Optimizing Diffusion Imaging Protocols for Structural Connectomics in Mouse Models of Neurological Conditions

Abstract

Network approaches provide sensitive biomarkers for neurological conditions, such as Alzheimer's disease (AD). Mouse models can help advance our understanding of underlying pathologies, by dissecting vulnerable circuits. While the mouse brain contains less white matter compared to the human brain, axonal diameters compare relatively well (e.g., ~0.6 μm in the mouse and ~0.65-1.05 μm in the human corpus callosum). This makes the mouse an attractive test bed for novel diffusion models and imaging protocols. Remaining questions on the accuracy and uncertainty of connectomes have prompted us to evaluate diffusion imaging protocols with various spatial and angular resolutions. We have derived structural connectomes by extracting gradient subsets from a high-spatial, high-angular resolution diffusion acquisition (120 directions, 43-μm-size voxels). We have simulated protocols with 12, 15, 20, 30, 45, 60, 80, 100, and 120 angles and at 43, 86, or 172-μm voxel sizes. The rotational stability of these schemes increased with angular resolution. The minimum condition number was achieved for 120 directions, followed by 60 and 45 directions. The percentage of voxels containing one dyad was exceeded by those with two dyads after 45 directions, and for the highest spatial resolution protocols. For the 86- or 172-μm resolutions, these ratios converged toward 55% for one and 39% for two dyads, respectively, with <7% from voxels with three dyads. Tractography errors, estimated through dyad dispersion, decreased most with angular resolution. Spatial resolution effects became noticeable at 172 μm. Smaller tracts, e.g., the fornix, were affected more than larger ones, e.g., the fimbria. We observed an inflection point for 45 directions, and an asymptotic behavior after 60 directions, corresponding to similar projection density maps. Spatially downsampling to 86 μm, while maintaining the angular resolution, achieved a subgraph similarity of 96% relative to the reference. Using 60 directions with 86- or 172-μm voxels resulted in 94% similarity. Node similarity metrics indicated that major white matter tracts were more robust to downsampling relative to cortical regions. Our study provides guidelines for new protocols in mouse models of neurological conditions, so as to achieve similar connectomes, while increasing efficiency.

Keywords: MRI; brain; connectivity (graph theory); diffusion imaging; mouse model; neurodegenerative diseases.

FIGURE 1 |

The stability of the condition numbers increased, and the standard deviation decreased with angular resolution, although not monotonically, denoting that some sampling schemes are more robust to rotational variance, due to their geometrical symmetry properties.

FIGURE 2 |

The effect of spatial resolution (horizontal axis) and angular resolution (vertical axis) on the number of voxels with one, two, three, or four fibers (dyads) per voxels (A). (A) Effects for 12, 45, and 120 directions, chosen as examples for low-, medium-, and high-angular sampling. (B) Effects for sampling schemes between 12 and 120 at three spatial resolutions (43, 86, and 172 μm). These results illustrated the advantages of high-angular and spatial-resolution protocols in terms of sensitivity and stability.

FIGURE 3 |

The number of voxels with one, two, and three dyads varied per region, but differences relative to the reference protocol (high-spatial, high-angular resolution) consistently decreased with increasing number of angular directions (only 12, 45, 60, and 120 directions are shown for simplicity) and with increasing spatial resolution (i.e., smaller voxels; ranging from 43-μm linear dimension for the reference to 86 and 172 μm).

FIGURE 4 |

The fimbria connectivity mapped as a function of spatial and angular resolution. The connectivity of the left fimbria was reconstructed for protocols with 12, 45, 60, and 120 directions, at the full 43-μm resolution, clearly illustrating limitations of smaller angular sampling protocols at capturing projections though the hippocampus (white arrows) and amygdala (yellow arrows). Less clear were the effects of spatial resolution in the range 43–172 μm where SNR and partial volume effects both played a role. However, the projections through the hippocampus covered reduced areas, and projections into the alveus were partially lost in the lower resolution protocol (blue arrows). L, left; R, right.

FIGURE 5 |

The hippocampus connectivity mapped as a function of spatial and angular resolution. Hippocampal connectivity (the left hemisphere was seeded) was affected more by angular resolution, especially for cortical regions (white arrows), but also in the ability to retrieve cross hemispheric projections (yellow arrows). L, left; R, right.

FIGURE 6 |

Dyad dispersion as a measure of error. The dyad one dispersion shows decreasing errors for higher angular samples, with an inflection point at 45^◦ and increasing stability after 60^◦ (A). Similar errors were apparent for 43 and 86 μm, but the errors were larger for 172 μm. Dyad two showed a stronger effect of resolution, and larger errors, which also tapered off after more than 60 directions were acquired (B). LGN, lateral geniculate nucleus.

FIGURE 7 |

Adjacency matrices shown as chord diagrams for a subset of 13 regions relevant to neurodegenerative diseases showed qualitatively greater similarity to the reference connectome of 120 directions (A120) for 45 (A45) and 60 directions (A60) when compared to the similarity between 120 (A120) and 12 directions (A12). Spatial resolution also had an effect on the chord diagrams, in particular, at the level four times downsampling (S4; 172 μm), but this was less pronounced when comparing two times downsampling (S2; 86 μm) with fully sampled (S1; 43 μm) protocols. The chord diagrams showed that all protocols can capture the connectivity of the hippocampus (Hc) and its connecting fibers (fx, fornix; fi, fimbria), but shorter protocols have reduced sensitivity for smaller nuclei (LD, laterodorsal thalamic nuclei; LGN, lateral geniculate nuclei; LPO, lateral preoptic nucleus) and lack sensitivity required for cortical connectivity, e.g., for the cingulate (Cg) and entorhinal cortices (Ent).

FIGURE 8 |

Global connectome similarity. Spearman correlations among the connectomes obtained for three resolution levels (S1, fully sampled at 43-μm linear voxel dimension; S2, downsampled by a factor of 2–86 μm; S4, downsampled by a factor of 4–172 μm; and each of the 12, 45, 60, and 120 angular resolution schemes (A12, A45, A60, A120) indicated that the highest similarities were obtained between the 60 and 120 angular samples schemes for all spatial resolutions. While the patterns were similar, similarities were lower for the 45 and 120 angular sample schemes for all resolutions relative to 60- and 120-direction schemes. When comparing against the reference set, the median was 0.89 for sets with 45 directions, but 0.92 for sets with 60 directions; and the maximum for 45 directions was 0.91, but 0.94 for 60 directions. The global maximum 0.97 was obtained when comparing (S2, A60) vs. (S2, A120); or (S1, A45) vs. (S2, A45).

FIGURE 9 |

Vertex-based graph similarity showed that white matter tracts were more robust to downsampling relative to nodes representing gray matter and, in particular, cortical domains. Our subgraph’s regions of interest include the cingulate cortex (Cg), insular cortex (Ins), temporal association areas (TeA), entorhinal cortex (Ent), hippocampus (Hc), hypothalamus (Hyp), preoptic telencephalon (LPO), septum (Spt), lateral geniculate nucleus (LGN), fimbria (fi), fornix (fx), mamilothalamic tract (mt), and laterodorsal thalamic nuclei (LD). When comparing graphs for different spatial resolutions, the fi was most similar between 43- and 86-μm resolutions with a score of 0.85, and also relative to 172 μm with a score of 0.82, but most other graph nodes were not. Among angular sampling schemes, the fimbria was also robust, with a similarity score between the 12 and 120 directions of 0.5, followed by the fornix, hippocampus, and septum with 0.1. The cortical regions were most likely to be dissimilar when changing spatial or angular sampling schemes. Median similarity scores are shown for each graph comparison.