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De Gaetano A, Nagy I, Kiss D, Romanovski VG, Hardy TA. A simplified longitudinal model for the development of Type 2 Diabetes Mellitus. J Theor Biol 2024; 587:111822. [PMID: 38589006 DOI: 10.1016/j.jtbi.2024.111822] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Revised: 03/22/2024] [Accepted: 03/27/2024] [Indexed: 04/10/2024]
Abstract
Obesity and diabetes are a progressively more and more deleterious hallmark of modern, well fed societies. In order to study the potential impact of strategies designed to obviate the pathological consequences of detrimental lifestyles, a model for the development of Type 2 diabetes geared towards large population simulations would be useful. The present work introduces such a model, representing in simplified fashion the interplay between average glycemia, average insulinemia and functional beta-cell mass, and incorporating the effects of excess food intake or, conversely, of physical activity levels. Qualitative properties of the model are formally established and simulations are shown as examples of its use.
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Affiliation(s)
- Andrea De Gaetano
- Consiglio Nazionale delle Ricerche, CNR-IASI Rome and CNR-IRIB Palermo, Italy; Department of Biomatics, Óbuda University, Budapest, Hungary
| | - Ilona Nagy
- Department of Analysis and Operations Research, Institute of Mathematics, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary.
| | - Daniel Kiss
- John von Neumann Faculty of Informatics, Óbuda University, Budapest, Hungary
| | - Valery G Romanovski
- Center for Applied Mathematics and Theoretical Physics, University of Maribor, SI-2000, Maribor, Slovenia; Faculty of Electrical Engineering and Computer Science, University of Maribor, SI-2000, Maribor, Slovenia; Faculty of Natural Science and Mathematics, University of Maribor, SI-2000, Maribor, Slovenia
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2
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Ridout SA, Vellanki P, Nemenman I. A mathematical model for ketosis-prone diabetes suggests the existence of multiple pancreatic β-cell inactivation mechanisms. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.06.04.597343. [PMID: 38895272 PMCID: PMC11185683 DOI: 10.1101/2024.06.04.597343] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/21/2024]
Abstract
Ketosis-prone diabetes mellitus (KPD) is a subtype of type 2 diabetes, which presents much like type 1 diabetes, with dramatic hyperglycemia and ketoacidosis. Although KPD patients are initially insulin-dependent, after a few months of insulin treatment, ~ 70% undergo near-normoglycemia remission and can maintain blood glucose without insulin, as in early type 2 diabetes or prediabetes. Here, we propose that these phenomena can be explained by the existence of a fast, reversible glucotoxicity process, which may exist in all people but be more pronounced in those susceptible to KPD. We develop a simple mathematical model of the pathogenesis of KPD, which incorporates this assumption, and show that it reproduces the phenomenology of KPD, including variations in the ability for patients to achieve and sustain remission. These results suggest that a variation of our model may be able to quantitatively describe variations in the course of remission among individuals with KPD.
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Affiliation(s)
- Sean A. Ridout
- Department of Physics, Emory University, Atlanta, GA, USA
- Initiative in Theory and Modeling of Living Systems, Emory University, Atlanta, GA, USA
| | - Priyathama Vellanki
- Department of Internal Medicine, Division of Endocrinology, Emory University School of Medicine, Emory University, Atlanta, GA, USA
- Grady Health System, Atlanta, GA, USA
| | - Ilya Nemenman
- Department of Physics, Emory University, Atlanta, GA, USA
- Initiative in Theory and Modeling of Living Systems, Emory University, Atlanta, GA, USA
- Department of Biology, Emory University, Atlanta, GA, USA
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3
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Subramanian V, Bagger JI, Harihar V, Holst JJ, Knop FK, Villsbøll T. An extended minimal model of OGTT: estimation of α- and β-cell dysfunction, insulin resistance, and the incretin effect. Am J Physiol Endocrinol Metab 2024; 326:E182-E205. [PMID: 38088864 PMCID: PMC11193523 DOI: 10.1152/ajpendo.00278.2023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 08/28/2023] [Revised: 11/27/2023] [Accepted: 12/07/2023] [Indexed: 12/20/2023]
Abstract
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.
