Mathematical Modeling of Renal Tubular Glucose Absorption after Glucose Load

Andrea De Gaetano,Dimitris Eliopoulos,Thomas Hardy,Geltrude Mingrone,Simona Panunzi

doi:10.1371/journal.pone.0086963

Abstract

A partial differential Progressive Tubular Reabsorption (PTR) model, describing renal tubular glucose reabsorption and urinary glucose excretion following a glucose load perturbation, is proposed and fitted to experimental data from five subjects. For each subject the Glomerular Filtration Rate was estimated and both blood and urine glucose were sampled following an Intra-Venous glucose bolus. The PTR model was compared with a model representing the conventional Renal Threshold Hypothesis (RTH). A delay bladder compartment was introduced in both formulations. For the RTH model, the average threshold for glycosuria varied between 9.90±4.50 mmol/L and 10.63±3.64 mmol/L (mean ± Standard Deviation) under different hypotheses; the corresponding average maximal transport rates varied between 0.48±0.45 mmol/min (86.29±81.22 mg/min) and 0.50±0.42 mmol/min (90.62±76.15 mg/min). For the PTR Model, the average maximal transports rates varied between 0.61±0.52 mmol/min (109.57±93.77 mg/min) and 0.83±0.95 mmol/min (150.13±171.85 mg/min). The time spent by glucose inside the tubules before entering the bladder compartment varied between 1.66±0.73 min and 2.45±1.01 min.The PTR model proved much better than RTH at fitting observations, by correctly reproducing the delay of variations of glycosuria with respect to the driving glycemia, and by predicting non-zero urinary glucose elimination at low glycemias. This model is useful when studying both transients and steady-state glucose elimination as well as in assessing drug-related changes in renal glucose excretion.

Highlights

Throughout evolution, higher organisms developed complex and highly specific methods to regulate glucose homeostasis
Renal tubular cells have the ability to adapt their glucose reabsorption capacity depending on glucose filtration rate, this in turn depending on plasma glucose concentration
Low-affinity, high capacity sodium glucose cotransporter-2 (SGLT2) and high-affinity, low capacity sodium glucose cotransporter-1 (SGLT1), both located in the proximal tubule of the kidney, increase their activity in presence of increased tubular glucose load [4,5]

Summary

Introduction

Throughout evolution, higher organisms developed complex and highly specific methods to regulate glucose homeostasis. The glomerulus filters approximately 162 grams of glucose per day from plasma, all of which is reabsorbed in tubules under normal conditions [3] (see Figure 1A). In this way, urinary glucose loss is avoided and energy is preserved. Renal tubular cells have the ability to adapt their glucose reabsorption capacity depending on glucose filtration rate, this in turn depending on plasma glucose concentration. It has been observed that in non-diabetic individuals, with Glomerular Filtration Rate (GFR) between 90 and 120 mL/min per m2 Body Surface Area (BSA), essentially complete glucose reabsorptive capacity is maintained up to glucose blood concentrations of about 11 mM [2]. The blood glucose concentration at which this phenomenon is observed is commonly known as the Renal Glucose Threshold for excretion (RGT), and the approximately linear above-threshold relationship between hyperglycemia and glycosuria (excretion of glucose into the urine) has been extensively studied, in normal subjects as well as in patients with Type 1 and Type 2 Diabetes Mellitus [6,7,8]

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