High-dimensional morphometry

Disentangling normal aging from Alzheimer’s disease in structuralmagnetic resonance images

Marco Lorenzi a,*, Xavier Pennec a, Giovanni B. Frisoni b,c, Nicholas Ayache a, for theAlzheimer’s Disease Neuroimaging InitiativeyaAsclepios Research Project, INRIA Sophia Antipolis, Sophia Antipolis, Franceb IRCCS Fatebenefratelli, Brescia, ItalycMemory Clinic, University Hospitals and University of Geneva, Geneva, Switzerland

a r t i c l e i n f o

Article history:Received 7 May 2013Received in revised form 25 July 2014Accepted 28 July 2014Available online 6 September 2014

Keywords:Longitudinal atrophyHealthy agingDeformation based morphometryNonlinear registrationCSF Abeta42

a b s t r a c t

The morphology observed in the brains of patients affected by Alzheimer’s disease (AD) is a combinationof different biological processes, such as normal aging and the pathological matter loss specific to AD. Theability to differentiate between these biological factors is fundamental to reliably evaluate pathologicalAD-related structural changes, especially in the earliest phase of the disease, at prodromal and preclinicalstages. Here we propose a method based on non-linear image registration to estimate and analyze fromobserved brain morphologies the relative contributions from aging and pathology. In particular, we firstdefine a longitudinal model of the brain’s normal aging process from serial T1-weight magnetic reso-nance imaging scans of 65 healthy participants. The longitudinal model is then used as a reference for thecross-sectional analysis. Given a new brain image, we then estimate its anatomical age relative to theaging model; this is defined as a morphological age shift with respect to the average age of the healthypopulation at baseline. Finally, we define the specific morphological process as the remainder of theobserved anatomy after the removal of the estimated normal aging process. Experimental results from105 healthy participants, 110 subjects with mild cognitive impairment (MCI), 86 with MCI converted toAD, and 134 AD patients provide a novel description of the anatomical changes observed across the ADtime span: normal aging, normal aging at risk, conversion to MCI, and the latest stages of AD. Moreadvanced AD stages are associated with an increased morphological age shift in the brain and withstrong disease-specific morphological changes affecting mainly ventricles, temporal poles, the entorhinalcortex, and hippocampi. Our model shows that AD is characterized by localized disease-specific brainchanges as well as by an accelerated global aging process. This method may thus represent a moreprecise instrument to identify potential clinical outcomes in clinical trials for disease modifying drugs.

! 2015 Elsevier Inc. All rights reserved.

1. Introduction

The objective of computational anatomy when applied toneurodegenerative diseases, such as Alzheimer’s disease (AD), is tounderstand the pathological changes affecting brain morphology(Frisoni et al., 2010; Scahill et al., 2002). However, the morphology

of the brain affected by AD is not completely related to the disease,especially in asymptomatic and prodromal stages, because thebrain structure is also the result of patient phenotype and clinicalhistory. In a brain affected by AD, we can identify 2 major processescontributing to morphological changes: normal aging and AD pa-thology itself.

! Age-related anatomical changes. It is known that aging is relatedto progressive impairment of neural mechanisms (Burke andBarnes, 2006), to chemical alterations in the brain, and tochanges in cognition and behaviour (Hof and Mobbs, 1984). Ithas been observed that morphological changes in the agingbrain are heterogeneous and primarily lead to gray matter lossin frontal, temporal, and parietal areas (Long et al., 2012; Sowellet al., 2003).

* Corresponding author at: INRIA Sophia Antipolis, Asclepios Research Project,Sophia Antipolis, France. Tel.: þ33 4 92 38 76 60; fax: þ33 4 92 38 76 69.

E-mail address: marco.lorenzi@inria.fr (M. Lorenzi).y Data used in preparation of this article were obtained from the Alzheimers

Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). As such, theinvestigators within the ADNI contributed to the design and implementation ofADNI and/or provided data but did not participate in analysis or writing of thisreport. A complete listing of ADNI investigators can be found at: http://adni.loni.usc.edu/wp-content/uploads/how_to_apply/ADNI_Acknowledgement_List.pdf.

Contents lists available at ScienceDirect

Neurobiology of Aging

journal homepage: www.elsevier .com/locate/neuaging

0197-4580/$ e see front matter ! 2015 Elsevier Inc. All rights reserved.http://dx.doi.org/10.1016/j.neurobiolaging.2014.07.046

Neurobiology of Aging 36 (2015) S42eS52

! Disease-related anatomical changes. AD is a neurodegenerativedisease characterized by the cooccurrence of different phe-nomena. It starts with the deposition of amyloid plaques andtau proteins in neurofibrillary tangles, which is followed by thedevelopment of function brain loss, and finally by widespreadstructural atrophy (Jack et al., 2010). The typical pattern of braintissue loss seen in AD mirrors tau deposition (Thompson et al.,2003) and involves primarily hippocampi, the entorhinal cor-tex, the posterior cingulate, and secondarily the temporal, pa-rietal, and frontal cortices (Frisoni et al., 2010). Aging is theprimary risk-factor in AD and leads to patterns of structural lossoverlapping the pathological ones. However, the magnitude ofbrain atrophy caused by AD is generally striking compared withnormal aging. As claimed in previous studies, AD is more likelyto be a pathological state concurrent to aging, identified byspecific biochemical and structural hallmarks (Barnes, 2011;Nelson et al., 2011).

