# Anatomical Labeling of Abdominal Blood Vessels

Definition In CA, anatomical labeling is important. Abdominal blood vessel labeling can be understood as the procedure to give labels to each branch (edge) of a graph structure representing the abdominal blood vessel network of a subject.

Let *b _{i}* be a branch of the graph showing an abdominal blood vessel network. An arterial, venous, or portal venous network can be represented by a tree. Here a set of anatomical label classes are written as

Also a set of branches to be labeled as

Machine Learning-Based Approach One approach for anatomical labeling is to employ machine learning [48, 190, 200].This process can be formulated as the process that finds the suitable category of a branch *b _{i}* from feature values

*f*of

_{i}*b*It can be written as

_{i}.

Of course, this approach assigns anatomical labels to each branch based on features computed locally. Global information is not considered. A process to correct labeling results will be necessary.

Practical Example of Anatomical Labeling As a given blood vessel region is expressed as a tree structure, likelihoods of candidate anatomical names for each branch in the tree structure are computed using a machine learning-based method. Possible branching patterns are expressed in a graph called a bifurcation graph, a graph structure that is different from the tree structure used to represent the blood vessel region. Each node of the bifurcation graph expresses each anatomical name, and each edge expresses a possible bifurcation. The edges are assigned weights based on the likelihoods of the branches in the tree structure. The directed spanning tree of the bifurcation graph represents a branching pattern. The optimum branching pattern is obtained by computing the directed maximum spanning tree. Each branch in the tree structure is labeled based on the branching pattern.

This algorithm was evaluated using 50 sets of abdominal CT volume data. The recall and precision rates of abdominal arteries were 89.3% and 92.9%, and the recall and precision rates of the hepatic portal system were 86.0% and 86.3%, respectively. Examples of results of automated anatomical labeling are shown in Fig. 3.93. In this experiment, 80.8% of the branching patterns of major bloodvessels that have branching variations were obtained correctly.

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**Fig. 3.93 **Examples of results of automated anatomical labeling. (**a**) Abdominal arteries. (**b**) Hepatic portal system