Multivariate Analysis of Structural and Diffusion Imaging in Traumatic Brain Injury

Rationale and Objectives

Diffusion tensor (DT) and T1 structural magnetic resonance images provide unique and complementary tools for quantifying the living brain. We leverage both modalities in a diffeomorphic normalization method that unifies analysis of clinical datasets in a consistent and inherently multivariate (MV) statistical framework. We use this technique to study MV effects of traumatic brain injury (TBI).

Materials and Methods

We contrast T1 and DT image-based measurements in the thalamus and hippocampus of 12 TBI survivors and nine matched controls normalized to a combined DT and T1 template space. The normalization method uses maps that are topology-preserving and unbiased. Normalization is based on the full tensor of information at each voxel and, simultaneously, the similarity between high-resolution features derived from T1 data. The technique is termed symmetric normalization for MV neuroanatomy (SyNMN). Voxel-wise MV statistics on the local volume and mean diffusion are assessed with Hotelling’s T__2 test with correction for multiple comparisons.

Results

TBI significantly (false discovery rate P < .05) reduces volume and increases mean diffusion at coincident locations in the mediodorsal thalamus and anterior hippocampus.

Conclusions

SyNMN reveals evidence that TBI compromises the limbic system. This TBI morphometry study and an additional performance evaluation contrasting SyNMN with other methods suggest that the DT component may aid normalization quality.

Traumatic brain injury (TBI) is the most frequent cause of death and disability in individuals ages 15–24 and is also prevalent in older adults ( ). TBI, most commonly caused by automotive accidents and falls, occurs at a rate of approximately 1 in 600 per year in the general population ( ), whereas up to 10% of soldiers returning from Iraq may suffer from some form of TBI ( ). Even mild TBI may lead to significant behavioral changes ( ) and is very likely to be under-reported, particularly by those who have experienced concussion ( ). In consequence, up to 2% of individuals in the United States live with TBI-related disability. Thus, focus on TBI as a public health concern is increasing, along with further development of sensitive tools for assessing axonal and cortical injury ( ), tracking recovery from these injuries ( ) and predicting outcome ( ).

Traditional T1 imaging may be used to uncover in vivo effects of TBI in the cortex and deep gray matter structures. Neuronal atrophy, from concussion, was detected with T1 imaging and linked to ongoing depression ( ), whereas TBI-related reductions in gray matter concentration have also been correlated with attention deficits ( ). Hippocampal volume may be reduced by TBI ( ), along with the basal forebrain ( ). The thalamus appears to undergo injury during or after TBI as assessed postmortem ( ), through finite element models of TBI ( ) and through large-deformation tensor-based morphometry of control and subject populations ( ). An additional postmortem report has indicated involvement of the mediodorsal thalamus, which has connections to the prefrontal cortex ( ). This finding has also been validated at the cellular level through neuropathology ( ) and through histochemical staining and explicit neuronal counts ( ). TBI effects in the hippocampus have also been verified neuropathologically ( ).

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Figure 1

An overview of the steps required in our multivariate processing for population analysis of tensor and scalar components. The Jacobian measures local volume of neuroanatomy, whereas tensor-derived scalars relate to the integrity of cellular structure. Multivariate tests enable relationships between these variables to enhance statistical power for detecting group differences.

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Materials and methods

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Theory for Multivariate Image Processing

Multivariate datasets

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$Figure 2, Here we see one slice from the template T1 ( left ) and T1 plus diffusion tensor (DT) ( right ) after intramodality distortion correction. The RGB channel intensity is weighted by the fractional anisotropy (FA) and indicates principal fiber direction going left-to-right ( red ), going bottom-to-top ( green ), and going in-and-out of the page ( blue ) which are superimposed on the T1 image in the right panel .$

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Symmetric diffeomorphic registration

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Dshape((x,0),(x,1))=minυ∫10∥υ(x,t)∥dt. D

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D2shape((x,0),(x,1))+Dsimilarity((x,1),I,J). D

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Symmetric DT Diffeomorphic Registration

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∥D1−D2∥DV=Tr((D1−D2)2)−13(Tr(D1)−Tr(D2))2.−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√ ‖

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∥IDT(1(x))−JDT(2(x))∥2DV, ‖

(

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where we apply the transformations Φ 1 and Φ 2 to the DT images. Local deformations of the DT image should preserve orientation of white matter fibers in relation to the anatomy. Thus, to warp and reorient the DT images, we use the preservation of principle directions method, as given by Alexander and Gee ( ). Preservation of principle directions guarantees that tensors properly reorient under a warping.

