Synopsis

Several brain diseases show prominent, regionally-specific atrophy over time, which is often predictive of patient outcomes. However, reliable estimation of atrophy rates typically relies on repeated observations over several years. This is incompatible with clinical practice in terms of cost and prognosis utility. Here, we propose a statistical regularization approach to dramatically improve the quality of regional atrophy estimates, using only two longitudinal measurements. We evaluate the approach on open data from 43 MR scanners and 599 subjects, showing that we halve the error in most regions, while maintaining discriminability between controls and Alzheimer patients.

Introduction

Materials and Methods

We used a subset of the TADPOLE dataset⁵, comprising 1.5T ADNI⁶ T1-weighted MPRAGE images with uniform preprocessing (gradwarp correction, B1 correction, and N3) from 178 controls (CN), 284 patients with mild cognitive impairment (MCI), and 138 AD patients, distributed between 43 ADNI sites (Figure 1), and up to 9 longitudinal acquisitions. We registered each subject’s images to their first time point using affine registration. Focusing on regions of particular interest for dementia, we computed volumes for cortical gray matter, brain, ventricles, hippocampus, putamen, and left and right temporal lobe gray matter with the MorphoBox prototype⁷. We also used diagnosis at baseline, sex, and age at time of acquisition.

We assumed log-linearity of atrophy due to the elderly study sample (IQR 71-80 years). Using only the CN subjects, we trained a mixed-effects model with random intercepts and random slopes - in lme4⁸ notation: log(volume) ~ 1 + Age + Sex + (1 + Age | Subject), which accounts for longitudinal measurements. “Long-term” atrophy rate in percent change per year is then directly given by the coefficient for Age. We used a parametric bootstrap with 200 resamplings to establish 5th/95th percentiles around the Age coefficient, yielding a reference range for atrophy.

For each region, relative percent change $$$p$$$ was computed as $$$p=\frac{V_{new}-V_{old}}{V_{old}}$$$, from which naïve “short-term” annual atrophy rates $$$r$$$ were computed as $$$r=\frac{p}{d}365$$$, with $$$d$$$ the time in days between the two acquisitions.

To obtain the regularized estimate $$$r_{reg}$$$, we used a shrinkage estimator of the rate of atrophy, thus trading lower variance for increased bias: $$$r_{reg}=(1-\lambda) r + \lambda m$$$, where $$$m$$$ is the fixed-effect coefficient for Age in the long-term random effects model trained on healthy controls. Equivalently, $$$m$$$ is the mean of the distribution of subject-specific long-term atrophy estimates. $$$\lambda$$$ can be computed analytically from the variance of the random effects and the total measurement variance. This could also be set in cross-validation by minimizing mean absolute error (MAE). Here, without loss of generality, we set $$$ \lambda = 0.5$$$ a priori for all structures.

Results

Long-term reference range

On average, the “long-term” estimates for atrophy rate across regions for controls stood between -0.5%/year and -0.2%/year (excluding ventricles). The hippocampus had more marked atrophy, estimated between -0.6%/year and -0.4%/year. Ventricular enlargement was estimated between 2.8% and 3.5% per year (Figure 2). These figures are in line with biological plausibility and extant literature31.

Error reduction

The shrunk short-term estimators of atrophy had approximately half the error (as measured by MAE) than the naïve short-term estimators (Figure 3). In all regions, the shrunk estimators on average moved towards the long-term estimator. For the ventricles, the mean absolute error was reduced from 4.5% to 2.2% by the shrunk short term estimator, bringing the estimation error below the long-term hypertrophy rate estimate (4.3% annual volume change). This suggests that the estimator can be used to distinguish between artefactual variation (apparent volume change) and actual ventricular enlargement, although other regions still have estimation error above the expected annual change. This trend held across diagnosis status (Figure 4).

Clinical discrimination

To evaluate atrophy rates as an imaging marker, we computed the area under the receiver-operating characteristic (ROC) curve (AUC) for the discrimination between CN and AD subjects, using image pairs more than 364 days apart. Consistent with the literature, hippocampal atrophy is the best predictor (AUC 75%). Other regions give worse performance but are significantly above chance (Figure 5).

Conclusions

Acknowledgements

References

1. Smith, S. M. et al. Longitudinal and cross-sectional analysis of atrophy in Alzheimer’s disease: Cross-validation of BSI, SIENA and SIENAX. NeuroImage 36, 1200–1206 (2007).

2. Fox, R. J. et al. Phase 2 Trial of Ibudilast in Progressive Multiple Sclerosis. N. Engl. J. Med. 379, 846–855 (2018).

3. Ledig, C., Schuh, A., Guerrero, R., Heckemann, R. A. & Rueckert, D. Structural brain imaging in Alzheimers disease and mild cognitive impairment: biomarker analysis and shared morphometry database. Sci. Rep. 8, (2018).

4. Schott, J. M. et al. Combining short interval MRI in Alzheimer’s disease. J. Neurol. 253, 1147–1153 (2006).

5. Marinescu, R. V. et al. TADPOLE Challenge: Prediction of Longitudinal Evolution in Alzheimer’s Disease. (2018).

6. Jack, C. R. et al. Update on the magnetic resonance imaging core of the Alzheimer’s disease neuroimaging initiative. Alzheimers Dement. 6, 212–220 (2010).

7. Schmitter, D. et al. An evaluation of volume-based morphometry for prediction of mild cognitive impairment and Alzheimer’s disease. NeuroImage Clin. 7, 7–17 (2015).

8. Bates, D., Mächler, M., Bolker, B. & Walker, S. Fitting Linear Mixed-Effects Models Using lme4. J. Stat. Softw. 67, (2015).