QSP Models of Diabetes Therapies

1. What Is a QSP Model of Diabetes?

Quantitative systems pharmacology (QSP) uses mechanistic mathematical models to connect pharmacology with physiology, disease biology, biomarkers, and clinical outcomes. Unlike a model focused only on drug concentration or a single response endpoint, a QSP model attempts to represent a network of interacting biological processes.

Diabetes is a natural setting for this type of modeling because glucose regulation is inherently a dynamic system. Glucose production, glucose utilization, insulin secretion, insulin action, glucagon signaling, incretin effects, renal glucose handling, body weight, and beta-cell function interact over multiple time scales.

2. What Questions Can Diabetes QSP Models Answer?

A diabetes QSP model can address questions spanning molecular pharmacology, physiology, disease progression, treatment response, and combination therapy.

These questions illustrate a major distinction between conventional exposure-response analysis and QSP. An exposure-response model may quantify the relationship between drug exposure and HbA1c, whereas a QSP model attempts to explain that relationship through intermediate biological mechanisms.

3. The Biological System Being Modeled

Glucose homeostasis emerges from interactions among several physiological processes. A QSP model does not necessarily need to represent every molecular pathway, but it should include the processes necessary to address the scientific question.

The important point is that these components are not independent. Insulin affects several tissues, glucose affects insulin secretion, glucagon affects hepatic glucose production, and changes in body weight can feed back into insulin sensitivity and energy balance.

4. From Physiology to Differential Equations

At the heart of a QSP model is a collection of state variables that change over time. A generic physiological state can be represented by a vector:

Here, the variables might represent glucose, insulin, beta-cell functional state, insulin sensitivity, and another hormone or physiological state. The exact definitions depend on the model.

The system can then be represented abstractly as:

where \(\mathbf{x}\) represents physiological states, \(\mathbf{u}\) represents external inputs such as meals or drug administration, and \(\boldsymbol{\theta}\) represents model parameters.

5. A Simplified Glucose–Insulin Model

A useful conceptual starting point is to describe glucose as a balance between glucose entering the system and glucose leaving the system.

Here, \(R_a\) can represent glucose appearance from meals or other sources, \(R_{hep}\) can represent net hepatic glucose output, and \(R_{periph}\) can represent peripheral glucose utilization.

Insulin can then influence peripheral glucose disposal and hepatic glucose production. A simplified representation might be:

and:

These equations are deliberately simplified. Real QSP models may distinguish multiple tissues, compartments, hormone concentrations, receptor signaling states, nonlinear responses, delays, and disease progression.

The value of the simplified model is conceptual: it demonstrates how a drug can affect glucose indirectly by changing one or more physiological mechanisms rather than acting on glucose itself.

6. Representing Insulin Resistance

Insulin resistance can be represented in a QSP model by changing parameters governing insulin-mediated glucose disposal or suppression of endogenous glucose production.

For example, if \(S_I\) represents insulin sensitivity, a simplified model might write:

A reduction in \(S_I\) therefore reduces insulin-mediated glucose disposal for the same insulin and glucose concentrations.

A disease model can go further by allowing insulin sensitivity to change over time:

where \(W\) could represent body weight or another metabolic state.

7. Modeling Beta-Cell Function

Progressive impairment of pancreatic beta-cell function is an important component of many models of diabetes progression. QSP models can represent both insulin secretion and the changing capacity of the beta-cell system.

A simplified secretion relationship might be written as:

where \(S_\beta\) represents beta-cell secretory capacity and \(g(G)\) describes the glucose dependence of secretion.

The beta-cell state itself can be modeled dynamically:

The exact form is model-dependent. The important QSP concept is that disease progression can be represented as a changing biological state rather than as a static baseline covariate.

8. How Diabetes Therapies Enter a QSP Model

A therapy is represented by linking drug exposure to one or more biological mechanisms. The model can then propagate those mechanistic effects through the glucose-regulation network.

