The impact of mathematical modeling on the understanding of diabetes and related complications

Integrated modeling of labile and glycated hemoglobin with glucose for enhanced diabetes detection and short-term monitoring

Metabolic biomarkers, particularly glycated hemoglobin and fasting plasma glucose, are pivotal in the diagnosis and control of diabetes mellitus. Despite their importance, they exhibit limitations in assessing short-term glucose variations. In this study, we propose labile hemoglobin as an additional biomarker, providing insightful perspectives into these fluctuations. By utilizing datasets from 40,652 retrospective general participants and conducting glucose tolerance tests on 60 prospective pediatric subjects, we explored the relationship between plasma glucose and labile hemoglobin. A mathematical model was developed to encapsulate short-term glucose kinetics in the pediatric group. Applying dimensionality reduction techniques, we successfully identified participant subclusters, facilitating the differentiation between diabetic and non-diabetic individuals. Intriguingly, by integrating labile hemoglobin measurements with plasma glucose values, we were able to predict the likelihood of diabetes in pediatric subjects, underscoring the potential of labile hemoglobin as a significant glycemic biomarker for diabetes research.

Unique Challenges in Diabetic Foot Science

In the past 30 years, there has been a rapid influx of information pertaining to the diabetic foot (DF) coming from numerous directions and sources. This article discusses the current state of the DF literature and challenges it presents to clinicians with its associated increase in knowledge on their derivations, complications, and interventions. Further, we attempt to provide tips on how to navigate and criticize the current literature to encourage and maximize positive outcomes in this challenging patient population.

Mathematical modeling in autoimmune diseases: from theory to clinical application

The research & development (R&D) of novel therapeutic agents for the treatment of autoimmune diseases is challenged by highly complex pathogenesis and multiple etiologies of these conditions. The number of targeted therapies available on the market is limited, whereas the prevalence of autoimmune conditions in the global population continues to rise. Mathematical modeling of biological systems is an essential tool which may be applied in support of decision-making across R&D drug programs to improve the probability of success in the development of novel medicines. Over the past decades, multiple models of autoimmune diseases have been developed. Models differ in the spectra of quantitative data used in their development and mathematical methods, as well as in the level of "mechanistic granularity" chosen to describe the underlying biology. Yet, all models strive towards the same goal: to quantitatively describe various aspects of the immune response. The aim of this review was to conduct a systematic review and analysis of mathematical models of autoimmune diseases focused on the mechanistic description of the immune system, to consolidate existing quantitative knowledge on autoimmune processes, and to outline potential directions of interest for future model-based analyses. Following a systematic literature review, 38 models describing the onset, progression, and/or the effect of treatment in 13 systemic and organ-specific autoimmune conditions were identified, most models developed for inflammatory bowel disease, multiple sclerosis, and lupus (5 models each). ≥70% of the models were developed as nonlinear systems of ordinary differential equations, others - as partial differential equations, integro-differential equations, Boolean networks, or probabilistic models. Despite covering a relatively wide range of diseases, most models described the same components of the immune system, such as T-cell response, cytokine influence, or the involvement of macrophages in autoimmune processes. All models were thoroughly analyzed with an emphasis on assumptions, limitations, and their potential applications in the development of novel medicines.

An extended minimal model of OGTT: estimation of α- and β-cell dysfunction, insulin resistance, and the incretin effect

Loss of insulin sensitivity, α- and β-cell dysfunction, and impairment in incretin effect have all been implicated in the pathophysiology of type 2 diabetes (T2D). Parsimonious mathematical models are useful in quantifying parameters related to the pathophysiology of T2D. Here, we extend the minimum model developed to describe the glucose-insulin-glucagon dynamics in the isoglycemic intravenous glucose infusion (IIGI) experiment to the oral glucose tolerance test (OGTT). The extended model describes glucose and hormone dynamics in OGTT including the contribution of the incretin hormones, glucose-dependent insulinotropic polypeptide (GIP), and glucagon-like peptide-1 (GLP-1), to insulin secretion. A new function describing glucose arrival from the gut is introduced. The model is fitted to OGTT data from eight individuals with T2D and eight weight-matched controls (CS) without diabetes to obtain parameters related to insulin sensitivity, β- and α-cell function. The parameters, i.e., measures of insulin sensitivity, a1, suppression of glucagon secretion, k1, magnitude of glucagon secretion, γ2, and incretin-dependent insulin secretion, γ3, were found to be different between CS and T2D with P values < 0.002, <0.017, <0.009, <0.004, respectively. A new rubric for estimating the incretin effect directly from modeling the OGTT is presented. The average incretin effect correlated well with the experimentally determined incretin effect with a Spearman rank test correlation coefficient of 0.67 (P < 0.012). The average incretin effect was found to be different between CS and T2D (P < 0.032). The developed model is shown to be effective in quantifying the factors relevant to T2D pathophysiology.NEW & NOTEWORTHY A new extended model of oral glucose tolerance test (OGTT) has been developed that includes glucagon dynamics and incretin contribution to insulin secretion. The model allows the estimation of parameters related to α- and β-cell dysfunction, insulin sensitivity, and incretin action. A new function describing the influx of glucose from the gut has been introduced. A new rubric for estimating the incretin effect directly from the OGTT experiment has been developed. The effect of glucose dose was also investigated.

A mechanistic modeling platform of SGLT2 inhibition: Implications for type 1 diabetes

Type 1 diabetes mellitus (T1DM) is an autoimmune disease characterized by abnormally high blood glucose concentrations due to dysfunction of the insulin-producing beta-cells in the pancreas. Dapagliflozin, an inhibitor of renal glucose reabsorption, has the potential to improve often suboptimal glycemic control in patients with T1DM through insulin-independent mechanisms and to partially mitigate the adverse effects associated with long-term insulin administration. In this work, we have adapted a systems pharmacology model of type 2 diabetes mellitus to describe the T1DM condition and characterize the effect of dapagliflozin on short- and long-term glycemic markers under various treatment scenarios. The developed platform serves as a quantitative tool for the in silico evaluation of the insulin-glucose-dapagliflozin crosstalk, optimization of the treatment regimens, and it can be further expanded to include additional therapies or other aspects of the disease.

