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Nonlinear associations of neurite density and myelin content with age revealed using multicomponent diffusion and relaxometry magnetic resonance imaging

Most magnetic resonance imaging (MRI) studies investigating the relationship between regional brain myelination or axonal density and aging have relied upon nonspecific methods to probe myelin and axonal content, including diffusion tensor imaging and relaxation time mapping. While these studies have provided pivotal insights into changes in cerebral architecture with aging and pathology, details of the underlying microstructural alterations have not been fully elucidated. In the current study, we used the BMC-mcDESPOT analysis, a direct and specific multicomponent relaxometry method for imaging of myelin water fraction (MWF), a marker of myelin content, and NODDI, an emerging multicomponent diffusion technique, for neurite density index (NDI) imaging, a proxy of axonal density. We investigated age-related differences in MWF and NDI in several white matter brain regions in a cohort of cognitively unimpaired participants over a wide age range. Our results indicate a quadratic, inverted U-shape, relationship between MWF and age in all brain regions investigated, suggesting that myelination continues until middle age followed by a decrease at older ages, in agreement with previous work. We found a similarly complex regional association between NDI and age, with several cerebral structures also exhibiting a quadratic, inverted U-shape, relationship. This novel observation suggests an increase in axonal density until the fourth decade of age followed by a rapid loss at older ages. We also observed that these age-related differences in MWF and NDI vary across different brain regions, as expected. Finally, our study indicates no significant association between MWF and NDI in most cerebral structures investigated, although this association approached significance in a limited number of brain regions, indicating the complementary nature of their information and encouraging further investigation. Overall, we find evidence of nonlinear associations between age and myelin or axonal density in a sample of well-characterized adults, using direct myelin and axonal content imaging methods.


Introduction
Biophysical axonal integrity and appropriate myelin content are necessary components for proper central nervous system (CNS) function. Extensive literature has demonstrated a functional and metabolic coupling between these two microstructural components, with loss or degeneration of either compartment may lead to the age-related cognitive decline, motor impairments, and autonomic dysfunction observed in the elderly. Among the numerous agerelated alterations observed in the brain parenchyma, myelin loss and axonal damage have been shown to be biological hallmarks of various neurogenerative diseases such as multiple sclerosis and dementia (MacKay et al., 2009, Bartzokis, 2011, Medana et al., 2003. However, the mechanisms underlying these cerebral microstructural changes remain poorly understood. Therefore, it is crucial to characterize changes in myelin content and axonal density that occur with normal aging and in the absence of clinically detectable pathology, to identify alterations that originate from pathological processes. Indeed, throughout the lifespan, the human brain experiences notable structural alterations in white matter (WM) and gray matter (GM). Postmortem histological studies have shown that myelin and axonal degeneration are among the main sequelae of aging and may be associated with concomitant motor and cognitive decline, as well as likely being closely linked to a myriad of age-associated neurodegenerative disorders and dementias (Flynn et al., 2003, Kolasinski et al., 2012, Bronge et al., 2002, Pannese, 2011, Stassart et al., 2018, Tang et al., 1997, Marner et al., 2003. Although histologic preparations have provided invaluable insight into normal brain aging, this method is available only for post-mortem studies, while a great deal interest attaches to longitudinal evaluation of brain aging. Thus, there remains a great deal of interest in non-invasive investigation of human brain microstructure.
