The present study aimed to assess the repeatability of ADC measurements derived in a diffusion phantom and in brains of healthy volunteers. The diffusion phantom, previously described by Dietrich et al. comprises four glass vials with a 68 mm diameter, containing liquids of varying diffusivities, namely water, acetone, polyethylene glycol (PEG), and dimethyl sulfoxide (DMSO) [36]. The volunteer cohort consisted of eleven individuals (six male and five female), with a median age of 29 years (range 23–38 years). The study was conducted according to the guidelines of the Declaration of Helsinki and was approved by the Institutional Review Board of the Medical Faculty of the LMU University Hospital, LMU Munich (reference number: 22-0954). Informed consent was obtained from all volunteers participating in the study.

Imaging was conducted at a 0.35 T MRIdian MR-linac system (ViewRay Inc., Oakwood Village, OH, USA) [28] at the Department of Radiation Oncology at the LMU University Hospital (LMU Munich). Prior to image acquisition, the treatment delivery system and MRI scanner were decoupled to operate the MR-linac in quality assurance mode to allow for modification of the sequence parameters, and the gantry angle was set to 0°. The diffusion phantom was stored in the treatment room ahead of time to ensure thermal equilibrium. For both diffusion phantom and volunteer scans, the head and neck receiver coils of the system were used, following the setup procedure described by Konnerth et al. but without using a thermoplastic mask [37].

Before systematically imaging volunteers following the scanning protocol described below, the parameters of the DWI pulse sequence were optimized for brain imaging for one volunteer. For this purpose, a prototype single-shot EPI DWI pulse sequence provided by the vendor was adapted in terms of b-values, number of averages, spatial resolution, field-of-view, repetition time, and bandwidth, all while simultaneously considering image quality, spatial resolution, and acquisition time. Two sequence variants were chosen for further investigation: one with a focus on a high spatial resolution (“highRes”), and the other with a focus on a high signal-to-noise ratio (“highSNR”). The respective sequence parameters are summarized in Table 1. The acquisition time for both sequence variants was approximately 6.5 min. The rationale behind this was to ensure that the DWI scan could be obtained within the timeframe allocated for reviewing and adapting the treatment plan between the acquisition of the daily setup MRI scan and the initiation of treatment delivery, thus avoiding any extension of the overall treatment fraction time in clinical practice.

For both sequence variants, axial diffusion-weighted images at five different diffusion weightings (b-values) were acquired (0, 100, 250, 500, 800 s/mm2), where the diffusion gradient was subsequently applied in the three cardinal directions (phase, read, slice). While the acquisition times and the field-of-view were similar for both variants, the main differences were in the number of averages (9 for highRes vs. 11 for highSNR), slice thickness and number (20 slices of 5 mm versus 14 slices of 7 mm), and in-plane voxel size (acquisition matrix voxel size of 3.0 × 3.0 mm2 versus 3.5 × 3.5 mm2). For both variants, zero-filling interpolation was applied before image reconstruction to obtain an image in-plane resolution of 1.5 × 1.5 mm2 and 1.75 × 1.75 mm2 for highRes and highSNR, respectively.

The remaining ten volunteers were scanned with these two sequence variants in a test–retest study [32, 34, 35], following the scanning protocol described below.

A test–retest study with an intermediate out-of-scanner break and repositioning was conducted to assess the repeatability of ADC measurements within the diffusion phantom and ten volunteers. During initial positioning at the MR-linac, the position of the projected virtual isocenter indicated by lasers outside of the scanner bore [28] was marked on adhesive tape attached to the phantom or volunteers’ foreheads, and the respective treatment couch positions were recorded.