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Affiliation(s)
- Vijaya Subramanian
- Institute for Computational Medicine, Johns Hopkins University, Baltimore, Maryland, United States
| | - Jonatan I Bagger
- Center for Clinical Metabolic Research, Gentofte Hospital, University of Copenhagen, Hellerup, Denmark
- Novo Nordisk Foundation Center for Basic Metabolic Research, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark
- Clinical Research, Steno Diabetes Center Copenhagen, Herlev, Denmark
| | - Vinayak Harihar
- Department of Biophysics, Johns Hopkins University, Baltimore, Maryland, United States
- Biophysics Graduate Group, University of California, Berkeley, California, United States
| | - Jens J Holst
- Novo Nordisk Foundation Center for Basic Metabolic Research, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark
- Department of Biomedical Sciences, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark
| | - Filip K Knop
- Center for Clinical Metabolic Research, Gentofte Hospital, University of Copenhagen, Hellerup, Denmark
- Novo Nordisk Foundation Center for Basic Metabolic Research, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark
- Clinical Research, Steno Diabetes Center Copenhagen, Herlev, Denmark
- Department of Clinical Medicine, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark
| | - Tina Villsbøll
- Center for Clinical Metabolic Research, Gentofte Hospital, University of Copenhagen, Hellerup, Denmark
- Clinical Research, Steno Diabetes Center Copenhagen, Herlev, Denmark
- Department of Clinical Medicine, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark
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Zhao Y, Jing W, Li L, Zhao S, Yamasaki M. Dynamical modeling the effect of glucagon-like peptide on glucose-insulin regulatory system based on mice experimental observation. Math Biosci 2023; 366:109090. [PMID: 37890522 DOI: 10.1016/j.mbs.2023.109090] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2023] [Revised: 10/17/2023] [Accepted: 10/18/2023] [Indexed: 10/29/2023]
Abstract
As an emerging global epidemic, type 2 diabetes mellitus (T2DM) represents one of the leading causes of morbidity and mortality worldwide. Existing evidences demonstrated that glucagon-like peptide-1 (GLP-1) modulate the glucose regulatory system by enhancing the β-cell function. However, the detailed process of GLP-1 in glycaemic regulator for T2DM remains to be clarified. Thus, in this study, we propose an Institute of Cancer Research (ICR) mice high fat and cholesterol dietary experimental data-driven mathematical model to investigate the secretory effect of GLP-1 on the dynamics of glucose-insulin regulatory system. Specifically, we develop a mathematical model of GLP-1 dynamics as part of the interaction model of β-cell, insulin, and glucose dynamics. The parameter estimation and data fitting are in agreement with the data in mice experiments In addition, uncertainty quantification is performed to explore the possible factors that influence the pathways leading to the pathological state. Model analyses reveal that the high fat or high cholesterol diet stimulated GLP-1 plays an important role in the dynamics of glucose, insulin and β cells in short-term. These results show that enhanced GLP-1 may mitigate the dysregulation of glucose-insulin regulatory system via promoting the β cells function and stimulating secretion of insulin, which offers an in-depth insights into the mechanistic of hyperglycemia from dynamical approach and provide the theoretical basis for GLP-1 served as a potential clinical targeted drug for treatment of T2DM.
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Affiliation(s)
- Yu Zhao
- School of Public Health, Ningxia Medical University, Ningxia, Yinchuan 750004, China; Ningxia Key Laboratory of Environmental Factors and Chronic Disease Control, 1160 Shengli Street, Xingqing District, Yinchuan 750001, China.
| | - Wenjun Jing
- School of Statistics, Shanxi University of Finance and Economics, Taiyuan, Shanxi, 030006, China
| | - Liping Li
- School of Public Health, Ningxia Medical University, Ningxia, Yinchuan 750004, China; Ningxia Key Laboratory of Environmental Factors and Chronic Disease Control, 1160 Shengli Street, Xingqing District, Yinchuan 750001, China
| | - Shi Zhao
- JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China
| | - Masayuki Yamasaki
- Faculty of Human Sciences, Shimane University, Shimane, 6908504, Japan.