The table is intentionally conceptual. A QSP model should not assume that a drug class has a single mechanism. For example, the biological effects represented for a particular therapy depend on the scientific question, evidence base, and intended use of the model.

9. Modeling Insulin Therapy

Insulin provides a relatively intuitive example of how pharmacology can be connected to a glucose–insulin system.

A simple model can separate exogenous insulin input from endogenous insulin secretion:

The exogenous component can itself be linked to an administration model:

The resulting insulin concentration or effect can then modify glucose disposal and hepatic glucose production.

More sophisticated models can distinguish rapid-acting and basal insulin, absorption from subcutaneous tissue, insulin kinetics, insulin action, delayed effects, and the relationship between insulin dosing and hypoglycemia risk.

10. Modeling GLP-1 Receptor Agonists

GLP-1 receptor agonists provide an example of a therapy whose effects can span several physiological pathways. Depending on the model, these may include glucose-dependent insulin secretion, glucagon regulation, gastric processes, appetite, food intake, and body weight.

A simplified receptor-effect relationship can be represented as:

The resulting effect can then be connected to downstream physiological processes. For example:

A more comprehensive QSP model can simultaneously represent glycemic and weight-related pathways. This is useful when the scientific question concerns the interaction between glucose control, energy intake, body weight, and insulin sensitivity.

Importantly, model structure should be supported by evidence. A QSP model should distinguish established mechanisms from hypotheses or phenomenological relationships introduced because they improve representation of observed data.

11. Modeling SGLT2 Inhibition

SGLT2 inhibitors illustrate how a QSP model can incorporate an organ-level mechanism that directly changes glucose disposition.

In a simplified representation, filtered glucose can be partitioned into reabsorbed and excreted glucose:

An SGLT2 inhibitor can then be represented as reducing the capacity for renal glucose reabsorption:

The resulting increase in urinary glucose excretion changes whole-body glucose balance. In a broader model, this can propagate into plasma glucose, insulin requirements, body weight, and other endpoints.

12. Modeling Metformin

Metformin is a particularly useful example for QSP because its pharmacology is not naturally summarized by a single simple downstream effect. Mechanistic work has described effects across tissues and metabolic pathways, including effects relevant to hepatic glucose production and intestinal biology.

A QSP representation might therefore include one or more mechanistic effect terms rather than treating metformin as a generic direct glucose-lowering input:

The individual components should only be included when they are supported by the purpose and evidence base of the model. Adding biological detail simply because it is available can increase parameter uncertainty without improving the model's ability to answer the intended question.

13. Linking Pharmacokinetics to Pharmacological Effect

QSP models often need a PK layer because the biological effect of a therapy depends on drug exposure over time.

A conceptual drug-development chain is:

For a simple exposure-response relationship:

the concentration \(C(t)\) generated by the PK model becomes the input to the pharmacological effect model.

In a QSP model, however, the effect may not stop at a single response variable. Target engagement can influence intermediate signaling states, which then influence physiological states such as insulin secretion or glucose utilization.

14. Connecting Hidden States to Biomarkers

Many biologically important QSP states are not directly observable. The model therefore needs an observation layer that connects latent mechanisms to measured data.

Here, \(y_j(t)\) represents an observed biomarker or clinical measurement, while \(h_j(\cdot)\) maps the underlying model states to that observation.

This distinction between model state and observable is fundamental to QSP. A model may estimate an underlying biological state that cannot be measured directly, but the inference is only useful if the available observations contain sufficient information about that state.

15. Why QSP Is Useful for Combination Therapies

Diabetes therapies frequently act through different biological mechanisms. A systems model can represent those mechanisms simultaneously and investigate how their effects propagate through the same physiological network.

Suppose two drugs act through distinct mechanisms \(M_1\) and \(M_2\). A simplified model might contain:

The combined treatment effect does not necessarily have to equal the arithmetic sum of two independently estimated clinical effects. The system can generate nonlinear interactions because each therapy changes the physiological state in which the other therapy operates.

