## 2 Methods and Materials  
### Subjects  
A total of 20 DCE-MRI examinations were available for experiments [16]. The data sets were collected from 10 healthy volunteers. Each subject was imaged twice, seven days apart (further, these examinations will be referred to as Session 1 and 2). The acquisition sequence used the standard 3D fast low-angle shot (FLASH) spoiled gradient recalled echo technique with the following parameters: TR = 2.36 ms, TE = 0.8 ms, FA = 20\({}^{\circ}\), in-plane resolution = 2.2 \(\times\) 2.2 mm\({}^{2}\), slice thickness = 3 mm, acquisition matrix = 192 \(\times\) 192, number of slices = 30. Prior to image acquisition, patients were administered 0.025 mmol/kg of GdDOTA at 3 mL/s flow rate. The contrast agent was injected intravenously. Then, 74 volumetric scans were gathered in 2.3 s time intervals.  
Every image series was registered in the time domain using the b-splines method, as implemented in the Insight Toolkit (ITK) library [17]. Specifically, we used Slicer 3D software to accomplish the task. For every study, the same reference frame was used as a fixed volume that every other (moving) volume was matched to. B-splines registration was performed fully automatically, i.e., no fiducial points were marked over tissues of interest. Furthermore, the procedure was launched in a multi-stage configuration. In each stage, various settings of grid size and subsampling rates were used. For a detailed interpretation of these parameters, the reader is referred to the ITK documentation. In short, they allow the registration of images at different scales--starting from coarse matching and then refining the outcome.  
A common practice in DCE series analysis is to interpolate the measured signal so as to achieve a higher temporal resolution and capture more precisely the critical phases of the perfusion process, such as, e.g., bolus arrival time or the peak of the signal enhancement [10]. As such, we applied cubic spline interpolation to the observed intensity time courses, and then resampled the interpolated signal curves at 0.4 milliseconds intervals.  
As stated in the introduction, analysis of the DCE images leads to estimation of the GFR. Thus, in order to validate the obtained estimates against ground-truth values, volunteers underwent iohexol clearance tests. The measurement was carried out by administrating a dose of 5 mL of iohexol (300 mg I/mL; Omnipaque 300, GE Healthcare), and then acquiring a venous blood sample after 4 h.  
No specific diet was imposed on the participating subjects, but they were asked to abstain from alcohol and high-protein meals, avoid exhausting physical exertion, be normally hydrated at least 2 days before examination, and have no caffeine on the examination day. Apart from these restrictions, participants were instructed to retain their ordinary habits concerning the type and amount of consumed food so as to assure stable examination conditions. All subjects gave their informed consent for inclusion before they participated in the study. The study was conducted in accordance with the Declaration of Helsinki, and the protocol was approved by the Regional Committees for Medical Research Ethics Western Norway (REC West 2012/1869).