White matter microstructure across the adult lifespan: A mixed longitudinal and cross-sectional study using advanced diffusion models and brain-age prediction

The macro- and microstructural architecture of human brain white matter undergoes substantial alterations throughout development and ageing. Most of our understanding of the spatial and temporal characteristics of these lifespan adaptations come from magnetic resonance imaging (MRI), including diffusion MRI (dMRI), which enables visualisation and quantification of brain white matter with unprecedented sensitivity and detail. However, with some notable exceptions, previous studies have relied on cross-sectional designs, limited age ranges, and diffusion tensor imaging (DTI) based on conventional single-shell dMRI. In this mixed cross-sectional and longitudinal study (mean interval: 15.2 months) including 702 multi-shell dMRI datasets, we combined complementary dMRI models to investigate age trajectories in healthy individuals aged 18 to 94 years (57.12% women). Using linear mixed effect models and machine learning based brain age prediction, we assessed the age-dependence of diffusion metrics, and compared the age prediction accuracy of six different diffusion models, including diffusion tensor (DTI) and kurtosis imaging (DKI), neurite orientation dispersion and density imaging (NODDI), restriction spectrum imaging (RSI), spherical mean technique multi-compartment (SMT-mc), and white matter tract integrity (WMTI). The results showed that the age slopes for conventional DTI metrics (fractional anisotropy [FA], mean diffusivity [MD], axial diffusivity [AD], radial diffusivity [RD]) were largely consistent with previous research, and that the highest performing advanced dMRI models showed comparable age prediction accuracy to conventional DTI. Linear mixed effects models and Wilk’s theorem analysis showed that the ‘FA fine’ metric of the RSI model and ‘orientation dispersion’ (OD) metric of the NODDI model showed the highest sensitivity to age. The results indicate that advanced diffusion models (DKI, NODDI, RSI, SMT mc, WMTI) provide sensitive measures of age-related microstructural changes of white matter in the brain that complement and extend the contribution of conventional DTI.


Introduction 62
The architecture of human brain white matter undergoes constant remodelling throughout life. 63 Age-related trajectories of white matter macro-and microstructure typically reflect increases in 64 anisotropy and decreases in diffusivity during childhood, adolescence and early adulthood 65 (Krogsrud et  Smith, Vidaurre, et al., 2019) utilised dMRI. However, the brain-age prediction accuracy of 115 advanced diffusion models such as RSI and NODDI are not known. 116 Including cross-sectional and longitudinal data obtained from 573 healthy individuals 117 (with 702 multi-shell dMRI datasets) aged 18-94 years, the primary aim of this study was to 118 offer a comprehensive description of normative age-related white matter trajectories in 119 adulthood by comparing relevant curve parameters such as key deflection points and rate of 120 change as well as age prediction accuracy of different dMRI metrics, with a particular focus on 121 relatively novel parameters based on advanced (DKI, NODDI, RSI, SMT mc, and WMTI) and 122 conventional (DTI) diffusion models of white matter coherence and microstructure. 123 First, we estimated the trajectories of each of the diffusion metrics across the age range. 124 Secondly, we utilised three separate methods to compare the age-sensitivity of the diffusion 125 models: i) we used linear mixed effect (lme) models including age, sex, and timepoint, ii) for 126 each model, we ran fits with and without age terms and compared the fit likelihood values 127 using Wilk's theorem (Wilks, 1938), iii) we used machine learning to predict age based on the 128 diffusion metrics, and compared the prediction accuracy of the models. Thirdly, we looked at 129 the derivatives of each function of the lme models' age curve to identify the point of change in 130 trajectory for each diffusion metric. Based on previous work characterising age differences and 131 longitudinal changes with a range of diffusion MRI metrics (Benitez et

154
Histogram representing density of data points.

Diffusion MRI processing 166
Processing steps followed a previously described pipeline (Maximov et  We selected 20 scalar metrics from the six models (DTI, DKI, NODDI, RSI,