Magnetic resonance imaging (MRI) has been widely used in clinical and preclinical investigations of the brain, and has provided pivotal data characterizing structural and functional cerebral changes with disease and aging (Gunning-Dixon et al., 2009). Parameters derived from diffusion tensor imaging (DTI) in particular, along with, to a lesser extent, relaxation time imaging, have been found to follow complex and nonlinear trajectories with age in WM and GM (Inano et al., 2011, Bartzokis et al., 2003, Yeatman et al., 2014, Fjell et al., 2009, Arshad et al., 2016, Sullivan and Pfefferbaum, 2006, Saito et al., 2009). However, the underlying structural mechanisms responsible for these findings are difficult to define due to the sensitivity of conventional MRI indices to a number of tissue properties, including hydration, macromolecular content, axonal density, myelin content, iron content, and architectural features such as fiber crossing and fanning. To address these limitations, more advanced analysis methods based on multicomponent relaxometry or diffusion have been introduced to improve both sensitivity and specificity of MR-based myelination and axonal density studies (MacKay et al., 1994, MacKay and Laule, 2016, Laule et al., 2008, Laule et al., 2006. Using multicomponent relaxometry analysis, Mackay and colleagues pioneered in-vivo MR imaging of myelin water fraction (MWF) (MacKay et al., 1994, MacKay andLaule, 2016), which has been histologically validated as a proxy for myelin content (Laule et al., 2008, Laule et al., 2006. This approach has been extensively applied to characterize cerebral demyelinating diseases and neurodevelopment , Flynn et al., 2003, Borich et al., 2013, Laule et al., 2004, Sirrs et al., 2007, Dean et al., 2017. However, multicomponent relaxometry is unable to distinguish between intracellular water fraction, a proxy of axonal density, and extracellular water fraction due to their similar relaxation times. To overcome this difficulty, Zhang and colleagues have introduced a new multicomponent diffusion technique to map intracellular water in brain, called neurite orientation dispersion and density imaging (NODDI) (Zhang et al., 2012). NODDI is based on a compartmental model of water diffusion incorporating intracellular water, that is, water within neurites, extracellular water, and a compartment consisting of less restricted water from the cerebral spinal fluid volume. NODDI has gained rapid popularity and has been shown to provide reliable and specific information about neurite density and dispersion in studies of aging (Kunz et al., 2014, Nazeri et al., 2015, Kodiweera et al., 2016, Grussu et al., 2015, Jelescu et al., 2015, Grussu et al., 2017, as well as in investigations of neurologic disorders (Timmers et al., 2016, Timmers et al., 2015, Mitchell et al., 2019, Churchill et al., 2017, Churchill et al., 2019, Adluru et al., 2014, Winston et al., 2014, Wen et al., 2015.
To the best of our knowledge, only a single pioneering study has sought to jointly investigate alterations in myelin content and axonal density with age through a combination of multicomponent relaxometry and diffusion analysis . Based on multiecho imaging for MWF mapping and NODDI for neurite density index (NDI) imaging, Billiet and colleagues observed increases in NDI with age in several cerebral WM regions. While their observations agree with those of Chang and colleagues, , they do not support Merluzzi and colleagues' observation of decreased NDI in different cerebral WM structures . This discrepancy may be attributable to differences in the study cohorts. In addition, and surprisingly, Billiet's study showed no difference in MWF with age; this disagrees with various MWF-based studies revealing a quadratic, inverted U-shaped, association between MWF and age in WM (Arshad et al., 2016, Bouhrara et al., 2020a, Bouhrara et al., 2020b. It remains unclear whether this discrepancy is due to differences in cohort characteristics or the MR methodology used to measure MWF, emphasizing the need for additional studies. In the current study, we investigated the pattern of myelination and axonal density in normative aging in a cohort of well-characterized cognitively unimpaired participants (n = 58), across the extended age range of 21 to 83 years. Our measure of MWF was conducted using the Bayesian Monte Carlo analysis of multi-component driven equilibrium singlecomponent observation of T 1 and T 2 (BMC-mcDESPOT) method Spencer, 2017). BMC-mcDESPOT generates a high-resolution whole brain MWF map with high accuracy and precision, and has been previously applied to provide evidence of myelin loss in mild cognitive impairment and dementia and to investigate brain myelin maturation and aging as well as the association between cerebral blood flow and myelin content , Bouhrara et al., 2020a, Bouhrara et al., 2020b, Bouhrara et al., 2020c. Our measure of NDI was conducted using the NODDI approach (Zhang et al., 2012). Our main goals are to characterize age-related differences in regional brain myelination and axonal density, to investigate the association between MWF and NDI, to provide further insights into regional brain maturation and aging over the adult lifespan, and to demonstrate the feasibility and utility of combining NODDI and BMC-mcDESPOT for advanced clinical investigations.

