Synopsis

Keywords: Brain Connectivity, Diffusion/other diffusion imaging techniques

Tractography is a method to reconstruct white matter microstructure from DWI information and connectomics maps this reconstruction to a graph representation. We compute modularity, assortativity, global efficiency, and average betweenness centrality on this graph. We model changes in these measures with age and sex using DWI for healthy patients from two sites. Data from different sites requires harmonization to remove site-effects. We compare performances of ComBat and LinearRISH harmonization techniques at reducing CoV and removing confounding site-effects from associated linear models. We find that ComBat is effective at both and using LinearRISH in addition acts synergistically at harmonizing site differences.

INTRODUCTION

Diffusion weighted imaging (DWI) is a non-invasive, in-vivo imaging modality ¹. Tractography is a method to reconstruct white matter microstructure from DWI information ^2–4. Connectomics is the mapping of this reconstruction to a graph representation called a connectome ⁵. Using this graph representation, we can use established graph theory analyses to understand the connectivity of the brain. Graph theory measures (GTMs) quantify brain community, resilience, efficiency, and centrality⁶. Ideally, larger patient populations yield greater statistical power to detect these changes. Large human imaging studies often achieve this by leveraging imaging collected from multiple sites. Unfortunately, data from different sites are often not directly comparable due to differences in data acquisition and/or scanners and introduce confounding differences for graph theory analysis ^{7 8,9}. Two common approaches to removing these effects are LinearRISH and Combined association testing (e.g., ComBat) ¹⁰. The impact of these harmonization methods on graph theoretical analysis is not well understood (Figure 1).

METHODS

We characterize four complex GTMs (modularity, characteristic path length, global efficiency, and betweenness centrality) in 117 participants from the Baltimore Longitudinal Study of Aging (BLSA) with 1:1 sex and age matched participants from the Vanderbilt Memory and Aging Project (VMAP). The population contains healthy patients aged 59 to 92 with 64 women. We evaluate two harmonization techniques, ComBat (feature harmonization) and LinearRISH (DWI harmonization), on their ability to harmonize site differences while preserving microstructural changes associated with aging.

Tractography and connectomics
For tractography, we used the MRTrix default probabilistic tracking algorithm¹¹. We generated 10 million streamlines per acquisition. After, we converted the tractogram to a connectome using the Desikan-Killany atlas ¹² with 84 cortical parcellations from Freesurfer ¹³.
We compute modularity, average betweenness centrality, assortativity, and global efficiency for each connectome using the Brain Connectivity Toolbox (BCT) Matlab implementation ⁶.

Harmonization
We used the Matlab implementation of ComBat to perform feature-level harmonization on the GTMs ¹⁴. ComBat creates a multivariate linear mixed effects regression model whose parameters are optimized with an empirical Bayes approach. Such model corrects for multiplicative and additive site effects. It is a computationally inexpensive harmonization method and is performed at the end of processing on the GTM data (Figure 1).
LinearRISH is a harmonization technique that scales rotation invariant features of DWI to remove scanner specific differences in white matter for a group of age matched subjects ¹⁵. It is applied before tractography and consists of: extracting spherical harmonic (SH) coefficients for all orders l=0,2,4,6 and degrees, registering to common space, computing the scale map (Φ) from VMAP to BLSA, registering and applying the scale map to VMAP SH coefficients, and finally converting back to the signal intensity domain.

Performance evaluation
First, we characterize across dataset coefficients of variation (CoV), a common metric used in harmonization studies ⁷. Coefficient of variation (CoV) of a group of measurements is the ratio of the standard deviation and mean multiplied by 100¹⁶. Here, we compare CoV before and after each harmonization technique is applied to VMAP and BLSA.
We fit linear models with site, age, and sex effect variables with the following formula:
$$$ GTM = 1 + Sex+Age+Site $$$

RESULTS

While both methods reduced CoV for all measures, only ComBat reduced CoV for assortativity (Figure 2). Modularity and average betweenness centrality experience a stronger decrease when ComBat and LinearRISH are used in combination indicating they behave synergistically for certain GTMs.
In Table 1 we report the linear model coefficients of each effect (age, sex, and site) with their significance. Effective harmonization techniques will remove site-related contributions. We examine the linear model site effect significance before and after harmonization.

DISCUSSION

No harmonization method achieves lowest CoV consistently across all graph measures; however, ComBat improves CoV from baseline for each GTM. LinearRISH has similar performance to ComBat in all measures except assortativity where it introduces a significant increase in variation. The combined harmonization offers some additional improvement to variation in all except assortativity.
Without harmonization, each GTM has a significant site effect present and confounding the model. After applying ComBat alone or with LinearRISH, the site effect is no longer significant. For very strong covariates (age in modularity and average betweenness centrality) we find similar effect sizes across harmonization methods. ComBat and LinearRISH seem to be additive. However, LinearRISH alone is not enough for three of the four GTMs studied. Weaker effects (age in assortativity and global efficiency) disappear when using LinearRISH. This could be caused by a biasing effect in the DWI that LinearRISH corrects.
In summary, ComBat is effective at decreasing CoV of data from multiple sites and removing significant site effect from derived data models. ComBat and LinearRISH have the capacity to work synergistically and create a combined decrease in variation and increase in model strength.
We advise caution when implementing these methods. LinearRISH is applied before tractography and thus affects downstream tasks. In future studies we hope to characterize the potential bias introduced in RISH template construction.

CONCLUSION

Overall, we recommend harmonizing multi-site studies with ComBat with LinearRISH but caution to check the assumptions for each method to ensure neither introduces additional confounding bias.

Acknowledgements

This work was conducted in part using the resources of the Advanced Computing Center for Research and Education at Vanderbilt University, Nashville, TN. This work was supported by the National Institutes of Health (NIH) under award numbers K01EB032989, K24-AG046373, K01-AG073584, and R01-AG034962, the National Science Foundation (NSF) under award number 2040462, the Alzheimer’s Association under award IIRG-08-88733, the Vanderbilt Clinical Translational Science Awards UL1-TR000445 and UL1-TR002243, and Vanderbilt’s High-Performance Computer Cluster for Biomedical Research under award S10-OD023680. This research was conducted with the support from the Intramural Research Program of the National Institute on Aging of the NIH. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH or NSF.

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