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Previous reports have described the use of magnetic resonance imaging (MRI) to estimate single-kidney extraction fraction (EF) and glomerular filtration rate (GFR), by measuring the concentration difference of intravenously injected Gd-chelate ([Gd]) in the renal artery and renal vein from measurements of blood T1. Problematic is the fact that [Gd] measurements in the renal artery are often inaccurate due to the small size, tortuousness and motion of the vessel. Consequently, the [Gd] in the inferior vena cava (IVC) below the renal vein ostia (i.e., the infrarenal IVC) has been used instead of the renal artery [Gd], based on the assumption that the [Gd] in the infrarenal IVC is the same as it is in the renal artery. However, this assumption has neither been theoretically nor experimentally investigated. Herein, we describe new difference and differential equation pharmacological models that can predict the biodistribution of Gd-chelate throughout the extracellular space. Assuming known average normal blood flows and GFR, our models predict that the infrarenal IVC [Gd] is 3.2% to 4.7% greater than the renal artery [Gd], and that the EF estimate using this IVC measurement is overestimated by 14.2%-20.0%. To support these predictions, algebraic equations are derived which show that the infrarenal IVC must develop a relatively high [Gd] in order to satisfy Gd flux constraints within the vascular system. These results suggest that the infrarenal IVC [Gd] is not a valid substitute for the renal artery [Gd].