Participants
Participants were drawn from two ongoing healthy aging cohorts of the National Institute on Aging (NIA). Eleven volunteers recruited from the Baltimore Longitudinal Study of Aging (BLSA) (Shock, 1985, Ferrucci, 2008, and forty seven from the Genetic and Epigenetic Signatures of Translational Aging Laboratory Testing (GESTALT) were enrolled. The study populations, experimental design, and measurement protocols of the BLSA have previously been reported (Shock, 1985, Ferrucci, 2008. The BLSA is a longitudinal cohort study funded and conducted by the National Institute on Aging (NIA) Intramural Research Program (IRP). Established in 1958, the BLSA enrolls community-dwelling adults with no major chronic conditions or functional impairments at enrollment. The GESTALT study is also a study of healthy volunteers, initiated in 2015 and funded and conducted by the NIA IRP. The goal of the BLSA and GESTALT studies is to evaluate multiple biomarkers related to aging. We note that the inclusion and exclusion criteria for these two studies are essentially identical. Participants underwent testing at the NIA's clinical research unit and were excluded if they had metallic implants, neurologic, or significant medical disorders. In addition, all participants underwent a Mini Mental State Examination (MMSE). The final cohort consisted of 58 cognitively unimpaired volunteers (mean ± standard deviation MMSE = 29.2 ± 1.0) ranging in age from 21 to 83 years (45.4 ± 18.3 years), including 31 men (42.9 ± 17.5 years) and 27 women (48.3 ± 19.1 years). Age and MMSE did not differ significantly between men and women. Experimental procedures were performed in compliance with our local Institutional Review Board, and participants provided written informed consent.

Data acquisition
All experiments were performed with a 3T whole body Philips MRI system (Achieva, Best, The Netherlands) using the internal quadrature body coil for transmission and an eightchannel phased-array head coil for reception. We emphasize that all MRI studies and ancillary measurements were performed with the same MRI system, running the same pulse sequences, at the same facility, and directed by the same investigators for both BLSA and GESTALT participants.

NODDI for NDI mapping-Diffusion-weighted images (DWI)
were acquired using a single-shot echo planar imaging sequence: repetition time (TR) / echo time (TE) of 10000 / 67 ms, two b-values of 700 and 2000 s/mm 2 , each encoded in 32 diffusionweighting gradient directions, two images with b of 0 s/mm 2 , field-of-view (FoV) of 240 mm × 208 mm × 150 mm, acquisition matrix of 120 × 120 × 50, acquisition voxel size of 2 mm × 2 mm × 3 mm, and SENSE factor of 2. All images were reconstructed to a voxel size of 2 mm × 2 mm × 2 mm. The total acquisition time was ~12 min.

BMC-mcDESPOT for MWF mapping-3D
spoiled gradient recalled echo (SPGR) images were acquired with flip angles (FAs) of [2 4 6 8 10 12 14 16 18 20]°, TR/TE of 5/1.37 ms, and acquisition time of 5 min, as well as 3D balanced steady state free precession (bSSFP) images were acquired with FAs of [2 4 7 11 16 24 32 40 50 60]°, TR/TE of 5.8/2.8 ms, and acquisition time of ~6 min. The bSSFP images were acquired with radiofrequency excitation pulse phase increments of 0 or π in order to account for offresonance effects (Deoni, 2011). All SPGR and bSSFP images were acquired with matrix size of 150 × 130 × 94, acquisition voxel size of 1.6 mm × 1.6 mm × 1.6 mm, and SENSE factor of 2. Further, the double-angle method (DAM) was used to correct for excitation radio frequency inhomogeneity (Stollberger and Wach, 1996). This makes use of two fast spinecho images acquired with flip angles of 45° and 90°, TR/TE of 3000/102 ms, acquisition voxel size of 2.6 mm × 2.6 mm × 4 mm, and acquisition time of ~4 min. All images were acquired with FOV of 240 mm × 208 mm × 150 mm and reconstructed to a voxel size of 2 mm × 2 mm × 2 mm. The total acquisition time was ~21 min.

NDI and MWF mapping
For each participant, an NDI map was generated using the NODDI analysis as described previously (Zhang et al., 2012). Specifically, all DW images were registered to the averaged b 0 image and corrected for motion and eddy current distortion artifacts using the Artefact Correction in Diffusion MRI (ACID) toolbox (http://diffusiontools.com/) (Mohammadi et al., 2010). The NODDI analysis was conducted on the registered images using the NODDI toolbox (https://www.nitrc.org/projects/noddi_toolbox), a multi-shell diffusion analysis package which enables the estimation of three separate water compartments, namely intracellular (i.e. NDI), extracellular, and cerebrospinal fluid.
