Subjects
This study was approved by the institutional review board of Erasmus MC, Rotterdam, The Netherlands. Informed consent was obtained from all subjects.
Two subject groups were included in this study. Group I consisted of 11 patients (age 52.2 ± 11.0 years, seven male) with early-stage knee osteoarthritis (knee complaints > 3 months, visual analogue pain scale > 20 mm and Kellgren–Lawrence grade I or II on radiography [9]). Group II consisted of ten healthy controls (age 26.7 ± 8.6 years, four male).
Imaging protocol
Images were acquired on a 3-T MRI (Discovery MR750; General Electric Healthcare, Milwaukee, WI, USA). The three-dimensional (3D) protocol for T1-weighted imaging consisted of an inversion recovery fast spoiled gradient-recalled echo (FSPGR) sequence with five TIs (100; 200; 400; 800; 2,100 ms) [10]. The repetition time (TR) was the inversion time plus the time after read-out (TS = 3.9 ms). Other parameters were: flip angle =15°, echo time = 1.5 ms, field of view = 15 × 15 cm, slice thickness = 3 mm, slice spacing = 3 mm, in-plane voxel size = 0.6 × 0.6 mm, number of slices in the sagittal plane = 36. The dGEMRIC MR protocol lasted approximately 15 min.
In patients, the dGEMRIC protocol [10] was performed twice with an interval of 7 days (range 5–14 days). A double dose (0.2 mmol/kg) of Magnevist (Bayer, Berlin, Germany) was injected intravenously. Next, the patients were asked to cycle for 10 min on a home trainer to promote contrast agent distribution into and throughout the knee and the cartilage [11]. After cycling, there was a delay of 80 min before the participants underwent MRI. An open design three-channel knee coil (Flick Engineering Solutions, Winterswijk, The Netherlands) was used, which enabled imaging of patients with a large knee diameter. Controls underwent MRI with the standard eight-channel knee coil (General Electric Healthcare) requiring a knee diameter less than 14 cm. For the controls, no contrast agent was used, and the second MR examination was acquired after a short break and repositioning of the knee.
Definition of regions of interest
For each subject, two regions of interest (ROIs) on the femoral and tibial cartilage were outlined by a trained researcher with a medical degree (J.vT.). The femoral cartilage ROI consisted of the adjacent trochlear, weight-bearing and posterior cartilage of the femur, and the tibial cartilage ROI consisted of the weight-bearing tibial plateau cartilage. The ROI outlining was performed on the central slice through the medial and lateral tibiofemoral joint, for both the first and second MR examination, resulting in eight cartilage ROIs per subject.
T1 calculation and uncertainty estimate
The T1 map was reconstructed by voxelwise fitting of the relationship SI(TI) = S0·(1-A·exp(-TI/T1) + exp(-TR/T1)) [10] to the T1-weighted images acquired at a range of inversion times. The fitting was performed with a maximum likelihood estimator of T1, S0 (fully relaxed signal) and A (inversion efficiency), which takes into account the Rician distribution of the data because, for magnitude MR images, this is more accurate than the commonly used normal distribution [12].
The uncertainty of the estimated parameters at each voxel can be expressed by the Cramér–Rao lower bound (CRLB), which gives a lower bound for the variance [12–14]. The square root of the T1 CRLB (CRLBσ) can therefore be interpreted as a lower bound for the standard deviation of the T1 value, which quantifies how noise on the MR signal propagates to uncertainty of the estimated T1 value. In quantitative MRI, CRLBσ has previously been used for optimisation of MR sequences [15–17], but it can also be used as an indicator of misalignment. Misalignment of the T1-weighted images, especially at tissue boundaries, results in biologically implausible values of S0, A and T1, often associated with a high uncertainty, which is expressed by CRLBσ. The T1 calculations were performed using in-house developed Matlab software (R2008a; The MathWorks, Natick, MA, USA), which produces both the T1 map and the CRLBσ map. As a summary statistic for the CRLBσ values, we computed the 90% percentile (90%-CRLBσ) over all voxels in each annotated ROI; the lower this value, the better. We also computed the 90%-CRLBσ over all voxels in all ROIs together, to obtain a single measure per subject.
Registration of T1-weighted images
All T1-weighted images were registered in 3D with respect to that T1-weighted image showing the highest contrast between cartilage and surrounding synovial fluid, and between cartilage and bone cortex (FSPGRTI = 2,100). Registrations were performed using Elastix software [18] using a rigid transformation model (translations and rotations). Femoral and tibial regions were registered separately based on subvolumes containing only the specific bone and surrounding tissue to allow correction for motion of the knee joint (Fig. 1). The registration was optimised over 1,000 iterations with localised mutual information (LMI) as a similarity measure [19]. Per iteration, LMI was calculated using 2,048 random samples obtained from a sample region of size 50 × 50 × 50 mm. Cubic B-spline interpolation was used when applying the deformation to the moving image. The exact registration settings can be found on the parameter file database on the Elastix website: http://elastix.isi.uu.nl/wiki.php.
T1 maps were calculated with and without registration. A Wilcoxon signed rank test was used to test for a significant effect of registration on the 90%-CRLBσ values.
Registration between the first and second MR examinations
To align the FSPGRTI = 2,100 images from the first and second MR examinations, registration was performed with the same method as in the previous section. Based on this registration, the T1 maps from the second MR examination were transformed to the T1 maps obtained in the initial study. The result of this alignment was compared with the reference standard of manually selecting matching slices, which was performed by a trained researcher (J.vT.) visually inspecting FSPGRTI=2,100 images from the first and second MR examinations for matching slices.
Analysis of the reproducibility between the first and second MR examinations was based on correlations of a weighted mean T1 value per ROI. A weighted mean was computed to reduce the effect of outliers which are, for example, caused by bone voxels accidently included in the cartilage ROIs. As outliers are expected to have a high CRLBσ, the reciprocal of the CRLBσ was used as the weight of each voxel to reduce their effect.
The reproducibility of the weighted mean T1 values was assessed using the intraclass correlation coefficient (ICC), Pearson’s correlation coefficient and total least squares regression. In these analyses we treated the four ROIs on each image as independent measurements. The ICC describes the resemblance of two sets of data with identical units and an equal variance [20, 21], and can therefore be used to measure the agreement between the first and the registered second MR examination. A total least squares fit [22, 23] was performed to estimate a linear relation between measurements obtained at the two examinations. A fit with a slope significantly different from 1 would imply a systematic difference.