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. 2015 Jul 15:115:224-34.
doi: 10.1016/j.neuroimage.2015.04.051. Epub 2015 May 8.

Regional flux analysis for discovering and quantifying anatomical changes: An application to the brain morphometry in Alzheimer's disease

M Lorenzi  1 , N Ayache  2 , X Pennec  3 ; Alzheimer's Disease Neuroimaging Initiative (ADNI)
Collaborators, Affiliations

Regional flux analysis for discovering and quantifying anatomical changes: An application to the brain morphometry in Alzheimer's disease

M Lorenzi et al. Neuroimage. .

Abstract

In this study we introduce the regional flux analysis, a novel approach to deformation based morphometry based on the Helmholtz decomposition of deformations parameterized by stationary velocity fields. We use the scalar pressure map associated to the irrotational component of the deformation to discover the critical regions of volume change. These regions are used to consistently quantify the associated measure of volume change by the probabilistic integration of the flux of the longitudinal deformations across the boundaries. The presented framework unifies voxel-based and regional approaches, and robustly describes the volume changes at both group-wise and subject-specific level as a spatial process governed by consistently defined regions. Our experiments on the large cohorts of the ADNI dataset show that the regional flux analysis is a powerful and flexible instrument for the study of Alzheimer's disease in a wide range of scenarios: cross-sectional deformation based morphometry, longitudinal discovery and quantification of group-wise volume changes, and statistically powered and robust quantification of hippocampal and ventricular atrophy.

Keywords: Alzheimer's disease; Demons; Longitudinal atrophy; Non-linear registration; Optimization.

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Figures

Fig. 1.
Fig. 1.
Helmholtz decomposition of the average longitudinal trajectory in AD, and pressure potential and divergence maps associated to the irrotational component. The divergence describes the critical regions of local expansion and contraction.
Fig. 2.
Fig. 2.
Topology of pressure fields. Black arrows indicate the irrotational component. The pressure field summarizes the observed contraction/expansion processes.
Fig. 3.
Fig. 3.
We can draw analogies between the flux analysis and the study anticyclones and depressions fronts in meteorological charts. Critical regions are identified by extremal pressure points, and are such that the flux (wind) across the boundaries is maximum.
Fig. 4.
Fig. 4.
Cross-sectional comparison of the average volume changes in AD patients vs healthy controls. Top: statistical comparison of the log-Jacobian determinant (TBM), significance is assessed at p < 0.05 corrected for family-wise error. Bottom: difference ΔFlux between the group-wise probability of the critical regions, and statistical assessment by permutation test (2000 bootstrap samples). The map of volume differences described by ΔFlux is strikingly similar to the one obtained with TBM after correction for multiple comparisons.
Fig. 5.
Fig. 5.
Group-wise comparison of critical regions. Top: probabilistic estimation of the critical regions of joint maximal expansion and contraction for AD and healthy subjects. Bottom: probabilistic estimation of the critical regions of specific volume change in AD compared to healthy subjects.
Fig. 6.
Fig. 6.
Sample critical regions associated to the AD average pressure map. Pressure extrema map to anatomically relevant areas for AD, and show an asymmetric distribution between left and right hemispheres.
Fig. 7.
Fig. 7.
From group-wise to patient specific quantification. The figure shows a sample of critical regions for the probabilistic integration of the flux estimated for a specific AD patients. Red regions: expanding critial regions. Blue regions: contracting critical regions.
Fig. 8.
Fig. 8.
Average regional flux for the most discriminative regions between AD and MCI (green) with respect to healthy controls (blue). The resulting atrophy patterns of AD and MCI are characterized by several common regions, denoting similar underlying anatomical process. In particular, common regions of longitudinal volume change are located in temporal areas and in ventricles/temporal horns of hippocampi.
Fig. 9.
Fig. 9.
Prior region of longitudinal atrophy in AD. A) Prior anatomical areas for the hippocampal (purple and green), and ventricular (yellow and red) expansion and contraction. B) Average divergence map for the longitudinal atrophy in AD. C) Ventricular and hippocampal mask for the extraction of the maximal/minimal divergence areas.
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