Using the FSL software, all SPGR, bSSFP, and DAM images for each participant were linearly registered to the SPGR image acquired at FA of 10°, and the derived transformation matrix was then applied to the original SPGR, bSSFP, and DAM images. A MWF map was then generated using the BMC-mcDESPOT analysis from the registered SPGR, bSSFP, and DAM datasets Spencer, 2017). Briefly, BMC-mcDESPOT assumes a two-component system consisting of a short relaxation component, corresponding to the signal of water trapped within the myelin sheets, and a long relaxation component, corresponding to intra/extra cellular water. Analysis was performed explicitly accounting for nonzero TE as incorporated into the TE-corrected-mcDESPOT signal model .

Regions-of-interest segmentation
The averaged SPGR image over FAs for each participant was registered using nonlinear registration to the Montreal Neurological Institute (MNI) standard space image and the derived transformation matrix was then applied to the MWF map for that participant. Similarly, the averaged DW image obtained with b of 0 was registered using nonlinear registration to the MNI image and the derived transformation matrix was then applied to the NDI map. Twenty-one WM regions of interest (ROIs) were defined from the MNI structural atlas and the Johns Hopkins University ICM-DTI-81 atlas, including: whole brain (WB) WM, frontal lobes (FL) WM, parietal lobes (PL) WM, temporal lobes (TL) WM, occipital lobes (OL) WM, cerebellum (CRB) WM, body of corpus callosum (BCC), genu of corpus callosum (GCC), splenium of corpus callosum (SCC), internal capsules (IC), cerebral peduncle (CP), anterior corona radiata (ACR), posterior corona radiata (PCR), anterior thalamic radiation (ATR), posterior thalamic radiation (PTR), inferior fronto-occipital fasciculus (IFOF), superior fronto-occipital fasciculus (SFOF), inferior longitudinal fasciculus (ILF), superior longitudinal fasciculus (SLF), forceps minor (Fm), and forceps major (FM). All ROIs were eroded to reduce partial volume effects and imperfect image registration using the FSL tool fslmaths. Finally, the mean MWF and NDI values in each ROI of each participant were calculated.

Statistical analysis
To investigate the effects of age and sex on MWF and NDI, multi linear regression was applied using the mean MWF or NDI within each ROI as the dependent variable and sex, age, and age 2 as the independent variables, after mean age centering. Mean age centering was performed by subtracting the mean age value calculated over all subjects from the age of each subject. In all cases, the interactions between sex and age or age 2 were found to be non-significant and were therefore omitted from the model. The threshold for statistical significance was p < 0.05 after correction for multiple ROI comparisons using the false discovery rate (FDR) method (Benjamini, 2010, Benjamini andHochberg, 1995).
Moreover, for each ROI, ANOVA analysis was performed to test for differences between mean MWF or NDI values averaged over participants within the age intervals of 20-29, 30-49, 50-69, and 70-89 years. Post-hoc Bonferroni correction was applied at the significance level of 0.1 to account for multiple comparisons across age intervals.
Further, for each ROI, Pearson correlation was conducted to examine the relationships between NDI and MWF. Finally, we investigated the association between NDI and MWF using multi linear regression analysis with the mean NDI within each ROI as the dependent variable and the MWF within the ROI, age, and sex as the independent variables. The threshold for statistical significance was p < 0.05 after correction for multiple ROI comparisons using the FDR method.

Results
Figs. 1 and 2 show average NDI or MWF maps by age decade over the adult lifespan for three representative axial slices. Visual inspection indicates increases in NDI or MWF values from early adulthood through middle age (i.e. 40-49 years), followed by reduced NDI or MWF in several brain regions, consistent with progressive increases in myelin content or axonal density followed by reductions at older ages. Furthermore, we note that different regions exhibit different patterns in the association of NDI or MWF with age, with the parietal lobes exhibiting greater NDI values while the occipital and parietal lobes exhibiting greater MWF as compared to the more anterior brain regions.
Figs. 3 and 4 show, respectively, quantitative results for NDI and MWF values from all participants as a function of age for the indicated 21 WM regions. These results show increasing NDI or MWF until middle age followed by decreases in NDI or MWF with age in most examined ROIs, in agreement with Figs. 1 and 2. The best-fit curves indicate that while the fundamental inverted U-shaped relationship between NDI or MWF and age was consistent across all ROIs, the age curves displayed regional variation. Furthermore, in agreement with Fig. 2, the highest MWF values were found in the occipital and parietal lobes, with the frontal and temporal lobes exhibiting overall lower MWF values, while for NDI, the highest values were seen in the parietal lobes, in agreement with Fig. 1.
