Phantom- and simulation-based validation of combined diffusion relaxometry in ex vivo ADRD white matter

Purpose: In principle, combined T2–Diffusion (D) MRI has the microstructural and chemical sensitivity to detect axonal and myelin water changes in Alzheimer’s disease and related dementias (ADRD), but its practical implementation may be hindered by demanding hardware requirements. This work assesses the feasibility and accuracy of T2–D for ex vivo analysis of WM lesions in ADRD tissue.

A thawed ex vivo brain sample from the Michigan Brain Bank and a T2–D phantom were scanned at 7T using a combined diffusion relaxometry (CDR) sequence. A non-negative least squares (NNLS) conventional data processing pipeline was used to disentangle water pools with unique T2–D signatures. Simulations examined the effects of minimum TE and SNR on recovery of myelin water (short T2, slow diffusion).

Across tissue types, T2–D data consistently resolved three spectral components. Phantom experiments showed detection of short T2 and slow diffusion features similar to those observed in ADRD ex vivo tissue, and confirmed CDR’s ability to accurately resolve multiple components. Simulations indicated reliable T2–D recovery for myelin with SNR > 30 dB and minimum TE < 25 ms.

Strong T2 and D weighting could be combined to capture the expected axonal, myelin, and extracellular (EC) regions in T2–D space. The observed short-T2, restricted-D components are therefore unlikely to be artifacts and instead support interpretations as physically meaningful myelin and axonal water signatures.