Being able to separately model healthy aging and AD wouldallow us to describe a given anatomy as being composed of distinctand concurrent factors. Such a decomposition would be extremelyinteresting not only to improve the understanding of the diseasebut also for clinical purposes, such as for early diagnosis and for thedevelopment of drugs targeting the atrophy specific to the pa-thology. It is important to notice that, although brought oncompletely different biological mechanisms, aging and AD oftenmap to common areas, and the correct identification of therespective contributions can be difficult, especially in morpho-metric studies. Moreover, it is plausible that these phenomena arenot completely independent and may overlap to create a positive“feedback” process. Thus, the onset of pathological changes maylead to accelerated global aging in the long term (Fjell et al., 2012),and vice versa.

A reliable estimate of the aging component is also important formodeling the evolution of the disease and for subsequent statisticalanalysis. When comparing the longitudinal observations fromdifferent clinical groups, at different aging stages, it is crucial tocorrectly position the observations on the time axis. This is notstraightforward because the disease appears at different ages andchronologically older brains may have greater structural integritythan younger ones affected by the pathology. Therefore, it might beof practical interest to compute an index of age shift “relative” to areference anatomical model.

The idea of modeling the time course of AD with respect toclinical and demographic factors was proposed in previous statis-tical studies (Ito et al., 2012; Samtani et al., 2012; Yang et al., 2011).However, these works were limited to scalar observations such asclinical scores and demographics and thus do not provide anexplicit model which relates structural changes in the entire brainto the disease and aging. Moreover, the disease progression wasidentified by clinical measures and was not therefore explicitlyassociated with a temporal time course.

Although imaging-based surrogate measures of aging have beenprovided by different methodological studies (Davatzikos et al.,2009; Franke et al., 2010; Konukoglu et al., 2013), the idea ofseparately investigating aging and residual morphological changeshas not been proposed before.

The objective of this work is to introduce a framework to identifyand disentangle the brain anatomical changes related to normalaging from those related to other biological processes, such as AD.In particular, our framework is based on the hypothesis that relatesthe development of AD to the abnormal accumulation of beta-amyloid (Ab) peptide in the brain (Jack et al., 2010). We thusdefine “normal aging” as the morphological brain evolution whichis not caused by Ab. This evolution is modeled by nonlinear

registration and is used as a reference to characterize observedanatomy as a contribution from normal morphological aging(normal aging process) plus a specific morphological process thatencodes the subject’s specific variability such as pathological traits.We test our framework on healthy participants positive to the ce-rebrospinal fluid (CSF) Ab42marker, in participants affected bymildcognitive impairment (MCI) and in AD patients.

The method is based on diffeomorphic nonlinear registrationand is detailed in Section 2. In Section 3, we show that such aframework provides a meaningful and accurate description ofanatomical brain changes across the stages of AD, characterized byincreased morphological aging plus specific and local atrophyfeatures.

2. Methods

The proposed method relies on specific modeling assumptionswhich are summarized here:

! The model of normal aging is derived from imaging data byapplying a registration-based protocol detailed in Section 2.1. Inparticular, we assume that normal aging can be modeledthrough nonlinear registration as a smooth and continuousprocess that can be extrapolated backward and forward in timebeyond the observed imaging follow-up time. Moreover, weassume that normal aging is a constant process in time, thatdoes not accelerate nor deceleratewith respect to the biologicalage of the elderly population. We show in Sections 3.4. and 3.5.that these simple assumptions lead to plausible experimentalresults compared with imaging and clinical data, and that theproposed model is a generalization of the classical linearmixed-effect (LME) modeling of univariate data used in longi-tudinal studies (Fitzmaurice et al., 2011).

! We define the specific morphological process as the remainder ofthe observed anatomy modulo the normal aging process. Thus,the specific morphological process encodes the morphologicaltraits that cannot be described by the model of normal aging. Inthis study we aim to show that this specific process providesvaluable information for discriminating pathological traitsspecific to AD across the whole disease time span (Section 3.6).

The framework was developed in the following way. Wewant tomodel the anatomy represented by a magnetic resonance image, Ik,acquired for a given subject k. For this purpose we describe theanatomical changes with respect to a reference anatomical tem-plate, T, through nonlinear image registration. This work is based ondiffeomorphic registration parameterized by stationary velocityfields (SVFs) (Lorenzi et al., 2013). The nonlinear registration settingestimates one-to-one smooth deformations that spatially align theanatomies represented by pairs of images. These deformations arecompletely identified voxel-wise by tangent velocities in thedeformation space (Arsigny et al., 2006).

As illustrated in Fig. 1, we parameterize the subject-to-templatedeformation fk by the flow of a SVF wk, which is denotedfk ¼ expðwkÞ. In this framework the observed anatomical changesare entirely encoded in the SVF wk.

Because the space of SVFs is a linear vector space (contrarily tothe space of deformations that it generates), we assume thatwk canbe decomposed into the algebraic sum of the normal deformationparameter wk

age plus a specific deformation parameter wkspecific

(Fig. 2).The proposed framework analyzes these different components

by processing the observed anatomy in different modeling steps asdescribed in the following sections.

