A

BC

D E

x

y

z

w

Normal/eMCI Normal/lMCI eMCI/lMCI Normal/AD eMCI/AD lMCI/AD0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Two groups to be discriminatedC

lassific

atio

n e

rro

r

Raw matrices

Augmented

Raw + Augmented

Iman Aganj,1 Gautam Prasad,2 Priti Srinivasan,1 Anastasia Yendiki,1 Paul M. Thompson,2 Bruce Fischl1,3

1 Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School2 Laboratory of Neuro Imaging, Institute for Neuroimaging and Informatics, University of Southern California

3 Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology

10 20 30 40 50 60 70

10

20

30

40

50

60

70

10 20 30 40 50 60 70

10

20

30

40

50

60

70

Diffusion MRI tractography Augmented connectivity matrix Healthy/disease classificationStructural connectivity matrix

Background: The complete map of connectivityamong different brain areas, known as theconnectome [1], can be used to study how brainarchitecture and function are influenced by geneticfactors, and change during development and withdisease. Standard approaches to compute structuralconnectivity often define the connection strengthbetween two brain regions based on thetractography streamlines between them. Such adirect fiber bundle is expected to be the major signalcarrier between the two brain areas; however, multi-synaptic neural pathways – those relayed throughother regions –may also provide connectivity [2–4].Methods: Here we propose to use the mathematicaltools developed for the analysis of resistive electricalcircuits (Kirchhoff’s circuit laws [5]) to account forindirect multi-synaptic neural pathways, augmentingthe information offered by direct brain connectivity,and increasing both the accuracy of connectomicstudies and potentially the consistency betweenstructural and functional networks. We model themultiple pathways connecting two regions startingwith two simple cases, shown in the graphical figureon the right. Case 1: two different fiber bundlesconnecting regions A and B, with connectivitymeasures 𝑥 and 𝑦, are considered to have the totalconnectivity 𝐶𝐴,𝐵 ≔ 𝑥 + 𝑦 . Case 2: indirectconnections between the two regions C and E areconsidered to contribute a total connectivity smallerthan each of 𝑧 and 𝑤, as 1 𝐶𝐶,𝐸 ≔ 1 𝑧 + 1 𝑤.Next, we exploited the similarity of these two basiccases to those of the electrical circuits made solely ofresistors, and calculated the total connectivitybetween pairs of regions similarly to well-developedtechniques in electronics (without suggesting thatthe resistive circuit is an appropriate model for thebrain’s biological wiring).

Data Processing: Diffusion MR images of 200subjects from the second phase of the Alzheimer’sDisease Neuroimaging Initiative (ADNI-2 [6]),composed of 50 cognitively normal controls, 74 earlyMCI (eMCI) subjects, 39 late MCI (lMCI) subjects, and37 Alzheimer’s disease (AD) patients, werepreprocessed [3], and segmented into 68 corticalregions automatically using FreeSurfer [7]. Theorientation distribution functions in constant solidangle [8] were constructed and used as input to theHough-transform global probabilistic tractography[9], resulting in close to 10,000 fibers per subject.The raw connectivity matrices were calculated, alongwith the proposed augmented network matrices thataccount for indirect as well as direct connections.Using the Brain Connectivity Toolbox [1], 35 networkmeasures from each matrix were computed. SupportVector Machines were trained for each type ofnetwork (raw, augmented, and both combined) andeach pair of groups, and the classification error wascomputed via leave-one-out cross-validation.Results: Combining raw and augmented matricesresulted in the best classification among Normal,eMCI, and lMCI (bar plot on the right), suggestingthat original and augmented networks containcomplementary information. A paired right-tailedWilcoxon signed rank test revealed significantlysmaller Normal/eMCI/lMCI classification error forthe proposed (combined) method than the standard(raw) method (p = 0.005). For AD vs. Normal andlMCI, the combined network augmentation did notchange the results, possibly because directconnections in AD patients are different enough forclassification to work well without considering multi-synaptic connections. The eMCI/AD classification isthe only one (out of six) where the combinedmethod degraded the results by overfitting.

Acknowledgments: Project supported by theNational Institutes of Health.

References:1. Rubinov & Sporns, Neuroimage, 2010.2. Honey et al, Proc. National Academy of Sciences, 2009.3. Prasad et al, Proc. IEEE ISBI, 2013.4. Deligianni et al, Proc. IEEE ISBI, 2011.5. Bakshi & Bakshi, Electric Circuits, 2008.6. http://adni.loni.usc.edu7. Fischl, Neuroimage, 2012.8. Aganj et al,Magnetic Resonance in Medicine, 2010.9. Aganj et al,Medical Image Analysis, 2011.