Combined diffusion relaxometry, T2–D, Alzheimer’s disease, ex vivo tissue, phantoms 1 |. INTRODUCTION ADRDs are leading causes of morbidity in aging populations,1 characterized by cognitive decline and functional impairment.2,3 While neuronal loss in gray matter (GM) is a hallmark of Alzheimer’s disease (AD), the contribution of white matter (WM) lesions has been increasingly recognized.4,5,6,7 Clinically, WM hyperintensities on T2 FLAIR imaging are used as sensitive markers of WM lesions,8,9,10 and diffusion weighted imaging is widely used to detect microstructural abnormalities.11,12 However, these techniques individually cannot readily separate axonal, extracellular, and myelin water pools.13,14,15 Combined diffusion relaxometry (CDR) uses both T2 and diffusion measurements to distinguish between biological water environments.16 CDR data are commonly represented as a two-dimensional T2–D spectrum, obtained via an inverse 2D Laplace transform (ILT), which decomposes the measured signal into multiple T2–D pairs (or spectral components).17,18 They can represent the distinct signal contributions associated with different microstructural and chemical environments in tissue. This technique has found applications ranging from obstetrics to neurology.19,20,21,22 T2–D imaging is conceptually well suited for separating WM water pools of interest in AD, but the components of greatest interest impose competing acquisition requirements. Sensitivity to axonal water benefits from strong diffusion weighting (high b values), whereas detecting myelin water requires short TEs. However, achieving high b values often requires longer diffusion-encoding gradients, thereby increasing the minimum achievable echo time (TEmin).23 These inherent tradeoffs are further complicated by the achievable signal-to-noise ratio (SNR), as noise can corrupt the ability to resolve restricted diffusion coefficients.24 These considerations raise two practical questions: 1) should our T2–D fitting routine exclude the myelin water peak, which could affect the resolved axonal and EC component T2–D values and 2) what TEmin and SNR are required to reliably capture and disentangle both myelin and axonal water spectral components? In this work, we analyzed CDR data from an ADRD ex vivo brain sample and validated our observed spectral components using two complementary tools: (1) a phantom designed to systematically mimic components of interest, and (2) simulations of CDR datasets with varied acquisition parameters (TEmin) and hardware constraints (SNR). 2 |. METHODS 2.1 |. Ex Vivo Tissue Selection and Scanning Our process and procedures were compliant with and conducted with the approval of our university’s Institutional Biosafety Committee (IBC). A frozen ex vivo post-mortem brain from a donor who had a pathologically confirmed diagnosis of AD and cerebral atherosclerosis was selected from the Michigan Alzheimer’s Disease Research Center (MADRC). Frozen tissue was used to avoid formalin crosslinking, which is known to affect T2 and D.25,26 A sample containing both WM lesions and normal appearing white matter (NAWM) was dissected, guided by the pre-mortem T2 FLAIR scan, and prepared as described by Murguia et al..27 The sample was placed in a 40 mm Millipede quadrature coil and inserted into a 7.0 Tesla NMR/MRI small animal scanner (Varian/Agilent, Walnut Creek, CA, USA) with 40 mT/m gradients with a 115-mm inner diameter. The temperature was approximately 15–20°C to preserve the sample while scanning. Two rounds of voxel-wise, 3D gradient-echo shimming were performed. A two-shot center-out spin-echo EPI scan was performed using 380 pairs of b values (19 values, from 1.49 to ) and TEs (20 values, from 18.92 to 189.2 ms). Diffusion weighting was strengthened by using all three directional gradients simultaneously, achieving a gradient amplitude of , 4 ms duration, and 12 ms separation. The in-plane resolution was 0.547×0.547 mm (FOV = 35 × 35 mm, matrix size = 64 × 64). The TR was 2000 ms, and the scan time was 50 minutes. 2.2 |. Phantom Development and Scanning A phantom was designed to emulate multi-component systems (see Gatidis et al.).28,29 The phantom contained 15, 5 mm NMR tubes with different concentrations of polyethylene glycol 3350 (PEG) and gadolinium (Gd) contrast agent gadobenate dimeglumine MultiHance (Bracco Diagnostics Inc., Princeton, NJ, USA). The concentration of Gd changed the T2 values (5–100 ms) and the addition of 100 mM of PEG resulted in two different D values (approximately 1.5 and (Figure 1 A). A spin echo (non-EPI) T2–D sequence was performed using 132 pairs of b values (11, from 0 to ) and TEs (12, from 23 to 133 ms) (Figure 1 B). The diffusion weighting used a maximum gradient amplitude of , duration of 6 ms, and separation of 11.3 ms. The in-plane resolution was 0.547 × 0.547 mm. The TR was 6000 ms, and the scan time was approximately 14 hours. 2.3 |. Data Processing Non-negative least squares T2–D fitting NNLS fitting17,18 was applied to all datasets. Regions of interest (ROIs) were manually selected in MATLAB from the T2–D MR images. To avoid bias from the spatially varying phase in complex signal averaging, phase correction was applied by computing the circular mean phase over the ROI voxels and multiplying each complex image by the corresponding conjugate phasor to rotate the mean ROI phase toward zero. The real components of the corrected signal intensities were then averaged within each ROI and stored as the measured signal vector, . The 2D spectrum was estimated by solving | (1) | where is a dictionary containing the signal evolutions. Each column of corresponds to a unique (T2, D) pair, and each row corresponds to a specific (TE, b) acquisition, with entries given by17 | (2) | The T2 and D ranges used to construct were informed by prior observations and previous studies.21,27,30 A total of 120 T2 values and 121 diffusion coefficients were included. Non-negativity constraints and Tikhonov regularization were imposed to restrict solutions to physically meaningful values and to improve robustness to noise and numerical instability.31,32 The regularization parameter was selected in the range 10−6–10−5, guided initially by cross-validation and refined based on consistency with prior NMR experiments and the ability to resolve distinct components. Solutions were obtained using a built-in NNLS solver (MATLAB R2023a (MathWorks, Natick, MA, USA). Ground truth D and T2: 1D parametric fitting As the 2D NNLS fitting routines are ill-posed by nature, we needed to calculate ground truth measures for use in the phantom experiments. The one- and two-component phantom tubes were analyzed using mono or bi-exponential curve fitting, respectively. We used all acquired TEs and the first b value to estimate T2, and all acquired b values and the first TE to estimate D. The resulting coefficients, or parametric component fits, were treated as ground truth values. 2.4 |. Phantom Applications for WM Spectra Validation Components in the 2D spectrum characteristic of both lesioned and normal-appearing white matter (NAWM) tissue were emulated with the phantom by combining MR signals from individual tubes with known diffusion (D) and T2 coefficients. Tube signals were averaged together incrementally, allowing the contribution of each spectral feature to be examined in isolation. Example phantom application Here, we describe how the phantom can be used. In this example, we can set our goal arbitrarily to construct a spectrum that will include components with the following T2–D features: T2 shorter than the TEmin highly restricted D with a long T2 less restricted D with a long T2 First, reference spectra and ground truth parametric fits were calculated individually (section 2.3). Here, tube G8P0 was used to get a short T2 component (Figure 1C), and tube G7P1 was used for the other two components (Figure 1D). Next, the ROI-averaged signals from both tubes were combined and analyzed to produce a composite spectrum (Figure 1E). Finally, all three spectra (two individual fits and composite) can be visually compared to assess any spectral artifacts and to confirm the component placement is accurate and consistent between the spectra. NAWM and lesion To emulate NAWM and lesion spectral features, two different pairs of tubes were used. Tube selection was guided by representative NAWM and lesion spectra. Tubes G3P1 and G7P1 were used for NAWM, and tubes G2P0 and G5P1 for lesions. 