## Abstract

### Introduction

Understanding disease progression in Alzheimer’s disease (AD) awaits the resolution of three fundamental questions: first, can we identify the location of “seed” regions where neuropathology is first present? Some studies have suggested the medial temporal lobe while others have suggested the hippocampus. Second, are there similar atrophy rates within affected regions in AD? Third, is there evidence of causality relationships between different affected regions in AD progression?

### Methods

To address these questions, we conducted a longitudinal MRI study to investigate the gray matter (GM) changes in AD progression. Abnormal brain regions were localized by a standard voxel-based morphometry method, and the absolute atrophy rate in these regions was calculated using a robust regression method. Primary foci of atrophy were identified in the hippocampus and middle temporal gyrus (MTG). A model based upon the Granger causality approach was developed to investigate the cause–effect relationship over time between these regions based on GM concentration.

### Results

Results show that in the earlier stages of AD, primary pathological foci are in the hippocampus and entorhinal cortex. Subsequently, atrophy appears to subsume the MTG.

### Conclusion

The causality results show that there is in fact little difference between AD and age-matched healthy control in terms of hippocampus atrophy, but there are larger differences in MTG, suggesting that local pathology in MTG is the predominant progressive abnormality during intermediate stages of AD development.

### Similar content being viewed by others

## References

Chetelat G, Degranges B, Sayette VDL, Viader F, Eustache, Baron JC (2002) Mapping grey matter loss with voxel-based morphometry in mild cognitive impairment. NeuroReport 13:1939–1943

Karas G, Burton EJ, Rombouts SARB, Schijndel RAV, O'Brien JT, Scheltens PH, McKeith IG, Williams D, Ballard C, Barkhof F (2003) A comprehensive study of grey matter loss in patients with Alzheimer's disease using optimized voxel-based morphometry. Neuroimage 18:895–907

Ashburner J, Friston KJ (2000) Voxel-based morphometry-the methods. Neuroimage 11:805–821

Davies RR, Scahill VL, Graham A, Williams GB, Graham KS, Hodges JR (2008) Development of an MRI rating scale for multiple brain regions: comparison with volumetrics and with voxel-based morphometry. Neuroradiology 51:491–503

Kakeda S, Korogi Y (2010) The efficacy of a voxel-based morphometry on the analysis of imaging in schizophrenia, temporal lobe epilepsy, and Alzheimer's disease/mild cognitive impairment: a review. Neuroradiology 52:711–721

Takao H, Abe O, Ohtomo K (2010) Computational analysis of cerebral cortex. Neuroradiology 52:691–698

Hirata Y, Matsuda H, Nemoto K, Ohnishi T, Hirao K, Yamashita F, Asada T, Iwabuchi S, Samejima H (2005) Voxel-based morphometry to discriminate early Alzheimer's disease from controls. Neurosci Lett 382:269–274

Li X, Messé A, Marrelec G, Pélégrini-Issac M, Benali H (2010) An enhanced voxel-based morphometry method to investigate structural changes: application to Alzheimer’s disease. Neuroradiology 52:203–213

Chetelat G, Landeau B, Eustache F, Mezenge F, Viader F, de la Sayette V, Desgranges B, Baron JC (2005) Using voxel-based morphometry to map the structrual changes associated with rapid conversion in MCI: A longitudinal MRI study. Neuroimage 27:934–946

Nestor PJ, Schetens P, Hodges JR (2004) Advances in the early detection of Alzheimer's disease. Nat Rev Neurosci 7:s34–s41

Fox NC, Warrington EK, Freeborough PA, Hartikainen P, Kennedy AM, Stevens JM, Rossor MN (1996) Presymptomatic hippocampal atrophy in Alzheimer's disease: a longitudinal MRI study. Brain 119:2001–2007

Whitwell JL, Przybelski SA, Weigand SD, Knopman DS, Boeve BF, Petersen RC, Jack CR Jr (2007) 3D maps from multiple MRI illustrate changing atrophy patterns as subjects progress from mild cognitive impairment to Alzheimer's disease. Brain 130:1777–1786