Combination simulations should nevertheless be treated as model-based hypotheses. They require appropriate validation before being interpreted as evidence of clinical benefit.

16. Modeling Diabetes Progression

One of the major advantages of a mechanistic disease model is the ability to represent changing physiology over time.

For example, beta-cell functional capacity might be represented by:

Insulin sensitivity could similarly be represented as a dynamic state:

The resulting model can distinguish between:

• an intervention that changes glucose immediately;
• an intervention that changes insulin sensitivity over weeks or months;
• an intervention that alters a disease-process state;
• and an intervention whose apparent effect depends on disease stage.

This distinction can be important when interpreting longitudinal clinical data because the observed response may reflect both the treatment effect and the changing underlying disease state.

17. Worked Example: A Simplified Diabetes QSP Simulation

Consider a hypothetical patient represented by a simplified glucose–insulin model. Assume that before treatment:

• baseline glucose is \(G_0=180\) mg/dL;
• insulin sensitivity is represented by \(S_I=0.50\) in model-specific units;
• beta-cell secretory capacity is represented by \(S_\beta=0.70\);
• the patient receives a therapy that increases effective insulin sensitivity by 20% in the model.

Step 1: Represent the treatment effect

Step 2: Propagate the change through glucose disposal

Using the simplified relationship:

the treatment increases the coefficient multiplying insulin-mediated glucose disposal from 0.50 to 0.60.

Step 3: Allow the system to evolve

The model numerically solves the coupled differential equations for glucose, insulin, and any other included states. The resulting trajectory might show glucose declining toward a new dynamic range rather than jumping instantaneously to a fixed target.

Step 4: Generate an observable

A longer-term model could translate simulated glucose exposure into an HbA1c-related output:

The exact observation function must be specified and validated against the data used to construct the model.

18. How Are Diabetes QSP Models Parameterized?

A QSP model can draw parameters from many sources, including biochemical experiments, animal studies, human physiology studies, clinical pharmacology analyses, biomarker data, and clinical trials.

One of the defining features of QSP is this integration of evidence across biological scales. A model can provide a common mathematical framework in which evidence from different experimental levels is connected.

19. Representing Inter-Individual Variability

A single deterministic QSP model describes one parameter set. Clinical populations, however, contain patients with different physiological characteristics.

Individual parameters can be represented as:

where \(\theta_{pop}\) represents a population value and \(\eta_i\) represents an individual deviation.

Covariates can also be incorporated:

This creates a bridge between mechanistic systems pharmacology and population-level modeling. Patient characteristics can modify physiological states or parameters, allowing simulations to explore heterogeneous treatment responses.

20. Sensitivity Analysis in Diabetes QSP

Large QSP models can contain many parameters. Sensitivity analysis asks which parameters have the greatest influence on a selected model output.

A local sensitivity can be expressed conceptually as:

Large absolute values indicate that relatively small proportional changes in a parameter can have relatively large effects on the output.

For diabetes models, sensitivity analysis might ask:

• Which parameters most influence fasting glucose?
• Which mechanisms determine the simulated HbA1c response?
• Which parameters control treatment response heterogeneity?
• Which biological measurements would most reduce uncertainty?
• Which mechanisms are important for a combination-treatment prediction?

21. Identifiability and Model Complexity

A biologically detailed model is not automatically a well-informed model. If several parameters produce similar predictions, the available data may not contain enough information to estimate them uniquely.

Two related concepts are important:

• Structural identifiability: whether parameters could theoretically be uniquely determined from ideal observations.
• Practical identifiability: whether the available data are sufficiently informative to estimate the parameters with useful precision.

For example, if two mechanisms affect glucose in nearly identical ways and only sparse glucose measurements are available, the data may support the combined effect without distinguishing the individual mechanisms.

22. How Are QSP Models Evaluated?

Model development should include multiple forms of evaluation rather than relying on a single measure of fit.