A Review of Quantitative Systems Pharmacology Models of the Coagulation Cascade: Opportunities for Improved Usability

Despite the numerous therapeutic options to treat bleeding or thrombosis, a comprehensive quantitative mechanistic understanding of the effects of these and potential novel therapies is lacking. Recently, the quality of quantitative systems pharmacology (QSP) models of the coagulation cascade has improved, simulating the interactions between proteases, cofactors, regulators, fibrin, and therapeutic responses under different clinical scenarios. We aim to review the literature on QSP models to assess the unique capabilities and reusability of these models. We systematically searched the literature and BioModels database reviewing systems biology (SB) and QSP models. The purpose and scope of most of these models are redundant with only two SB models serving as the basis for QSP models. Primarily three QSP models have a comprehensive scope and are systematically linked between SB and more recent QSP models. The biological scope of recent QSP models has expanded to enable simulations of previously unexplainable clotting events and the drug effects for treating bleeding or thrombosis. Overall, the field of coagulation appears to suffer from unclear connections between models and irreproducible code as previously reported. The reusability of future QSP models can improve by adopting model equations from validated QSP models, clearly documenting the purpose and modifications, and sharing reproducible code. The capabilities of future QSP models can improve from more rigorous validation by capturing a broader range of responses to therapies from individual patient measurements and integrating blood flow and platelet dynamics to closely represent in vivo bleeding or thrombosis risk.

MATHEMATICAL MODEL FOR PREDICTING FASTING BLOOD GLUCOSE LEVEL IN DIABETES MELLITUS PATIENTS

OBJECTIVE

The aim: To substantiate the use of data on patients' lifestyle, parameters of blood glucose, heart rate, blood pressure and bread units to build a mathematical model for predicting fasting blood glucose level in diabetes mellitus patients to improve existing measures for diabetes prevention.

PATIENTS AND METHODS

Materials and methods: An open database consisting of the studied parameters of 359 people was used in the research. The linear regression method was used to predict fasting blood glucose level in diabetes mellitus patients. The statistical software IBM SPSS Statistics Version 23 was chosen for calculations.

RESULTS

Results: To calculate the coefficients of the linear regression equation, stepwise elimination of parameters was chosen. The analysis of the coefficients of influence of independent variables on dependent showed that the greatest effect on the change in glucose level had value of consumed bread units. The model for women diagnosed with type 2 diabetes showed the highest accuracy.

CONCLUSION

Conclusions: Mathematical modeling made it clear that any malnutrition or health disorders can lead to a significant change in glucose levels. The obtained models consist of a number of parameters, some of which might depend on the presence of concomitant diseases. Further studies should focus on the optimal combination of various parameters taking into account methods of treating comorbidities.

Optimization of trial duration to predict long-term HbA1c change with therapy: A pharmacometrics simulation-based evaluation

Glycated hemoglobin (HbA1c) is the main biomarker of diabetes drug development. However, because of its delayed turnover, trial duration is rarely shorter than 12 weeks, and being able to predict long-term HbA1c with precision using data from shorter studies would be beneficial. The feasibility of reducing study duration was therefore investigated in this study, assuming a model-based analysis. The aim was to investigate the predictive performance of 24- and 52-week extrapolations using data from up to 4, 6, 8 or 12 weeks, with six previously published pharmacometric models of HbA1c. Predictive performance was assessed through simulation-based dose-response predictions and model averaging (MA) with two hypothetical drugs. Results were consistent across the methods of assessment, with MA supporting the results derived from the model-based framework. The models using mean plasma glucose (MPG) or nonlinear fasting plasma glucose (FPG) effect, driving the HbA1c formation, showed good predictive performance despite a reduced study duration. The models, using the linear effect of FPG to drive the HbA1c formation, were sensitive to the limited amount of data in the shorter studies. The MA with bootstrap demonstrated strongly that a 4-week study duration is insufficient for precise predictions of all models. Our findings suggest that if data are analyzed with a pharmacometric model with MPG or FPG with a nonlinear effect to drive HbA1c formation, a study duration of 8 weeks is sufficient with maintained accuracy and precision of dose-response predictions.

A Glucose-Only Model to Extract Physiological Information from Postprandial Glucose Profiles in Subjects with Normal Glucose Tolerance

BACKGROUND

Current mathematical models of postprandial glucose metabolism in people with normal and impaired glucose tolerance rely on insulin measurements and are therefore not applicable in clinical practice. This research aims to develop a model that only requires glucose data for parameter estimation while also providing useful information on insulin sensitivity, insulin dynamics and the meal-related glucose appearance (GA).

METHODS

The proposed glucose-only model (GOM) is based on the oral minimal model (OMM) of glucose dynamics and substitutes the insulin dynamics with a novel function dependant on glucose levels and GA. A Bayesian method and glucose data from 22 subjects with normal glucose tolerance are utilised for parameter estimation. To validate the results of the GOM, a comparison to the results of the OMM, obtained by using glucose and insulin data from the same subjects is carried out.

RESULTS

The proposed GOM describes the glucose dynamics with comparable precision to the OMM with an RMSE of 5.1 ± 2.3 mg/dL and 5.3 ± 2.4 mg/dL, respectively and contains a parameter that is significantly correlated to the insulin sensitivity estimated by the OMM (r = 0.7) Furthermore, the dynamic properties of the time profiles of GA and insulin dynamics inferred by the GOM show high similarity to the corresponding results of the OMM.

CONCLUSIONS

The proposed GOM can be used to extract useful physiological information on glucose metabolism in subjects with normal glucose tolerance. The model can be further developed for clinical applications to patients with impaired glucose tolerance under the use of continuous glucose monitoring data.

Mathematical modeling reveals differential dynamics of insulin action models on glycerol and glucose in adolescent girls with obesity

Under healthy conditions, the pancreas responds to a glucose challenge by releasing insulin. Insulin suppresses lipolysis in adipose tissue, thereby decreasing plasma glycerol concentration, and it regulates plasma glucose concentration through action in muscle and liver. Insulin resistance (IR) occurs when more insulin is required to achieve the same effects, and IR may be tissue-specific. IR emerges during puberty as a result of high concentrations of growth hormone and is worsened by youth-onset obesity. Adipose, liver, and muscle tissue exhibit distinct dose-dependent responses to insulin in multi-phase hyperinsulinemic-euglycemic (HE) clamps, but the HE clamp protocol does not address potential differences in the dynamics of tissue-specific insulin responses. Changes to the dynamics of insulin responses would alter glycemic control in response to a glucose challenge. To investigate the dynamics of insulin acting on adipose tissue, we developed a novel differential-equations based model that describes the coupled dynamics of glycerol concentrations and insulin action during an oral glucose tolerance test in female adolescents with obesity and IR. We compared these dynamics to the dynamics of insulin acting on muscle and liver as assessed with the oral minimal model applied to glucose and insulin data collected under the same protocol. We found that the action of insulin on glycerol peaks approximately 67 min earlier (p < 0.001) and follows the dynamics of plasma insulin more closely compared to insulin action on glucose as assessed by the parameters representing the time constants for insulin action on glucose and glycerol (p < 0.001). These findings suggest that the dynamics of insulin action show tissue-specific differences in our IR adolescent population, with adipose tissue responding to insulin more quickly compared to muscle and liver. Improved understanding of the tissue-specific dynamics of insulin action may provide novel insights into the progression of metabolic disease in patient populations with diverse metabolic phenotypes.