Linear mixed effects models (lme) 247
To investigate the relationship between age and global mean skeleton values for each diffusion 248 metric, lme analyses were performed using the lme function (Bates & Pinheiro, 1998)

in R (R 249
Core Team, 2012). In fitting the model, we scaled (z normalised) each variable and entered 250 age, orthogonalised age 2 , sex, and timepoint (TP) as fixed effects. Subject ID was entered as a 251 random effect. For each diffusion metric M, we employed the following function: 252 253 ! = # + % × #'( + ) × #'( ! + +(, + -. (1) 254 255 where A is the intercept, B is the age coefficient, and C is the coefficient of the orthogonalised 256 quadratic age term (expressed as poly(age,2)[,2] in R). Age curves were obtained with 257 predictions from the fitted model using the predict function in R and used for age curve 258 trajectory figures. Visual inspection of residual plots did not reveal any obvious deviations 259 from homoscedasticity or normality. The significance threshold was set at p < 0.05, and the 260 results were corrected for multiple comparisons using the false discovery rate (FDR) 261 adjustment (Benjamini & Hochberg, 1995). 262 To investigate the rate of change for each of the age curves at any point, we calculated 263 their derivatives using numerical differentiation with finite differences (Burden & Faires, 2011). To compare the age-sensitivity of the models, we ran lme fits with and without age 265 terms, and calculated the difference in likelihood ratios (Glover & Dixon, 2004). The 266 significance of the age dependence was calculated using Wilk's theorem (Wilks, 1938) as 267 /2(2 ! − 2 " ), where L2 is the likelihood ratio obtained from the models with age terms, and 268 L1 is the likelihood ratio obtained from the models without age terms. 269 NODDI, RSI, SMT mc, WMTI), predicted age was estimated in a 10-fold cross validation, 277 assigning a model-specific brain age estimate to each individual, as well as a multimodal brain 278 age estimate based on all diffusion features. To investigate the prediction accuracy of each 279 model, correlation analyses were run for predicted versus chronological age, and model-280 specific R 2 , root mean square error (RMSE) and mean absolute error (MAE) were calculated. 281 To statistically compare the prediction accuracy of the models, Z tests for correlated samples 282 (Zimmerman, 2012) were run on the model-specific correlations between predicted and 283 chronological age in a pairwise manner using 284 285 5 = (6 m1 − 6 m2 )/89 m1 ! + 9 m2 ! − 2:9 m1 9 m2 , 286 287 where "m1" and "m2" represent model 1 and model 2, the b terms represent the beta value 288 from the regression fit, the s terms represent their errors, and r represents the correlation 289 between the two sets of associations. In order to assess the complementary value of the 290 different models, we computed the correlations between the brain age predictions (Figure 6). 291 The predictions were first corrected for age-bias using linear models (Le et al., 2018), and the 292 residuals were used in the correlation analysis. 293 To evaluate the importance of each diffusion modality in the multimodal model, we ran an 294 additional prediction model including only mean-skeleton values to reduce the number of 295 highly correlated features in the regressor input, and calculated a) the proportion of the total 296 weight contributed by each modality, where weight represents the number of times a feature is 297 used to split the data across all trees, and b) gain values, which represent the improvement in accuracy added by a feature to the branches it is on. To assess the significance of the general 299 model performance, average RMSE was calculated for the multimodal model using cross 300 validation with ten splits and ten repetitions and compared to a null distribution calculated 301 from 1000 permutations. 302 SMT mc intra, and WMTI awf metrics following similar trajectories. RSI rD, NODDI ISOFV, 327 RSI FA fine, and WMTI axIAD metrics followed decreasing trajectories from the offset. SMT 328 mc extramd and extratrans, and WMTI radEAD followed similar trajectories to MD and RD. 329 NODDI OD revealed a steady increase until older age where the slope stabilised thereafter.      Age -0.66 *** 0.46 *** 0.03 0.59 *** -0.12 * -0.24 *** -0.32 *** -0.33 *** 0.48 *** 0.67 *** -0.48 *** -0.69 *** -0.54 *** 0.50 *** 0.56 *** -0.26 *** -0.49 *** 0.15 *** -0.58 *** 0.57 *** Age 2 -0.17 *** 0.34 *** 0.40 *** 0.29 *** -0.44 *** -0.26 *** -0.18 *** -0.33 *** 0.10 * -0.08 -0.37 *** -0.15 *** -0.11 * 0.21 *** 0.35 *** -0.27 *** -0.26 *** 0.14 *** 0.11 * 0.21 ***