Our statistical analysis, presented in Table 1, showed significant effects of age on NDI in four of the brain regions evaluated, namely, the cerebellum, genu of CC, cerebral peduncles, and forceps major (Table 1). Here, the effect of age on NDI in the anterior corona radiata, superior fronto-occipital fasciculus, and forceps minor was significant before FDR correction. Similarly, the quadratic effect of age, age 2 , was significant (p < 0.05) or close to significance (p < 0.1) in various brain structures (Table 1). Here, the effect of age 2 on NDI in the occipital lobes, superior longitudinal fasciculus, and forceps major was significant before FDR correction. Moreover, our statistical analyses indicate that all ROIs exhibited nonsignificant interactions between age 2 and sex or age and sex on NDI. Sex effect on NDI was not significant in any of the ROIs. However, the genu of CC, longitudinal fasciculus, and forceps exhibited a significant sex effect before FDR. In these brain regions, women had 2 to 6 % higher NDI values than men. Furthermore, the effect of age on MWF was significant or close to significance in several ROIs while the quadratic effect of age, age 2 , was significant or close to significance in all ROIs except the genu of CC (Table 1). Moreover, our statistical analyses indicate that all ROIs exhibited non-significant interactions between age 2 and sex or age and sex on MWF. Sex effect on MWF was not significant in any ROI. However, the parietal lobes, splenium, and forceps major all exhibited a close to significant effect of sex before FDR. In these brain regions, women had ~8% higher MWF values than men. Finally, for each ROI exhibiting significant age 2 effect, we determined the specific year at which MWF or NDI peaked (Table 1). As seen, the MWF of the occipital lobes, parietal lobes, cerebral peduncles, and cerebellum reached a maximum at later ages as compared to all other WM structures, while the parietal lobes, internal capsules, and superior frontooccipital fasciculus reached a maximum NDI at later ages as compared to other WM structures.
The ANOVA analysis comparing the regional mean NDI or mean MWF values averaged over participants within age intervals indicated that for most ROIs (Fig. 5), there was a statistically significant variation in NDI or MWF values across age intervals. The post hoc analysis indicated that significance was mainly between age-intervals 20-29, 30-49, or 50-69 and 70-89.
Finally, Fig. 6 shows the weak Pearson correlations between MWF and NDI for all ROIs. The nominal significance in occipital and temporal lobes, and genu of corpus callosum did not survive the FDR correction. This illustrates the unique information these metrics provide and highlights the potential of NODDI and BMC-mcDESPOT to provide complementary insights. Finally, the association between NDI and MWF while accounting for age and sex as covariates indicated significant associations in several brain structures, namely, the whole brain, occipital lobes, temporal lobes, genu of CC, and inferior longitudinal fasciculus. However, significance did not survive FDR correction.

Discussion
In this cross-sectional study, we investigated the association between NDI, a measure of neurite density, and MWF, a measure of myelin content, and age in several cerebral WM structures in a healthy adult population spanning a wide age range. NDI was derived from NODDI (Zhang et al., 2012), a multicomponent diffusion analysis method, while MWF was derived from BMC-mcDESPOT, a multicomponent relaxometry method Spencer, 2017). Our results revealed widespread WM microstructural differences as a function of age as well as regional variations between the NDI and MWF measures; we attribute this to different aspects of microstructural changes over adulthood.