Analysis of wearable time series data in endocrine and metabolic research

Many hormones in the body oscillate with different frequencies and amplitudes, creating a dynamic environment that is essential to maintain health. In humans, disruptions to these rhythms are strongly associated with increased morbidity and mortality. While mathematical models can help us understand rhythm misalignment, translating this insight into personalised healthcare technologies requires solving additional challenges. Here, we discuss how combining minimally invasive, high-frequency biosampling technologies with wearable devices can assist the development of hormonal surrogates. We review bespoke algorithms that can help analyse multidimensional, noisy, time series data and identify wearable signals that could constitute clinical proxies of endocrine rhythms. These techniques can support the development of computational biomarkers to support the diagnosis and management of endocrine and metabolic conditions.

Examining Type 1 Diabetes Mathematical Models Using Experimental Data

Type 1 diabetes requires treatment with insulin injections and monitoring glucose levels in affected individuals. We explored the utility of two mathematical models in predicting glucose concentration levels in type 1 diabetic mice and determined disease pathways. We adapted two mathematical models, one with β-cells and the other with no β-cell component to determine their capability in predicting glucose concentration and determine type 1 diabetes pathways using published glucose concentration data for four groups of experimental mice. The groups of mice were numbered Mice Group 1–4, depending on the diabetes severity of each group, with severity increasing from group 1–4. A Markov Chain Monte Carlo method based on a Bayesian framework was used to fit the model to determine the best model structure. Akaike information criteria (AIC) and Bayesian information criteria (BIC) approaches were used to assess the best model structure for type 1 diabetes. In fitting the model with no β-cells to glucose level data, we varied insulin absorption rate and insulin clearance rate. However, the model with β-cells required more parameters to match the data and we fitted the β-cell glucose tolerance factor, whole body insulin clearance rate, glucose production rate, and glucose clearance rate. Fitting the models to the blood glucose concentration level gave the least difference in AIC of 1.2, and a difference in BIC of 0.12 for Mice Group 4. The estimated AIC and BIC values were highest for Mice Group 1 than all other mice groups. The models gave substantial differences in AIC and BIC values for Mice Groups 1–3 ranging from 2.10 to 4.05. Our results suggest that the model without β-cells provides a more suitable structure for modelling type 1 diabetes and predicting blood glucose concentration for hypoglycaemic episodes.

A systems biology analysis of lipolysis and fatty acid release from adipocytes in vitro and from adipose tissue in vivo

Lipolysis and the release of fatty acids to supply energy fuel to other organs, such as between meals, during exercise, and starvation, are fundamental functions of the adipose tissue. The intracellular lipolytic pathway in adipocytes is activated by adrenaline and noradrenaline, and inhibited by insulin. Circulating fatty acids are elevated in type 2 diabetic individuals. The mechanisms behind this elevation are not fully known, and to increase the knowledge a link between the systemic circulation and intracellular lipolysis is key. However, data on lipolysis and knowledge from in vitro systems have not been linked to corresponding in vivo data and knowledge in vivo. Here, we use mathematical modelling to provide such a link. We examine mechanisms of insulin action by combining in vivo and in vitro data into an integrated mathematical model that can explain all data. Furthermore, the model can describe independent data not used for training the model. We show the usefulness of the model by simulating new and more challenging experimental setups in silico, e.g. the extracellular concentration of fatty acids during an insulin clamp, and the difference in such simulations between individuals with and without type 2 diabetes. Our work provides a new platform for model-based analysis of adipose tissue lipolysis, under both non-diabetic and type 2 diabetic conditions.

Improved Methods for Mid-Term Blood Glucose Level Prediction Using Dietary and Insulin Logs

Background and Objectives: The daily lifestyle management of diabetes requires accurate predictions of the blood glucose level between meals. The objective of this study was to improve the accuracy achieved by previous work, especially on the mid-term, i.e., 120 to 180 min prediction horizons, for insulin-dependent patients. Materials and Methods: An absorption model-based method is proposed to train an artificial neural network with the bolus and basal insulin dosing and timing, the baseline blood glucose level, the maximal glucose infusion rate, and the total carbohydrate content as parameters. The approach was implemented in various algorithmic setups, and it was validated on data from a small-scale clinical trial with continuous glucose monitoring. Results: Root mean square error results for the mid-term horizons are 1.72 mmol/L (120 min) and 1.95 mmol/L (180 min). The accuracy of the proposed model measured on the clinical data is better than the accuracy reported by any other currently available and comparable models. Conclusions: A relatively short (ca. two weeks) training sample of a continuous glucose monitor and dietary/insulin log is sufficient to provide accurate predictions. For the outpatient application in practice, a hybrid model is proposed that combines the present mid-term method with the authors’ previous work for short-term predictions.

An Updated Organ-Based Multi-Level Model for Glucose Homeostasis: Organ Distributions, Timing, and Impact of Blood Flow

Glucose homeostasis is the tight control of glucose in the blood. This complex control is important, due to its malfunction in serious diseases like diabetes, and not yet sufficiently understood. Due to the involvement of numerous organs and sub-systems, each with their own intra-cellular control, we have developed a multi-level mathematical model, for glucose homeostasis, which integrates a variety of data. Over the last 10 years, this model has been used to insert new insights from the intra-cellular level into the larger whole-body perspective. However, the original cell-organ-body translation has during these years never been updated, despite several critical shortcomings, which also have not been resolved by other modeling efforts. For this reason, we here present an updated multi-level model. This model provides a more accurate sub-division of how much glucose is being taken up by the different organs. Unlike the original model, we now also account for the different dynamics seen in the different organs. The new model also incorporates the central impact of blood flow on insulin-stimulated glucose uptake. Each new improvement is clear upon visual inspection, and they are also supported by statistical tests. The final multi-level model describes >300 data points in >40 time-series and dose-response curves, resulting from a large variety of perturbations, describing both intra-cellular processes, organ fluxes, and whole-body meal responses. We hope that this model will serve as an improved basis for future data integration, useful for research and drug developments within diabetes.

A mathematical model of food intake

The metabolic, hormonal and psychological determinants of the feeding behavior in humans are numerous and complex. A plausible model of the initiation, continuation and cessation of meals taking into account the most relevant such determinants would be very useful in simulating food intake over hours to days, thus providing input into existing models of nutrient absorption and metabolism. In the present work, a meal model is proposed, incorporating stomach distension, glycemic variations, ghrelin dynamics, cultural habits and influences on the initiation and continuation of meals, reflecting a combination of hedonic and appetite components. Given a set of parameter values (portraying a single subject), the timing and size of meals are stochastic. The model parameters are calibrated so as to reflect established medical knowledge on data of food intake from the National Health and Nutrition Examination Survey (NHANES) database during years 2015 and 2016.

