Elektronika 2009-11.pdf - Instytut Systemów Elektronicznych

The presented methodology draws upon the method of
determining the location of a point on the surface of our planet
in the system of geographic coordinates, where a similar cartographic
projection is used to make topographic maps. This
representation of mutual spatial relationships between the
analysed arteries yields a convenient access to and a unanimous
description of all elements of the vascular structure.
As the structure of coronary vascularization may be characterised
by three different types of artery distribution over the
heart surface, in the following part we will propose a grammar
for the left dominance artery distribution. The left dominance
artery distribution is present in on average 10...14% of cases,
with a variety of intermediate forms possible. Before we define
the representation of the analysed image in the form of IE
graphs, we have to introduce the following order relationship
1 ≤ 2 ≤ 3 ≤ … ≤ 24 and α ≤ β ≤ γ ≤ … ≤ µ in the set of Г edge
labels shown in Fig. 1. This way, we index all peaks according
to the ≤ relationship in the set of edge labels which connect
the main peak marked 1 to the adjacent peaks and we index
in the ascending order (i = 2, 3, …, n). This gives us IE graphs
for the right and the left coronary arteries, respectively, presented
in Fig. 1.
When graphs shown in Fig. 1 are represented by their
characteristic descriptions, they look as follows:
For the right coronary artery:
The graph structure created in this way will form elements
of a graph language defining the spatial topology of the heart
muscle vascularization including its possible morphological
changes.
For IE graphs defined as above, in order to locate the
place where stenoses occur in the case of a balanced artery
distribution, the graph grammar may take the following form:
for the right coronary artery:
G P = (S, ∆, Γ, P, Z)
S = {ST, RCA, PI, RM, C_Right},
D = {ST, RCA, PI, RM},
G = {16η, 11ι, 12λ, 14ε}
The start graph Z and the set of productions shown in Fig. 2.
for the left coronary artery:
G L = (S, ∆, Γ, P, Z)
S = {ST, LCA, LM_CX, L_LAD, CX, LM, L, LAD, C_Left,
C_Left_ant, C_Left_circum}
For the left coronary artery:
ST 1 RCA 2 PI 3 RM 4 ST 1 LCA 2 LM_CX 3 L_LAD 4 CX 5 LM 6 L 7 LAD 8
1 2 1 - 1 2 2 2 1 - 1 -
16η 11ι 12λ 1ε - 2κ 13ι 16ι 13θ 1λ 2λ 18ι 22κ - 23η -
2 3 4 4 - 2 3 4 5 6 7 8 6 - 8 -
Fig. 1. The representation of the right (A) and the left (B) coronary artery using IE graphs
Rys. 1. Reprezentacja prawej (A) oraz lewej (B) tętnicy wieńcowej za pomocą grafów IE
10 ELEKTRONIKA 11/2009