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Conceptual Volume Combination Expression Attribute

Tag (3010,000C) Conditionally Required (1C) ConceptualVolumeCombinationExpression 1 Unlimited Text (UT)

Symbolic expression specifying the combination of Conceptual Volumes as a text string consisting of Conceptual Volume Constituent Index (3010,000D) values, combination operators and parentheses.

Required if Conceptual Volume Combination Flag (3010,000E) equals YES.

See Section 10.34.1.1.

Section 10.34.1.1

10.34.1.1 Conceptual Volume Combination Expression

For Conceptual Volumes specified as a combination of other Conceptual Volumes, the combination logic is specified by the text string value of the Conceptual Volume Combination Expression (3010,000C).

A nested list notation is used to apply geometric operators to a set of Conceptual Volumes.

The first element of the list shall be one of the following geometric operators:

UNION

geometric union of two or more arguments

INTERSECTION

geometric intersection of two or more arguments

NEGATION

geometric inverse of a single argument

SUBTRACTION

geometric subtraction of second argument from the first

XOR

geometric exclusive disjunction of two arguments

Note

The result of a NEGATION operation is well-defined only if used as an operand to an INTERSECTION. NEGATION without context to an INTERSECTION results in an infinite Volume.

Subsequent elements shall specify arguments of the geometric operator. An argument is either a Conceptual Volume Constituent Index (3010,000D) value (i.e., positive integer) or a parenthesized list of operations.

The grammar for the Conceptual Volume Combination Expression (<sexpr>) is shown below in BNF (Backus Naur Form) :

```<sexpr>         :: <cv> | <list>
<cv>            :: 1 | 2 | 3 | …
<list>          :: ( <op1><sp><sexpr> ) |
( <op2><sp><sexpr><sp><sexpr> ) |
( <op3><sp><args> )
<args>          :: <sexpr><sp><sexpr> | <args><sp><sexpr>
<op1>           :: NEGATION
<op2>           :: SUBTRACTION | XOR
<op3>           :: UNION | INTERSECTION
<sp>            :: 0x20
```

Examples:

1. Union of paired organs 1 and 2 (disjoint)

Figure 10.34.1.1-1. Conceptual Volume Example of Union of Disjoint Volumes

Conceptual Volume Combination Expression (3010,000C):

(UNION 1 2)

Items in Conceptual Volume Constituent Sequence (3010,0008):

Table 10.34.1.1-1. Conceptual Volume Example of Union of Disjoint Volumes

Conceptual Volume Constituent Index (3010,000D)

Conceptual Volume

1

Right Lung

2

Left Lung

2. Union of paired organs 1 and 2 (non-disjoint)

Figure 10.34.1.1-2. Conceptual Volume Example of Union of Non-disjoint Volumes

Conceptual Volume Combination Expression (3010,000C):

(UNION 1 2)

Items in Conceptual Volume Constituent Sequence (3010,0008) :

Table 10.34.1.1-2. Conceptual Volume Example of Union of non-disjoint Volumes

Conceptual Volume Constituent Index (3010,000D)

Conceptual Volume

1

Spinal Cord PRV

2

Left Lung

3. Union of two organs 1 and 2 with excluded volume 3 using NEGATION

Figure 10.34.1.1-3. Conceptual Volume Example of Intersection and Negation

Conceptual Volume Combination Expression (3010,000C):

(INTERSECTION (UNION 1 2) (NEGATION 3) )

Items in Conceptual Volume Constituent Sequence (3010,0008):

Table 10.34.1.1-3. Conceptual Volume Example of Intersection and Negation

Conceptual Volume Constituent Index (3010,000D)

Conceptual Volume

1

Heart

2

Left Lung

3

CTV

4. Union of paired organs 1 and 2, with exclusion of multiple volumes 3, 4 and 5

Figure 10.34.1.1-4. Conceptual Volume Example of Intersection and Union

Conceptual Volume Combination Expression (3010,000C):

(INTERSECTION (UNION 1 2) (NEGATION (UNION 3 4 5) ))

Note

This combination can be expressed alternatively as:

(SUBTRACTION (UNION 1 2) (UNION 3 4 5) )

Items in Conceptual Volume Constituent Sequence (3010,0008):

Table 10.34.1.1-4. Conceptual Volume Example of Intersection and Union

Conceptual Volume Constituent Index (3010,000D)

Conceptual Volume

1

R Lung

2

L Lung

3

Node 1

4

Node 2

5

CTV

5. Intersection of overlapping volumes 1 and 2

Figure 10.34.1.1-5. Conceptual Volume Example of Intersection of Non-disjunct Volumes

Conceptual Volume Combination Expression (3010,000C):

(INTERSECTION 1 2)

Items in Conceptual Volume Constituent Sequence (3010,0008):

Table 10.34.1.1-5. Conceptual Volume Example of Intersection of non-disjunct Volumes

Conceptual Volume Constituent Index (3010,000D)

Conceptual Volume

1

Rectum

2

Prostate PTV

6. Intersection of disjoint volumes 1 and 2

Figure 10.34.1.1-6. Conceptual Volume Example of Intersection of Non-disjunct Volumes

Conceptual Volume Combination Expression (3010,000C):

(INTERSECTION 1 2)

Items in Conceptual Volume Constituent Sequence (3010,0008):

Table 10.34.1.1-6. Conceptual Volume Example of Intersection of disjunct Volumes

Conceptual Volume Constituent Index (3010,000D)

Conceptual Volume

1