Jens H. Jensen

Purpose: To compare the dependence on b ‐value of the spherical harmonic powers for the diffusion MRI signal in white matter to theoretical predictions from the stick model of water diffusion within axons. Methods: Diffusion MRI data were acquired at 3 T in three healthy adults with 10 b ‐value shells ( b = 1000–10 000 s/mm ² ) and 64 directions per shell. For every b ‐value, the signal was expanded in spherical harmonics for all even degrees l up to l = 6, and the harmonic power for each degree was calculated. These were compared in selected white matter regions of interest to the theoretical predictions of the stick model, which depend on just two adjustable parameters: the intra‐axonal diffusivity and an amplitude factor for each degree. The intra‐axonal diffusivity was estimated independently using triple diffusion encoding MRI, leaving the amplitude factor as the sole fitting parameter. Results: Close agreement between experiment and theory was found for b 4000 s/mm ² , the threshold where extra‐axonal water signal is expected to be strongly suppressed, for total cerebral white matter as well as separately within the genu, body, and splenium of the corpus callosum. These findings extend prior studies that either considered only the l = 0 harmonic power or treated the intra‐axonal diffusivity as a fitting parameter. Conclusion: In white matter, the b ‐value dependence of the diffusion MRI signal's even degree spherical harmonic powers up to l = 6 are relatively well‐described by the stick model of axons for b 4000 s/mm ² .

Diffusion MRI (dMRI) methods including diffusion tensor imaging (DTI) and more advanced models including diffusional kurtosis imaging (DKI) and fiber ball white matter modeling (FBWM) probe various aspects of white matter (WM) microstructure. However, the associations between these variables and myelin content remain largely unknown. We examined this issue using ViSTa myelin water imaging (MWI), which estimates the proportion of tissue water associated with myelin using the apparent myelin water fraction (aMWF) and examined correlations with dMRI variables across heterogeneous deep WM regions. Four healthy adults underwent anatomical MRI, multishell dMRI, and ViSTa‐MWI. We computed DTI, DKI, FBWM, and aMWF metrics within a binarized deep WM atlas and callosal subregions (the genu and splenium) and evaluated associations between dMRI and aMWF using voxel‐wise block‐permutation Spearman correlations. Across WM regions, axonal water fraction ( ρ = 0.68), mean kurtosis ( ρ = 0.63), and radial kurtosis ( ρ = 0.62) had stronger correlations with aMWF than conventional DTI metrics. Correlations for dMRI variables were consistently higher within the splenium (mean | ρ | = 0.68) compared to the genu (mean | ρ | = 0.56), reflecting stronger associations with aMWF in an earlier‐myelinating region with denser axonal packing and reduced fiber dispersion. DTI, DKI, and FBWM variables all correspond with aMWF. Select DKI and FBWM variables demonstrated the strongest associations with aMWF and were more sensitive than conventional DTI metrics. Correlations for all metric families were stronger within the splenium compared to the genu, presumably reflecting the high density of myelination in this region. These results help to clarify the biophysical interpretation of dMRI microstructural parameters by determining how strongly they are influenced by myelin content. This preliminary examination helps to clarify the roles of dMRI variables for future studies of WM integrity and reinforces the use of DKI and FBWM.

Purpose: To derive a quantitative relationship between the mean Kärger model (KM) water exchange rate and the mean intercellular water transition rate applicable to brain and other complex biological tissues. Theory and Methods: The mean KM water exchange rate applies to any KM, accommodates an arbitrary number of compartments, and can be estimated from the time dependence of the diffusional kurtosis. The mean intercellular water transition rate for a tissue is the average rate at which water leaves all cellular compartments and enters the extracellular space. It is shown that these two quantities are proportional to each other provided the exchange dynamics are uniform throughout an imaging voxel and the compartmental diffusivities and residence times are not correlated, with a proportionality coefficient depending on the diffusivities and compartmental water fractions. This relationship is illustrated for several white matter regions having highly aligned axons using diffusional kurtosis imaging (DKI) data from four healthy volunteers. Results: For parallel axons, the proportionality coefficient simply reduces to the extracellular water fraction, which allows estimates for the KM exchange rates obtained with DKI to be translated into estimates for the axonal water transition rate. The axonal transition rate is found to vary from 0.83 s ⁻¹ in the posterior limb of the internal capsule to 2.00 s ⁻¹ in the body of the corpus callosum. Conclusion: Under mild assumptions, the mean KM water exchange rate is proportional to the mean intercellular water transition rate. This provides a practical method for estimating intercellular water transition rates from DKI.