Simulation-Based Evaluation of Treatment Adjustment to Exercise in Type 1 Diabetes

Regular exercise is beneficial and recommended for people with type 1 diabetes, but increased glucose demand and changes in insulin sensitivity require treatment adjustments to prevent exercise-induced hypoglycemia. Several different adjustment strategies based on insulin bolus reductions and additional carbohydrate intake have been proposed, but large inter- and intraindividual variability and studies using different exercise duration, intensity, and timing impede a direct comparison of their effects. In this study, we use a mathematical model of the glucoregulatory system and implement published guidelines and strategies in-silico to provide a direct comparison on a single 'typical' person on a standard day with three meals. We augment this day by a broad range of exercise scenarios combining different intensity and duration of the exercise session, and different timing with respect to adjacent meals. We compare the resulting blood glucose trajectories and use summary measures to evaluate the time-in-range and risk scores for hypo- and hyperglycemic events for each simulation scenario, and to determine factors that impede prevention of hypoglycemia events. Our simulations suggest that the considered strategies and guidelines successfully minimize the risk for acute hypoglycemia. At the same time, all adjustments substantially increase the risk of late-onset hypoglycemia compared to no adjustment in many cases. We also find that timing between exercise and meals and additional carbohydrate intake during exercise can lead to non-intuitive behavior due to superposition of meal- and exercise-related glucose dynamics. Increased insulin sensitivity appears as a major driver of non-acute hypoglycemic events. Overall, our results indicate that further treatment adjustment might be required both immediately following exercise and up to several hours later, but that the intricate interplay between different dynamics makes it difficult to provide generic recommendations. However, our simulation scenarios extend substantially beyond the original scope of each model component and proper model validation is warranted before applying our in-silico results in a clinical setting.

Mathematical Modeling for the Physiological and Clinical Investigation of Glucose Homeostasis and Diabetes

Mathematical modeling in the field of glucose metabolism has a longstanding tradition. The use of models is motivated by several reasons. Models have been used for calculating parameters of physiological interest from experimental data indirectly, to provide an unambiguous quantitative representation of pathophysiological mechanisms, to determine indices of clinical usefulness from simple experimental tests. With the growing societal impact of type 2 diabetes, which involves the disturbance of the glucose homeostasis system, development and use of models in this area have increased. Following the approaches of physiological and clinical investigation, the focus of the models has spanned from representations of whole body processes to those of cells, i.e., from in vivo to in vitro research. Model-based approaches for linking in vivo to in vitro research have been proposed, as well as multiscale models merging the two areas. The success and impact of models has been variable. Two kinds of models have received remarkable interest: those widely used in clinical applications, e.g., for the assessment of insulin sensitivity and β-cell function and some models representing specific aspects of the glucose homeostasis system, which have become iconic for their efficacy in describing clearly and compactly key physiological processes, such as insulin secretion from the pancreatic β cells. Models are inevitably simplified and approximate representations of a physiological system. Key to their success is an appropriate balance between adherence to reality, comprehensibility, interpretative value and practical usefulness. This has been achieved with a variety of approaches. Although many models concerning the glucose homeostasis system have been proposed, research in this area still needs to address numerous issues and tackle new opportunities. The mathematical representation of the glucose homeostasis processes is only partial, also because some mechanisms are still only partially understood. For in vitro research, mathematical models still need to develop their potential. This review illustrates the problems, approaches and contribution of mathematical modeling to the physiological and clinical investigation of glucose homeostasis and diabetes, focusing on the most relevant and stimulating models.

Effects of resistant starch on glycaemic control: a systematic review and meta-analysis

The effects of resistant starch on glycaemic control are controversial. In this study, a systematic review and meta-analysis of results from nineteen randomised controlled trials (RCT) was performed to illustrate the effects of resistant starch on glycaemic control. A literature search was conducted on PubMed, Scopus and Cochrane electronic databases for related publications from inception to 6 April 2020. Key inclusion criteria were: RCT; resistant starch as intervention substances and reporting glucose- and insulin-related endpoints. Exclusion criteria were: using type I resistant starch or a mixture of resistant starch and other functional food ingredients as intervention; using substances other than digestible starch as controls. The effect of resistant starch on fasting plasma glucose was significant (effect size (ES) –0·09 (95 % CI –0·13, −0·04) mmol/l, P = 0·001) compared with digestible starch. Subgroup analyses revealed that the ES was larger when the dosage of resistant starch was more than 28 g/d (ES –0·16 (95 % CI –0·24, –0·08) mmol/l, P < 0·001) or the intervention period was more than 8 weeks (ES –0·12 (95 % CI –0·18, –0·06) mmol/l, P < 0·001). The effect on homoeostatic model assessment (HOMA)-insulin resistance (IR) was significant (ES –0·33 (95 % CI –0·51, –0·14), P = 0·001). However, the effects on other insulin-related endpoints were not significant, including fasting plasma insulin, four endpoints from the frequently sampled intravenous glucose tolerance test (insulin sensitivity index, acute insulin response, disposition index and glucose effectiveness) and HOMA-β. The current study indicated moderate effects of resistant starch on improving glycaemic control.

Type 2 diabetes progression: A regulatory network approach

In order to elucidate central elements underlying type 2 diabetes, we constructed a regulatory network model involving 37 components (molecules, receptors, processes, etc.) associated to signaling pathways of pancreatic beta-cells. In a first approximation, the network topology was described by Boolean rules whose interacting dynamics predicted stationary patterns broadly classified as health, metabolic syndrome, and diabetes stages. A subsequent approximation based on a continuous logic analysis allowed us to characterize the progression of the disease as transitions between these states associated to alterations of cell homeostasis due to exhaustion or exacerbation of specific regulatory signals. The method allowed the identification of key transcription factors involved in metabolic stress as essential for the progression of the disease. Integration of the present analysis with existent mathematical models designed to yield accurate account of experimental data in human or animal essays leads to reliable predictions for beta-cell mass, insulinemia, glycemia, and glycosylated hemoglobin in diabetic fatty rats.

Mathematical model of blood glucose dynamics by emulating the pathophysiology of glucose metabolism in type 2 diabetes mellitus

Mathematical modelling has established itself as a theoretical tool to understand fundamental aspects of a variety of medical-biological phenomena. The predictive power of mathematical models on some chronic conditions has been helpful in its proper prevention, diagnosis, and treatment. Such is the case of the modelling of glycaemic dynamics in type 2 diabetes mellitus (T2DM), whose physiology-based mathematical models have captured the metabolic abnormalities of this disease. Through a physiology-based pharmacokinetic-pharmacodynamic approach, this work addresses a mathematical model whose structure starts from a model of blood glucose dynamics in healthy humans. This proposal is capable of emulating the pathophysiology of T2DM metabolism, including the effect of gastric emptying and insulin enhancing effect due to incretin hormones. The incorporation of these effects lies in the implemented methodology since the mathematical functions that represent metabolic rates, with a relevant contribution to hyperglycaemia, are adjusting individually to the clinical data of patients with T2DM. Numerically, the resulting model successfully simulates a scheduled graded intravenous glucose test and oral glucose tolerance tests at different doses. The comparison between simulations and clinical data shows an acceptable description of the blood glucose dynamics in T2DM. It opens the possibility of using this model to develop model-based controllers for the regulation of blood glucose in T2DM.

