Layout of anatomical structures and blood vessels based on the foundational model of anatomy

2.1 The foundational model of anatomy

The Foundational Model of Anatomy (FMA) ontology [1, 2] is an open-source knowledge resource for biomedical informatics serving as a domain ontology that represents the structural organisation of the entire human body. The FMA distinguishes itself from traditional anatomical sources by providing a detailed, symbolic representation of anatomical entities and their relationships, supporting various applications in biomedical informatics. With over 75,000 classes and extensive relational data, the FMA facilitates cross-disciplinary integration and standardisation in anatomy representation. It structures anatomical information across different levels of abstraction into four main components: (1) Anatomy Taxonomy (AT), (2) Anatomical Structural Abstraction (ASA), (3) Anatomical Transformation Abstraction (ATA), and (4) Metaknowledge (Mk). This classification facilitates the detailed representation and understanding of the human body’s anatomy for various applications in medical and other research fields.

2.2 Treemap layout

For the visualisation pipeline (see Section 4 and Figure 5), we need to display the hierarchical relationship of the underlying anatomical system in a way that is easy to read and fast to interpret. For this a treemap layout has been proven useful [3, 6]. A treemap layout is a layout algorithm that recursively maps nodes of a tree into a, in our case, two-dimensional (2D) space, with the additional restriction to display the parent-child relationships of the underlying graph by placing a child node inside the layout area of its parent node [5]. A second condition that has to be fulfilled for a treemap layout is that the layout elements of any sibling nodes, i.e., nodes with the same parent node, must not overlap.

Over the years, several treemap layout algorithms have been created with different goals, such as achieving a circular layout [7], focusing on different attributes like weight, or preserving neighbourhoods. For the visualisation pipeline used here, we focus on the subclass of treemap layout algorithms that allocate nodes to a rectangular reference space. One of the first algorithms, the Slice & Dice algorithm introduced by Johnson and Shneiderman [8] follows the approach of recursively splitting the reference space along one axis, resulting in horizontal or vertical slices. Due to the limitation of only being able to split the reference space along one axis, this treemap layout approach may contain numerous thin and long slices, leading to a vast number of splitting treemap layout algorithms proposed [5]. For example, the Squarrified algorithm [9], extending the Interactive Dynamic Map algorithm [10], was introduced, focusing on achieving an aspect ratio of the to-be-created rectangular subdivision of one, or the Golden Rectangle layout approaching the golden ratio [11].

In addressing the trade-off between order preservation and aspect ratio, we note that conventional algorithms often compromise visual quality by incorporating various parameters not needed for our specific use case. Consequently, we propose a simplified treemap algorithm, the Grid-Layout, primarily focusing on enhancing visual quality. This approach deliberately overlooks many common parameters considered in existing algorithms, simplifying the overall approach and enabling the optimisation of the visualisation. A brief overview of this algorithm is outlined in Section 4, and a visualisation is shown in Figure 2.

2.3 Network layout

Network layout algorithms provide methods to display complex network data, including biological networks, in a comprehensible manner [12–14]. These algorithms aim to represent networks – comprising nodes and edges – in a way that conveys the structure of the data and allows to analyse it with low effort. Common approaches include force-directed algorithms [15, 16], which simulate physical forces among nodes and edges to position closely related nodes together while dispersing unrelated ones. Another approach is the hierarchical layout [17], which arranges nodes into levels based on their connectivity, often used in organisational charts or tree structures. An alternative method is circular layout [18], ideal for emphasising cyclic structures in data. Orthogonal layouts [19] arrange nodes and edges in a grid format, ensuring that all connections between nodes are represented by horizontal or vertical line segments. Each algorithm has its strengths and restrictions. Recent advancements have introduced hybrid algorithms that combine features of multiple techniques to handle specific data characteristics and layout methods with constraints [20–23], improving the visual outcomes of network visualisations and supporting important aspects such as mental-map preserving layout [24, 25].

2.4 Edge routing

Edge routing is the part in network visualisation that determines the paths between nodes for connection representation to produce a clear depiction in which edges and paths are easy to follow and the network structure is easily perceived. Typical goals for edge routing are to minimise edge crossings, edge length, and overlap with nodes, thereby reducing visual clutter and improving readability [26]. Effective edge routing is crucial when dealing with complex graphs where a straight-line connection between nodes would result in an unreadable and potentially confusing drawing.

There are several strategies and styles for edge routing, including orthogonal routing [27], where edges follow right-angle paths; spline routing, where edges are drawn using curved lines such as Bézier curves [28]; and polyline routing [29], where edges are piecewise linear but not necessarily orthogonal. The choice of strategy and style often depends on the application and the specific requirements for the visualisation, such as whether the graph is directed or undirected, the density of the graph, and the need for highlighting certain pathways or structures within the graph.

Advanced edge routing algorithms also take into account aesthetic criteria and constraints, such as minimising the number of bends in an edge to reduce visual complexity or using edge bundling [30, 31] to group similar edges together, which can help in revealing higher-level structures within the graph. Edge routing can be particularly challenging in dynamic graphs where the nodes and edges change over time, requiring the routing algorithm to adapt while maintaining a stable and mental-map preserving layout.

