Identifying locations susceptible to micro-anatomical reentry using a spatial network representation of atrial fibre maps

Figures

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  Fig 1. A schematic illustrating our approach. Left column: (A) In the healthy atrial myocardium, cardiomyocytes (pink cells) are well coupled along and across the principle fibre directions, such that the longest reentrant loop is too short to sustain micro-anatomical reentry (green arrows). (B) Over time, the atria accumulate interstitial fibrosis (yellow cells) forming short segments of electrically isolated fibre. (C) The length of these segments grows as more interstitial fibrosis accumulates until the isolated segments are sufficiently long to harbour micro-reentry (blue arrows). We hypothesise that the accumulation of interstitial fibrosis can be modelled as a spatial network. Right column: Nodes (yellow points) representing a group of cardiomyocytes are connected to their neighbours along fibres (red links) and across fibres (blue links). If the density of interstitial fibrosis is low, there are many transverse (blue) links. We model the increase in the density of interstitial fibrosis as the progressive removal of transverse links, and equate the micro-anatomical reentrant substrate to regions of the spatial network where a loop exists that is longer than one refractory…

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  Fig 2. A schematic showing the construction of spatial networks from atrial imaging data. (A) An image based model of the atria is derived from atrial imaging. The model, represented by a mesh of voxels, is coupled with vectors representing the underlying fibre orientation at each point. (B) In the fibre model, a spatial network is generated where nodes (yellow points) are connected with probability 1 along fibre tracts (pink edges), and low probability across fibre tracts (blue edges). (C) In the fibre-less null model, the probability of forming an edge is not biased by the underlying fibre orientation.

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  Fig 3. A 2D schematic showing the conversion of local fibre orientation vectors into global fibre tracts which are seeded with nodes and coupled into a spatial network. (A) Each image-based model provides a vector field for the local fibre orientation. (B) Beginning from a set of random seed points (red circles), fibres are generated using tractography, propagating forward and backwards in the direction of the local orientation vector. (C) Nodes (yellow circles) are placed at approximately equal intervals along the fibres. (D) Nodes are coupled to neighbouring nodes with probability 1 if nodes are adjacent and in the same fibre (pink edges), and according to a monotonically decreasing function of distance, p(x;r, c), otherwise (blue edges). Nodes which are close together (green arrows) are more likely to be connected than those which are far apart (red arrows). (E) By applying a discrete diffusion model (see section 3.4) to the network, we identify the micro-reentrant substrate by observing where conduction block (red/orange circle) results in a wavefront (white circle) reentering a blocked fibre.

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  Fig 4. A 2d schematic demonstrating the construction of the spatial network using the fibre-less null model. The process is similar to Fig 3 where steps (A) and (B) are skipped. (A) Nodes are distributed uniformly in each voxel. (B) Nodes are connected according to a monotonically decreasing function of distance, p(x;r, c), Eq (1), where c is a characteristic distance (dashed circle). There is no directional bias in the connection probability (blue edges only). Nodes which are closer together than the characteristic distance (green arrows) are more likely to be connected than those which are far apart (red arrows). (C) The micro-reentrant substrate is identified using the DDM.

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  Fig 5. The micro-reentrant substrate for the human atria at low (left column), medium (middle) and high global risk of micro-reentry (right). A: Superior view. B: Posterior view. C: Inferior view. D: Cut-through. E: Superior right atrial zoom. IVC/SVC: Inferior/superior vena cava. PRA/PLA: Posterior right/left atrium. RAA/LAA: Right/left atrial appendage. TV/MV: Tricuspid/mitral valve opening. CS: Coronary sinus. FO: Fossa ovalis. PM: Pectinate muscles. CT: Crista terminalis. IAS: Inter-atrial septum. RIPV/LIPV/RSPV/LSPV: Right/left, inferior/superior, pulmonary vein.

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  Fig 6. The micro-reentrant substrate for the human atria using the fibre-less null model at low (left column), medium (middle) and high global risk of micro-reentry (right). A: Superior view. B: Posterior view. C: Inferior view. D: Cut-through. E: Superior right atrial zoom. See Fig 5 for labels.

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  Fig 7. The number of independent spatial clusters identified as at local risk of micro-anatomical reentry. Data for the fibre model (blue points) and the fibre-less null model (orange crosses) for (A) the human atria, (B) the healthy sheep atria, and (C) the HF sheep atria, as a function of the global risk parameter, λ. Each clustering value is calculated from 1000 sampled micro-reentrant circuits. Error bars from bootstrapping.

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  Fig 8. The occupied voxel fraction averaged over voxels where micro-reentry is detected. Data for the fibre model (blue points) and the fibre-less null model (orange crosses) for (A) the human atria, (B) the healthy sheep atria, and (C) the HF sheep atria, as a function of the global risk parameter, λ. The dashed line in each subfigure is the average value of the occupied voxel fraction for all the voxels in the atrial geometry.

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  Fig 9. A view of the human superior right atrium illustrating factors influencing the spatial distribution of local risk. Risk regions for (A) the fibre model, and (B) the fibre-less null model. (C) The occupied voxel fraction (OVF). (D) The longitudinal connection fraction in the fibre model (LCF). Regions (1–4) are referenced in the main text. Colourbar limits: OVF ∈ [0.3, 0.9], LCF ∈ [0.4, 0.8].

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  Fig 10. The distribution of LCF and OVF values in the human atria at low (A-C) and high (D-F) global risk. (A) & (D) The distribution across all the voxels in the human atria. (B) & (E) The distribution weighted by the local risk of reentry in each voxel for the fibre model. (C) & (F) The equivalent for the fibre-less null model. Note, the LCF is not defined for the fibre-less null model, but for illustrative purposes we include the LCF for the equivalent fibre model. Dashed lines: median. Dotted lines: 10th, 25th, 75th and 90th percentiles. Colourbar indicates voxel density relative to distribution maximum; regions in grey correspond to a relative density of zero. Red crosses: weighted mean of distribution.