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SU‐FF‐J‐22: An Image Based Statistical Shape Model and Its Application in Radiotherapy Margin Design
Author(s) -
Zhou S,
Yan H,
Wang Z,
Yoo S,
Das S,
Yin F,
Anscher M,
Marks L
Publication year - 2006
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.2240801
Subject(s) - margin (machine learning) , computer science , probability distribution , gaussian , medical imaging , point (geometry) , artificial intelligence , mathematics , statistics , physics , geometry , machine learning , quantum mechanics
Purpose: A novel imaging based model is proposed to describe the stochastic nature of the shape and location of a volume of interest (VOI). Based on the VOIs in sequential patient images, the model can predict the probability that a specific point will belong to the VOI. An application of the model is in customized radiotherapy margin design. Methods: N sequential patient images taken on‐board or online contain all VOI information immediately before or during the treatment sessions. Typically these images are already registered in the radiation device coordinates, a signed distance transform (SDT) will be applied to the VOI boundary in each image to generate a distance map d ( r⃗ ). The sign of d ( r⃗ ) indicates whether the point r⃗ is inside (negative) or outside (positive) the VOI. The VOI shape/location random variation around its mean will propagate through SDT into d ( r⃗ ). It is reasonable to assume that d ( r⃗ ) is Gaussian and its measured values are independent from each other. Consequently, t =μ ( r ⃗ )− d ̄ ( r ⃗ ) s ( r ⃗ )obeys Student's t‐distribution, with N − 1 degrees of freedom. Here d̄ ( r⃗ ) μ( r⃗ ), and s ( r⃗ ) are the sample mean, the expected mean, and sample variance of d ( r⃗ ). By definition of level‐set theory, before any more measurement, a point belongs to the expected VOI if and only if μ( r⃗ ) ⩽ 0. The probability that a point x⃗ belongs to the VOI can be estimated by Pr VOI( r ⃗ )= Pr ( μ ( r ⃗ ) ⩽ 0 ) = Pr ( t ⩽ − d ( r ⃗ ) / s ( r ⃗ ) ) . When the VOI is clinical tumor volume (CTV) we can use Pr VOI( r ⃗ ) to design our radiation field margin after a cut‐off coverage probability p is specified. All points in space with Pr VOI( r ⃗ )⩾ p are included as part of the expected CTV. Thus we effectively generated a planning tumor volume (PTV). Conclusion: The model has been tested on real clinical cases. The results show that it is robust and easy to use. The customized probability/imaging based non‐uniform margin obtained through this model should be extremely useful in image guided radiation treatment.