After setup, the same scanning protocol was followed for both the phantom and volunteers. First, a 3D-MRI dataset was acquired with a clinical balanced steady-state free precession (bSSFP) sequence (TrueFISP; sagittal slices; slice thickness: 1.5 mm; in-plane resolution: 1.49 × 1.49 mm2; TR/TE: 3.84/1.92 ms; bandwidth: 532 Hz/pixel; flip angle: 60°; field-of-view (LR × AP × SI): 216 × 268 × 280 mm3). This was followed by acquisition of the two DWI sequence variants detailed above (Scan 1; test). Subsequently, the phantom or volunteer were moved out of the scanner bore for a break between scans of at least 5 min. For this, the phantom was removed from, and volunteers were instructed to step off the treatment couch. After the break, the phantom or volunteers were repositioned by moving the treatment couch to the same position as during initial scanning and with the aid of the laser positioning system and marked positions. Subsequently, another 3D-MRI dataset and the two DWI sequence variants were acquired (Scan 2; retest). All acquired data were exported in DICOM format for offline analysis.

All ADC maps were reconstructed offline with an in-house Python script (Python 3.8.10). The geometric mean values of the direction-specific diffusion-weighted images were calculated and fitted pixel-wise with the Python package scipy.optimize.minimize (scipy version 1.3.3; optimizer L-BFGS-B) using the monoexponential function (with two fit parameters):

$$S\left( b \right) = S_ \exp \left( }} \right),$$

(1)

with the signal S0 at b = 0 and S(b) at b-value b, and the ADC. This resulted in four ADC maps for the diffusion phantom and for each volunteer (two sequence variants for both Scan 1 and Scan 2).

For the diffusion phantom and each volunteer, the duration of the outside-scanner break, defined as the time span between the end of sequence variant highSNR in Scan 1 and start of imaging in Scan 2, was calculated.

For analysis of the ADCs, all 3D-MRI datasets and ADC maps were imported into a research version of the treatment planning system RayStation 10B (version 10.1.100.0; RaySearch Laboratories, Stockholm, Sweden). The pre- and post-break 3D-MRI datasets were rigidly registered using the automatic intensity-based rigid registration with correlation coefficient as image similarity measure implemented in the treatment planning system. The results of the registration were visually inspected in overlay plots. The resulting translation vectors and rotations were applied to the ADC maps acquired after the break to map all ADC maps to the same frame-of-reference.

Contouring was performed on the 3D-MRI dataset of Scan 1. For the diffusion phantom, the four vials were contoured, and the contours were contracted by 7 mm for sampling the ADCs in the center of the four liquids contained in the vials (water, DMSO, acetone, and PEG). For the volunteers, the cerebral ventricles were segmented, and the contours were contracted by 2 mm to sample the ADCs within the cerebrospinal fluid (CSF). Additionally, four cylindrical regions-of-interest (ROIs) with a 1 cm radius, a 2.5 cm height, and a volume of 7.9 cm3 located to the left (ROIleft) and right (ROIright) of the ventricles and in the posterior right brain hemisphere (ROIpost) and anterior left hemisphere (ROIant) were defined in regions of relatively homogenous image contrast as observed on the 3D-MRI dataset. All structures were propagated to the four registered ADC maps for the diffusion phantom and each volunteer, respectively.

The average ADCs (mean ± 1σ) within each of the ROIs on each dataset were extracted and compared to literature values. Concerning the diffusion phantom, literature values were retrieved from a study in which the identical diffusion phantom was scanned at a diagnostic 1.5 T MRI scanner at a room temperature of 24 °C with different sequences [36]. The range of ADCs measured with a single-shot EPI DWI pulse sequence in three diffusion directions (read, phase, slice) was considered for comparison. For evaluation of the ADCs in the CSF and the cylindrical ROIs within the volunteers’ brains, reference values were obtained from a publication quantifying the ADCs in various regions of the brains of healthy volunteers [38]. As the cylindrical ROIs contained mixtures of white and gray matter tissue, the overall range of ADCs reported for these two tissue types was considered.

