A multi-compartment model for pathological connectomes

Abstract

Brain connectivity analysis is pivotal to understanding mechanisms underpinning neurological diseases. However, current methodologies for quantitatively mapping the connectivity in vivo face challenges when focal lesions are present and can introduce strong biases in the estimates. We present a novel approach to address these challenges by introducing a multi-compartment description of the connectome, which explicitly incorporates lesion information during the estimation process. We extended the Convex Optimization Modeling for Microstructure Informed Tractography (COMMIT) framework to integrate an additional tissue compartment in voxels affected by pathology, allowing us to infer accurately the contributions of streamlines passing through lesions and to provide unbiased connectivity estimates. We evaluated the effectiveness of our approach on data from healthy subjects of the Human Connectome Project, in which we artificially introduced focal lesions to simulate pathology with varying levels of axonal damage. We also tested the performances obtained when comparing healthy subjects with patients affected by multiple sclerosis. Results demonstrate that our approach significantly enhances sensitivity to pathological changes even at low degeneracy levels compared with state-of-the-art techniques, thus representing a significant step forward to advance our understanding of neurodegenerative diseases.

Keywords: Brain networks; Connectomics; Convex Optimization Modeling for Microstructure Informed Tractography; Focal lesions; Multi-compartment models; Neurodegenerative diseases.

Figure 1.

Example of local alterations of the neuronal tissue due to pathology: Normal-appearing WM is highlighted in green, whereas pathological tissue is in red. Clearly, if some fibers traverse both areas, as depicted here with the blue streamline, the fundamental assumption made by existing techniques, “a streamline represents a group of axons with the same trajectory and constant microstructural properties” cannot be satisfied in this situation; hence, assuming invariance of the microstructural parameters along a particular streamline will cause a mismatch between the streamline itself and the measured dMRI signal.

Figure 2.

Synthetic example illustrating the error-compensation mechanism when using a generic microstructure-informed tractography method without accounting for lesions in the model. On the left, the connection strengths of the three exemplar bundles (middle panel) are reported, along with the corresponding fiber-density voxelwise map, in the absence of pathology, whereas on the right, we show these quantities as estimated when a focal lesion is present (red star-like shape). Due to the lack of considering the pathology in the model, the effect of the lesion is reflected not only on the bundles actually affected by pathology (underestimation, orange) but, potentially, also on the healthy ones (overestimation, green; underestimation, blue).

Figure 3.

Cartoon example to illustrate how to augment the signal forward model of COMMIT to account for lesions. The upper panels display a simulated configuration consisting of two crossing bundles and a focal lesion, a possible tractogram reconstructed with tractography, and a two-compartment model to describe streamline contributions and lesion damage, respectively. Below are reported: the vector y with the data measured in the three voxels; the matrix $\tilde{\mathbf{A}}$ encoding the streamline contributions, that is, A; and tissue damage in each affected voxel (only one in this case), that is, L.

Figure 4.

Axial slices of T1 images showing lesions modeled as spherical objects within the WM in which the signal is locally altered by the pathology. The positions and extents of the lesions were randomly set such that the total amount of “pathological” voxels covers 5% of the WM volume as reported in the literature for samples of MS patients. We simulated five levels of tissue damage: none (i.e., healthy subject), mild (25% reduction), moderate (50% reduction), severe (75% reduction), and profound (100% reduction).

Figure 5.

Root mean squared error of the fit without (left) and with (right) explicit modeling of the lesions. The red circles indicate the position and extent of the simulated lesions, clearly showing a modest error in the fit when using the model without considering an explicit compartment for the lesioned tissue, with potentially severe consequences on all estimated coefficients.

Figure 6.

Comparison of global network measures as estimated by state-of-the-art connectomics approaches (left, without lesion compartment) and the proposed multi-compartment connectomes (right, with lesion compartment), as a function of the degree of lesion damage. The asterisks in the figure represent the level of significance (*p ≤ 0.05, **p ≤ 0.01, ***p ≤ 0.001). The results of the permutation test are reported in Table 1.

Figure 7.

Comparison of global network measures of the connectomes estimated using the standard method (without lesion compartment) and our proposed approach (with lesion compartment). Asterisks represent the significance level (*p ≤ 0.05, **p ≤ 0.01, ***p ≤ 0.001) computed using a robust linear model corrected for sex, age, network density, and WM volume.