2.5 |. Simulations for Investigating the Effects of Experimental Noise and Minimum TE Data for the T2–D experiment was simulated for a myelin water pool (T2 = 7 ms and ). The same number of TEs, the maximum TE (209 ms), and the b values from the ex vivo tissue scans were retained for all datasets, but each simulation used a different combination of TEmin and SNR. The TEmin values ranged from 5 to 50 ms, and SNR values from 10 to 50 dB. A total of 120 T2–D spectra were generated using the processing pipeline described in section 2.3. To assess both the precision and accuracy of the resolved spectral component locations, we defined metrics called “spread” and “bias,” respectively. Before calculating these metrics, our spectral peaks were thresholded to exclude points with a value (spectrum intensity) below 50 percent of the maximum intensity. Bias: The centroid of the myelin water spectral component was calculated as | (3) | along the T2 axis, and likewise along the D axis. Here, is the weight at pixel is the T2 coefficient at pixel , and denotes the number of pixels within the range where the peak is expected to appear. These centroids were subtracted from the true coefficients to obtain a bias metric. For example, in the T2 dimension, | (4) | Spread: The spread, or width, of the spectral peaks in the D and T2 dimensions was determined by first identifying the longest connected sequence of spectral bin in each direction. The spread was then calculated as the difference between the maximum and minimum D and T2values. The minimum spread that could be assigned was the spectral bin width. The data are displayed as spread and bias maps using contour plots. 3 |. RESULTS 3.1 |. Ex vivo tissue The spectra derived for NAWM, lesions, and GM consistently showed three peaks (Figure 2). We will refer to the tissue spectral features as Components 1–3, defined by their T2–D properties as such: Component 1: Short T2, appearing below the TEmin, speculated to be related to myelin water Component 2: Longer T2, speculated to be extracellular (EC) water Component 3: Same T2 as Component 2, but with a restricted diffusion coefficient located near the lower boundary of the signal evolution dictionary, speculated to be axonal water. Normal Appearing White Matter: Components 2 and 3 had T2s between 25 – 30 ms (Figure 2 B). Component 1 had a T2 value around 6 – 10 ms, less than half the TEmin. Components 1 and 2 had diffusion coefficients between . The fitting routine pinned component 3 consistently at the slowest diffusion coefficient,. Lesions: Components 2 and 3 had T2s between 25 – 50 ms (Figure 2 C). Component 1 appeared closer to the TEmin than was seen with the NAWM. The diffusion coefficients for all three peaks were similar to the NAWM results. Gray Matter: The spectra for gray matter (GM) were similar to those of the lesions; however, on average, all three peaks appeared at slightly longer T2s. 3.2 |. Phantom Lesion spectrum validation We were able to use phantom tube G2P0 (Figure 3B) to derive a component with a T2 similar to that of the lesion’s Component 2 (Figure 3A). Additionally, we were able to replicate the diffusion coefficients, which varied by approximately two orders of magnitude, for the lesion’s Components 1 and 3 with tube G5P1 (Figure 3C). In the composite, phantom-derived spectrum from tubes G5P1 and G2P0, all components retained their relative positions. The slow diffusion or short T2 features did not prevent the resolution of coexisting components under the acquisition and reconstruction conditions. NAWM spectrum validation We were able to use phantom tube G7P1 (Figure 4B) to derive a component with a short-T2, which was less than half the TEmin, similar to the NAWM’s Component 1 (Figure 4A). As this tube also contained PEG, it exhibited a faint secondary component at a similar T2, but with substantially slower diffusion. Components 2 and 3 from the NAWM were replicated using tube G3P1 (Figure 4C). The combined spectrum resolved three distinct components with centroids consistent with those observed in the corresponding single-tube spectra (Figure 4D). Therefore, allowing our NNLS algorithm to fit the NAWM component 1, speculated to be myelin, did not significantly impact the other components. 3.3 |. Simulations Figure 5 summarizes the effects of TEmin and SNR on the diffusion and T2 coefficients resolved from the simulated CDR data. Increasing TEmin and decreasing SNR resulted in progressive elongation of the components along the diffusion dimension, as quantified by the diffusion peak spread (Figure 5A). Substantial broadening 1–2 orders of magnitude relative to an ideal discrete component was observed primarily at the lowest tested SNR (10 dB) and for TEmin values exceeding 25 ms. The diffusion bias plot (Figure 5B) indicates that, across conditions, the diffusion centroid appeared either faster or slower than the true diffusion value. At higher SNRs combined with longer TEmin, the diffusion centroid was biased toward faster apparent diffusion coefficients. Conversely, for short TEmin values (5–10 ms) and reduced SNR, the centroid shifted toward more restricted diffusion relative to the ground truth. As TEmin increased beyond this ideal range, the apparent diffusion progressively overestimated the true diffusion coefficient. Along the T2 dimension, the centroid systematically shifted toward shorter T2 values with increasing TEmin and decreasing SNR (Figure 5C,D). Reductions in SNR produced a more pronounced effect on T2 centroid bias than increases in TEmin. For SNR values below 20 dB, the T2 centroid deviated by approximately 1–2 ms toward shorter relaxation times. 4 |. DISCUSSION We evaluated the feasibility and accuracy of using CDR at 7T for studying WM spectral features in ex vivo ADRD tissue. We first briefly characterized NAWM and lesioned tissue T2–D spectral components, recreated them with phantoms to identify unwanted component interactions and artifacts, and ran simulations to determine if the practical achievable SNR and TEmin can capture WM features of interest. Our ex vivo tissue CDR analysis consistently exhibited multiple components, including short-T2 and restricted-diffusion features. The results align with prior human WM T2–D studies at 3T30 and 7T21,33 that also report consistent multi-component spectra. Differences in T2 and diffusion coefficients across studies are plausibly explained by physiology (in vivo vs ex vivo) and tissue preparation (fixed vs thawed). Our phantom allowed us to emulate T2–D components that were observed in NAWM and lesioned tissue. Through the iterative process of creating the composite spectra, we found that the component speculated to be myelin water does not significantly bias the estimations of the axonal or EC water features. Finally, based on simulations, we found that reliable short-T2 recovery required SNR > 30 dB and TEmin < 25 – 30 ms. When SNR is lower or TEmin is longer, centroid bias and peak broadening increase, and low-amplitude features near the TEmin limit warrant greater scrutiny.