Chan D, Janssen JC, Whitwell JL, Watt HC, Jenkins R, Frost C, Rossor MN, Fox NC (2003) Change in rates of cerebral atrophy over time in early-onset Alzheimer's disease: longitudinal MRI study. Lancet 362:1121–1122

Schott JM, Fox NC, Frost C, Scahill RI, Jassen JC, Chan D, Jenkins R, Rossor MN (2003) Assessing the onset of structural change in familial Alzheimer's disease. Ann Neurol 53:181–188

Fox NC, Schott JM (2004) Imaging cerebral atrophy: normal ageing to Alzheimer's disease. Lancet 363:392–394

Schuff N, Woerner N, Boreta L, Kornfield T, Shaw LM, Trojanowski JQ, Thompson PM, Jack CR Jr, Weiner MW (2009) MRI of hippocampal volume loss in early Alzheimer's disease in relation to ApoE genotype and biomarkers. Brain 132:1067–1077

Ridha BH, Barnes J, Barlett JW, Godolt A, Pepple T, Rossor MN, Fox NC (2006) Tracking atrophy progression in familial Alzheimer's disease: a serial MRI study. Lancet Neurol 5:824–834

Schill RI, Frost C, Jenkins R, Whitwell JL, Rossor MN, Fox NC (2003) A longitudinal study of brain volume changes in normal aging using serial registered magnetic resonance imaging. Arch Neurol 60:989–994

Zeger SL, Liang KY (1991) Feedback models for discrete and continuous time series. Stat Sin 1:51–64

Diggle PJ, Heagerty P, Liang KY, Zeger S (2003) Analysis of longitudinal data, 2nd edn. Oxford University Press, Oxford

Whitwell JL (2008) Longitudinal imaging: change and causality. Curr Opin Neurol 21:410–416

Granger C (1969) Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37:424–438

Braak H, Braak E (1996) Evolution of the neuropathology of Alzheimer's disease. Acta Neurol Scand Suppl 165:3–12

Jack CR Jr, Weigand SD, Shiung MM, Przybelski SA, O'Brien PC, Gunter JL, Knopman DS, Boeve BF, Smith GE, Petersen RC (2008) Atrophy rates accelerate in Amnestic mild cognitive impairment. Neurology 70:1740–1752

Jack CR Jr, Shiung MM, Gunter JL, O'Brien PC, Weigand SD, Knopman DS, Boeve BF, Ivnik RJ, Smith GE, Cha RH, Tangalos EG, Petersen RC (2004) Comparison of different MRI atrophy rate measures with clinical disease progression in AD. Neurology 62:591–600

Resnick SM, Pham DL, Kraut MA, Zonderman AB, Davatzikos C (2003) Longitudinal magnetic resonance imaging studies of older adults: a shrinking brain. J Neurosci 23:3295–3301

Marcus DS, Fotenos AF, Csernansky JG, Morris JC, Buckner RL (2009) Open access series of imaging studies: longitudinal MRI data in nondemented and demented older adults. J Cog Neurosci 22(12):2677–2678

Marcus DS, Wang TH, Parker J, Csernansky JG, Morris JC, Buckner RL (2007) Open Access Series of Imaging Studies (OASIS): cross-sectional MRI data in young, middle aged, nondemented, and demented older adults. J Cog Neurosci 19:1498–1507

Morris JC (1997) Clinical dementia rating: A reliable and valid diagnostic and staging measure for dementia of the Alzheimer type. Int Psychogenatrics 9(suppl 1):173–176

Morris JC (1993) The clinical dementia rating (CDR): Current version and scoring rules. Neurology 43:2412b–2414b

Talairach J, Tournoux P (1998) Coplanar stereotaxic atlas of the human brain. Thieme, Stuttgart

Smith SM (2002) Fast robust automated brain extraction. Hum Brain Mapp 17:143–155

Zhang Y, Brady M, Smith SM (2001) Segmentation of brain MR images through a hidden Markov random field model and the expectation maximization. IEEE Trans Med Imag 21:45–47

Jenkinson M, Smith SM (2001) A global optimisation method for robust affine registration of brain images. Med Image Anal 5:143–156

Rueckert D, Sonda LI, Hayes C, Hill DLG, Leach MO, Hawkes DJ (1999) Non-rigid registration using free-form deformations: application to breast MR images. IEEE Trans Med Imag 18:712–721

