The random walk model of intrafraction movement

Area of Science:

• Medical Physics
• Radiation Oncology
• Stochastic Processes

Background:

• Intrafraction movement in radiation therapy can significantly impact treatment accuracy.
• Current methods for accounting for this movement, such as planning target volume (PTV) margins, may be suboptimal.
• Understanding movement as a stochastic process is crucial for refining these margins.

Purpose of the Study:

• To model intrafraction movement as a stochastic process driven by random external forces.
• To evaluate the impact of a proposed three-dimensional random walk model on optimal PTV margins.
• To provide a quantitatively correct explanation for experimental findings in radiation therapy.

Main Methods:

• Developed a three-dimensional random walk model for intrafraction movement.
• Calculated properties of the random walk, including fraction-average population density distributions for displacements.
• Integrated these distributions into established optimal margin recipes.

Main Results:

• The random walk model suggests PTV margins approximately 30% smaller than those derived from end-of-fraction Gaussian fits.
• Identified key characteristics of random walks in clinical data, such as displacement standard deviation scaling with the square root of time.
• Accounting for non-Gaussian corrections from the random walk model reduced least squares errors in experimental comparisons by about 50%.

Conclusions:

• A random walk model provides a more accurate and efficient approach to understanding and quantifying intrafraction movement.
• This model leads to reduced PTV margins, potentially improving treatment precision and reducing dose to healthy tissues.
• The findings support the use of stochastic process modeling for optimizing radiation therapy margins.