BioModels-15 years of sharing computational models in life science

Computational modelling has become increasingly common in life science research. To provide a platform to support universal sharing, easy accessibility and model reproducibility, BioModels (https://www.ebi.ac.uk/biomodels/), a repository for mathematical models, was established in 2005. The current BioModels platform allows submission of models encoded in diverse modelling formats, including SBML, CellML, PharmML, COMBINE archive, MATLAB, Mathematica, R, Python or C++. The models submitted to BioModels are curated to verify the computational representation of the biological process and the reproducibility of the simulation results in the reference publication. The curation also involves encoding models in standard formats and annotation with controlled vocabularies following MIRIAM (minimal information required in the annotation of biochemical models) guidelines. BioModels now accepts large-scale submission of auto-generated computational models. With gradual growth in content over 15 years, BioModels currently hosts about 2000 models from the published literature. With about 800 curated models, BioModels has become the world’s largest repository of curated models and emerged as the third most used data resource after PubMed and Google Scholar among the scientists who use modelling in their research. Thus, BioModels benefits modellers by providing access to reliable and semantically enriched curated models in standard formats that are easy to share, reproduce and reuse.

Nonlinear Analysis for a Type-1 Diabetes Model with Focus on T-Cells and Pancreatic β-Cells Behavior

Type-1 diabetes mellitus (T1DM) is an autoimmune disease that has an impact on mortality due to the destruction of insulin-producing pancreatic β -cells in the islets of Langerhans. Over the past few years, the interest in analyzing this type of disease, either in a biological or mathematical sense, has relied on the search for a treatment that guarantees full control of glucose levels. Mathematical models inspired by natural phenomena, are proposed under the prey–predator scheme. T1DM fits in this scheme due to the complicated relationship between pancreatic β -cell population growth and leukocyte population growth via the immune response. In this scenario, β -cells represent the prey, and leukocytes the predator. This paper studies the global dynamics of T1DM reported by Magombedze et al. in 2010. This model describes the interaction of resting macrophages, activated macrophages, antigen cells, autolytic T-cells, and β -cells. Therefore, the localization of compact invariant sets is applied to provide a bounded positive invariant domain in which one can ensure that once the dynamics of the T1DM enter into this domain, they will remain bounded with a maximum and minimum value. Furthermore, we analyzed this model in a closed-loop scenario based on nonlinear control theory, and proposed bases for possible control inputs, complementing the model with them. These entries are based on the existing relationship between cell–cell interaction and the role that they play in the unchaining of a diabetic condition. The closed-loop analysis aims to give a deeper understanding of the impact of autolytic T-cells and the nature of the β -cell population interaction with the innate immune system response. This analysis strengthens the proposal, providing a system free of this illness—that is, a condition wherein the pancreatic β -cell population holds and there are no antigen cells labeled by the activated macrophages.

A Novel Synthetic Model of the Glucose-Insulin System for Patient-Wise Inference of Physiological Parameters From Small-Size OGTT Data

Existing mathematical models for the glucose-insulin (G-I) dynamics often involve variables that are not susceptible to direct measurement. Standard clinical tests for measuring G-I levels for diagnosing potential diseases are simple and relatively cheap, but seldom give enough information to allow the identification of model parameters within the range in which they have a biological meaning, thus generating a gap between mathematical modeling and any possible physiological explanation or clinical interpretation. In the present work, we present a synthetic mathematical model to represent the G-I dynamics in an Oral Glucose Tolerance Test (OGTT), which involves for the first time for OGTT-related models, Delay Differential Equations. Our model can represent the radically different behaviors observed in a studied cohort of 407 normoglycemic patients (the largest analyzed so far in parameter fitting experiments), all masked under the current threshold-based normality criteria. We also propose a novel approach to solve the parameter fitting inverse problem, involving the clustering of different G-I profiles, a simulation-based exploration of the feasible set, and the construction of an information function which reshapes it, based on the clinical records, experimental uncertainties, and physiological criteria. This method allowed an individual-wise recognition of the parameters of our model using small size OGTT data (5 measurements) directly, without modifying the routine procedures or requiring particular clinical setups. Therefore, our methodology can be easily applied to gain parametric insights to complement the existing tools for the diagnosis of G-I dysregulations. We tested the parameter stability and sensitivity for individual subjects, and an empirical relationship between such indexes and curve shapes was spotted. Since different G-I profiles, under the light of our model, are related to different physiological mechanisms, the present method offers a tool for personally-oriented diagnosis and treatment and to better define new health criteria.

Modelling the effects of glucagon during glucose tolerance testing

Background

Glucose tolerance testing is a tool used to estimate glucose effectiveness and insulin sensitivity in diabetic patients. The importance of such tests has prompted the development and utilisation of mathematical models that describe glucose kinetics as a function of insulin activity. The hormone glucagon, also plays a fundamental role in systemic plasma glucose regulation and is secreted reciprocally to insulin, stimulating catabolic glucose utilisation. However, regulation of glucagon secretion by α-cells is impaired in type-1 and type-2 diabetes through pancreatic islet dysfunction. Despite this, inclusion of glucagon activity when modelling the glucose kinetics during glucose tolerance testing is often overlooked. This study presents two mathematical models of a glucose tolerance test that incorporate glucose-insulin-glucagon dynamics. The first model describes a non-linear relationship between glucagon and glucose, whereas the second model assumes a linear relationship.

Results

Both models are validated against insulin-modified and glucose infusion intravenous glucose tolerance test (IVGTT) data, as well as insulin infusion data, and are capable of estimating patient glucose effectiveness (s_G) and insulin sensitivity (s_I). Inclusion of glucagon dynamics proves to provide a more detailed representation of the metabolic portrait, enabling estimation of two new diagnostic parameters: glucagon effectiveness (s_E) and glucagon sensitivity (δ).

Conclusions

The models are used to investigate how different degrees of pax‘tient glucagon sensitivity and effectiveness affect the concentration of blood glucose and plasma glucagon during IVGTT and insulin infusion tests, providing a platform from which the role of glucagon dynamics during a glucose tolerance test may be investigated and predicted.

Determination of physiological parameters for endogenous glucose production in individuals using diurnal data

Background

Triple tracer meal experiments used to investigate organ glucose-insulin dynamics, such as endogenous glucose production (EGP) of the liver are labor intensive and expensive. A procedure was developed to obtain individual liver related parameters to describe EGP dynamics without the need for tracers.