M. Lorenzi et al. / Neurobiology of Aging 36 (2015) S42eS52 S43

2.1. Estimation of the normal aging model

This section describes the procedure based on nonlinear regis-tration used to create the reference model of the average group-wise longitudinal changes in healthy controls. As in the case ofclassical univariate linear mixed-effects modeling, we define a hi-erarchical model in which the subject specific trajectories ofmorphological changes are random realizations of an underlyingnormal aging process m0 (Fig. 3). The model is defined by thefollowing levels:

1. Given the SVF m0ðtÞ describing the group-wise aging process inthe template space T0, the subject-specific trajectories ofhealthy controls (in the template space) are realizationsm0ðtÞ þ εS, where εS is the random variation from the fixedeffect m0.

2. The SVF describing the subject-specific trajectory mSðtÞ is ob-tained by an intersubject spatial change of coordinates from thetemplate space to the subject-specific coordinate system.

3. The trajectories mS(t) at points ti describe a time series of lon-gitudinal images ISti . In particular we assume that the acquisi-tion baseline time of each subject is the same within thepopulation (t0¼0), which equates to assuming that the agingprogression is constant with respect to biological age.

Given the observed subject-specific trajectories of the anatom-ical changes defined by the series ISti , we estimate the group-wisetrajectory m0 by solving the inverse problem specified by theaforedescribed hierarchical model (Fig. 3). Please note that, as forlinear mixed-effects modeling, our model assumes that the errorsof the subject-to-template registration are similar for all the sub-jects. The model allows as well missing data and unequal samplingof trajectories by opportunely modeling inter and intrasubjectvariability. Details of the practical estimation of the normal agingtrajectory m0 using non-linear registration are given in Appendix A.

In the following sections, we assume that normal aging evolveslinearly in time according to the average group-wise SVF m0, so thatit is parameterized by the trajectory m0(t) ¼ tm0. Note that theresulting longitudinal normal aging process exp(tm0) is non-linear.

2.2. Identification and extraction of the morphological age shift

Now that we have defined the normal aging model in a longi-tudinal setting, let us switch to a purely cross-sectional design:

given an image Ik of a subject k, we want to differentiate betweenthe morphological patterns caused by normal aging and thoserelated to different biological processes.

Given the trajectory tm0, wewant to project the subject’s anatomyIk on the “closest” point to determine its relative progression stage tkwith respect to the normal aging process (Fig. 2). By projecting theSVF, which parameterizes the subject-to-template deformationexp(wk), orthogonally onto the normal aging trajectory1, we obtainthe decomposition wk ¼ wk

age þwkspecific ¼ tkm0 þwk

specific.In such a decomposition the time point tk is the morphological

age shift of the subject k with respect to the template T (which hasthe average age of the healthy control population), defined by theprojection on the longitudinal model tm0. The SVF wk

specific includesthe specific morphological changes that cannot be related to thenormal aging process (Fig. 2). The time shift tk defines the pro-jection on the longitudinal normal evolution tm0 and is defined asthe whole brain average of the voxel-by-voxel projections:tk ¼ hwk;m0iðxÞ=km0k

2ðxÞ. Once tk is determined, the specific defor-

mation parameter is simply defined voxel-wise aswk

specific ¼ wk & tkm0. The removal of the normal deformationparameter tkm0 allows us to directly compare the remainingparameter wk

specific across subjects.

2.3. Identification and analysis of the specific morphological process

Let us turn now to the analysis of the specific deformationparameter wk

specific across subjects. This component defines themorphological changes that cannot be attributed to the normalaging process.

2.3.1. Divergence associated with the specific deformationparameter

Our diffeomorphic registration encodes observedmorphologicalchanges as dense diffeomorphic deformation fields parameterizedby SVF. Volume changes are measured in a closed region by the fluxof SVF across the boundary: the inward (resp. outward) flow ofvectors across the boundary measures the apparent volume loss(resp. gain) (see Fig. 1 for an illustrative example). More precisely,these local atrophy/growth processes are quantified by a scalarmap: the divergence V,wk

specific associated with the specific defor-mation parameter wspecific (Lorenzi et al., 2012).

Fig. 1. The SVFwk (blue arrows) parameterizes the underlying transformation. In particular, thefinal displacement is obtained by locally following the flow-lines (as shown for instanceby the green and red streams) identified by the SVF. The flux of the SVF across the boundaries of regions (e.g., black circles) measures the apparent regional volume change encoded bythe deformation. Abbreviation: SVF, stationary velocity field. (For interpretation of the references to color in this Figure, the reader is referred to the web version of this article.)

1 In the present work the projection is based on the standard L2 metric.

M. Lorenzi et al. / Neurobiology of Aging 36 (2015) S42eS52S44

2.3.2. Discriminative analysis of the specific deformation parameterWe test the ability of the divergence maps V,wspecific to discrim-

inate between a set of patients P and a control group C. Because this isa scalar map, we can use classical univariate methods.