Age sensitivity estimated using lme models 381
Results from the lme models revealed significant main effects of age on the global mean 382 skeleton values for all diffusion metrics (see Table 2). An examination of the fixed effects 383 estimates (β) and t-statistics for the age term allows for interpretation of the extent and 384 direction of the linear association with age. Overall, the FA fine compartment of the RSI model 385 was most sensitive to age (β(125) = -0.69, t = -21.97, p < 0.001). NODDI OD was the second 386 most sensitive to age (β(125) = 0.67, t = 21.62, p < 0.001). The model least sensitive to age was 387 DTI AD (β(125) = 0.03, t = 0.71, p = 1). For conventional DTI metrics, FA was the most age  3.6. Age sensitivity estimated using brain age 400 The model performances for the multimodal and model-specific brain age predictions are 401 shown in Table 4. SI Figures 8 and 9 show the associations between predicted age and 402 chronological age for each of the models. Figure 6 shows the pairwise correlations between 403 predicted age for each model. Pairwise differences in the age prediction accuracy of the models 404 are shown in Figures 7 and 8. SI Figure 1 shows the RMSE of the multimodal model prediction 405 compared to a null distribution obtained from calculating 1000 permutations. 406     accuracy between DTI and RSI, and WMTI and NODDI did not survive correction for multiple 457 comparisons. Figure 6 showed correlation coefficients of mean r = 0.59 (Std = 0.09) between 458 the DTI, RSI, NODDI, SMT and WMTI predictions, while the DKI showed lower correlations 459 with the other model predictions (mean r = 0.29, Std = 0.04). 460 To evaluate the relative importance of each modality, we ran an additional multimodal 461 model including only mean-skeleton values to reduce the number of highly correlated features 462 in the regressor input. Table 5 shows the total gain and the proportion of weight contributed by 463 each modality to the total weight, indicating their relative contribution in the model training. 464 The results revealed that the machine favoured the NODDI model in the training. 465 466