Reference intervals, defined as intervals containing a new observation with a specified probability relative to reference data, would be clinically useful in assessing brain magnetic resonance imaging (MRI). Brain charts, which are estimates of MRI phenotypes across covariates such as age and sex, can be used to construct reference intervals. However, the reference data used to fit intervals often differ from a new sample in terms of study design, MRI acquisition, and image preprocessing. Application of MRI reference intervals to new samples remains a challenging problem. Here, we propose a new method called reference interval calibration via conFormal prediction (ReForm) that adjusts reference intervals for a new sample. Our method builds on recent work in conformal prediction, which yields intervals with guaranteed coverage for new observations. Through resampling experiments in Lifespan Brain Chart Consortium cortical thickness data, we compare ReFormed reference intervals with refitting intervals, statistical harmonization methods, and model-based adjustment of intervals. Notably for patient privacy concerns, ReForm does not require sharing of reference data. Yet, our empirical results demonstrate that ReForm controls FPR similarly or better than alternative methods that require sharing reference data. Finally, we provide recommendations for practical applications of ReForm and an R package (https://github.com/andy1764/ReForm) for calibrating reference intervals using ReForm.

Neuroimaging is vital in quantifying brain atrophy due to typical aging and due to neurodegenerative diseases. To collect large samples necessary to model lifespan brain development, research consortiums aggregate images acquired across multiple study sites. Previous studies have demonstrated that this multi‐site study design can lead to site‐related bias, necessitating harmonization of these “site effects.” However, current methodologies are unable to generalize to new sites outside the original harmonized sample, limiting translation to new sites or clinical practice. Here, we propose a method called ComBat‐Predict (CB‐Predict) building upon the ComBat method for site effect adjustment, which extends to data from a new site with smaller sample sizes and unknown site effects. In data from the Alzheimer's Disease Neuroimaging Initiative, our proposed method mitigates bias and yields high accuracy in predicting cortical thickness measures when generalizing the model to new data. Furthermore, we demonstrate that our proposed harmonization method can reduce site‐related variance in centile scores estimated using data from the Lifespan Brain Chart Consortium. Altogether, our results demonstrate that CB‐Predict effectively harmonizes new sites and thereby enables effective translation of neuroimaging models to additional samples.

Intercompartmental water exchange in brain and other biological tissue can be probed in vivo with diffusion MRI (dMRI). We assess the accuracy of a recently proposed method for estimating a mean exchange rate by performing Monte Carlo simulations of random walkers through a packing of permeable, randomly placed, parallel cylinders to model water exchange within axonal fiber bundles. The diffusivity and kurtosis of the full system are calculated for a broad range of diffusion times and model parameters. The mean exchange rate is estimated from the logarithmic derivative of the kurtosis with respect to the diffusion time and compared with the exchange rate predicted by the Kärger model (KM), which is exact in certain limits. The mean exchange rate is also compared with the reciprocal exchange time obtained by conventional fitting of the kurtosis time dependence to a two‐compartment KM, with a high correlation being found between the two quantities. The estimates from the logarithmic derivative are in good agreement with the KM predictions when the exchange time is long in comparison to the compartment traversal times, which corresponds to barrier‐limited exchange. Compared to the standard procedure of fitting the kurtosis to the KM over a broad range of diffusion times, using the logarithmic derivative reduces the data acquisition burden by only requiring a narrow range of times and increases generality in that number of compartments need not be specified. This method may be useful for estimating the mean exchange rate from the kurtosis time dependence measured with dMRI.

