Extracting the gradient component of the gamma index using the Lie derivative method

Area of Science:

• Medical Physics
• Radiotherapy Dosimetry
• Image Analysis

Background:

• The gamma index (γ) is widely used for dose evaluation in radiotherapy but has limitations in assessing dose-gradient regions.
• These limitations are particularly problematic in stereotactic radiotherapy (SRT), hindering accurate error detection.

Purpose of the Study:

• To develop a novel evaluation method combined with the gamma index (γ) to identify clinically significant dose-gradient errors.
• To address the limitations of the standard gamma index in evaluating dose deviations in critical regions.

Main Methods:

• Utilized Lie derivatives from differential geometry to define L, S, and U metrics for evaluating dose distribution deviations.
• Combined these metrics with the gamma index (γ) as γL, γS, and γU, and introduced a threshold value σ.
• Validated the method in ideal SRT and clinical cases using radiochromic films, comparing with MGI, χ, and SSIM.

Main Results:

• The proposed γL, γS, and γU metrics, particularly γL with threshold σ, effectively identified dose-gradient error regions missed by standard γ analysis.
• The S-metric indicated robust deviation and dose-gradient influence, while also measuring similarity.
• Traditional metrics (MGI, χ, SSIM) failed to detect clinically relevant regions.

Conclusions:

• The Lie derivative method offers a novel perspective for identifying gradient-induced errors in radiotherapy dose evaluations.
• This approach enhances the clinical significance and accuracy of gamma index (γ) analysis, especially in complex scenarios like SRT.
• The method shows promise for improved quality assurance in radiation therapy.