1. Internal consistency. Does the model behave coherently across physiological states and limiting cases?
2. Calibration. Can the model reproduce the datasets used for parameter estimation?
3. Visual predictive checks. Do simulated trajectories reproduce important features of observed data?
4. External validation. Can the model reproduce data that were not used during development?
5. Sensitivity analysis. Which assumptions and parameters drive the predictions?
6. Predictive qualification. Is the model sufficiently credible for the intended application?

QSP model credibility is therefore tied to the intended use. A model used to generate a mechanistic hypothesis may require a different level of evidence than a model intended to support a consequential drug-development decision.

Current regulatory and model-informed drug-development programs increasingly emphasize fit-for-purpose evaluation of quantitative models rather than assuming that one universal validation standard applies to every application.

23. What Can Diabetes QSP Models Simulate?

Once a model has been appropriately developed and evaluated, simulations can explore conditions that may not yet have been directly studied.

• Alternative dose levels or exposure profiles.
• Different dosing schedules.
• Changes in insulin sensitivity.
• Different levels of beta-cell function.
• Variation in baseline glucose control.
• Changes in body weight or metabolic state.
• Combination therapies acting through different mechanisms.
• Potential biomarker trajectories.
• Mechanistic explanations for heterogeneous treatment response.
• Hypotheses about which biological measurements would be most informative in a future study.

Simulation is especially powerful when the model integrates mechanisms that would otherwise be difficult to study simultaneously in a clinical trial.

24. Worked Concept: Combining Two Mechanistically Different Therapies

Consider a hypothetical model containing two therapies:

• Therapy A: increases insulin sensitivity.
• Therapy B: increases urinary glucose excretion.

The first therapy could modify:

while the second could modify:

The whole-body glucose equation becomes:

Because the two treatments enter different terms, the model can explore their simultaneous effects without requiring that the combined response be specified in advance.

The simulation can then be compared with clinical combination-treatment data when available. If the observed combination response differs systematically from the model prediction, that discrepancy can provide information about missing mechanisms, incorrect assumptions, or parameter uncertainty.

25. Prediction Is Not the Same as Certainty

Every QSP prediction contains uncertainty. Sources include uncertain parameters, measurement error, structural assumptions, missing mechanisms, and uncertainty about how well the model generalizes to a new population or treatment condition.

A useful conceptual decomposition is:

Simulation should therefore be performed over plausible parameter distributions or scenarios when uncertainty is material, rather than presenting one deterministic trajectory as though it were known with certainty.

26. A Practical Workflow for Building a Diabetes QSP Model

1. Define the scientific question. Decide what the model is intended to explain or predict.
2. Define the system boundary. Identify which tissues, pathways, biomarkers, and outcomes need to be represented.
3. Build the physiological model. Represent glucose, insulin, relevant hormones, tissue processes, and disease states.
4. Add disease mechanisms. Introduce insulin resistance, beta-cell dysfunction, altered renal handling, or other processes required by the question.
5. Add the pharmacology. Connect drug exposure to molecular targets and downstream mechanisms.
6. Connect mechanisms to observations. Map model states to glucose, insulin, HbA1c, weight, biomarkers, and other measured endpoints.
7. Parameterize from evidence. Integrate experimental, preclinical, clinical, and literature information.
8. Calibrate and evaluate. Test whether the model reproduces relevant observations.
9. Perform sensitivity and uncertainty analysis. Identify the parameters and assumptions that control predictions.
10. Validate where possible. Compare predictions with independent data.
11. Simulate the intended application. Use the model only within the scope for which its credibility has been established.

This workflow emphasizes a central QSP principle: the model should be built around the scientific question rather than around the maximum amount of biological detail that can be represented.

27. QSP vs PK/PD vs Population PK

These modeling approaches overlap, but they answer different types of questions.

These are not mutually exclusive categories. A diabetes QSP model may contain a PK model and pharmacodynamic relationships as components of a larger mechanistic system.

