As part of a larger, ethically approved (NHS Research Ethics Committee UK no. 21/NS/0128), analyses were performed on a complete cohort of 20 participants (M: 14, F: 6, aged 74.0 ± 6.0, 63–85 years) with clinically determined moderate or severe cerebral small vessel disease (SVD) [13]. Participants attended two visits 30 days apart (mean: 32 ± 7.8, 21–56 days) and underwent a 3 T MRI (Philips 3 T Achieva dStream) and a separate FCI scan on each visit. First, the impact of employing different model fitting techniques on R1 tissue contrast was evaluated in regions of white matter hyperintensities (WMHs) of presumed vascular origin as a proxy for SVD [13]. Second, using the best analysis approach, repeatability and magnitude of R1 contrast (effect size) were determined.

The general FCI technique has previously been reported [10]. A brief description is provided in Fig. 1 to describe the specific approach used in this study. Field-cycling images were acquired across four evolution magnetic field strengths (\(_^)\) of 0.2, 2, 20, and 200 mT. Using the mark II FCI scanner, evolution field strengths were applied for five different evolution times, with evolution times spaced across a logarithmic scale to cover the expected range of brain tissue R1 values. These 20 images were acquired for a single image slice, with an echo time (TE) of 16 ms, matrix size of 90 × 90, and slice thickness of 10 mm. An in-plane resolution of 3.1 × 3.1 mm2 and 2.8 × 2.8 mm2 was obtained for 16 and 24 scans, respectively. The total acquisition time, to collect all 20 FCI contrasts of a single brain image slice, was 30 min. FCI data were processed to remove ghosting artefacts caused by instability in the main magnet current supply [14]. Two participants were recalled after their first scan (one after 7 days; the other after 10 days) to repeat their FCI scans, due to scanner hardware failure.

Field-Cycling Imaging (FCI) experiment. A Mark II FCI scanner configured for brain imaging. B 3T tissue label map co-registered to FCI space. Regions of white matter (WM), grey matter (GM), and white matter hyperintensity (WMH) are delineated. R1 map at evolution field strength of 0.2 mT and dispersion slope maps are shown for visits 1 and 2. C Pulse sequence diagram. FCI acquires images at multiple magnetic evolution field strengths and evolution times. Pre-polarised evolution recovery: to maximise available magnetisation (\(}_})\) prior to the evolution phase for evolution field strengths ≤ 100 mT a pre-polarisation phase is completed at field strength \(}_^}\), (200 mT in this study). After time point \(}_\), \(}_}\) relaxes at a given evolution field (\(}_^}\)) for a specified evolution time (\(}_}\)). \(}_}(}_})\) is then detected at detection field \(}_^}.\) \(}_\) and \(}_^}\) represent the equilibrium magnetisation for \(}_^}\) and \(}_^}\), respectively. Non-polarised evolution recovery: Typically for fields > 100 mT no pre-polarisation phase is needed as sufficient magnetisation will be generated from the evolution stage alone to yield adequate signal-to-noise ratio. The main magnetic field is disabled for approximately one second between shots to prevent overheating of the resistive magnet amplifiers. Therefore, no residual transverse or longitudinal magnetisation persists from shot to shot

3 T MRI data were collected using a 3 T Philips Achieva dStream scanner (Best, NL), using a 32-channel head coil. T1-weighted images were acquired with repetition time (TR) of 8.1 ms, TE of 3.7 ms, acquired matrix size of 256 × 240, acquired voxel size of 1 × 1 × 1 mm3, and reconstructed voxel size of 0.67 × 0.67 × 1  mm3. Fluid attenuation inversion recovery (FLAIR) images were acquired with TR of 4800 ms, inversion time (TI) of 1650 ms, TE of 340 ms, acquired matrix size of 224 × 224, acquired voxel size of 1.12 × 1.12 × 1.12 mm3, and reconstructed voxel size of 0.63 × 0.63 × 0.63 mm3.

Tissue label maps of white matter (WM), grey matter (GM), and white matter hyperintensities (WMHs) were generated from the T1W and FLAIR images obtained at 3 T MRI using standard automated approaches [15]. The FLAIR images and tissue labels were then co-registered to images obtained from FCI using a two-step manual approach in 3D Slicer 5.6.1 [16] and in-house scripts written in MATLAB (R2023a, The MathWorks, USA). First, landmarks placed across multiple slices of the FLAIR image volume and the mean FCI single slice image were used to inform a rigid-body translation so that the orientation of the FLAIR and tissue label image volumes matched the orientation of the FCI image. The location of the FLAIR image slice that matched most closely the FCI image was then used to inform the down sampling of the 3T images to match the FCI image slice thickness. Subsequently, a landmark informed non-linear deformation was performed to match the geometry of the down sampled 3T single slice images to the FCI image.