In most of the cerebral structures examined, we observed a quadratic, inverted U-shaped, association between NDI and age (Fig. 3). Although this relationship was statistically significant in a limited number of brain structures (Table 1), it likely reflects an increase in axonal density throughout young to middle age and a decrease afterwards. These results may help to some extent in reconciling the apparent discrepancies in NDI results in the literature. Indeed, in pioneering studies, Billiet and colleagues and Chang and colleagues have observed increases in NDI with age in a number of cerebral WM regions , while Merluzzi and colleagues observed decreases in NDI in several WM regions . However, the age range of the cohorts in these studies was relatively limited. Although Billiet's study incorporated a wide age range, it did not include subjects above the age of 70 and incorporates only a few subjects over 60 years, while Chang's cohort was composed primarily of relatively young subjects in the age range of 7-63. Finally, Merluzzi's cohort included only subjects over 45 years. These limitations in previous studies may have precluded detection of the nonlinear, more biologically plausible, associations of NDI with age that we observed. Indeed, nonlinear patterns with age in various WM brain structures (Inano et al., 2011, Bartzokis et al., 2003, Yeatman et al., 2014, Fjell et al., 2009, Arshad et al., 2016, Sullivan and Pfefferbaum, 2006, Saito et al., 2009) have been found using conventional quantitative MRI methods. However, while these previous studies may provide some experimental support to our observation, we note that conventional MRI measures, although sensitive to axonal water signal, are also sensitive to a number of tissue properties, including hydration, macromolecular content, iron content, myelin content, and architectural features such as fiber crossing and fanning, rendering them nonspecific to any underlying tissue propriety. Furthermore, it must be recognized recognized that other technical factors may have contributed further to the discrepancy between studies, including our current investigation, such as differences in acquisition parameters, cohort sizes, image manipulations (for example, image registration and segmentation), and statistical methods. As an example, the NODDI model does not explicitly account for different transverse relaxation times in different tissue compartments; this makes it highly echo-time-dependent; this has been shown to significantly bias NODDIderived measures, including NDI (Gong et al., 2020). Another potential source of discrepancy is the dependence of the statistical models adopted on the variables used in the final regression model. Finally, the specific values of NDI and MWF parameters, their significance, and trends with age will exhibit some variability as a function of sampling density within age groups, range of ages incorporated, and consistency of data (Fjell et al., 2010).
In agreement with previous work, our results indicate a significant quadratic association between MWF and age in most cerebral WM regions examined (Fig. 4). These results are consistent with Arshad and colleagues' and Bouhrara and colleagues' recent studies indicating an inverted U-shape pattern of MWF values with age in different WM regions (Arshad et al., 2016, Bouhrara et al., 2020a. The quadratic association between MWF and age is attributed to the process of myelination from youth through middle age, followed by demyelination in later years (Arshad et al., 2016, Bouhrara et al., 2020a, Bartzokis et al., 2010; this pattern is in agreement with postmortem observations (Tang et al., 1997, Peters, 2002. As expected, we found that different regions exhibit both similarities and differences in associations between MWF and age, with most regions peaking at the fifth life decade with the occipital and parietal lobes exhibited delayed demyelination as compared to the other lobes. This pattern is consistent with the retrogenesis hypothesis (first in-last out), in which posterior brain regions are spared from degeneration as compared to anterior brain regions (Stricker et al., 2009, Brickman et al., 2012, Raz, 2000, Bender et al., 2016. These findings are consistent with studies based on myelin-sensitive, but nonspecific, MRI methods such as DTI and relaxation times (Yeatman et al., 2014, Saito et al., 2009, Bartzokis et al., 2010, Okubo et al., 2017, and strongly motivate additional longitudinal studies. In contrast to De Santis and colleagues' observation (De Santis et al., 2014), our results did not find a significant correlation between NDI and MWF in any of the 21 ROIs studied (Fig.  6). This discrepancy is likely due to several methodological factors. First, unlike our study, De Santis and colleagues' study was conducted in a small cohort size (N = 17) spanning a limited age range of young subjects (mean age = 24.2 ± 2.8 years). Second, in their study, axonal density was estimated from the composite hindered and restricted model of diffusion, CHARMED (Assaf and Basser, 2005). There are fundamental differences between the NODDI and CHARMED models (Winston, 2015). One important example is that the NODDI signal model incorporates three compartments while CHARMED incorporates only two. Further, in NODDI, the intracellular component is modelled as sticks with orientation approximated using the Watson distribution to account for dispersion, while CHARMED does not model orientation dispersion, which can lead to an underestimation of axonal density. Further, while in both methods the extracellular component is modelled by anisotropic Gaussian diffusion, NODDI incorporates a third component corresponding to cerebrospinal fluid modelled by isotropic diffusion. Lastly, De Santi and colleagues used conventional mcDESPOT to map MWF (Deoni et al., 2008); parameter estimates obtained in this way can show a great deal of variability with respect to noise , Lankford and Does, 2013, West et al., 2019. Our Bayesian implementation greatly stabilizes these parameter estimates, thereby permitting markedly improved MWF determination Spencer, 2017).