Nichols TE, Hayasaka S (2003) Controlling the familywise error rate in functional neuroimaging: a comparative reviews. Stat Meth Med Res 12:419–446

Tzourio-Mazoyer N, Landeau B, Papathanassiou D, Crivello F, Etard O, Delcroix N, Mazoyer B, Joliot M (2002) Automated anatomical labelling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. Neuroimage 15:273–289

Huber PJ (1981) Robust statistics. Wiley, Hoboken

Bryk AS, Raudenbush SW (1992) Hierarchical linear models: applications and data analysis methods. Sage, New Delhi

Sullivan LM, Dukes KA, Losina E (1999) Tutorial in biostatistics: An introduction to hierarachical linear modelling. Statist Med 18:855–888

Draganski B, Gaser C, Busch V, Schuierer G, Bogdahn U, May A (2004) Changes in grey matter induced by training. Nature 427:311–312

Draganski B, Gaser C, Kempermann G, Kuhn HG, Winkler J, Buchel C, May A (2006) Temporal and spatial dynamics of brain structure changes during extensive learning. J Neurosci 26:6314–6317

Salat DH, Tuch DS, van der Kouwe AJW, Greve DN, Pappu V, Lee SY, Hevelonea ND, Zalet AK, Growdon JH, Corkin S, Fischl B, Rosasa HD (2010) White matter pathology isolates the hippocampal formation in Alzheimer's disease. Neurobiol Aging 31:244–256

Zhang Y, Schuff N, Du AT, Rosen HJ, Kramer JH, Gorno-Tempini ML, Miller BL, Weiner MW (2009) White matter damage in frontotemporal dementia and Alzheimer's disease measured by diffusion MRI. Brain 132:2579–2592

Fellgiebel A, Wille P, Muller MJ, Winterer G, Scheurich A, Vucurevic G, Schmidt LG, Stoeter P (2004) Ultrastructural hippocampal and white matter alterations in mild cognitive impairment: a diffusion tensor imaging study. Dement Geriatr Cogn Disord 18:101–108

Muller MJ, Greverus D, Dellani PR, Weibrich C, Wille PR, Scheurich A, Stoeter P, Fellgiebel A (2005) Functional implications of hippocampal volume and diffusivity in mild cognitive impairment. Neuroimage 28:1033–1042

Chetelat G, Villain N, Desgranges B, Eustache F, Baron JC (2009) Posterior cingulate hypometabolism in early Alzheimer's disease: what is the contribution of local atrophy versus disconnection? Brain 132:1–2

Vincent JL, Snyder AZ, Fox MD, Shannon BJ, Andrews JR, Raichle ME, Buckner RL (2006) Coherent spontaneous activity identifies a hippocampal-parietal memory network. J Neurophysiol 96:3517–3531

Seeley WM, Crawford RK, Zhou J, Miller BL, Greicius MD (2009) Neurodegenerative diseases target large-scale human brain networks. Neuron 62:42–56

Haan WD, Pijnenburg YL, Strijers RLM, Made YVD, Flier WMVD, Scheltens P, Stam CJ (2009) Functional neural network analysis in frontotemporal dementia and Alzheimer's disease using EEG and graph theory. BMC Neurosci 10:1–12

Stam CJ, Haan WDE, Daffertshofer A, Jones BF, Manshanden I, Van Cappellen V, Van Walsum AM, Montez T, Verbunt JPA, de Munck JC, Van Dijk BW, Berendse HW, Scheltens P (2009) Graph theoretical analysis of magnetoencephalographic functional connectivity in Alzheimer's disease. Brain 132:213–224

Celone K, Calhoun V, Dickerson B, Atri A, Chua EF, Miller SL, DePeau K, Rentz DM, Selkoe DJ, Blacker D, Albert MS, Sperling RA (2006) Alterations in memory networks in mild cognitive impairment and Alzheimer's Disease: an independent component analysis. J Neurosci 26:10222–10231

Supekar K, Menon V, Rubin D, Musen M, Greicius MD (2008) Network analysis of Intrinsic functional brain connectivity in Alzheimer's Disease. PLoS Comput Biol 4:1–11