Discussion 469
Ageing confers a range of structural brain alterations, affecting micro-and macrostructural 470 properties of the neurocircuitry supporting cognitive and other complex brain functions. In the 471 current mixed cross-sectional and longitudinal study, we compared age sensitivity and brain 472 white matter age trajectories across the adult lifespan based on advanced and conventional 473 dMRI models. The results from our comprehensive analysis approach, including age-curve 474 trajectories, linear mixed effects models, Wilk's theorem analysis, and brain age prediction, 475 showed high age sensitivity for all diffusion metrics, with comparable sensitivity between the 476 highest performing advanced dMRI models and conventional DTI, and a moderate benefit of 477 including all metrics in the same model. The mixed effects analyses and corresponding 478 derivatives revealed variations in age trajectories between models, indicating that they may be 479 sensitive to different underlying aspects of white matter ageing. 480 Our results showed that FA plateaued around the third decade with a steady decline in 481 slope following the age of ~40, and an accelerated decrease in senescence (Figure 3). The other 482 mark, where the trajectories subsequently increase following a steady period. While these 484 results to a large extent correspond with trajectories observed in previous studies (Cox et  informs us about the estimated rate of change at specific ages, in addition to the differential 510 sensitivity between different metrics during different life phases. Although diffusion imaging 511 cannot give direct access to neuronal processes on a cellular level, the varying estimated 512 trajectories in advanced dMRI models potentially reflect differential involvement of the 513 putative biological underpinnings during the different phases of brain ageing. Thus, metric-514 specific differences may reflect age-related pathological changes behind each dMRI model, 515 helping us better pinpoint the age at which decline in white matter microstructure begins, 516 which has important implications for interventive strategies aimed at promoting healthy 517 ageing. 518 Although recent research has validated FA and RD metrics of DTI as being sensitive 519 markers to myelin (Lazari & Lipp, 2020), caution must be exerted in interpreting specific 520 underlying biology on the basis of DTI alone . With this in mind, 521 combining tissue models such as NODDI, WMTI, RSI, and SMT mc may hold promise in 522 jointly reflecting measures more relatable to the neurobiological underpinnings of brain ageing. properties than conventional DTI (Jensen et al., 2005). 541 In theory, the partly non-overlapping assumptions and biophysical properties of the 542 different diffusion MRI models offer a more comprehensive and complete view of the 543 manifold biological processes in brain development, ageing, and disorders when considered 544 jointly. In general, our findings of higher age prediction accuracy when combining different 545 models supports this view. However, not surprisingly, the relatively high correlations and 546 similar age-related trajectories of several of the different metrics also suggest a certain level of 547 redundancy. Further studies are needed to test the hypothesis that combining various diffusion 548 MRI models of brain macro-and microstructure increases the feasibility and precision of 549 multimodal data-driven brain phenotyping approaches (e.g. "fingerprinting") towards more 550 specific clinical applications and prediction (Alnaes et al., 2018). With this in mind, including 551 the advanced models may not only improves specificity compared to conventional DTI, but 552 potentially provides additional information related to changes in myelination and axonal Some methodological limitations must also be addressed. One concern is that of 588 averaging over regions of interests and the entire white matter skeleton, which is complicated 589 by the direction and magnitude of age associations varying regionally. Recent findings 590 (Tønnesen et al., 2020) found that the global mean skeleton model outperformed region of 591 interest-based single-metric models, providing evidence for relevant information required for 592 brain age prediction is captured at a global level. Indeed, previous studies have suggested that 593 regional DTI-based indices of brain aging reflect relatively global processes ( The study also included a relatively large sample and benefitted from all participants 611 having been scanned with the same MRI scanner. Additionally, with cross-sectional studies 612 being limited by between-subject variance and possible cohort effects (Schaie, 2005), the 613 current study profits from a mixed cross-sectional and longitudinal design, where participants 614 can be used as their own baseline (Sexton et al., 2014). However, the longitudinal aspect of our 615 study had some limitations, including the short interval duration, and the low sample size 616 compared to the cross-sectional sample. Consequently, the main results were largely driven by 617 cross sectional data despite the mixed cross-sectional and longitudinal nature of the design. 618 Future research should aim to adopt fully longitudinal designs over several time points in order 619 to evaluate individual differences in change over time, preferably over wide age ranges. 620 Although the advanced dMRI models offered new insight into age sensitivity (such as 621 the relatively high performance of RSI and NODDI for age prediction) and differences in age trajectories, the biological interpretation of these metrics require further validation. Continued 623 development and validation of more optimal diffusion models that better reflect biological 624 properties of the brain is needed, and future research should take into account the impact of a 625 range of potential factors that may mediate brain and cognitive development (Alnaes et al., 626 2020) and ageing (Lindenberger, 2014), such as pre-and perinatal events, socio-demographical 627 factors, education, lifestyle, cardiometabolic risk factors, and genetics. 628 In conclusion, characterising changes in white matter microstructure over the human 629 lifespan is critical for establishing robust models of normative neurodevelopment and ageing, 630 which in turn can help us to better understand deviations from healthy age trajectories. The 631 current study demonstrates that while advanced and conventional dMRI models show 632 comparable age-sensitivity, multi-shell diffusion acquisition and advanced dMRI models can 633 contribute to measuring multiple, complementary aspects of white matter characteristics. 634