Some of the WM brain structures studied exhibited a potential association between NDI and MWF after controlling for age and sex in the multi-linear regression analysis. However, this association did not survive FDR correction. This could be due to study characteristics, including a potentially underpowered study or lack of availability of very young participants (<20 years old) in accordance with the inclusion and exclusion criteria of the BLSA and GESTALT studies. Indeed, studies have shown that myelination is in part modulated by axonal activity (Mensch et al., 2015, Wake et al., 2011. Moreover, aside from acting as an electric insulator, oligodendrocytes, the cells that produce and maintain myelin, may provide substantial metabolic support to underlying axons (Simons and Nave, 2015). However, other facts argue against an association between NDI and MWF, including the fact that a numerical majority of cerebral axons are unmyelinated (Stassart et al., 2018), in addition to the appearance of tiny axons at older ages (Marner et al., 2003). Further, some studies suggest that myelin loss does not lead to axonal degeneration in a long-lived model of chronic demyelination (Smith et al., 2013). Therefore, it remains unclear whether the maturation of axons and of the myelination pattern of the brain are mechanistically associated or represent two independent neurological processes. In terms of degenerative processes, increasing evidence suggest that axonal degeneration occurs before the onset of clinical symptoms in several age-related diseases including dementias (Kanaan et al., 2013). However, as for multiple sclerosis, it is unclear whether axonal damage is independent of, or secondary to, demyelination in dementia. Further studies probing changes in myelin and axonal content using larger cohorts, and especially longitudinal studies, are required to fully elucidate the relationship between axonal density and myelin. These studies will be of critical importance for the development of specific therapeutic strategies supporting myelin and axonal simultaneous homeostatic phenotype.
Our calculated NDI and MWF mean values were overall in good agreement with those previously reported (Arshad et al., 2016, MacKay and Laule, 2016, Dean et al., 2017, Dvorak et al., 2019. However, we note that mcDESPOT, including BMC-mcDESPOT, provides somewhat higher MWF values as compared to multiple spin echo (MSE)-based methods . Indeed, various experimental and physiological factors that are not incorporated into the MSE or mcDESPOT signal models could account for this discrepancy. This includes, but is not limited to, magnetization transfer between macromolecules and free water protons, longitudinal relaxation time effects resulting from use of short repetition times in MSE, exchange between water pools, J-coupling, off-resonance, spin locking, water diffusion within different compartments, and internal gradients. Further, as noted above, NDI measures from NODDI are biased due to T 2 -weighting that is not accounted for in the underlying signal model (Gong et al., 2020). In addition, the intrinsic diffusivity for NODDI is fixed to 1.7 μm 2 /ms (Zhang et al., 2012). Although this value has been shown to be appropriate for adult brain WM, it has also been demonstrated that it is likely to be an overestimate for adult brain gray matter (GM) or infant brain WM and GM (Guerrero et al., 2019). These represent major challenges in MR imaging studies of myelin content and axonal density, and further technical developments are required to improve accuracy of both myelin content and axonal density imaging.
Although our work used advanced methodology, certain limitations remain. While our cohort spanned a wide age range, it does not include very young participants (< 20 years old), due to the inclusion and exclusion criteria of the BLSA and GESTALT studies. Inclusion of younger participants may influence the shape of MWF and NDI age-related trajectories (Fjell et al., 2010) and the assessment of their maxima with respect to age. We also note that it was not feasible to obtain optimal uniform sampling across all age intervals in this convenience sample of participants in ongoing research protocols, although all decades were well-represented. Moreover, our dataset is cross-sectional, so that the quadratic trends with age observed here require further validation through longitudinal studies. Such work, motivated by the present results, is underway. Finally, our work did not investigate differences with age or sex in MWF or NDI in GM regions; this was due to the facts that NDI determination using NODDI has been found to be unreliable in GM regions (Guerrero et al., 2019), while accurate determination of MWF in GM is highly problematic due to the small amount of myelin in GM (Bonny et al., 2020.