Results

The development used an existing formula describing the EGP dynamics comprising 4 parameters defined from glucose, insulin and C-peptide dynamics arising from triple meal studies. The method employs a set of partial differential equations in order to estimate the parameters for EGP dynamics. Tracer-derived and simulated data sets were used to develop and test the procedure. The predicted EGP dynamics showed an overall mean R² of 0.91.

Conclusions

In summary, a method was developed for predicting the hepatic EGP dynamics for healthy, pre-diabetic, and type 2 diabetic individuals without applying tracer experiments.

Simulation Software for Assessment of Nonlinear and Adaptive Multivariable Control Algorithms: Glucose - Insulin Dynamics in Type 1 Diabetes

A simulator for testing automatic control algorithms for nonlinear systems with time-varying parameters, variable time delays, and uncertainties is developed. It is based on simulation of virtual patients with Type 1 diabetes (T1D). Nonlinear models are developed to describe glucose concentration (GC) variations based on user-defined scenarios for meal consumption, insulin administration, and physical activity. They compute GC values and physiological variables, such as heart rate, skin temperature, accelerometer, and energy expenditure, that are indicative of physical activities affecting GC dynamics. This is the first simulator designed for assessment of multivariable controllers that consider supplemental physiological variables in addition to GC measurements to improve glycemic control. Virtual patients are generated from distributions of identified model parameters using clinical data. The simulator will enable testing and evaluation of new control algorithms proposed for automated insulin delivery as well as various control algorithms for nonlinear systems with uncertainties, time-varying parameters and delays.

A novel fast-slow model of diabetes progression: Insights into mechanisms of response to the interventions in the Diabetes Prevention Program

Several models for the long-term development of T2DM already exist, focusing on the dynamics of the interaction between glycemia, insulinemia and β-cell mass. Current models consider representative (fasting or daily average) glycemia and insulinemia as characterizing the compensation state of the subject at some instant in slow time. This implies that only these representative levels can be followed through time and that the role of fast glycemic oscillations is neglected. An improved model (DPM15) for the long-term progression of T2DM is proposed, introducing separate peripheral and hepatic (liver and kidney) insulin actions. The DPM15 model no longer uses near-equilibrium approximation to separate fast and slow time scales, but rather describes, at each step in slow time, a complete day in the life of the virtual subject in fast time. The model can thus represent both fasting and postprandial glycemic levels and describe the effect of interventions acting on insulin-enhanced tissue glucose disposal or on insulin-inhibited hepatic glucose output, as well as on insulin secretion and β-cell replicating ability. The model can simulate long-term variations of commonly used clinical indices (HOMA-B, HOMA-IR, insulinogenic index) as well as of Oral Glucose Tolerance or Euglycemic Hyperinsulinemic Clamp test results. The model has been calibrated against observational data from the Diabetes Prevention Program study: it shows good adaptation to observations as a function of very plausible values of the parameters describing the effect of such interventions as Placebo, Intensive LifeStyle and Metformin administration.

Translation Between Two Models; Application with Integrated Glucose Homeostasis Models

PURPOSE

For some biological systems, there exist several models with somewhat different features and perspectives. We propose an evaluation method for NLME models by analyzing real and simulated data from the model of main interest using a structurally different, but similar, NLME model. We showcase this method using the Integrated Glucose Insulin (IGI) model and the Integrated Minimal Model (IMM). Additionally, we try to map parameters carrying similar information between the two models.

METHODS

A bootstrap of real data and simulated datasets from both the IMM and IGI models were analyzed with the two models. Important parameters of the IMM were mapped to IGI parameters using a large IMM simulated dataset analyzed under the IGI model.

RESULTS

Comparison of the parameters estimated from real data and data simulated with the IMM and analyzed with the IGI model demonstrated differences between real and IMM-simulated data. Comparison of the parameters estimated from real data and data simulated with the IGI model and analyzed with the IMM also demonstrated differences but to a lower extent. The strongest parameter correlations were found for: insulin-dependent glucose clearance (IGI) ~ insulin sensitivity (IMM); insulin-independent glucose clearance (IGI) ~ glucose effectiveness (IMM); and insulin effect parameter (IGI) ~ insulin action (IMM).

CONCLUSIONS

We demonstrated a new approach to investigate models' ability to simulate real-life-like data, and the information captured in each model in comparison to real data, and the IMM clinically used parameters were successfully mapped to their corresponding IGI parameters.

Mathematical Modelling of Endocrine Systems

Hormone rhythms are ubiquitous and essential to sustain normal physiological functions. Combined mathematical modelling and experimental approaches have shown that these rhythms result from regulatory processes occurring at multiple levels of organisation and require continuous dynamic equilibration, particularly in response to stimuli. We review how such an interdisciplinary approach has been successfully applied to unravel complex regulatory mechanisms in the metabolic, stress, and reproductive axes. We discuss how this strategy is likely to be instrumental for making progress in emerging areas such as chronobiology and network physiology. Ultimately, we envisage that the insight provided by mathematical models could lead to novel experimental tools able to continuously adapt parameters to gradual physiological changes and the design of clinical interventions to restore normal endocrine function.

Modeling of Diabetes and Its Clinical Impact

Understanding all aspects of diabetes treatment is hindered by the complexity of this chronic disease and its multifaceted complications and comorbidities, including social and financial impacts. In vivo studies as well as clinical trials provided invaluable information for unraveling not only metabolic processes but also risk estimations of, for example, complications. These approaches are often time- and cost-consuming and have frequently been supported by simulation models. Simulation models provide the opportunity to investigate diabetes treatment from additional viewpoints and with alternative objectives. This review presents selected models focusing either on metabolic processes or risk estimations and financial outcomes to provide a basic insight into this complex subject. It also discusses opportunities and challenges of modeling diabetes.

Comparison of Power, Prognosis, and Extrapolation Properties of Four Population Pharmacodynamic Models of HbA1c for Type 2 Diabetes

Reusing published models saves time; time to be used for informing decisions in drug development. In antihyperglycemic drug development, several published HbA1c models are available but selecting the appropriate model for a particular purpose is challenging. This study aims at helping selection by investigating four HbA1c models, specifically the ability to identify drug effects (shape, site of action, and power) and simulation properties. All models could identify glucose effect nonlinearities, although for detecting the site of action, a mechanistic glucose model was needed. Power was highest for models using mean plasma glucose to drive HbA1c formation. Insulin contribution to power varied greatly depending on the drug target; it was beneficial only if the drug target was insulin secretion. All investigated models showed good simulation properties. However, extrapolation with the mechanistic model beyond 12 weeks resulted in drug effect overprediction. This investigation aids drug development in decisions regarding model choice if reusing published HbA1c models.

Sensor-Augmented Pump-Based Customized Mathematical Model for Type 1 Diabetes

BACKGROUND

Simulations using mathematical models are important for studying, developing, and improving therapies for people with type 1 diabetes.