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Yildirim V, Sheraton VM, Brands R, Crielaard L, Quax R, van Riel NA, Stronks K, Nicolaou M, Sloot PM. A data-driven computational model for obesity-driven diabetes onset and remission through weight loss. iScience 2023; 26:108324. [PMID: 38026205 PMCID: PMC10665812 DOI: 10.1016/j.isci.2023.108324] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2023] [Revised: 08/22/2023] [Accepted: 10/20/2023] [Indexed: 12/01/2023] Open
Abstract
Obesity is a major risk factor for the development of type 2 diabetes (T2D), where a sustained weight loss may result in T2D remission in individuals with obesity. To design effective and feasible intervention strategies to prevent or reverse T2D, it is imperative to study the progression of T2D and remission together. Unfortunately, this is not possible through experimental and observational studies. To address this issue, we introduce a data-driven computational model and use human data to investigate the progression of T2D with obesity and remission through weight loss on the same timeline. We identify thresholds for the emergence of T2D and necessary conditions for remission. We explain why remission is only possible within a window of opportunity and the way that window depends on the progression history of T2D, individual's metabolic state, and calorie restrictions. These findings can help to optimize therapeutic intervention strategies for T2D prevention or treatment.
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Affiliation(s)
- Vehpi Yildirim
- Department of Public and Occupational Health, Amsterdam University Medical Centers, University of Amsterdam, 1081 BT Amsterdam, the Netherlands
- Institute for Advanced Study, University of Amsterdam, 1012 GC Amsterdam, the Netherlands
| | - Vivek M. Sheraton
- Institute for Advanced Study, University of Amsterdam, 1012 GC Amsterdam, the Netherlands
- Computational Science Lab, University of Amsterdam, 1098 XH Amsterdam, the Netherlands
- Center for Experimental and Molecular Medicine, Amsterdam University Medical Centers, 1100 DD Amsterdam, the Netherlands
| | - Ruud Brands
- AMRIF B.V., Agro Business Park, 6708 PW Wageningen, the Netherlands
- Institute for Risk Assessment Sciences, Utrecht University, 3584 CL Utrecht, the Netherlands
| | - Loes Crielaard
- Department of Public and Occupational Health, Amsterdam University Medical Centers, University of Amsterdam, 1081 BT Amsterdam, the Netherlands
- Institute for Advanced Study, University of Amsterdam, 1012 GC Amsterdam, the Netherlands
| | - Rick Quax
- Institute for Advanced Study, University of Amsterdam, 1012 GC Amsterdam, the Netherlands
- Computational Science Lab, University of Amsterdam, 1098 XH Amsterdam, the Netherlands
| | - Natal A.W. van Riel
- Department of Biomedical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, the Netherlands
- Department of Experimental and Vascular Medicine, Amsterdam University Medical Centers, 1100 DD Amsterdam, the Netherlands
| | - Karien Stronks
- Department of Public and Occupational Health, Amsterdam University Medical Centers, University of Amsterdam, 1081 BT Amsterdam, the Netherlands
- Institute for Advanced Study, University of Amsterdam, 1012 GC Amsterdam, the Netherlands
| | - Mary Nicolaou
- Department of Public and Occupational Health, Amsterdam University Medical Centers, University of Amsterdam, 1081 BT Amsterdam, the Netherlands
- Institute for Advanced Study, University of Amsterdam, 1012 GC Amsterdam, the Netherlands
| | - Peter M.A. Sloot
- Institute for Advanced Study, University of Amsterdam, 1012 GC Amsterdam, the Netherlands
- Computational Science Lab, University of Amsterdam, 1098 XH Amsterdam, the Netherlands
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Sugimoto H, Hironaka KI, Yamada T, Sakaguchi K, Ogawa W, Kuroda S. DI/cle, a Measure Consisting of Insulin Sensitivity, Secretion, and Clearance, Captures Diabetic States. J Clin Endocrinol Metab 2023; 108:3080-3089. [PMID: 37406246 PMCID: PMC10655546 DOI: 10.1210/clinem/dgad392] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 02/02/2023] [Revised: 06/26/2023] [Accepted: 06/30/2023] [Indexed: 07/07/2023]
Abstract