include our small tissue sample size and use of a single diffusion encoding direction. Anisotropic tissue will require multiple directions (e.g., for powder-averaging),24 which will increase scan time. Future studies include optimizing the number and placement of TE and b value combinations, extending to a larger cohort, and comparing spectra results with histology of the tissue. For future studies, we suggest: 1) evaluating SNR to ensure the fitting routine is not resolving components biased by noise, 2) using the component centroid T2–D values to interpret the spectra, not the spread, and 3) treating features near the TEmin boundary and low-intensity components as candidates requiring additional validation. 5 |. CONCLUSION This work used phantom and simulation-based validation to evaluate short-T2 and restricted-diffusion components observed in combined T2–diffusion MRI of ex vivo ADRD WM. Across NAWM, lesions, and GM, three consistent spectral components were observed, including a component with T2 shorter than the TEmin and a component with highly restricted diffusion. Phantom experiments demonstrated that components with T2 values around 10 ms and components near the lower bound of diffusion sensitivity were recoverable and did not induce spurious spectral components when combined with longer-T2 compartments. Complementary simulations showed that, under experimentally relevant SNRs and TEmins, spectral centroids remained minimally biased and peak broadening remained limited. Together, these results indicate that the observed short-T2 and restricted-diffusion components are unlikely to arise solely from acquisition limitations. Instead, they reflect resolvable and reproducible features of the underlying signal, supporting their interpretation as biologically meaningful signatures that could be consistent with myelin-associated and axonal water compartments in ADRD WM. ACKNOWLEDGMENTS We thank Ulrich Scheven for his contributions to helpful discussions on CDR and guidance scanning on the 7T Varian animal scanner. Funding Information This work was supported by NIH; grant P30AG072931-03S1 Footnotes Financial disclosure None reported.

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