METHODS

The Medtronic CareLink^® database was used to create virtual patients with a variety of inter-insulin sensitivities, meal absorption rates, pharmacokinetics, age, and gender. In addition, intra-insulin sensitivities of the virtual patients change over a 24-h cycle.

RESULTS

A total of 2087 virtual patients were developed. The time percentage between 70 and 180 mg/dL of the CareLink uploads and the simulated virtual patients was 72.4% (18.6) and 74.1% (16.9), respectively. The time percentage <70 mg/dL of the real continuous glucose monitoring from CareLink uploads and the simulated virtual patients was 1% (2.4) and 1.7% (4.1), respectively. A simulation study with the virtual patients predicted the glycemic distribution after 2 h of insulin suspension as reported in the ASPIRE (Automation to Simulate Pancreatic Insulin Response) clinical trial. The 3 months outcomes of Medtronic's hybrid closed-loop 670G system pivotal trial were also predicted in a simulation study. The time percentage <70 mg/dL was 3.4% and 3.1%, and the time percentage between 71 and 180 mg/dL was 73.8% and 77.7% for 93 pivotal study adults (>18 years) and 90 adult (>28 years) virtual patients, respectively.

CONCLUSION

The Medtronic CareLink database was utilized to generate a large number of virtual patients with a variety of insulin sensitivities, pharmacokinetics, and meal absorption rates. This new simulation model can be potentially used to evaluate and prognosticate the outcomes of studies of artificial pancreas algorithms and systems.

A closed-loop multi-level model of glucose homeostasis

BACKGROUND

The pathophysiologic processes underlying the regulation of glucose homeostasis are considerably complex at both cellular and systemic level. A comprehensive and structured specification for the several layers of abstraction of glucose metabolism is often elusive, an issue currently solvable with the hierarchical description provided by multi-level models. In this study we propose a multi-level closed-loop model of whole-body glucose homeostasis, coupled with the molecular specifications of the insulin signaling cascade in adipocytes, under the experimental conditions of normal glucose regulation and type 2 diabetes.

METHODOLOGY/PRINCIPAL FINDINGS

The ordinary differential equations of the model, describing the dynamics of glucose and key regulatory hormones and their reciprocal interactions among gut, liver, muscle and adipose tissue, were designed for being embedded in a modular, hierarchical structure. The closed-loop model structure allowed self-sustained simulations to represent an ideal in silico subject that adjusts its own metabolism to the fasting and feeding states, depending on the hormonal context and invariant to circadian fluctuations. The cellular level of the model provided a seamless dynamic description of the molecular mechanisms downstream the insulin receptor in the adipocytes by accounting for variations in the surrounding metabolic context.

CONCLUSIONS/SIGNIFICANCE

The combination of a multi-level and closed-loop modeling approach provided a fair dynamic description of the core determinants of glucose homeostasis at both cellular and systemic scales. This model architecture is intrinsically open to incorporate supplementary layers of specifications describing further individual components influencing glucose metabolism.

Agent-based modeling of the interaction between CD8+ T cells and Beta cells in type 1 diabetes

We propose an agent-based model for the simulation of the autoimmune response in T1D. The model incorporates cell behavior from various rules derived from the current literature and is implemented on a high-performance computing system, which enables the simulation of a significant portion of the islets in the mouse pancreas. Simulation results indicate that the model is able to capture the trends that emerge during the progression of the autoimmunity. The multi-scale nature of the model enables definition of rules or equations that govern cellular or sub-cellular level phenomena and observation of the outcomes at the tissue scale. It is expected that such a model would facilitate in vivo clinical studies through rapid testing of hypotheses and planning of future experiments by providing insight into disease progression at different scales, some of which may not be obtained easily in clinical studies. Furthermore, the modular structure of the model simplifies tasks such as the addition of new cell types, and the definition or modification of different behaviors of the environment and the cells with ease.

The promises of quantitative systems pharmacology modelling for drug development

Recent growth in annual new therapeutic entity (NTE) approvals by the U.S. Food and Drug Administration (FDA) suggests a positive trend in current research and development (R&D) output. Prior to this, the cost of each NTE was considered to be rising exponentially, with compound failure occurring mainly in clinical phases. Quantitative systems pharmacology (QSP) modelling, as an additional tool in the drug discovery arsenal, aims to further reduce NTE costs and improve drug development success. Through in silico mathematical modelling, QSP can simulate drug activity as perturbations in biological systems and thus understand the fundamental interactions which drive disease pathology, compound pharmacology and patient response. Here we review QSP, pharmacometrics and systems biology models with respect to the diseases covered as well as their clinical relevance and applications. Overall, the majority of modelling focus was aligned with the priority of drug-discovery and clinical trials. However, a few clinically important disease categories, such as Immune System Diseases and Respiratory Tract Diseases, were poorly covered by computational models. This suggests a possible disconnect between clinical and modelling agendas. As a standard element of the drug discovery pipeline the uptake of QSP might help to increase the efficiency of drug development across all therapeutic indications.

Disease Progression Modeling: Key Concepts and Recent Developments

Disease modeling involves the use of mathematical functions to describe quantitatively the time course of disease progression. In order to characterize the natural progression of disease, these models generally incorporate longitudinal data for some biomarker(s) of disease severity or can incorporate more direct measures of disease severity. Disease models are also often linked to pharmacokinetic-pharmacodynamic models so that the influence of drug treatment on disease progression can be quantified and evaluated. Regulatory agencies have embraced disease progression models as powerful tools that can be used to improve drug development productivity. This article provides a brief overview of key concepts in disease progression modeling followed by illustrative examples from models for Alzheimer's disease. Finally, recent novel applications in which disease progression models have been linked to cost-effectiveness analysis and genomic analysis are described.

A Simple Mathematical Model for Wound Closure Evaluation

The incidence of ulcers associated to type 2 diabetes mellitus (T2DM) increases every year. We introduce and explore a new mathematical algorithm to evaluate wound-healing in foot ulcers associated to T2DM. Fifteen patients (nine women and six men), mean age of 70 ± 16 years were included. The evolution of their wounds followed-up for a period of 18-45 days. According to the Wagner grading system the ulcers were grade I (5 patients), grade II (9 patients), and grade III (1 patient). Clinically, the type of the ulcers was neuroischemic (12 patients) and neuropathic (3 patients). A new parameter is introduced, the "continuous linear healing rate" Dc that was more accurate with higher values and requires less quantifications than usual formulas to make a wound-healing projection.

A Six-Stage Workflow for Robust Application of Systems Pharmacology

Quantitative and systems pharmacology (QSP) is increasingly being applied in pharmaceutical research and development. One factor critical to the ultimate success of QSP is the establishment of commonly accepted language, technical criteria, and workflows. We propose an integrated workflow that bridges conceptual objectives with underlying technical detail to support the execution, communication, and evaluation of QSP projects.