We calculated the voxel-by-voxel map of the effect sizeassociated with the average group-wise divergenceES ¼ ðmeanðV,wP

specÞ &meanðV,wCspecÞÞ=sdðV,wP

specÞ, which qua-ntifies the difference between volume changes modeled in pa-tients and controls. We then chose a set of relevant regions for AD(hippocampi, medial temporal lobes, posterior cingulate, andventricles), where we identified the voxels of maximal positiveand negative effect sizes. Regions were propagated in our refer-ence space from the AAL-labeled MNI template (Tzourio-Mazoyeret al., 2001). These voxels were inflated and symmetrized withrespect to the sagittal midline to define a set of group-wise mostdiscriminative regions. Finally Fisher discriminant analysis wasperformed on the corresponding regional average divergencevalues associated with patients and controls. The discriminativeanalysis was performed by leave-one-out cross validation (500permutations).

3. Experiments and results

3.1. Experimental data

Data used in the preparation of this article were obtained fromthe Alzheimer’s Disease Neuroimaging Initiative (ADNI) database(adni.loni.usc.edu). The ADNI was launched in 2003 by the NationalInstitute on Aging, the National Institute of Biomedical Imaging and

Bioengineering, the Food and Drug Administration, private phar-maceutical companies, and nonprofit organizations, as a $60million, 5-year public-private partnership. The Principal Investi-gator of this initiative is Michael W. Weiner, MD, VAMedical Centerand University of California San Francisco. ADNI is the result of ef-forts of many coinvestigators from a broad range of academic in-stitutions and private corporations, and participants have beenrecruited from more than 50 sites across the United States andCanada. For up-to-date information, visit www.adni-info.org.

3.2. Baseline characteristics

We chose ADNI structural MRIs from 65 healthy participantswith normal levels of CSF Ab42 (>192 pg/mL, group Ab&); 40healthy participants with abnormal levels (group Abþ); 86 par-ticipants with mild cognitive impairment who subsequentlyconverted to AD (group MCIconv); 110 MCI participants whoremained stable during the observation period (group MCIstable);and 134 AD patients (group AD). Demographic as well clinicalinformation was based on ADNI data updated to March 2012, witha follow-up period of 3 years from baseline. Baseline socio-demographical and clinical information for the different groupsare shown in Table 1.

3.3. Analysis of normal aging and specific morphological processes

Previous studies show that healthy elderly subjects with patho-logical CSF Ab42 levels (<192 pg/mL) have a more pronounced pro-gression of brain atrophy (Fjell et al., 2010, Tosun et al., 2010), which

Fig. 3. Hierarchical framework for the estimation of the group-wise model of normal aging. For a given subject, the follow-up longitudinal images are nonlinearly registered to thebaseline to estimate the associated SVF (A). The subject-specific trajectory mS of the longitudinal morphological progression is estimated from the series of SVF with a linear model intime (B). Finally the group-wise model is computed as the mean of the transported subject-specific trajectories (C). Abbreviation: SVF, stationary velocity field. (For interpretation ofthe references to color in this figure, the reader is referred to the web version of this article.)

Fig. 2. An observed anatomy can be described in terms of normal aging plus a specific morphological process. (For interpretation of the references to color in this figure, the reader isreferred to the web version of this article.)

M. Lorenzi et al. / Neurobiology of Aging 36 (2015) S42eS52 S45

might be a marker of the presymptomatic stage of AD. We thereforedefined the normal agingmodel byconsideringonly theAb groupas areferencenormalpopulation.The longitudinalobservations (baseline,6,12,24,and36months) available for theAbgroupwereconsideredtomodel a reference healthy evolution m0 normalized to an anatomicalreference template T according to Section 2.1. The average follow-uptime for the Ab group was 18.32 months ('11.47) and the averagenumber of follow-up acquisitions per participant was 4.46 ('0.8): 40participants had 5 scans (thus the complete set of longitudinal im-ages), 17 had 4 scans, 6 had 3 scans, and only 2 had 2 scans.

The template T was estimated as in Guimond et al. (2000) fromthe pooled healthy group. Therefore, the reference age of thetemplate is 75.41 years, which corresponds to the average age ofhealthy participants.

To unbias the analysis with respect to the healthy Ab population,we centered the SVFs by subtracting the average subject-to-template SVF of the Ab group. The unbiased SVF was thenanalyzed by following the framework proposed in Sections 2.2. and2.3. The effectiveness of the specific morphological process inencoding information relevant to the pathology was tested byperforming 2 different discriminative analyses for the classificationbetween AD versus healthy, and MCIconv versus MCIstable.

3.4. Longitudinal model of normal aging

The reference model of normal aging estimated for the Ab groupis shown in Fig. 4A. The estimated normal aging process is char-acterized mainly by ventricular growth and by a correspondingapparent atrophy in surrounding regions. Volume loss is wide-spread in temporal areas and characterizes the shrinkage ofhippocampi. Interestingly, themodel displays an important atrophypattern in the cerebellum, which is in agreement with observationspreviously reported in the literature (Koller et al., 1981; Luft et al.,1999; Torvik et al., 1986). Finally, other regions of volume losswere localized in the superior frontal cortex and in the cuneus, inagreement with previous findings on longitudinal atrophy in theADNI healthy cohort (Fjell et al., 2009).