Prior to voxel wise fitting of acquired FCI imaging data, images were motion corrected and denoised. Motion correction was performed using a rigid-body spatial transformation to the mean FCI image using SPM12 [17]. After motion correction, images were denoised using a pretrained denoising convolutional neural network (dnCNN) approach contained within MATLAB, introduced in R2017b [18]. The supplementary materials available online contain further details of the denoising, and motion correction approaches used.

The most effective model fitting approach to inform reliable quantification of multi-field R1 measurements in brain from FCI was investigated. R1 maps were generated at each evolution field by fitting models with increasing complexity to the signal vs evolution time data in each voxel, from which a value of R1 is assigned to each voxel for every field (see Table 1). The base model describing the evolution of the signal during the field-cycling experiment was derived from Maxwell’s equations separately for when the pre-polarisation field was used (field strengths of 0.2, 2, 20 mT) and not used (200 mT) [10]. Model F1 was used to fit the data acquired at each field independently, and data acquired from multiple fields were fitted simultaneously using four different models (S1–S4). First, because the suitability of simultaneously fitting data from all fields was unknown, data acquired with pre-polarisation at 0.2, 2, and 20 mT were fitted simultaneously, and data acquired at 200 mT were fitted separately (Model S1). Second, data acquired from all fields were fitted simultaneously (Model S2). Then, a Rician noise term was added to the base model in an attempt to more accurately model the noise floor in the acquired data (Model S3). An additional weighting parameter, β, was added to Model S4 as an estimated correction to the magnetisation recovery occurring during both the ramp between evolution and detection fields, and the exposure to readout field before detection. Subsequently, to quantify the field dependence of the R1 measurements, quantitative maps of the R1 dispersion slope, b, were generated by fitting the power law dispersion model to the multi-field R1 values on a voxel-by-voxel basis by R1 = a(\(_^\))b.

To identify which fitting model was best suited for analysis of brain FCI data, tissue region image contrast and dispersion model adherence were compared. Co-registered 3 T tissue maps were used to extract the R1 values from WM, GM, and WMH regions and statistical analyses were performed using SPSS (IBM, V29.0.1.0). Performance of fitting models was evaluated for R1 maps obtained at the lowest field strength of 0.2 mT (R10.2) because visual inspection confirmed this field had the greatest image contrast between WM and WMH regions (see Fig. 2). First, the image contrast between WMH and WM regions, quantified as the degree of separation between histogram distributions of R10.2 values (\(IC=\frac_- _}_}\)), was compared (n = 20, visit 1). Second, the adherence of the calculated R10.2 values to the dispersion power law model was quantified as mean goodness-of-fit (R2) from WMH regions (n = 20, visit 1). Significant difference between fitting models was examined using within-subjects ANOVA and post hoc paired t-tests with significance level after Bonferroni correction set to 0.01. Models S3 and S4 were expected to improve the model fit due to the inclusion of additional free parameters, but due to potential overfitting, the impact on image contrast and adherence was unknown.

R1 contrast at each field strength. Box and whisker plots of R1 contrast between regions of white matter and white matter hyperintensity obtained at 0.2, 2, 20, and 200 mT (n = 20, scan visit 1). Each dot represents a single participant. Cohort mean ± standard deviation values are shown

For the identified best R1 mapping approach, repeatability of mean R10.2 values and dispersion slope, b, extracted from regions of WM, GM, and WMH, were examined by the 95% limits of agreement using the Bland–Altman method and intraclass correlation coefficient (ICC), for a two-way mixed model of absolute values for single measures (n = 19, visits 1 and 2). Paired t-tests were performed to determine whether there was no significant bias between visit 1 and visit 2 for tissue averaged values of R10.2 and dispersion slope. The magnitude of Cohen’s d effect size was evaluated between tissue averaged values to examine the extent of R10.2 and dispersion slope image contrast between different tissue regions using Paired t-test (n = 20, visit 1). In this analysis, larger values of Cohen’s d indicate larger differences between the tissue groups compared to the extent of variability across each tissue group. Cohen’s d values greater than 0.5 and 0.8 are commonly considered to reflect medium and large effect sizes, respectively. One case of visit 2 data was excluded from the repeatability analysis due to failure of the automated 3 T MRI preprocessing pipeline used to generate tissue label maps.