A critical review of mathematical models and data used in diabetology

Boutayeb, Abdesslam; Chetouani, Abdelaziz

doi:10.1186/1475-925x-5-43

Cited by 104 publications

(54 citation statements)

References 87 publications

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“…Mathematical models can be used effectively to estimate disease prevalence and help understand factors affecting disease development risk. The majority of diabetesrelated mathematical models explain clinical aspects of glucosee insulin dynamics, whereas few models have been specific to the epidemiology of diabetes [3]. Diabetes prevalence varies significantly with age implying the mechanisms underlying risk of developing diabetes could be age specific.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, a mathematical representation calculating diabetes incidence rates within the model itself can provide a better option for an efficient and more accurate prediction of diabetes prevalence. Mathematical models also allow for estimating parameters and determining sensitivities [3]. A model representing all major population mechanisms such as births, deaths, aging, migration, and diabetes incidence will help to assess relative sensitivities or strength of associations of each of these mechanisms to diabetes prevalence.…”

Section: Introductionmentioning

confidence: 99%

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A mathematical model for determining age-specific diabetes incidence and prevalence using body mass index

Appuhamy

Kebreab

2013

Annals of Epidemiology

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a b s t r a c tPurpose: Few models have been developed specifically for the epidemiology of diabetes. Diabetes incidence is critical in predicting diabetes prevalence. However, reliable estimates of disease incidence rates are difficult to obtain. The aim of this study was to propose a mathematical framework for predicting diabetes prevalence using incidence rates estimated within the model using body mass index (BMI) data. Methods: A generic mechanistic model was proposed considering birth, death, migration, aging, and diabetes incidence dynamics. Diabetes incidence rates were determined within the model using their relationships with BMI represented by the Hill equation. The Hill equation parameters were estimated by fitting the model to National Health and Nutrition Examination Survey (NHANES) 1999e2010 data and used to predict diabetes prevalence pertaining to each NHANES survey year. The prevalences were also predicted using diabetes incidence rates calculated from the NHANES data themselves. The model was used to estimate death rate parameters and to quantify sensitivities of prevalence to each population dynamic. Results: The model using incidence rate estimates from the Hill equations successfully predicted diabetes prevalence of younger, middle-aged, and older adults (prediction error, 20.0%, 9.64%, and 7.58% respectively). Diabetes prevalence was positively associated with diabetes incidence in every age group, but the associations among younger adults were stronger. In contrast, diabetes prevalence was more sensitive to death rates in older adults than younger adults. Both diabetes incidence and prevalence were strongly sensitive to BMI at younger ages, but sensitivity gradually declined as age progressed. Younger and middle aged adults diagnosed with diabetes had at least a two-fold greater risk of death than their nondiabetic counterparts. Nondiabetic older adults were found to be under slightly higher death risk (0.079) than those diagnosed with diabetes (0.073). Conclusions: The proposed model predicts diagnosed diabetes incidence and prevalence reasonably well using the link between BMI and diabetes development risk. Ethnic group and gender-specific model parameter estimates could further improve predictions. Model prediction accuracy and applicability need to be comprehensively evaluated with independent data sets.Published by Elsevier Inc. IntroductionDiabetes prevalence is rising dramatically worldwide and is expected to rise from 366 million in 2011 to 552 million by 2030 [1]. More than 10% of world health care expenditure and about 14% of U.S. healthcare costs are attributable to diabetes [2]. Quantifying diabetes prevalence is important to allow rational planning of prevention programs and allocating resources for people affected by diabetes [2]. Mathematical models can be used effectively to estimate disease prevalence and help understand factors affecting disease development risk. The majority of diabetesrelated mathematical models explain clinical aspects of glucosee insulin dynamics, wh...

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A mathematical model for determining age-specific diabetes incidence and prevalence using body mass index

Appuhamy

Kebreab

2013

Annals of Epidemiology

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“…For blood glucose control, it is important to estimate blood glucose response to insulin as accurately as possible. Mathematical models of glucoseinsulin metabolism have been developed [3] since 1960s starting with Bolie [4]. Recent trends of studies are towards 1) models for patients in a specific state, and 2) models of blood glucose excursion after a meal including not only carbohydrates but also fat and/or protein.…”

Section: Mathematical Models Of Glucose-insulin Metabolismmentioning

confidence: 99%

Recent Trends in Blood Glucose Control Studies

2015

Automat Control Physiol State Func

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Diabetes mellitus is a disease of the endocrine system in which blood glucose levels are constantly above the normal range. Since insulin-dependent diabetic patients require insulin administration to maintain blood glucose levels within the normal range, automatic blood glucose control methods to reduce the burden of such open-loop insulin therapy have been studied. In this review, we first introduce some important mathematical models of glucoseinsulin metabolism, followed by some representative blood glucose control systems, where most of them use model predictive control as control algorithm, developed to date and discuss their implications in the near future.

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“…Several mathematical models of the GIG regulatory system are used for theoretical and clinical applications to diabetes control (Makroglou et al, 2006;Boutayeb and Chetouani, 2006), but, no theoretical model has been developed to discuss the role of the brain in the brain glucose homeostasis within the healthy or the diabetes, both of which are generally under varying stresses. Also, neither the effect of brain nor that of stress is included in any currently existing quantitative models of GIG regulatory system.…”

Section: Hypothesis Of Brain Glucose Homeostasismentioning

confidence: 99%

A Control-Theoretical Approach to Model-Based Medicine

Gaohua

Kimura

2008

IFAC Proceedings Volumes

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This paper discusses the notion of model-based medicine which is expected to give a solution to various difficulties in clinical medical systems based upon the familiar methodology of control science. The model-based medicine relies essentially on an integrated model of the visceral system of human body that includes various functional subsystems such as respiration, circulation, thermal, digestion, urinary, endocrine/neuronal systems as its component. We introduce an example of such integrated models of human body developed in our laboratory. Some novel results which enhance the effect of therapy are presented concerning brain hypothermia treatments based on the model. In the latter half of the paper, we propose a new hypothesis on the cause of diabetes based on the integrated model, as well as clinical evidence. We think the real cause of elevation of blood glucose is the homeostasis of glucose concentrations in the brain. In other words, the elevation of blood sugar itself is not as harm as people think, because it is an outcome of control of the brain sugar. Long-term effect of psychological stress is shown to cause diabetes based on our model.

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A critical review of mathematical models and data used in diabetology

Cited by 104 publications

References 87 publications

A mathematical model for determining age-specific diabetes incidence and prevalence using body mass index

A mathematical model for determining age-specific diabetes incidence and prevalence using body mass index

Recent Trends in Blood Glucose Control Studies

A Control-Theoretical Approach to Model-Based Medicine

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