From the quantitative point of view, the average relative annualvolume change in selected ROIs was &0.54% and &0.4% for hippo-campi and medial temporal lobes respectively, and þ1.3% in theventricles. These results are compatible with those reported inseveral longitudinal morphometric studies (Fjell et al., 2009, Foxand Schott, 2004; Jack et al., 2004; Risacher et al., 2010).

Fig. 4B provides a statistical assessment of the ability of theproposed aging model to describe the observed group-wise longi-tudinal anatomical changes. We compared the change in brainvolume associated with the normal aging model, Fig. 4A, to thelongitudinal brain volume changes measured in the Ab- group.Brain volume was quantified as the ratio between gray þ whitematter tissue and total intracranial volume (gray þ white þ CSFareas). Tissue segmentation was performed with the FAST toolavailable in the FSL suite (Zhang et al., 2001).

For the sake of comparison, we also compared the progressionassociated with our model to the classical LME of the scalar mea-sures of brain volumes. We observed that the brain volume pro-gression associated with the model of normal aging is close to thatmodeled by LME, and almost entirely falls into the 95% confidenceinterval within the age range (65e90). These results indicate thatthe hierarchical model described in Section 2. is compatible withclassical approaches of longitudinal analysis while providing amore comprehensive description of the whole brain dynamicsassociated with morphological change.

Fig. 4C shows the extrapolation of the longitudinal model intime. The progression follows the model highlighted in Fig. 4A andis in fact characterized bymajor ventricles enlargement and bymildatrophy spread in the temporal areas.

3.5. Morphological age shift

Fig. 4C provides a qualitative illustration of morphological ageestimated with respect to the normal aging model. We see that themorphological age shift correctly temporally aligns the subject’sbrains relative to the aging model.

The statistical analysis reported in Table 2 shows that themorphological age shift is significantly correlated with the biolog-ical one, and with neuropsychological scores. Men have a signifi-cantly greater morphological age shift than women. This result isconsistent with previous studies reporting a general acceleratedaging process in men across the whole life span (Coffey et al., 1998;Mann et al., 2011).

Finally, positive Apoe4 is not generally correlated with themorphological age shift, even though a significant negative corre-lation was measured in healthy participants Ab&, and in stable MCI(Supplementary Table S2).

Interestingly, Fig. 4C shows that the morphological age shift isonly partially related to biological aging. In fact, more pronouncedanatomical changes are depicted here in advanced stages of themodel, and thus they identify virtually older anatomies.

For this reason, even though the considered groups did notsignificantly differ in age, the morphological age shift increases asthe clinical condition gets closer to AD. As shown in Fig. 5, Abþ, MCIand AD become virtually older compared with healthy Ab& (p-values in the boxes). MCIconv are significantly older than MCIstable(p ¼ 0.035), indicating a possible accelerated aging process inducedby the progression of AD.

3.6. Analysis of the specific individual process

Fig. 6 shows the average specific deformation parameterswk

specific associated with different groups. The morphologicalchanges specific to healthy Abþ are mild, whereas the changesspecific to the MCI converters are more pronounced and map to thefrontal cortex, ventricles, temporal poles, entorhinal cortex, andhippocampi. The same pattern is observed in AD patients.

Table 1Average baseline sociodemographic and clinical scores for the participants included in the study

Healthy Ab& Healthy Abþ MCI stable MCI converters AD p-value

No. participants 65 40 110 86 134Age at baseline 74.94 (5.31) 76.29 (5.29) 75.05 (7.42) 73.79 (7.45) 75.14 (7.38) 0.49Education 15.46 (2.76) 15.91 (3.28) 15.62 (2.82) 15.87 (2.79) 14.77 (3.08) 0.02Gender (% males) 54 54 68 70 52 0.05MMSE 28.96 (1.04) 29.18 (0.93) 27.6 (1.8) 26.74 (1.59) 23.44 (1.9) <0.001Modified ADAS-cog 6.18 (2.85) 7.08 (3.18) 10.24 (4.16) 12.92 (4.43) 18.27 (5.98) <0.001APOE4 (% positives) 10 48.6 49.4 73 66 <0.001

Standard deviations are shown in parentheses. Last column: p-values for the differences between averages across groups (analysis of variance).Key: AD, Alzheimer’s disease; MCI, mild cognitive impairment, MMSE, mini-mental state examination.

M. Lorenzi et al. / Neurobiology of Aging 36 (2015) S42eS52S46

In Fig. 6A, second row, we notice that changes in clinical con-dition (from Abþ, toMCIconv and AD) are associated with larger andmore intense atrophy patterns. We notice an increasing pattern ofgrowth in the CSF regions, as well as a complementary pattern ofatrophy mapping onto hippocampi, temporal areas, and cortices.Interestingly, the average atrophy patterns of the specific parame-ters are very similar and compatible with those associated with thefull SVF (Supplementary Fig. S1).

Fig. 6B shows the effect size between the divergence maps of MCIconverters versus stable, and of AD versus healthy controls. As ex-pected, the effect sizebetweenADandhealthycontrols is greater thanthat between MCI converters and stables, indicating the larger vari-ability in the MCI group. In Supplementary Fig. S1, we show that the

effect size obtained from the specific atrophy component is slightlygreater (around ventricles and in the white matter) than the oneobtainedwith thewhole SVF (thuswhen considering normal agingþspecific deformation processes) when we compared MCI stableversus converters. Whenwe compared ADwith healthy controls, theeffect size associated with thewhole SVF generally is greater inwhitematter and mildly lower in the temporal horns of the hippocampi.

