three submodels, followed by its equations and a corresponding model output.

A Hovorka glucoregulatory model

B Tuning of the Extended Kalman Filter

The Extended Kalman Filter configuration specifies initial-state, process-noise, and measurement-noise settings.

Tuning of the Extended Kalman Filter

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