Greicius MD, Srivastava G, Reiss A, Menon V (2004) Default-mode network activity distinguishes Alzheimer's Disease from healthy aging: Evidence from functional MRI. Proc Nat Acad Sci 101:4637–4642

Lemieux L (2008) Causes, relationships and explanations: the power and limitations of observational longitudinal imaging studies. Curr Opin Neurol 21:391–392

Bullmore E, Sporns O (2009) Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci 10:186–198

Good C, Johnsrude IS, Ashburner J, Henson RN, Friston KJ, Frackowiak RS (2001) A voxel-based morphometric study of ageing in 465 normal adult human brains. Neuroimage 14:21–36

Faes L, Nollo G, Chon KH (2008) Assessment of Granger causality by nonlinear model identification: application to short-term cardiovascular variability. Ann Biomed Eng 36:381–395

Shaman P, Stine RA (1998) The bias of autoregressive coefficient estimators. J Am Stat Assoc 83:842–848

Li X, Marrelec G, Hess RF, Benali H (2010) A nonlinear identification method to study effective connectivity in functional MRI. Med Image Analy 14:30–38

Wernerheim C (2000) Cointegration and causality in the exports-GDP nexus: the post-war evidence for Canada. Empirical Econ 25:111–125

Oxley L, Greasley D (1998) Vector autoregression, cointegration and causality: testing for causes of the British industrial revolution. Appl Econ 30:1387–1397

Doornik J (1996) Testing vector error autocorrelation and heteroscdasticity. The Econometric Society 7th World Congress, Tokyo, 1996.

Durbin J (1970) Testing for serial correlation in least squares regression when some of the regressors are lagged dependent variables. Econometrica 38:410–421

Breslow NE, Clayton DG (1993) Approximate inference in generalized linear mixed models. J Am Stat Assoc 88:9–25

Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J Roy Stat Soc B 39:1–38

Laird NM, Lange N, Stram D (1987) Maximum likelihood computations with repeated measures: Application of the EM algorithm. J Am Stat Assoc 82:97–105

Laird NM, Ware JH (1982) Random-effects models for longitudinal data. Biometrics 38:963–974

Worsley K, Liao CH, Aston J, Petre V, Duncan GH, Morales F, Evans AC (2002) A general statistical analysis for fMRI data. Neuroimage 15:1–15

Liang KY, Zeger SL (1986) Longitudinal data analysis using generalized linear models. Biometrika 73:13–22, Neuroimage 11:805–821

## Acknowledgments

This study is supported under the CNRT award by the Northern Ireland Department for Employment and Learning through its "Strengthening the All-Island Research Base" initiative. The authors thank Dr. Randy Buckner and his colleagues for making their OASIS data available to us. They were supported by Grants No.: P50 AG05681, P01 AG03991, R01 AG021910, P50 MH071616, U24 RR021382, and R01 MH56584.

### Conflict of Interest

We declare that we have no conflict of interest.

## Author information

### Authors and Affiliations

### Corresponding author

## Appendices

### Appendix 1: AR model within subjects for effective connectivity study

For the subjects who have at least three longitudinal scans, we assume the brain GM concentration is an autoregressive (AR) function, i.e., the GM change at a later time point is related to the GM at a previous time point. This is a reasonable assumption [16], and based on this assumption, for each affected region *i*, we have:

where *t* is the time, *y*
_{
i
}(*t*) is current GM concentration value; *y*
_{
i
}(*t − 1*) is the previous GM concentration value; *a*
_{
i
} is the AR coefficient; and *e*
_{
i
}(*t*) is the model error (Gaussian noise). For two-connected regions, we can consider the mutual interaction between these regions (for example hippocampus and MTG as shown in Fig. 2); we thus have a GCM as follows [19, 22]:

where *y*
_{1}(*t*) and *y*
_{2}(*t*) are the current averaged GM concentration in hippocampus and MTG, respectively, and *y*
_{
1
}(*t − 1*), *y*
_{2}(*t − 1*) are the corresponding previous average GM concentration in hippocampus and MTG regions as shown in Fig. 3b. If a subject has been scanned only twice over time, we cannot estimate the coefficients based on individual subjects. Equation A2 has two parameters, but two “visits” can only produce one equation. Assuming for each subject, left and right hemispheres have the same model within each subject (Fig. 5), we can build a general linear model for each subject and combine the left and right hemisphere regional GM concentration within this model, i.e. first-level analysis for Eq. A2 [39]:

where *Y* = [*y*
_{2,1}(*t*), *y*
_{2,2}(*t*), …, *y*
_{2,n}(*t*)]′, \( n = (V - 1) \times 2 \), where *V* is the total number of visits (we multiply by 2 because we combine the left and right hemisphere GM concentrations within the model); *X*
_{1} = [*y*
_{1,1}(*t − 1*), *y*
_{1,2}(*t − 1*), …, *y*
_{1,n}(*t − 1*)]′, *X*
_{2} = [*y*
_{2,1}(*t − 1*), *y*
_{2,2}(*t − 1*), …, *y*
_{2,n}(*t − 1*)]′. *X*
_{2} represents the AR term of *y*
_{2}(*t*), and *X*
_{1} denotes the influence from the other connected region and \( e(t) = [{e_{{2,1}}}(t),{e_{{2,2}}}(t), \cdots, {e_{{2,n}}}(t)]{}^{\prime}\sim N(0,\sigma {}^2) \). The estimated GM concentration response is:

where \( \widehat{\beta } \) can be estimated by:

and *X* = [*X*
_{1}, *X*
_{2}], and *X*
^{+} is the Moore–Penrose pseudoinverse of the matrix. To study the influence from MTG to hippocampus, we swap the *y*
_{2}(*t*) and *y*
_{1}(*t*) in Eq. A2.

### Appendix 2: Granger model for the effective connectivity

Granger causality analysis [61, 62] is derived based on *F* statistics. For Eq. A2, the test for determining Granger causality (GC) is: (1) *y*
_{1}(*t*) is GC of *y*
_{2}(*t*) [61], if *b*
_{1} = 0 in Eq. A2 is not true. Given the data, we reach this conclusion if *b*
_{1} = 0 is rejected. (2) Similarly, *y*
_{2}(*t*) is GC of *y*
_{1}(*t*) can be investigated by reversing the input–output roles of the two series. *F* statistics (see Appendix 3) are developed to detect significant relations within subject, and *t* statistics are developed for between-subjects analysis (Appendix 4).

### Appendix 3: *F* test (within subject)

After the covariates and their coefficients *b*
_{1} and *b*
_{2} in Eqs. A3/A4 have been estimated by the least squares method in Appendix 1 from the GM concentration response, the *F* test [63] is applied to test the inference of the connectivity between different regions. Accordingly from Eq. A4, we partitioned the coefficients \( \widehat{\beta } \) as: \( \widehat{\beta } = ({\widehat{\beta }_1}:{\widehat{\beta }_2}) \) and *X* = (*X*
_{1} : *X*
_{2}), we can write this test as:

For one GM concentration response, the *F* test on the causality is given by [64]:

where *s* is the column of *X*
_{2}; *k* is the column of *X*
_{1}; *n* is the total number of visits minus one (multiply by 2 if combining two hemispheres within the brain). \( R{}^2 = \frac{{{\text{RS}}{{\text{S}}_0} - {\text{RSS}}}}{{{\hbox{RS}}{{\hbox{S}}_0}}} \), where RSS_{0} (original system when *β*
_{2} = 0, without interaction terms for the two-connection network (Fig. 2)) and *RSS* are the residual sums of squares (when both the AR and feedback terms exists in the system), \( {\text{RS}}{{\text{S}}_0} = (Y - \widehat{Y}){}^\prime \times (Y - \widehat{Y}) \)(under *H*
_{0}); \( {\text{RSS}} = (Y - \widehat{Y}){}^\prime \times (Y - \widehat{Y}) \). Then, we apply Eq. A6 to test the influences between regions.