Finally, Table 3 shows regional and pooled accuracy of thespecific process in differentiating AD versus Ctrls, and MCIconvversus MCIstable. The fair classification results (91% sensitivity, 84%specificity for AD vs. Ctrls, and 67%, 63% for MCIconv vs. MCIstable)indicate the ability of the specific parameter to encode informa-tion relevant to the disease condition. The provided classificationresults are significantly better than those given by pure chance (p< 0.001, McNemar’s c2 test) and are in line with those available inthe literature on the ADNI dataset (Chincarini et al., 2011;Cuingnet et al., 2011). We have thus shown that the specificdeformation parameter encodes specific pathological traits acrossthe whole disease time span, which are significantly discrimina-tive among the considered populations.

4. Conclusions

We proposed a method to describe brain anatomy as contribu-tions of 2 independent processes: morphological aging and a

Fig. 4. (A) Normal aging model. Top: The average SVF describes the group-wise trajectory of normal aging observed in the healthy Ab group (blue arrows indicate magnitude anddirection of the trajectory). Bottom: average 1-year volume changes associated to the model of normal aging. The model leads to local relative volume changes ranging fromaround þ4% for the expansion of ventricles, to &4% for the relative volume loss in temporal areas. (B) Observed versus modeled brain volume changes in the Ab&cohort. Black line:fitted slope (and 95% confidence interval) for the linear mixed-effects model (LME) on the observed subject-specific trajectories of scalar volumes (colored lines). Red dots: pro-gression of brain volume changes associated to the normal aging model and associated fitted slope (red line). Brain volume is quantified here by the ratio between gray þ whitematter tissue and total intracranial volume (gray þ white þ CSF areas). (C) Modeled longitudinal evolution extrapolated from &15 to 18 years, and corresponding observed normalanatomies with estimated morphological age and age shift (biological age in parenthesis). Abbreviations: CCF, cerebrospinal fluid; SVF, stationary velocity field. (For interpretation ofthe references to color in this Figure, the reader is referred to the web version of this article.)

Table 2Pearson’s correlation between sociodemographic/clinical scores and morphologicage shift (in bold significant correlation)

Pearson’s correlation p value

Age at baseline 0.4 <0.001Education 0.09 0.05Gender (male ¼ 1, female ¼ 0) 0.25 <0.001MMSE L0.2 <0.001ADAS-cog (modified) 0.23 <0.001APOE4 (# alleles) &0.04 0.4

Key: ADAS-cog, Alzheimer’s Disease Assessment Scale; MMSE, mini-mental stateexamination.

M. Lorenzi et al. / Neurobiology of Aging 36 (2015) S42eS52 S47

specific component. These components identify different clinicalstages, and are compatible with the hypothesis that points to theabnormal levels of CSF Ab42 as a presymptomatic marker of AD inthe early stages.

We showed that more advanced AD stages (from Abþ to MCIconverters, and finally to AD) are associated with both “virtuallyolder” brains, and with increased specific morphological changesnot related to the normal aging process. Thus, according to ourmodel, ADmight have an influence on the overall aging of the brainacting as an acceleration factor.

4.1. Relationship with classical morphometric studies

Compared with standard analysis approaches of group-wisestructural changes such as classical voxel/tensor-basedmorphometry (Good et al., 2002; Hua et al., 2008), or discrimi-native analysis (Chincarini et al., 2011; Cuingnet et al., 2011), ourmethod has the advantage of providing complementary infor-mation representing morphological aging and specific deforma-tion parameters that carry relevant biological meaning. For thisreason, the proposed method provides a novel way of interpretingmorphometric results. For instance, it may be of great interest toinvestigate the relationship between the morphological age shiftand specific changes in characterizing brain structural and clinicalreserve in preclinical/prodromal stages.

4.2. Combining cross-sectional and longitudinal analysis

Our method proposes cross-sectional comparison of brainimages by means of a previously defined longitudinal model ofmorphological changes. The statistical modeling of the inter-subject variability in computational anatomy is challenging, andthe interpretation of group-wise comparison results is alwaysbound to the statistical assumptions about the measured features(for instance, concerning the statistical distribution of the Jaco-bian/divergence values). In this study we showed that byremoving the aging component we increase the ability in

detecting specific group-wise differences. For this reason, theproposed method represents a novel and promising approach tothe appropriate modeling and interpretation of group-wiseanatomical variation.

We note in fact that the voxel-by-voxel analysis of the diver-gence maps in Section 3.6 is compatible with standard voxel/tensor-based morphometry approaches and leads to very similarresults to those provided by classical group-wise comparison (Goodet al., 2002; Hua et al., 2008). It is, however, providing a slightlygreater effect size when comparing MCIs. This indicates that theremoval of the normal aging process could enhance the estimationof pathological volume changes. When comparing AD with healthycontrols, the analysis of the specific morphological process providesa slightly larger effect size in the temporal horns but generallylower in the white matter. This latter result can be explained bynoting that the removal of the aging process aims to decorrelate themorphological changes explained by the aging model. In this waywe reduce, for instance, the effect of ventricles expansion, detect-able in tensor based morphometry as an apparent contraction inthe white matter.