CONTEXT Insulin clearance is implicated in regulation of glucose homeostasis independently of insulin sensitivity and insulin secretion. OBJECTIVE To understand the relation between blood glucose and insulin sensitivity, secretion, and clearance. METHODS We performed a hyperglycemic clamp, a hyperinsulinemic-euglycemic clamp, and an oral glucose tolerance test (OGTT) in 47, 16, and 49 subjects with normal glucose tolerance (NGT), impaired glucose tolerance (IGT), and type 2 diabetes mellitus (T2DM), respectively. Mathematical analyses were retrospectively performed on this dataset. RESULTS The disposition index (DI), defined as the product of insulin sensitivity and secretion, showed a weak correlation with blood glucose levels, especially in IGT (r = 0.04; 95% CI, -0.63 to 0.44). However, an equation relating DI, insulin clearance, and blood glucose levels was well conserved regardless of the extent of glucose intolerance. As a measure of the effect of insulin, we developed an index, designated disposition index/clearance, (DI/cle) that is based on this equation and corresponds to DI divided by the square of insulin clearance. DI/cle was not impaired in IGT compared with NGT, possibly as a result of a decrease in insulin clearance in response to a reduction in DI, whereas it was impaired in T2DM relative to IGT. Moreover, DI/cle estimated from a hyperinsulinemic-euglycemic clamp, OGTT, or a fasting blood test were significantly correlated with that estimated from 2 clamp tests (r = 0.52; 95% CI, 0.37 to 0.64, r = 0.43; 95% CI, 0.24 to 0.58, r = 0.54; 95% CI, 0.38 to 0.68, respectively). CONCLUSION DI/cle can serve as a new indicator for the trajectory of changes in glucose tolerance.
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Affiliation(s)
- Hikaru Sugimoto
- Department of Biochemistry and Molecular Biology, Graduate School of Medicine, The University of Tokyo, Tokyo 113-0033, Japan
| | - Ken-ichi Hironaka
- Department of Biological Sciences, Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan
| | - Tomoko Yamada
- Division of Diabetes and Endocrinology, Department of Internal Medicine, Kobe University Graduate School of Medicine, Hyogo 650-0017, Japan
| | - Kazuhiko Sakaguchi
- Division of Diabetes and Endocrinology, Department of Internal Medicine, Kobe University Graduate School of Medicine, Hyogo 650-0017, Japan
| | - Wataru Ogawa
- Division of Diabetes and Endocrinology, Department of Internal Medicine, Kobe University Graduate School of Medicine, Hyogo 650-0017, Japan
| | - Shinya Kuroda
- Department of Biochemistry and Molecular Biology, Graduate School of Medicine, The University of Tokyo, Tokyo 113-0033, Japan
- Department of Biological Sciences, Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan
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Subramanian V, Bagger JI, Holst JJ, Knop FK, Vilsbøll T. A glucose-insulin-glucagon coupled model of the isoglycemic intravenous glucose infusion experiment. Front Physiol 2022; 13:911616. [PMID: 36148302 PMCID: PMC9485803 DOI: 10.3389/fphys.2022.911616] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2022] [Accepted: 07/19/2022] [Indexed: 11/13/2022] Open
Abstract
Type 2 diabetes (T2D) is a pathophysiology that is characterized by insulin resistance, beta- and alpha-cell dysfunction. Mathematical models of various glucose challenge experiments have been developed to quantify the contribution of insulin and beta-cell dysfunction to the pathophysiology of T2D. There is a need for effective extended models that also capture the impact of alpha-cell dysregulation on T2D. In this paper a delay differential equation-based model is developed to describe the coupled glucose-insulin-glucagon dynamics in the isoglycemic intravenous glucose infusion (IIGI) experiment. As the glucose profile in IIGI is tailored to match that of a corresponding oral glucose tolerance test (OGTT), it provides a perfect method for studying hormone responses that are in the normal physiological domain and without the confounding effect of incretins and other gut mediated factors. The model was fit to IIGI data from individuals with and without T2D. Parameters related to glucagon action, suppression, and secretion as well as measures of insulin sensitivity, and glucose stimulated response were determined simultaneously. Significant impairment in glucose dependent glucagon suppression was observed in patients with