Conclusions
In this cross-sectional study examining sex differences and age-related alterations in neurite density and myelination across a wide age range of cognitively normal subjects, we showed that both neurite density and myelination in most ROIs studied follow complex patterns with age described by quadratic, inverted U-shape, relationships. Further, our results indicate that NODDI and BMC-mcDESPOT MRI provide complementary information regarding white matter integrity, and may be combined to investigate the underlying mechanisms of axonal and myelin damage in neurodevelopment and neurodegeneration. Neurite density index (NDI) maps represented as averaged participant maps calculated over age intervals. Results are shown for three representative slices. Visual inspection of NDI maps shows that NDI follow complex patterns with age with most regions exhibiting an increase in NDI values from early age until middle age followed by a more rapid decrease in several brain regions, while other regions exhibiting constant patterns. Myelin water fraction (MWF) represented as averaged participant maps calculated over age intervals. Results are shown for three representative slices. Visual inspection of MWF maps shows an increase in MWF values from early age until middle age followed by a more rapid decrease in several brain regions. This suggests progressive myelination continuing into middle age followed by a decline in myelin content at older ages. Regional neurite density index (NDI) trends as a function of age. For each ROI, the coefficient of determination, R 2 , is reported and * represents the significance of the overall model after FDR correction with * p < 0.05 or ** p < 0.01. Several regions investigated show an inverted U-shaped trend of NDI with age, while other regions showed constant or decreasing associations with age. WB: whole brain white matter, FL: frontal lobes, PL: parietal lobes, TL: temporal lobes, OL: occipital lobes, CRB: cerebellum, BCC: body of corpus callosum, GCC: genu of corpus callosum, SCC: splenium of corpus callosum, IC: internal capsules, CP: cerebral peduncle, ACR: anterior corona radiata, PCR: posterior corona radiata, ATR: anterior thalamic radiation, PTR: posterior thalamic radiation, IFOF: inferior fronto-occipital fasciculus, SFOF: superior fronto-occipital fasciculus, ILF: inferior longitudinal fasciculus, SLF: superior longitudinal fasciculus, Fm: forceps minor, FM: forceps major. Regional myelin water fraction (MWF) trends as a function of age. For each ROI, the coefficient of determination, R 2 , is reported and * represents the significance of the overall model after FDR correction with * p < 0.05 or ** p < 0.01. All regions investigated show an inverted U-shaped trend of MWF with age, but with differences in detail between regions. WB: whole brain white matter, FL: frontal lobes, PL: parietal lobes, TL: temporal lobes, OL: occipital lobes, CRB: cerebellum, BCC: body of corpus callosum, GCC: genu of corpus callosum, SCC: splenium of corpus callosum, IC: internal capsules, CP: cerebral peduncle, ACR: anterior corona radiata, PCR: posterior corona radiata, ATR: anterior thalamic radiation, PTR: posterior thalamic radiation, IFOF: inferior fronto-occipital fasciculus, SFOF: superior fronto-occipital fasciculus, ILF: inferior longitudinal fasciculus, SLF: superior longitudinal fasciculus, Fm: forceps minor, FM: forceps major. Post hoc family-wise error (Bonferroni) correction of the ANOVA results. A black square indicates a post-correction significant difference between the two corresponding age groups in mean NDI (top panel) or mean MWF (bottom panel), a gray square indicates a postcorrection close to significant difference, for each ROI, while a white squares indicate non significance. For example, in FL, there were post-correction statistically significant differences between the age intervals 50-69 and 70-89 in NDI and MWF. WB: whole brain white matter, FL: frontal lobes, PL: parietal lobes, TL: temporal lobes, OL: occipital lobes, CRB: cerebellum, BCC: body of corpus callosum, GCC: genu of corpus callosum, SCC: splenium of corpus callosum, IC: internal capsules, CP: cerebral peduncle, ACR: anterior corona radiata, PCR: posterior corona radiata, ATR: anterior thalamic radiation, PTR: posterior thalamic radiation, IFOF: inferior fronto-occipital fasciculus, SFOF: superior fronto-occipital fasciculus, ILF: inferior longitudinal fasciculus, SLF: superior longitudinal fasciculus, Fm: forceps minor, FM: forceps major. Pearson correlation between MWF and NDI in 21 WM ROIs. R 2 denotes the coefficient of determination. None of the correlations were statistically significant. WB: whole brain white matter, FL: frontal lobes, PL: parietal lobes, TL: temporal lobes, OL: occipital lobes, CRB: cerebellum, BCC: body of corpus callosum, GCC: genu of corpus callosum, SCC: splenium of corpus callosum, IC: internal capsules, CP: cerebral peduncle, ACR: anterior corona radiata, PCR: posterior corona radiata, ATR: anterior thalamic radiation, PTR: posterior thalamic radiation, IFOF: inferior fronto-occipital fasciculus, SFOF: superior frontooccipital fasciculus, ILF: inferior longitudinal fasciculus, SLF: superior longitudinal fasciculus, Fm: forceps minor, FM: forceps major.