4.3. Interpretation of aging and specific processes

Concerning the modeling of the specific deformation parameter,we note that by definition this component is highly heterogeneousacross the population because it includes normal anatomical vari-ability as well as pathological features. In this study we have shownthat despite this high variability, the specific deformation is able toaccurately describe anatomical features specific to AD. Thediscriminative analysis performed in Section 3.6. showed that thespecific deformation parameter includes specific pathological traitswhich characterize the whole disease time span. Future studiesbased on more sophisticated machine learning techniques, asproposed for instance in Chincarini et al., (2011) and Cuingnet et al.,(2011), may lead to improved classification results.

In our model, the morphological age shift is based on thewhole brain average of the projection on the normal aging model.Here, we make a precise assumption about the aging process,which is in fact defined globally. Therefore, accelerated aging isconstrained with respect to the whole brain normal aging model,and any local departure from it (for instance in some specificregions), is interpreted as a specific morphological change, inde-pendent from aging. Different MRI-based indices of brain aginghave been proposed in the past (Davatzikos et al., 2009; Frankeet al., 2010). Our model integrates these approaches into amore general description of the AD process. We note that themorphological age shift for AD patients is lower than the agingscore estimated in Franke et al. (2010) (4 vs. 10 years). In fact wehave shown that AD is characterized by a more pronouncedspecific and concurrent pattern of atrophy. In this case, the pre-sent result motivates and provides clinical outcomes for thedesign of disease-specific modifying drugs that do not have animpact on normal aging.

We observed aweak but significant positive correlation betweenmorphological age shift and years of education. The correlation issignificant and stronger when considered in healthy participantsonly (Supplementary Table S1). This latter finding could indicatethat morphologically older participants with high education aremore likely to appear cognitively healthy. Therefore, the morpho-logical age shift might represent a measure of cognitive and struc-tural reserve in normal aging (Coffey et al., 1999).

The proposed average model of aging assumes that the baselineacquisition time is unique for the healthy cohort, as already pro-posed in previous longitudinal studies of brain volume changes inAD, based on mixed-effects modeling (Ridha et al., 2006). We

Fig. 5. Box-plot of the group-wise morphological age shift estimated for the clinicalgroups. The morphological age shift describes statistically significant older brains(standard t-test, p-value in the boxes) with respect to the healthy Ab- for all the patientgroups. Interestingly, MCI converters are “virtually older” than the MCI stables (p ¼0.035). Abbreviation: MCI, mild cognitive impairment.

M. Lorenzi et al. / Neurobiology of Aging 36 (2015) S42eS52S48

showed in the experimental section that under these assumptionswe obtained similar results to those provided by classical univariateLME models, by correctly describing the temporal variability ofbrain changes in the healthy cohort. However, it will be of interestto explicitly account for the inter-subject baseline differences infuture studies. This amounts tomodifying the assumption about theconstant evolution in time of the healthy aging process.

Finally, the proposed model could be extended in future work toaccount for different evolution trajectories, and to explicitly modeldifferent neurodegenerative pathologies, and AD subtypes. Toconclude, our approach provides new insights that may help theunderstanding of AD dynamics and could thus represent a moreprecise instrument to identify outcomes in clinical trials for diseasemodifying drugs.

4.4. Limitations

Some methodological limitations should be considered in thisstudy. The proposed model of aging progression is based onnonlinear registration and is therefore estimated from image dataonly. This means that no biological/biomechanical information was

accounted in the definition of the average trajectory. Nonlinearregistration is driven by image intensities, thus it only modelsapparent observable anatomical changes. Moreover, nonlinear

Fig. 6. (A) First row: average specific deformation parameter not related to healthy aging (blue arrows indicate magnitude and direction of the deformation). MCI converters and ADpatients show a more pronounced pattern of morphological change mapping mainly to ventricles, temporal poles, the entorhinal cortex and hippocampi. Second row: associatedrelative volume change. Warm colors: apparent growth. Cool colors: apparent atrophy. (B) Effect size associated with the divergence maps of the specific deformation parameter.The effect size quantifies the magnitude of the difference between volume changes modeled in the 2 groups. AD patients and healthy controls show greater differences localized inhippocampi, temporal areas, and in the ventricles. These differences are milder when comparing MCI converters with stable. Abbreviations: AD, Alzheimer’s disease; MCI, mildcognitive impairment. (For interpretation of the references to color in this Figure, the reader is referred to the web version of this article.)

Table 3Regional classification accuracy for the leave-one-out discrimination

AD vs. Ctrls MCIconv vs. MCIStable

Sens Spec PPV NPV Sens Spec PPV NPV

All features 91 84 85 90 54 54 54 54MTL (&) 86 81 85 82 53 51 52 52MTL (þ) 73 77 76 74 57 57 57 57Hippocampi (&) 77 71 75 73 55 47 51 51Hippocampi (þ) 77 63 73 67 67 63 64 65Ventricles (þ) 65 69 68 66 61 43 52 52Ventricles (&) 68 69 69 68 58 56 57 57PC (&) 58 59 59 59 58 58 58 58PC (þ) 59 50 54 54 47 74 64 58

The analyzed features are the positive and negative flux (þ and &) of the specificparameter across the regions of interest.Bold values inidicate the highest discriminative results.Key: MCI, mild cognitive impairment; MTL, medial temporal lobes; NPV, negativepredictive value; PC, posterior cingulated; PPV, positive predictive value; SVF, sta-tionary velocity field.

