Modeling and Prediction of Abdominal Tumor Motion

Haobing Wang

Department of Computer Science

May 9th, 2003

Project Outline Topic and Goal Background and Motivation Methods Experiments Analysis Future Work

Topic and Goal Facilitate real-time tracking of the tumor

motion during radiotherapy and allow for for precise delivery of radiation dose to mobile tumors.

Find methods to model and predict abdominal tumor motion.

Background and Motivation Tumor position is modeled by tracking

surgically implanted clips surrounding the tumor.

The radiation beam has mechanical latency.

Template Matching Using DHMM DHMM: Deformable Hidden Markov

Model Given a pattern template, recognizing the

pattern in a new time series, allowing flexible deformation of time.

Template Matching Using DHMM Generalize the standard constant model and

allow each state to generate data in the form of a regression curve.

K-state segmental HMM each state of which corresponds to one segment in the piecewise linear representation of the template.

Template Matching Using DHMM Use a sinusoid as template

The DHMM automatically find the period whose shape is similar to a sinusoid. Then the sequence is found is used as the prediction of the next breathing period.

Experiments of DHMM Method

0 100 200 300 400 500

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Experiments of DHMM MethodPrediction of 100 frames

Analysis of DHMM Method

Average error and error variance is greater than 1 millimeter.

Although the computation time for each clip is around 5 minutes, it’s still cannot be done on-line.

Prediction by Curve Fitting A least square method to fit the data points

to a third order polynomial function: f(x) = b0 + b1x + b2x

2 + b3x3 . The set of

coefficients [bn] can be found by

minimizing the sum:

2

1

33

2210 )]([

N

kkkkk xbxbxbby

Examples of Curve Fitting

Prediction by Curve Fitting Suppose S is the shape function which

describes the trajectory of a single breathing period, and (t) is a weighing function. I use as a decay factor. So S(t) can be computed by:

Sk = f(t) + (1-tSk-1

Experiments of Curve FittingBob (clip 2)

Experiments of Curve FittingGary (clip 0)

Experiments of Curve FittingResults of predicting approximately 550 frames on average

Experiments of Curve FittingResults of predicting 100 frames

Comparison of Four MethodsPredicting 100 frames

Analysis of Curve Fitting

Gives better result. Average error is the best among the four methods, and error variation is the second to the best.

Computation is fast. Can be done on-line.

Future Work

Adjustment of duration of each breathing period.

Improvement of the performance of the clip tracker and patients’ breathing pattern.

Future Work