## 1 Introduction  
Monitoring the state of kidney functioning has become an increasingly important task in modern medical diagnostics. Failures in renal operation may impair physiological homeostasis, leading to the improper management of electrolytes, acid-base balance perturbation, or the deregulation of arterial blood pressure. Kidneys are responsible for blood filtration, and the removal of water-soluble waste products of metabolism and surplus glucose and other organic substances. Kidney diseases include, among others, acute kidney injury [1], chronic kidney disease (CKD) [2] and various cancers (e.g., renal cell carcinoma). Treatment depends on the pathological condition, and may require life-long dialysis, or kidney removal or transplantation. In any case, precise knowledge about kidney performance is needed for the proper diagnosis, treatment and follow-up prognosis. Especially in the case of CKD, which may be caused by longstanding hypertension or diabetes mellitus, it is important to continuously and precisely monitor renal function, since early detection of the disease allows the prevention of its development to the end stage. Tissue perfusion is a viable means of preserving cell nutrition, humoral communication and the elimination of waste products over a lifetime [3]. Thus information about local blood flow and the blood filtration taking part in the glomeruli plays a fundamental role in the diagnosis and follow-up of the aforementioned diseases. Routinely, renal diagnosis is accomplished through the creatinine clearance procedure, or by using the more specific bihexol clearance test. These tests lead to determination of the glomerular filtration rate (GFR)--the main indicator of kidney performance. However, neither procedure enables differentiation between left and right kidney function [4]. Dynamic contrast-enhanced (DCE) magnetic resonance imaging (MRI) is an alternative technique available for the assessment of kidney functioning [5; 6; 7]. The procedure requires the administration of a contrast agent (CA) intravenously, given as a bolus injection, whose passage through the abdominal arterial system and the capillary bed and tubular systems of the kidneys is measured. In contrast to conventional methods, DCE-MRI enables the estimation of GFR for a single kidney, ultimately at the voxel-level, and simultaneously it provides anatomical characteristics of the renal parenchyma. The estimation of renal filtration based on the DCE-MR images involves the pharmacokinetic (PK) modeling of the contrast agent, arriving from the abdominal aorta into a kidney artery, the renal parenchyma and the afferent arterioles of the renal corpuscles, and then passing from the glomerular capillaries through the filtration barrier into the Bowman's space and the tubular system, ending up in the renal pelvis, the ureter and then the bladder as a constituent of the urine. There have been numerous PK models proposed in the literature [8], which vary in (1) the number of tissue compartments, (2) the level of incorporating compartment-specific impulse residue functions, (3) the inclusion of the effect of tracer agent leakage from capillaries in cancerous cells, and (4) the way in which the delay and the broadening of peak CA concentration in the renal parenchyma, relative to the abdominal aorta, is modeled. In the case of the normal-state kidney, all recent models exploit a two-compartment approach [9]. In this setting, at any point in time, the contrast agent concentration in the tissue is the sum of concentrations in the intravascular (IV) and extracellular extravascular (EEV) compartments. In the present study, we used the two-compartment filtration model (2 CFM) proposed by [PERSON] et al. [10]. One approach to finding the PK model's parameters (defined below) is to fit the model-based signal intensity time course to the image data using a non-linear least-squares (NLLS) method. Depending on the model, various explicit parameters are used to characterize tracer agent kinetics.