T2D (duration of T2D: 8 (6–36) months) relative to weight matched control subjects (CS) without diabetes (k1 (mM)−1: 0.16 ± 0.015 (T2D, n = 7); 0.26 ± 0.047 (CS, n = 7)). Insulin action was significantly lower in patients with T2D (a1 (10 pM min)−1: 0.000084 ± 0.0000075 (T2D); 0.00052 ± 0.00015 (CS)) and the Hill coefficient in the equation for glucose dependent insulin response was found to be significantly different in T2D patients relative to CS (h: 1.4 ± 0.15; 1.9 ± 0.14). Trends in parameters with respect to fasting plasma glucose, HbA1c and 2-h glucose values are also presented. Significantly, a negative linear relationship is observed between the glucagon suppression parameter, k1, and the three markers for diabetes and is thus indicative of the role of glucagon in exacerbating the pathophysiology of diabetes (Spearman Rank Correlation: (n = 12; (−0.79, 0.002), (−0.73,.007), (−0.86,.0003)) respectively).
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Affiliation(s)
- Vijaya Subramanian
- Institute for Computational Medicine, Johns Hopkins University, Baltimore, MD, United States
- *Correspondence: Vijaya Subramanian, ; Jonatan I. Bagger,
| | - Jonatan I. Bagger
- Center for Clinical Metabolic Research, Herlev and Gentofte Hospital, University of Copenhagen, Hellerup, Denmark
- Novo Nordisk Foundation Center for Basic Metabolic Research, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark
- Clinical Research, Steno Diabetes Center Copenhagen, Herlev, Denmark
- *Correspondence: Vijaya Subramanian, ; Jonatan I. Bagger,
| | - Jens J. Holst
- Novo Nordisk Foundation Center for Basic Metabolic Research, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark
- Department of Biomedical Sciences, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark
| | - Filip K. Knop
- Center for Clinical Metabolic Research, Herlev and Gentofte Hospital, University of Copenhagen, Hellerup, Denmark
- Novo Nordisk Foundation Center for Basic Metabolic Research, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark
- Clinical Research, Steno Diabetes Center Copenhagen, Herlev, Denmark
- Department of Clinical Medicine, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark
| | - Tina Vilsbøll
- Center for Clinical Metabolic Research, Herlev and Gentofte Hospital, University of Copenhagen, Hellerup, Denmark
- Clinical Research, Steno Diabetes Center Copenhagen, Herlev, Denmark
- Department of Clinical Medicine, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark
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Yang B, Li J, Haller MJ, Schatz DA, Rong L. The progression of secondary diabetes: A review of modeling studies. Front Endocrinol (Lausanne) 2022; 13:1070979. [PMID: 36619543 PMCID: PMC9812520 DOI: 10.3389/fendo.2022.1070979] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 10/15/2022] [Accepted: 11/23/2022] [Indexed: 12/24/2022] Open
Abstract
Mathematical modeling has provided quantitative information consistent with experimental data, greatly improving our understanding of the progression of type 1 and type 2 diabetes. However, diabetes is a complex metabolic disease and has been found to be involved in crosstalk interactions with diverse endocrine diseases. Mathematical models have also been developed to investigate the quantitative impact of various hormonal disorders on glucose imbalance, advancing the precision treatment for secondary diabetes. Here we review the models established for the study of dysglycemia induced by hormonal disorders, such as excessive glucocorticoids, epinephrine, and growth hormone. To investigate the influence of hyperthyroidism on the glucose regulatory system, we also propose a hyperthyroid-diabetes progression model. Model simulations indicate that timely thyroid treatment can halt the progression of hyperglycemia and prevent beta-cell failure. This highlights the diagnosis of hormonal disorders, together withblood sugar tests, as significant measures for the early diagnosis and treatment of diabetes. The work recapitulates updated biological research on the interactions between the glucose regulatory system and other endocrine axes. Further mathematical modeling of secondary diabetes is desired to promote the quantitative study of the disease and the development of individualized diabetic therapies.