28. What Diabetes QSP Models Do Not Tell Us Automatically

QSP models can provide mechanistic insight, but their outputs remain conditional on the evidence and assumptions used to construct them.

• A mechanistic diagram is not proof of causality. A pathway included in a model may represent a hypothesis rather than an established causal relationship.
• More detail does not automatically mean more predictive accuracy.
• Parameter estimates depend on model structure and available data.
• Different models can sometimes reproduce the same clinical endpoint.
• Predictions outside the calibration domain require particular caution.
• Combination-treatment predictions are model-based hypotheses unless independently supported.
• Patient-level predictions require adequate representation of individual variability and sufficient information to characterize it.

29. Applications in Diabetes Drug Development

QSP and related model-informed approaches can contribute to several stages of drug development.

FDA describes quantitative systems pharmacology among the quantitative approaches that can support model-informed drug development, alongside population PK, PBPK, exposure-response models, and related methods.

30. Why Diabetes Is a Particularly Useful QSP Domain

Diabetes presents a multi-scale modeling problem: molecular targets influence cellular signaling, cellular processes influence tissue physiology, tissue physiology influences glucose regulation, and the resulting dynamics appear in clinical biomarkers and outcomes.

Reviews of systems pharmacology in type 2 diabetes have specifically highlighted the need to connect molecular, physiological, and disease-level organization within multi-level mathematical models.

This makes diabetes a useful domain for learning QSP because the model can be constructed progressively:

1. Start with glucose and insulin.
2. Add insulin sensitivity.
3. Add beta-cell function.
4. Add glucagon and incretin pathways.
5. Add renal glucose handling.
6. Add drug exposure and target engagement.
7. Add disease progression.
8. Add inter-individual variability.
9. Add multiple therapies and combination effects.
10. Validate against increasingly independent clinical datasets.

The resulting model becomes a quantitative framework for asking mechanistic questions across scales rather than a collection of disconnected pharmacological effects.

References

1. Bruno R, et al. Requirements for multi-level systems pharmacology models to reach end-usage: the case of type 2 diabetes. CPT: Pharmacometrics & Systems Pharmacology. 2016. doi:10.1002/psp4.12069.
2. Brunton LL, et al. Pharmacology of metformin — An update. Pharmacological Reviews. 2020. PMID: 31705902.
3. Abdel-Rahman SM, et al. Efficacy and safety of GLP-1 receptor agonists and SGLT2 inhibitors as adjuncts to insulin in type 1 diabetes: Systematic review and meta-analysis. Diabetes, Obesity and Metabolism. 2026. PMID: 41605813.
4. FDA. Quantitative Systems Pharmacology (QSP)-Based Dose Selection for Minimum Anticipated Biological Effect Level (MABEL) in First-in-Human (FIH) Trials. Draft Guidance. 2026.
5. FDA. Division of Pharmacometrics. U.S. Food and Drug Administration. Describes model-informed approaches including population PK, PBPK, exposure-response, QSP, and related quantitative models.
6. FDA. Leveraging Quantitative Methods and Modeling to Modernize Generic Drug Development and Review. Public Workshop. 2017.
7. Brunton LL, et al. Metformin: Antidiabetic actions from cells to tissues. Metabolism. 2026. PMID: 41819225.
8. Evans-Molina D, et al. Type 1 diabetes and adjunctive pharmacologic therapies. The literature on adjunctive metabolic therapies provides clinical context for mechanistic modeling of insulin, GLP-1 receptor agonists, SGLT2 inhibitors, and related interventions.

Where to Go Next

A natural progression is to study QSP Models of Glucose–Insulin Regulation in detail, followed by models of inflammatory and metabolic signaling, incretin therapies, insulin therapy, SGLT2 inhibition, beta-cell dynamics, body-weight regulation, and combination diabetes therapies.

The next tutorial can build directly on this framework by deriving a more detailed glucose–insulin QSP model, introducing meal inputs, insulin secretion, insulin resistance, hepatic glucose production, peripheral glucose disposal, and dynamic simulation.