Purpose: To demonstrate a method of reducing pulse duration effects for the diffusional kurtosis of the multi‐compartment Kärger model (KM) as estimated with a Stejskal‐Tanner DWI sequence.Theory and Methods: An effective diffusion time is introduced that corrects errors in the apparent diffusional kurtosis arising from a nonzero pulse duration δ for the multi‐compartment KM. The correction is exact to first order in the diffusion time Δ, and numerical calculations are used to assess how well it reduces pulse duration effects. Specifically, for the two‐compartment KM, the deviations of the apparent kurtosis obtained with the Stejskal‐Tanner sequence from the exact kurtosis are calculated for the full range of δ and Δ, and similar calculations are performed for the deviation in the derivative of the kurtosis with respect to Δ. For the general multi‐compartment KM, upper bounds on the maximum magnitude of the deviations are determined. Application of the correction to estimation of intercompartmental exchange rates is illustrated with several examples.Results: For the two‐compartment KM, the correction reduces the deviation of the apparent kurtosis and its time derivative for most values of δ and Δ. For the general multi‐compartment KM, the maximum deviation magnitude, relative to the initial kurtosis, is 2.26% for the uncorrected kurtosis and 0.57% after correction. The correction reduces the maximum deviation magnitude of the derivative from 46% to less than 1%.Conclusion: Pulse duration effects for the kurtosis of the multi‐compartment KM can be strongly suppressed by applying the effective diffusion time correction.

Diffusion MRI (dMRI) is widely used as a non‐invasive means of detecting changes in brain tissue microstructure. In our previous studies, we demonstrated the sensitivity of dMRI to capture brain microstructural alterations in the triple transgenic (3xTg‐AD) mice, particularly brain morphological abnormalities in 2‐month‐old mice, where dMRI was sensitive to myelin abnormalities, to microglia proliferation/activation, and to the larger number of basal forebrain cholinergic neurons previously described in this model at this young age. In this study, we extend our prior work by establishing the dMRI profile of several brain regions relevant to AD pathology in 2‐month‐old 3xTg‐AD and age‐matched controls (NC) and by investigating the effectiveness of these dMRI metrics in predicting group genotype using elastic net (EN) logistic regression modeling. EN has been shown to be a high‐performance and stable machine learning model for neuroimaging data. Our results demonstrated significant group differences in several ROIs, particularly in the corpus callosum (CC) where fractional anisotropy (FA) (p < 0.0001; d = −1.87), radial diffusivity (D_┴) (p < 0.0001; d = −1.33), and radial kurtosis (K_┴) (p < 0.0001; d = −1.34) were statistically significant and the most sensitive dMRI metrics to differentiate between the two groups, with large effect sizes (Cohen's d) values. Moreover, FA in the ventral hippocampus (VH) (p < 0.0001; d = 1.13) and fimbria (Fi) (p < 0.0001; d = −1.04) as well as mean diffusivity (MD) (p < 0.0001; d = 1.10) and D_┴ in the subiculum (Sub) (p < 0.0001; d = 1.12) were also statistically significant and able to clearly distinguish the two groups. Additionally, our results from the trained EN model indicate that FA in the VH, CC, and cingulate cortex (Ctx‐Cg) were the three best dMRI metrics to classify the 3xTg‐AD mice with an accuracy of 0.95. Sensitivity and specificity were also calculated to assess the goodness of prediction, resulting in 0.96 and 0.94, respectively.

Intercellular water exchange in brain is analyzed in terms of the multi-compartment Kärger model (KM), and the mean KM water exchange rate is used as a summary statistic for characterizing the exchange processes. Prior work is extended by deriving a stronger lower bound for mean exchange rate that can be determined from the time dependence of the diffusional kurtosis. In addition, an analytic formula giving the time dependence of the kurtosis for a model of thin cylindrical neurites is demonstrated, and this formula is applied to numerically test the accuracy of the lower bound for a range of model parameters. Finally, the lower bound is measured in vivo with diffusional kurtosis imaging for the dorsal hippocampus and cerebral cortex of 8-month-old mice. From the stronger lower bound, the mean KM exchange rate is found to be 46.1 ± 11.0 s-1 or greater in dorsal hippocampus and 20.5 ± 8.5 s-1 or greater in cortex.