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Affiliation(s)
- Boya Yang
- Department of Mathematics, University of Florida, Gainesville, FL, United States
| | - Jiaxu Li
- Department of Mathematics, University of Louisville, Louisville, KY, United States
| | - Michael J. Haller
- Department of Pediatrics, University of Florida, Gainesville, FL, United States
| | - Desmond A. Schatz
- Department of Pediatrics, University of Florida, Gainesville, FL, United States
| | - Libin Rong
- Department of Mathematics, University of Florida, Gainesville, FL, United States
- *Correspondence: Libin Rong,
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Chudtong M, Gaetano AD. A mathematical model of food intake. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:1238-1279. [PMID: 33757185 DOI: 10.3934/mbe.2021067] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
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.
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Affiliation(s)
- Mantana Chudtong
- Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
- Center of Excellence in Mathematics, the Commission on Higher Education, Si Ayutthaya Rd., Bangkok 10400, Thailand
| | - Andrea De Gaetano
- Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
- Consiglio Nazionale delle Ricerche, Istituto per la Ricerca e l'Innovazione Biomedica (CNR-IRIB), Palermo, Italy
- Consiglio Nazionale delle Ricerche, Istituto di Analisi dei Sistemi ed Informatica "A. Ruberti" (CNR-IASI), Rome, Italy
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10
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Mari A, Tura A, Grespan E, Bizzotto R. Mathematical Modeling for the Physiological and Clinical Investigation of Glucose Homeostasis and Diabetes. Front Physiol 2020; 11:575789. [PMID: 33324238 PMCID: PMC7723974 DOI: 10.3389/fphys.2020.575789] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2020] [Accepted: 11/04/2020] [Indexed: 12/21/2022] Open
Abstract
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.
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Affiliation(s)
- Andrea Mari
- Institute of Neuroscience, National Research Council, Padua, Italy
| | - Andrea Tura
- Institute of Neuroscience, National Research Council, Padua, Italy
| | - Eleonora Grespan
- Institute of Neuroscience, National Research Council, Padua, Italy
| | - Roberto Bizzotto
- Institute of Neuroscience, National Research Council, Padua, Italy
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11
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Abstract
Diabetes is a chronic, progressive disease that calls for longitudinal data and analysis. We introduce a longitudinal mathematical model that is capable of representing the metabolic state of an individual at any point in time during their progression from normal glucose tolerance to type 2 diabetes (T2D) over a period of years. As an application of the model, we account for the diversity of pathways typically followed, focusing on two extreme alternatives, one that goes through impaired fasting glucose (IFG) first and one that goes through impaired glucose tolerance (IGT) first. These two pathways are widely recognized to stem from distinct metabolic abnormalities in hepatic glucose production and peripheral glucose uptake, respectively. We confirm this but go beyond to show that IFG and IGT lie on a continuum ranging from high hepatic insulin resistance and low peripheral insulin resistance to low hepatic resistance and high peripheral resistance. We show that IFG generally incurs IGT and IGT generally incurs IFG on the way to T2D, highlighting the difference between innate and acquired defects and the need to assess patients early to determine their underlying primary impairment and appropriately target therapy. We also consider other mechanisms, showing that IFG can result from impaired insulin secretion, that non-insulin-dependent glucose uptake can also mediate or interact with these pathways, and that impaired incretin signaling can accelerate T2D progression. We consider whether hyperinsulinemia can cause insulin resistance in addition to being a response to it and suggest that this is a minor effect.
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Affiliation(s)
- Joon Ha
- Laboratory of Biological Modeling, National Institutes of Health, Bethesda, Maryland
| | - Arthur Sherman
- Laboratory of Biological Modeling, National Institutes of Health, Bethesda, Maryland
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