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2 Estimating an ideal resected region using the TDR

to compute perfused regions using Voronoi diagram. A Voronoi diagram is a way of dividing

space into a number of regions as shown in
Figure 3(a)
. A set of points (called seeds) is speci-

ied beforehand and for each seed there will be a corresponding region consisting of all points

closer to that seed than to any other. The corresponding regions are called Voronoi cells. In es-

timating perfused regions, a seed and Voronoi cell in a Voronoi diagram correspond to a point

on a portal vein and a region perfumed by the portal point, respectively, as shown in
Figure

3(b)
.
Note that, in
Figure 3(b)
,
portal-vein points (seeds) exist continuously, whereas seeds in

the original Voronoi diagram are located apart from each other. As a result, the liver region is

divided into small regions of the same number as the portal-vein points.

FIGURE 3
Computing perfused regions using Voronoi diagram.

The TDR of a portal-vein point
P
is defined as

(1)

where the denominator and enumerator are illustrated in
Figure 3(c)
.
The TDR reflects how

much the portal-vein point feed the tumor and is also affected by the tumor.

Given a tumor location, let us compute an ideal resected region by using the TDR, where the

ideal resected region means a minimum region including all subregions perfused by tumor-

FIGURE 4
Computing ideal resected region.

Step 1
: Among the portal-vein points with TDR larger than 0 on a branch, select the point

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