To assess the repeatability of the measurements of the mean ADC in the ROIs in the diffusion phantom, the absolute relative deviation Δ (in percent) was calculated as the absolute difference of the mean ADCs measured in Scan 1 (ADC1) and Scan 2 (ADC2) relative to their mean value [39]:

$$\Delta = \frac}_ - }_ } \right|}}}\left( }_ , }_ } \right)}} \cdot 100\% .$$

(2)

The deviation Δ was calculated for both sequence variants for each ROI of the diffusion phantom (water, DMSO, acetone, and PEG).

Following the Quantitative Imaging Biomarkers Alliance (QIBA) recommendations and definitions [32, 34, 35], the repeatability coefficient (RC) of the mean ADCs, measured in a test–retest scheme, was calculated for each ROI for the volunteers (CSF, ROIleft, ROIright, ROIpost, ROIant). The RC is a metric for the precision and quantifies the range within which 95% of differences between measurements of a biomarker under repeatability conditions within the same subject are expected to fall due to inherent measurement uncertainties [32]. For large sample sizes, the RC for repeated measurements of N subjects is defined as [33, 35, 40,41,42]:

$$} = 1.96 \cdot \sqrt 2 \cdot } = 1.96 \cdot \sqrt 2 \cdot \sqrt \mathop \sum \limits_^ \sigma_^ } ,$$

(3)

with the within-subject standard deviation wSD of the mean ADC within the ROI, the number of volunteers N, and the within-subject variances \(\sigma_^\). With two measurements (test and retest) for a given ROI and volunteer i, with mean values of ADCi,1 (Scan 1) and ADCi,2 (Scan 2), the within-subject variance is (ADCi,1-ADCi,2)2/2, and the RC can be written as:

$$} = 1.96 \cdot \sqrt ^ \left( }_ - }_ } \right)^ }}} .$$

(4)

For small sample sizes (N < 30), the factor of 1.96 needs to be adjusted, by using the critical value tdf of the Student’s t-distribution with N − 1 degrees of freedom (df) at a 95% confidence level, instead. Consequently, for this study, the RC calculation was adjusted accordingly:

$$} = t_}}} \cdot \sqrt ^ \left( }_ - }_ } \right)^ }}} .$$

(5)

The 95% confidence intervals [RCL, RCU] (CIs) for the RC were calculated using the 97.5th and 2.5th percentile values of a \(\chi^\) distribution. The lower and upper limits of the CIs, RCL and RCU, are given by [33]:

$$}_}} = } \cdot \sqrt }}}}}}^ \left( \right)}}} .$$

(6)

and

$$}_}} = } \cdot \sqrt }}}}}}^ \left( \right)}}} .$$

(7)

Furthermore, the relative repeatability coefficient (relRC; in %) was calculated [35, 42]:

$$\begin } & = t_}}} \cdot \sqrt 2 \cdot } \cdot 100\% = t_}}} \cdot \sqrt 2 \cdot \sqrt \mathop \sum \limits_^ \frac^ }}^ }}} \cdot 100\% \\ & = t_}}} \cdot \sqrt \mathop \sum \limits_^ \frac}_ - }_ } \right)^ }}}\left( }_ , }_ } \right)^ }}} \cdot 100\% , \\ \end$$

(8)

with the within-subject coefficient of variation wCV, and the mean value \(\mu_\) of ADCi,1 (Scan 1) and ADCi,2 (Scan 2). The 95% CIs of the relRC were calculated analogously to the CIs of the RC.

The RC and relRC values with the respective CIs were calculated for the CSF and each cylindrical ROI separately, using a critical value of t9 = 2.262 (N = 10 volunteers; df = N − 1 = 9). For better comparability with RCs reported in the literature, these metrics were additionally calculated for all four cylindrical ROIs within the brain tissue combined, using a critical value of t39 = 2.023 (4 ROIs for each volunteer; df = 40 − 1 = 39).

Additionally, Bland–Altman plots for the mean ADCs measured within the ROIs in the volunteers were generated for the CSF, and for the four cylindrical ROIs combined, and respective biases and limits of agreement (LoAs) at 95% confidence were determined [41].