Investigation of the age-at-onset heterogeneity in type 1 diabetes through mathematical modeling

Wang, Xujing; He, Zening; Ghosh, Soumitra

doi:10.1016/j.mbs.2006.03.021

Cited by 12 publications

(7 citation statements)

References 70 publications

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“…But it would be an interesting addition in a more elaborate model. (β cells have been modelled explicitly in other models; see, e.g., Wang et al (2006) and Mahaffy & Edelstein-Keshet (2007) for different approaches to modelling healthy β cells in T1D. )…”

Section: Discussionmentioning

confidence: 99%

Bifurcation analysis of an existing mathematical model reveals novel treatment strategies and suggests potential cure for type 1 diabetes

Nielsen

Pociot

Ottesen

2013

Mathematical Medicine and Biology

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Type 1 diabetes is a disease with serious personal and socioeconomic consequences that has attracted the attention of modellers recently. But as models of this disease tend to be complicated, there has been only limited mathematical analysis to date. Here we address this problem by providing a bifurcation analysis of a previously published mathematical model for the early stages of type 1 diabetes in diabetes-prone NOD mice, which is based on the data available in the literature. We also show positivity and the existence of a family of attracting trapping regions in the positive 5D cone, converging towards a smaller trapping region, which is the intersection over the family. All these trapping regions are compact sets, and thus, practical weak persistence is guaranteed. We conclude our analysis by proposing 4 novel treatment strategies: increasing the phagocytic ability of resting macrophages or activated macrophages, increasing the phagocytic ability of resting and activated macrophages simultaneously and lastly, adding additional macrophages to the site of inflammation. The latter seems counter-intuitive at first glance, but nevertheless it appears to be the most promising, as evidenced by recent results.

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Section: Discussionmentioning

confidence: 99%

Bifurcation analysis of an existing mathematical model reveals novel treatment strategies and suggests potential cure for type 1 diabetes

Nielsen

Pociot

Ottesen

2013

Mathematical Medicine and Biology

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Section: Modeling the Role Of Apcs In T1dmentioning

confidence: 99%

“…Further extensions of the Freiesleben De Blasio model were subsequently reported . More specifically, a direct description of β‐cells was included , instead of considering only the expression level of autoantigen(s). In this study, it was shown that disease dynamics of T1D critically depend on the rate of β‐cell turnover (i.e., the difference between β‐cell replication/neogenesis and death), which in turn depends on the organ developmental stage of the pancreas.…”

Section: Modeling the Role Of Apcs In T1dmentioning

confidence: 99%

“…Although the Freiesleben De Blasio model and these follow‐up studies provided important qualitative insights about the mechanisms underlying susceptibility, they were mostly phenomenological, and represented only an approximation of the real physiological system. For these reasons, several models were subsequently developed to address certain aspects of macrophage complicity in the initiation of the disease .…”

Section: Modeling the Role Of Apcs In T1dmentioning

confidence: 99%

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Autoimmune responses in T1DM: quantitative methods to understand onset, progression, and prevention of disease

et al. 2014

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Understanding the physiological processes that underlie autoimmune disorders and identifying biomarkers to predict their onset are two pressing issues that need to be thoroughly sorted out by careful thought when analyzing these diseases. Type1 diabetes (T1D) is a typical example of such diseases. It is mediated by autoreactive cytotoxic CD4+ and CD8+ T-cells that infiltrate the pancreatic islets of Langerhans and destroy insulin-secreting β-cells, leading to abnormal levels of glucose in affected individuals. The disease is also associated with a series of islet-specific autoantibodies that appear in high-risk subjects (HRS) several years prior to the onset of diabetes-related symptoms. It has been suggested that T1D is relapsing-remitting in nature and that islet-specific autoantibodies released by lymphocytic B-cells are detectable at different stages of the disease, depending on their binding affinity (the higher, the earlier they appear). The multifaceted nature of this disease and its intrinsic complexity make this disease very difficult to analyze experimentally as a whole. The use of quantitative methods, in the form of mathematical models and computational tools, to examine the disease has been a very powerful tool in providing predictions and insights about the underlying mechanism(s) regulating its onset and development. Furthermore, the models developed may have prognostic implications by aiding in the enrollment of HRS into trials for T1D prevention. In this review, we summarize recent advances made in determining T- and B-cell involvement in T1D using these quantitative approaches and delineate areas where mathematical modeling can make further contributions in unraveling certain aspect of this disease.

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“…Only recently has mechanistic modeling begun to explore specific pathways associated with the effects of T cells in the chain of events causing β -cell destruction that leads to T1DM (16). Work by Wang et al studied the heterogeneity between young- and adult-onset type 1 diabetes (17), and Entelos developed a large scale model of a virtual NOD mouse (18) are some examples.…”

Section: Introductionmentioning

confidence: 99%

Modeling dynamic changes in type 1 diabetes progression: Quantifying $\beta$-cell variation after the appearance of islet-specific autoimmune responses

Smith

Ciupe

Zou³

et al. 2009

Mathematical Biosciences and Engineering

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Type 1 diabetes (T1DM) is a chronic autoimmune disease with a long prodrome, which is characterized by dysfunction and ultimately destruction of pancreatic β-cells. Because of the limited access to pancreatic tissue and pancreatic lymph nodes during the normoglycemic phase of the disease, little is known about the dynamics involved in the chain of events leading to the clinical onset of the disease in humans. In particular, during T1DM progression there is limited information about temporal fluctuations of immunologic abnormalities and their effect on pancreatic β-cell function and mass. Therefore, our understanding of the pathoetiology of T1DM relies almost entirely on studies in animal models of this disease. In an effort to elucidate important mechanisms that may play a critical role in the progression to overt disease, we propose a mathematical model that takes into account the dynamics of functional and dysfunctional β-cells, regulatory T cells, and pathogenic T cells. The model assumes that all individuals carrying susceptible HLA haplotypes will develop variable degrees of T1DM-related immunologic abnormalities. The results provide information about the concentrations and ratios of pathogenic T cells and regulatory T cells, the timing in which β-cells become dysfunctional, and how certain kinetic parameters affect the progression to T1DM. Our model is able to describe changes in the ratio of pathogenic T cells and regulatory T cells after the appearance islet antibodies in the pancreas. Finally, we discuss the robustness of the model and its ability to assist experimentalists in designing studies to test complicated theories about the disease.

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Investigation of the age-at-onset heterogeneity in type 1 diabetes through mathematical modeling

Cited by 12 publications

References 70 publications

Bifurcation analysis of an existing mathematical model reveals novel treatment strategies and suggests potential cure for type 1 diabetes

Bifurcation analysis of an existing mathematical model reveals novel treatment strategies and suggests potential cure for type 1 diabetes

Autoimmune responses in T1DM: quantitative methods to understand onset, progression, and prevention of disease

Modeling dynamic changes in type 1 diabetes progression: Quantifying $\beta$-cell variation after the appearance of islet-specific autoimmune responses

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