### Appendix 4: Mixed effect model (first level: within subject)

Apart from the *F* test conducted within subjects, we can also inference an effect by defining a contrast matrix *c* and using the *t* statistics, we start from estimation of an effect:

*j* = 1,…, *n*, where *n* is the number of visits minus one (×2 if combine two hemispheres within the model in A3/A4). For example, we can select *c* = [0,1] at first level contrast to study the influence from MTG to hippocampus.

where \( \widehat{\sigma } = \sqrt {{r\prime r/v}} \), \( r = Y - X\widehat{\beta } \), \( v = m - {\hbox{rank}}(X) \)is the degree of freedom (*df*); \( m = 2(n - 1) \)is the total number of effect in Eq. A7 for two hemispheres.

### Appendix 4: Mixed effect model (second level: between subjects)

For the second-level analysis, a general linear mixed model [65] was adopted, i.e.:

where *E* = (*E*
_{1}, …, *E*
_{
n*
})′, *S* = (*S*
_{1}, …, *S*
_{
n
}), and *η* is normally distributed with zero mean and variance \( S + \sigma_{\rm{random}}^2 \) independently for *j* = 1, …, *n*. We want to compare the effects in VBM using covariates (*Z* is the design matrix for comparison in the general linear model):

If we are interested in the difference between two groups, we can set \( {I_{{{n_1}}}} = \left[ {1, \cdots, 1} \right]_{{1 \times n_1^{ * }}}^{\prime;} \),\( {I_{{{n_2}}}} = \left[ {1, \cdots, 1} \right]_{{1 \times n_2^{ * }}}^{\prime;} \),\( {O_2} = \left[ {0, \cdots, 0} \right]_{{1 \times n_2^{ * }}}^{\prime;} \), and \( {O_1} = \left[ {0, \cdots, 0} \right]_{{1 \times n_1^{ * }}}^{\prime;} \). In this study, \( n_1^{ * } = 34 \)(number of controls), \( n_2^{ * } = 20 \) (number of AD subjects).

To estimate *γ* in Eq. A9, we first use the restricted maximum likelihood [66, 67] algorithm to estimate \( \widehat{\sigma }_{\text{random}}^2 \). In the expectation maximization algorithm [67–69], let *S* = diag(*S*
_{1}, …, *S*
_{
n*
}) and **I** be the *n*
^{*}
*× n*
^{*} identity matrix (\( n{}^{ * } = n_1^{ * } + n_2^{ * } = 54 \) in this study). From (A9), we have the variance matrix of the effects vector **E** = (*E*
_{
1
}, …, *E*
_{
n
})′:

Define the weighted residual matrix:

Starting with an initial value of \( \sigma_{{random}}^2 = {\mathbf{E}^{{\prime;}}}{\mathbf{R}_{\rm{I}}}\mathbf{E/}{v^{*}} \) based on assuming that the fixed effects variances are zero. The updated estimate is:

where *p*
^{*} = rank(*Z*). Replace \( \sigma_{\rm{random}}^{{2}} \) with \( \widehat{\sigma }_{\text{random}}^2 \) in (A11) and iterate (A11–A13) to convergence. In practice, 10 iterations appear to be enough [69]. After convergence, step (A11) is repeated with \( \sigma_{\rm{random}}^{{2}} \) by \( \widehat{\sigma }^{2}_{{{\text{random}}}} \), then the estimate of *γ* is:

And its estimated variance matrix is:

In the case when the variances of *E* are not homogeneous across the level 2 unit (for example, different scanner), Eq. A15 should be replaced by other terms [40, 70]:

Finally, effects defined by a contrasts matrix (second level, **b** = [1 −1] in this study for control compared to AD) **b** in *γ* can be estimated by \( E^{ * } = b\widehat{\gamma } \) with standard deviation:

The *T* statistic is:

with a nominal *ν*
^{*}
*df* (\( v^{ * } = n{}^{*} - {\hbox{rank}}(Z) \)) can then be used to detect such an effect.

## Rights and permissions

## About this article

### Cite this article

Li, X., Coyle, D., Maguire, L. *et al.* Gray matter concentration and effective connectivity changes in Alzheimer’s disease: a longitudinal structural MRI study.
*Neuroradiology* **53**, 733–748 (2011). https://doi.org/10.1007/s00234-010-0795-1

Received:

Accepted:

Published:

Issue Date:

DOI: https://doi.org/10.1007/s00234-010-0795-1