Novel mathematical model for glucose transport in skeletal muscle interstitium

Physiology 2016 (Dublin, Ireland) (2016) Proc Physiol Soc 37, PCB314

Poster Communications: Novel mathematical model for glucose transport in skeletal muscle interstitium

R. J. Sove1, D. Goldman1, G. M. Fraser1

1. Medical Biophysics, Western University, London, Ontario, Canada.

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Type II diabetes is characterized by a decreased sensitivity to insulin resulting in an impairment in glucose uptake and high blood glucose concentrations [1]. Measures of insulin resistance involve blood glucose measurements following an insulin clamp [2]. These global measurements fail to account for the spatial complexity of glucose uptake into the muscle. Therefore, in this study, we developed a spatial mathematical model for glucose transport in skeletal muscle to assess the effects of insulin resistance on glucose uptake. The mathematical model describes the steady-state diffusive transport of both insulin and glucose in the interstitial space between capillaries and muscle fibers in skeletal muscle. The insulin and glucose concentration at the capillary wall was fixed to the blood insulin and glucose concentrations respectively. The insulin flux at the muscle fiber surface was specified according to Michaelis-Menton kinetics for the uptake of insulin into the fiber. Glucose uptake by the muscle fiber was specified to be linearly proportional to glucose concentration and insulin flux. In this work, the governing equations were solved on a two-dimensional cross-section of skeletal muscle orthogonal to capillary blood flow. The geometry was discretized using triangular elements and the governing equations were solved using a Galerkin finite element method. The resulting system of non-linear equations were iteratively linearized and solved using the generalized minimal residual method. Convergence was verified by successively refining the mesh to ensure the solution was independent of the choice of discretization. We simulated glucose and insulin transport for both fasting and post-prandial conditions by altering the blood insulin and blood glucose concentrations. Insulin resistance was simulated by decreasing the rate constant describing the kinetics of glucose uptake by a factor related to the severity of the resistance. Glucose concentration for fasting and post-prandial conditions for the case of no insulin resistance is shown in Figure 1. This figure shows the heterogeneous nature of glucose in the interstitial space. Glucose uptake rate was 165% higher in post-prandial conditions when compared to fasting conditions. The effect of insulin resistance on glucose uptake for both fasting and insulin resistance is shown in Figure 2. Overall, we wish to elucidate the importance of geometry on glucose transport. Here, we demonstrate how glucose uptake rates change with varying levels of insulin resistance in both fasting and post-prandial states. Additionally, capillary density may be altered in type II diabetics [3], and thus may be an important factor in glucose uptake. With this spatial model, we will be able to explore the effects of capillary density in various metabolic conditions.



Where applicable, experiments conform with Society ethical requirements.

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