# Equivalent Square (Open & Blocked Fields)

Determination of the equivalent square fields for rectangular and shielded fields is of great importance in radiotherapy centres and treatment planning software. This is accomplished using standard tables and empirical formulas. Tables are published by different agencies such as ICRU (International Commission on Radiation Units and measurements), which are based on experimental data; but there exist mathematical formulas that yield the equivalent square field of an irregular rectangular field which are used extensively in computation techniques for dose determination. These processes lead to some complicated and time-consuming formulas for which the current study was designed. In this work, considering the portion of scattered radiation in absorbed dose at a point of measurement, a numerical formula was obtained based on which a simple formula was developed to calculate equivalent square field. Using polar coordinate and inverse square law will lead to a simple formula for calculation of equivalent field. The presented method is an analytical approach based on which one can estimate the equivalent square field of a rectangular field and may be used for a shielded field or an off-axis point. Besides, one can calculate equivalent field of rectangular field with the concept of decreased scatter radiation with inverse square law with a good approximation.

Semi empirical methods have been developed to relate central axis depth dose data for square, rectangular, circular, and irregularly shaped fields. Although general methods (based on Clarkson's principle to be discussed later in this chapter) are available, simpler methods have been developed specifically for interrelating square, rectangular, and circular field data.

Day and others have shown that, for central axis depth dose distribution, a rectangular field may be approximated by an equivalent square or by an equivalent circle. Data for equivalent squares, taken from the Hospital Physicists' Association,

A simple rule-of-thumb method has been developed by Sterling et al. for equating rectangular and square fields. According to this rule, a rectangular field is equivalent to a square field if they have the same area/perimeter (A/P).

The following formulas are useful for quick calculation of the equivalent field parameters.

For rectangular fields: Where ais the field width and b is the field length.

For square fields a=b then,

A/P = a2/4a

= a/4

Where a is the side of the square.

For Circular Fields:

Although the concept of A/P is not based on sound physical principles, it is widely used in clinical practice and has been extended as a field parameter to apply to other quantities such as backscatter factors, tissue-air ratios, and even beam output in air or in phantom. The reader may, however, be cautioned against an indiscriminate use of A/P. For example, the A/P parameter, as such, does not apply to circular or irregularly shaped fields, although radii of equivalent circles may be obtained by the relationship. Questions:

1. Find the equivalent square fields size for width of 10 and length 15?

a) 12

b) 12.5

c) 13

d) 14.5

1. a) 12

References:

1. The physics of radiation therapy by F. M. Khan

2. A simple calculation method for determination of equivalent square field Seyed Ali Shafiei, Hadi Hasanzadeh, and Seyed Ahmad Shafiei StrengthsFinder 2.0 