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registration results are dependent on the registration model andmay potentially provide different results depending on the choiceof parameters, similarity measure and regularization scheme.However, we have already shown in previous work that LCC-Demons nonlinear registration provides reliable and meaningfulresults when applied to brain image registration problems, espe-cially for the longitudinal analysis of atrophy (Lorenzi et al., 2013).

Finally, only 3-year follow-up imaging data are available for thehealthy cohort, and therefore the group-wise evolutionwas limitedto a linear model in time for the SVF due to the lack of sufficientlongitudinal observations.

Disclosure statement

The authors have actual or potential conflicts of interest.

Acknowledgements

This work was partially funded by the European Research Council(ERC advanced Grant MedYMA 2011-291080), ANR blanc Karametriaand the EU project Care4Me. Data collection and sharing for thisproject was funded by the Alzheimer’s Disease Neuroimaging Initia-tive (ADNI; National Institutes of Health Grant U01 AG024904). ADNIis funded by the National Institute on Aging, the National Institute ofBiomedical Imaging and Bioengineering, and through generous con-tributions from the following: Alzheimer’s Association; AlzheimerDrug Discovery Foundation; BioClinica, Inc.; Biogen Idec Inc.; Bristol-Myers Squibb Company; Eisai Inc.; Elan Pharmaceuticals, Inc.; Eli Lillyand Company; F. Hoffmann-La Roche Ltd and its affiliated companyGenentech, Inc.; GE Healthcare; Innogenetics, N.V.; IXICO Ltd.; Jans-sen Alzheimer Immunotherapy Research & Development, LLC.;Johnson & Johnson Pharmaceutical Research & Development LLC.;Medpace, Inc.; Merck & Co., Inc.; Meso Scale Diagnostics, LLC.; Neu-roRx Research; Novartis Pharmaceuticals Corporation; Pfizer Inc.;Piramal Imaging; Servier; Synarc Inc.; and Takeda PharmaceuticalCompany. The Canadian Institutes of Health Research is providingfunds to support ADNI clinical sites in Canada. Private sector contri-butions are facilitated by the Foundation for the National Institutes ofHealth (www.fnih.org). The grantee organization is the NorthernCalifornia Institute for Research and Education, and the study is co-ordinated by the Alzheimer’s Disease Cooperative Study at the Uni-versity of California, San Diego. ADNI data are disseminated by theLaboratory for Neuro Imaging at the University of Southern Califor-nia. The authors thank Sheila and John Stark, and KristinMcLeod fortheir valuable help in proofreading the manuscript.

Appendix A. Supplementary data

Supplementary data associated with this article can be found,in the online version, at http://dx.doi.org/10.1016/j.neurobiolaging.2014.07.046.

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Appendix A.

Implementation of the hierarchical model of normal aging

This section describes the framework for the estimation of thegroup-wise longitudinal model of normal aging. Follow-up lon-gitudinal images were first rigidly aligned to the baseline one.The baseline image was then affine aligned to a previouslydefined anatomical template, which was estimated from thehealthy control population under study. Follow-up images wereresampled in the template space by composition of the estimatedrigid and affine transformations. For each subject S and timepoint t, the follow-up image ISt was nonlinearly registered to thealigned baseline IS0 with the LCC-Demons algorithm (Fig. 3A)(Lorenzi et al., 2013). The LCC-Demons estimates nonlineartransformations parameterized by SVFs (indicated here asexpðvSt Þ), such that IS0xISt +expðvSt Þ. The longitudinal morphologicaldifferences between baseline and follow-up images are in this

way encoded by the series of spatially dense SVFs vSt (Fig. 1). Foreach subject, a trajectory mS of the longitudinal morphologicalprogression was estimated from the series of SVFs with a modellinear in time2 (Fig. 3B). The trajectory mS represents the esti-mated longitudinal morphological changes associated to a givenpatient S, and it is identified by a SVF defined voxel-wise in theanatomical space of the patient. The direct voxel-by-voxel group-wise comparison of the trajectories is not possible, since theymust be normalized in a common reference template space T. Tonormalize the trajectories mS, we parallel transported them in thereference space of the anatomical template through the subject-to-template deformation. The parallel transport is a mathemat-ical tool used in the context of diffeomorphic registration forresampling a given velocity field in the template geometry(Lorenzi and Pennec, 2013). We therefore define the longitudinalmodel of normal aging in the template space T (fixed effect of thetrajectory) as the average trajectory m0 of the transported subject-specific trajectories mS (Fig. 3C).

2 Note that the model is linear in the SVF parameters, but nonlinear in thedeformation space. In particular, it always remains diffeomorphic, i.e. one-to-oneand spatially differentiable (smooth). The linear model was estimated by mini-mizing the classical least squared criterion

PktmS&vtSk2.

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