4.1 Treemap layout

For the first step of the visualisation pipeline, a directed acyclic graph (DAG) is divided into 24 sub-trees representing individual tiles based on the retrieved anatomical base data set. Each tile can be different in size or even be empty and is assigned to specific sections of the treemap. A global scaling factor regulates the size of each tile.

To enable a mechanism for reducing complexity and thereby customise the level of detail for specific applications, the microcirculations, which serve as connection points for the vascular layout mentioned later, can be limited to a predefined set. As a result, vascular treemap paths are created solely based on the selected set of microcirculations. Without such a selection, the treemap incorporates all microcirculations, treating them as potential connection points for the vascular layout.

Another way of simplifying the complexity of the system is to limit the level of detail shown within a tile in the treemap layout. This is done by filtering the nodes to be displayed based on their distance to the root node. In the context of the FMA, a global maximum distance can be set ranging from 1 to 16, adjusting the visibility of the nodes so that only those within the specified distance are displayed in the treemap layout.

Lastly, a tree mapping algorithm, chosen from three options (Grid-Layout, Slice&Dice, or Squarrified), generates the treemap within each tile, with additional space reserved for later vascular layout integration. The proposed grid layout algorithm is a specialised treemap algorithm that utilises the general properties of the hierarchical anatomical system. For our specific use case, we have simplified the overall algorithmic approach by not distinguishing the size or ordering of children of a parent node. This improves the overall readability and fast retrieval of information on the body’s hierarchical anatomical system through the treemap layout.

The algorithm generally operates on a tile-by-tile basis (i.e., separate on each subgraph), with each subgraph associated to a tile laid out independently. First, the root node is identified within the graph of the corresponding tile. Then, a treemap layout, starting at the root node, is carried out in a top-down approach, where the children of each node are allocated progressively smaller space in the corresponding tile. For the layout, two types of grids can be chosen: a dynamic grid that adapts to the children of the node and a fixed global grid for all tiles, with the user deciding which grid to use. With this approach, we aim, similar to the Squarrified algorithm, for an aspect ratio close to one. The result can be seen in Figure 2.

4.2 Vascular layout

In the second step of the visualisation pipeline, vascular data for the circulatory paths is integrated, enhancing the treemap with detailed vascular information. A vascular layout refers to the arrangement of a vascular graph representing the blood vessel system information. Vascular layouts are tied to the graph for the treemap layout, which must contain contact points, such as microcirculations, to connect with the vascular layout. Note that the information for the vascular and treemap layouts are distinct graphs and do not share any nodes. Edges in the vascular graph should be orthogonally oriented when possible. These segments are connected at specific points, termed bend points, which are calculated during the vascular layout process.

In general, the vascular layout should fit into the treemap representation, focusing on five main goals:

1. independence to simplify the overall problem by breaking it into manageable parts;

2. shortest paths to ensure direct and efficient routing without unnecessary detours;

3. anatomical accuracy to faithfully represent the actual structure of the vascular system, requiring precise positional data;

4. clarity to prevent overlapping and maintain clear distinctions between arteries and veins; and

5. completeness to fully match the layout of nodes and edges of the original graph, ensuring a thorough and accurate representation.

To enhance clarity in the layout, venous and arterial vessels are separated within each tile. A complete microcirculation is depicted with arterial edges (red, carrying oxygen-rich blood from the heart) and venous edges (blue, draining oxygen-poor blood toward the heart). In the treemap, blue (venous) vessels are always positioned on the right side, while red (arterial) vessels are placed on the left. The edges are routed to the tiles horizontally or vertically, through top or bottom channels, with a colour-coded separation (red at the top; blue at the bottom). This setup includes designated vascular channels above and below the treemap in each tile, ensuring the visibility of the treemap is maintained without interference. Since lower channels are reserved for blue (venous) paths, and upper channels are reserved for red (arterial) segments, L-shaped areas are created around the treemap based on the vessel type.

4.3 Vascular layout method

The integration of a vascular layout interconnected with the representation of an anatomical hierarchy can be divided into the four following steps:

1. identifying tile-specific transition points (called hubs);

2. generating internal layouts from the leaves of the vascular graph;

3. calculating positions for nodes outside the vascular graph; and

4. creating the external layout connecting to the heart chambers

It should be noted that the structure of the vascular graph is quite complicated with only a part of the nodes clearly assignable to specific tiles. The layout process has to deal with the layout within the tiles (separated between arterial and venous vessels), the connection of nodes within tiles to nodes outside tiles, and the overall connection of the vascular system to the heart.

4.3.1 Identifying tile-specific transition points

In the first step, to avoid overlapping paths and guide them through specific areas of the treemap to their target microcirculation, transition points (the so-called hubs, see Figure 6) are identified in the vascular graph. Starting from the leaves of the vascular graph, each leaf (end of a vascular path at a node within the treemap) is assigned a unique cluster ID based on its target microcirculation. The bottom-up approach propagates the cluster ID from the leaves to their parent nodes, identifying hubs (the end-point of this process) as nodes with a single cluster ID passed from their descendants within one tile. Hubs are inside tiles and represent points where paths converge from the leaves to the root, they are prioritised in the layout process. The hubs (see Figure 6) can be seen as starting points for vessels inside the tile. They are crucial in separating the layout process into internal and external tile layouts.

Figure 6:

Part of a vascular layout of a tile showing a vascular channel, hubs, and internal nodes.