# American Institute of Mathematical Sciences

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2009, 6(4): 753-778. doi: 10.3934/mbe.2009.6.753

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

 1 University of Michigan, Department of Mathematics, Center for Computational Medicine and Bioinformatics, 100 Washtenaw Ave, Ann Arbor, 48109-2218, United States 2 University of Michigan, Department of Mathematics, 530 Church St., Ann Arbor, 48109, United States 3 Duke University, Laboratory of Computational Immunology, Durham, NC 27708, United States 4 University of Michigan, Department of Surgery, C558 MSRB II, Ann Arbor, MI 48109, United States 5 University of Michigan, Departments of Internal Medicine and Human Genetics, School of Public Health, The Brehm Center for Type 1 Diabetes Research and Analysis, Center for Computational Medicine and Bioinformatics, 100 Washtenaw Ave, Ann Arbor, MI 48109-2219, United States 6 University of Michigan, Laboratory of Immunogenetics, Department of Internal Medicine, The Brehm Center for Type 1 Diabetes Research and Analysis, 1500 East Medical Center Drive, Ann Arbor, MI 48109, United States

Received  January 2009 Revised  July 2009 Published  September 2009

Type 1 diabetes (T1DM) is a chronic autoimmune disease with a long prodrome, which is characterized by dysfunction and ultimately destruction of pancreatic $\beta$-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 $\beta$-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 $\beta$-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 $\beta$-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 of 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.
Citation: Patrick Nelson, Noah Smith, Stanca Ciupe, Weiping Zou, Gilbert S. Omenn, Massimo Pietropaolo. Modeling dynamic changes in type 1 diabetes progression: Quantifying $\beta$-cell variation after the appearance of islet-specific autoimmune responses. Mathematical Biosciences & Engineering, 2009, 6 (4) : 753-778. doi: 10.3934/mbe.2009.6.753
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