Paracrine regulation of glucagon secretion: the β/α/δ model

The regulation of glucagon secretion in the pancreatic α-cell is not well understood. It has been proposed that glucose suppresses glucagon secretion either directly through an intrinsic mechanism within the α-cell or indirectly through an extrinsic mechanism. Previously, we described a mathematical model for isolated pancreatic α-cells and used it to investigate possible intrinsic mechanisms of regulating glucagon secretion. We demonstrated that glucose can suppress glucagon secretion through both ATP-dependent potassium channels (K_ATP) and a store-operated current (SOC). We have now developed an islet model that combines previously published mathematical models of α- and β-cells with a new model of δ-cells and use it to explore the effects of insulin and somatostatin on glucagon secretion. We show that the model can reproduce experimental observations that the inhibitory effect of glucose remains even when paracrine modulators are no longer acting on the α-cell. We demonstrate how paracrine interactions can either synchronize α- and δ-cells to produce pulsatile oscillations in glucagon and somatostatin secretion or fail to do so. The model can also account for the paradoxical observation that glucagon can be out of phase with insulin, whereas α-cell calcium is in phase with insulin. We conclude that both paracrine interactions and the α-cell's intrinsic mechanisms are needed to explain the response of glucagon secretion to glucose.

Requirements for multi-level systems pharmacology models to reach end-usage: the case of type 2 diabetes

We are currently in the middle of a major shift in biomedical research: unprecedented and rapidly growing amounts of data may be obtained today, from in vitro, in vivo and clinical studies, at molecular, physiological and clinical levels. To make use of these large-scale, multi-level datasets, corresponding multi-level mathematical models are needed, i.e. models that simultaneously capture multiple layers of the biological, physiological and disease-level organization (also referred to as quantitative systems pharmacology-QSP-models). However, today's multi-level models are not yet embedded in end-usage applications, neither in drug research and development nor in the clinic. Given the expectations and claims made historically, this seemingly slow adoption may seem surprising. Therefore, we herein consider a specific example-type 2 diabetes-and critically review the current status and identify key remaining steps for these models to become mainstream in the future. This overview reveals how, today, we may use models to ask scientific questions concerning, e.g., the cellular origin of insulin resistance, and how this translates to the whole-body level and short-term meal responses. However, before these multi-level models can become truly useful, they need to be linked with the capabilities of other important existing models, in order to make them 'personalized' (e.g. specific to certain patient phenotypes) and capable of describing long-term disease progression. To be useful in drug development, it is also critical that the developed models and their underlying data and assumptions are easily accessible. For clinical end-usage, in addition, model links to decision-support systems combined with the engagement of other disciplines are needed to create user-friendly and cost-efficient software packages.

Early BMP, Wnt and Ca(2+)/PKC pathway activation predicts the bone forming capacity of periosteal cells in combination with calcium phosphates

The development of osteoinductive calcium phosphate- (CaP) based biomaterials has, and continues to be, a major focus in the field of bone tissue engineering. However, limited insight into the spatiotemporal activation of signalling pathways has hampered the optimisation of in vivo bone formation and subsequent clinical translation. To gain further knowledge regarding the early molecular events governing bone tissue formation, we combined human periosteum derived progenitor cells with three types of clinically used CaP-scaffolds, to obtain constructs with a distinct range of bone forming capacity in vivo. Protein phosphorylation together with gene expression for key ligands and target genes were investigated 24 hours after cell seeding in vitro, and 3 and 12 days post ectopic implantation in nude mice. A computational modelling approach was used to deduce critical factors for bone formation 8 weeks post implantation. The combined Ca(2+)-mediated activation of BMP-, Wnt- and PKC signalling pathways 3 days post implantation were able to discriminate the bone forming from the non-bone forming constructs. Subsequently, a mathematical model able to predict in vivo bone formation with 96% accuracy was developed. This study illustrates the importance of defining and understanding CaP-activated signalling pathways that are required and sufficient for in vivo bone formation. Furthermore, we demonstrate the reliability of mathematical modelling as a tool to analyse and deduce key factors within an empirical data set and highlight its relevance to the translation of regenerative medicine strategies.

Quasi-Steady-State Analysis based on Structural Modules and Timed Petri Net Predict System's Dynamics: The Life Cycle of the Insulin Receptor

The insulin-dependent activation and recycling of the insulin receptor play an essential role in the regulation of the energy metabolism, leading to a special interest for pharmaceutical applications. Thus, the recycling of the insulin receptor has been intensively investigated, experimentally as well as theoretically. We developed a time-resolved, discrete model to describe stochastic dynamics and study the approximation of non-linear dynamics in the context of timed Petri nets. Additionally, using a graph-theoretical approach, we analyzed the structure of the regulatory system and demonstrated the close interrelation of structural network properties with the kinetic behavior. The transition invariants decomposed the model into overlapping subnetworks of various sizes, which represent basic functional modules. Moreover, we computed the quasi-steady states of these subnetworks and demonstrated that they are fundamental to understand the dynamic behavior of the system. The Petri net approach confirms the experimental results of insulin-stimulated degradation of the insulin receptor, which represents a common feature of insulin-resistant, hyperinsulinaemic states.

Glucose Homeostatic Law: Insulin Clearance Predicts the Progression of Glucose Intolerance in Humans

Homeostatic control of blood glucose is regulated by a complex feedback loop between glucose and insulin, of which failure leads to diabetes mellitus. However, physiological and pathological nature of the feedback loop is not fully understood. We made a mathematical model of the feedback loop between glucose and insulin using time course of blood glucose and insulin during consecutive hyperglycemic and hyperinsulinemic-euglycemic clamps in 113 subjects with variety of glucose tolerance including normal glucose tolerance (NGT), impaired glucose tolerance (IGT) and type 2 diabetes mellitus (T2DM). We analyzed the correlation of the parameters in the model with the progression of glucose intolerance and the conserved relationship between parameters. The model parameters of insulin sensitivity and insulin secretion significantly declined from NGT to IGT, and from IGT to T2DM, respectively, consistent with previous clinical observations. Importantly, insulin clearance, an insulin degradation rate, significantly declined from NGT, IGT to T2DM along the progression of glucose intolerance in the mathematical model. Insulin clearance was positively correlated with a product of insulin sensitivity and secretion assessed by the clamp analysis or determined with the mathematical model. Insulin clearance was correlated negatively with postprandial glucose at 2h after oral glucose tolerance test. We also inferred a square-law between the rate constant of insulin clearance and a product of rate constants of insulin sensitivity and secretion in the model, which is also conserved among NGT, IGT and T2DM subjects. Insulin clearance shows a conserved relationship with the capacity of glucose disposal among the NGT, IGT and T2DM subjects. The decrease of insulin clearance predicts the progression of glucose intolerance.