SIAM News Blog

Mathematical Modeling to Improve Understanding of Diabetic Complications in the Kidneys

By Ashlee N. Ford Versypt

Diabetes is the seventh leading cause of death in the United States, and nearly 10% of the population suffers from it. With this significant impact on public health and the complex dynamics of the related biochemistry, diabetes is a popular topic for mathematical modeling. 

Diabetic kidney disease, which is the primary cause for kidney failure, is a severe complication of diabetes. Although modeling of diabetic complications in the kidney is in its infancy compared to the mature application of insulin regulation, it is a promising approach that quantitatively describes the interacting processes in proposed mechanisms for the development and progression of kidney damage due to diabetes.

In a minisymposium presentation titled “Mathematical Modeling of Podocytes in Diabetic Kidney Disease” at the 2016 SIAM Conference on the Life Sciences, held in Boston this July, Ashlee Ford Versypt (School of Chemical Engineering, Oklahoma State University) presented a model for diabetic glucose-induced damage to podocyte cells in kidneys. In the early stages of diabetic kidney disease, kidney tissue damage is primarily focused in glomeruli, bundles of capillaries covered in podocyte cells within the filtration units (nephrons) of the kidney where blood is filtered to produce urine. Significant damage to glomeruli occurs before the leakage of proteins through glomeruli into urine in a clinical condition called proteinuria is detectable by non-invasive measurements. Continued damage ultimately leads to kidney failure. 

Slowing the rate of diabetic kidney disease’s progression before the occurance of irreversible glomerular injury through podocyte damage and loss is critical because these tissues cannot repair themselves. The renin-angiotensin system (RAS) is one of the most important biochemical pathways that impacts the health of podocyte cells (see Figure 1). This hormone system is responsible for regulating blood pressure and fluid balance throughout the body. In contrast to the systemic RAS, podocyte cells independently express the various hormones of RAS intracellularly, and thus can evade systemic pharmaceutical interventions designed to reduce concentrations of the hormone Angiotensin II. Intracellular accumulation of Angiotensin II in hyperglycemia has been linked to damage and death of podocyte cells.

Figure 1. The renin-angiontensin system (RAS) throughout the body is a different biochemical network than that expressed in podocytes cells, which is implicated in kidney damage in diabetic kidney disease. The Ford Versypt lab developed a mathematical model of the intracellular reaction network.

Ford Versypt’s lab model uses a system of ordinary differential equations (ODEs) to represent the kinetics of biochemical production of Angiotensin II intracellularly in podocytes as distinct from the systemic RAS. Parameterization of the model is challenging with sparse data. Due to a lack of time series data, the lab described a steady state network with glucose-sensitive parameters. Ford Versypt is enthusiastic that the model developed in this work will be a useful starting point for connecting with experimental researchers investigating the pathophysiology of diabetic kidney disease. These researchers may then design further experiments to improve understanding of the mechanisms of diabetic kidney disease. The long-term goal is to build increasingly sophisticated mathematical models to connect the various phenomena involved in the progression of diabetic complications in the kidneys. 

This article is based on a minisymposium talk entitled "Mathematical Modeling of Podocytes in Diabetic Kidney Disease" at the SIAM Conference on the Life Sciences, held in Boston this July.

  Ashlee N. Ford Versypt is an assistant professor of chemical engineering at Oklahoma State University and a member of the Harold Hamm Diabetes Center at the University of Oklahoma Health Sciences Center. Her research focuses on mathematical modeling of biomedical and pharmaceutical systems via differential equations and agent-based models. 
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