%0 Journal Article
%T A Radiotherapy Treatment Margin Formula When Systematic Positioning Errors are Relatively Small Compared to Random Positioning Errors: A First-Order Approximation
%A Kiyoshi Yoda
%J International Journal of Medical Physics,Clinical Engineering and Radiation Oncology
%P 193-196
%@ 2168-5444
%D 2017
%I Scientific Research Publishing
%R 10.4236/ijmpcero.2017.62017
%X A
radiotherapy treatment margin formula has been analytically derived when a
standard deviation (SD) of systematic positioning errors Ʃ is
relatively small compared to an SD of random positioning errors σ.
The margin formula for 0 </span><span style=\"font-family:Verdana;\">¡Ü</span><span style=\"font-family:Verdana;\"> &amp;#425; </span><span style=\"font-family:Verdana;\">¡Ü</span><span style=\"font-family:Verdana;\"> &amp;sigma; was calculated by linearly interpolating two boundaries at
&amp;#425; = 0 and &amp;#425; = &amp;sigma;, assuming that the van Herk margin
approximation of &lt;i&gt;k&lt;sub&gt;1&lt;/sub&gt;&lt;/i&gt;&amp;#425; +
&lt;i&gt;k&lt;sub&gt;2&lt;/sub&gt;&lt;/i&gt;&amp;sigma; is valid at &amp;#425;
= &amp;sigma;. It was shown that a margin formula for 0 </span><span style=\"font-family:Verdana;\">¡Ü</span><span style=\"font-family:Verdana;\"> &amp;#425; </span><span style=\"font-family:Verdana;\">¡Ü</span><span style=\"font-family:Verdana;\"> &amp;sigma; may be approximated
by &lt;i&gt;k&lt;sub&gt;1&lt;/sub&gt;&lt;/i&gt;&amp;sigma; +
&lt;i&gt;k&lt;sub&gt;2&lt;/sub&gt;&lt;/i&gt;&amp;#425;, leading to a more
general form of &lt;i&gt;k&lt;sub&gt;1&lt;/sub&gt;&lt;/i&gt;
max(&amp;#425;,&amp;sigma;) + &lt;i&gt;k&lt;sub&gt;2&lt;/sub&gt;&lt;/i&gt;
min(&amp;#425;,&amp;sigma;) which is a piecewise linear approximation for any
values of &amp;#425; and &amp;sigma;.
%K Treatment Margin
%K Systematic Positioning Errors
%K Random Positioning Errors
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=76361