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SyNMN with T1 and DT

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D2shape((x,0),(x,1))+DMVsim((x,1),I2,J2). D

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DMVsim(I2,J2,)=ω1(x)MI(IT1(1),JT1(2))+ω2(x)∥IDT(1)−JDT(2))∥2DV D

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where MI is the mutual information (defined in the usual way) and the ω__i weights each similarity term as a function of the domain. If this term is optimized, we write I 2 ( ϕ__1 (0.5)) ≈ J 2 ( ϕ__2 (0.5)). Our previous work in curve matching ( ) showed that weights that vary across the spatial domain allow results that may be superior to results found with constant weighting terms. These combined gradient functions, used at each iteration, are illustrated in Figure 5 . The sum of the weighting functions is always constrained to add to one. We also normalize each similarity derivative such that its maximum displacement, before weighting, is on the order of a single voxel. This latter step aids in making a fair combination of the different gradients.

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Cohort and Image Dataset

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Cohort

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Imaging Parameters

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Results

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Performance Evaluation

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Qualitative Assessment

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Quantitative Assessment of Optimization Performance

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Evaluation of Hippocampus Segmentation Quality

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Table 1

Dice Overlap between Labeled Hippocampi Generated by Expert Manual Segmentation and Automatic Segmentation by SyN with T1, SyNMN with DT and T1 data, and the Demons Method

Evaluation of Automated Hippocampus Segmentation Subject SyN Dice Left SyN Dice Right SyNMN Dice Left SyNMN Dice Right Demons Dice Left Demons Dice Right 1 0.776 0.837 0.821 0.818 0.732 0.802 2 0.790 0.889 0.805 0.878 0.778 0.862 3 0.854 0.833 0.888 0.836 0.837 0.841 4 0.819 0.834 0.879 0.851 0.831 0.834 5 0.793 0.878 0.835 0.903 0.773 0.828 6 0.853 0.887 0.876 0.866 0.822 0.853 7 0.826 0.834 0.857 0.813 0.779 0.813 8 0.857 0.861 0.871 0.874 0.847 0.830 9 0.922 0.910 0.905 0.924 0.823 0.824 tbi 10 0.862 0.858 0.838 0.857 0.800 0.846 tbi 11 0.873 0.893 0.887 0.863 0.854 0.881 tbi 12 0.840 0.872 0.868 0.856 0.799 0.846 tbi 13 0.789 0.838 0.781 0.873 0.682 0.723 tbi 14 0.786 0.814 0.786 0.799 0.694 0.792 tbi 15 0.882 0.886 0.862 0.885 0.801 0.762 tbi 16 0.868 0.887 0.871 0.862 0.861 0.859 tbi 17 0.898 0.880 0.905 0.886 0.791 0.877 tbi 18 0.860 0.895 0.891 0.906 0.790 0.858 tbi 19 0.860 0.849 0.871 0.869 0.790 0.856 tbi 20 0.883 0.882 0.899 0.838 0.790 0.807 tbi 21 0.786 0.878 0.812 0.880 0.789 0.681 Average 0.845 0.866 0.860 0.864 0.794 0.823t -Test vs. demons 6.49 6.91 0P value vs. demons 8.57E-08 2.20E-08 1

DT, diffusion tensor; SyN, symmetric normalization; SyNMN, symmetric normalization for multivariate neuroanatomy.

Aggregate performance difference, for both left and right hippocampi, is assessed by pairwise t -test. SyN and SyNMN show similar performance.

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Multivariate Effects of TBI

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Discussion

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Multivariate Analysis of Structural and Diffusion Imaging in Traumatic Brain Injury

Rationale and Objectives

Materials and Methods

Results

Conclusions

Materials and methods

Theory for Multivariate Image Processing

Multivariate datasets

Symmetric diffeomorphic registration

Symmetric DT Diffeomorphic Registration

SyNMN with T1 and DT

Cohort and Image Dataset

Cohort

Imaging Parameters

Results

Performance Evaluation

Qualitative Assessment

Quantitative Assessment of Optimization Performance

Evaluation of Hippocampus Segmentation Quality

Multivariate Effects of TBI

Discussion

References

Further Reading

Abstracts of Funded National Institutes of Health Grants

Advances in Radiological Image Analysis from MICCAI 2007

Automated 11 C-PiB Standardized Uptake Value Ratio