# SU‐FF‐J‐22: An Image Based Statistical Shape Model and Its Application in Radiotherapy Margin Design

Conference Paper

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, [formula omitted] 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 [formula omitted]. When the VOI is clinical tumor volume (CTV) we can use [formula omitted] to design our radiation field margin after a cut‐off coverage probability p is specified. All points in space with [formula omitted] 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. © 2006, American Association of Physicists in Medicine. All rights reserved.

### Full Text

### Duke Authors

### Cited Authors

- Zhou, S; Yan, H; Wang, Z; Yoo, S; Das, S; Yin, F; Anscher, M; Marks, L

### Published Date

- January 1, 2006

### Published In

### Volume / Issue

- 33 / 6

### Start / End Page

- 2025 -

### International Standard Serial Number (ISSN)

- 0094-2405

### Digital Object Identifier (DOI)

- 10.1118/1.2240801

### Citation Source

- Scopus