Gamma Index: Radiotherapy Dose Agreement Metric
The gamma index (γ) is a dimensionless quantity that evaluates whether measured dose distributions agree with planned ones within simultaneous dose-difference and distance-to-agreement (DTA) criteria. A point passes when γ ≤ 1, meaning the combined normalized discrepancy resides inside an ellipse defined by tolerances such as 3 percent/2 mm.
Clinical physicists summarise QA by reporting the percentage of evaluated points with γ ≤ 1. Regulatory bodies increasingly expect plans to meet thresholds like “95 percent of points pass 3 percent/2 mm,” so accurate calculation and documentation are essential.
Definition and Mathematics
For each evaluated location, gamma minimises the combined metric
γ = min { sqrt[(Δd/DTA)2 + (ΔD/DD)2] }
where Δd is the spatial separation between the measurement point and any reference point, ΔD is the dose difference, DTA is the allowed distance tolerance, and DD is the allowed dose-difference tolerance. Search algorithms (brute-force, k-d trees, or interpolated grids) evaluate nearby voxels until the minimum is identified.
Historical Background
Low, Harms, and Mutic introduced the gamma index in 1998 to resolve debates between dose-difference and DTA metrics in IMRT QA. Adoption accelerated as multi-leaf collimators enabled complex fluence maps that challenged film-only verification methods. Vendors now embed gamma evaluations into 2D array detectors, EPID-based solutions, and log-file analyses.
Recent guidelines from AAPM, ESTRO, and IAEA recommend reporting both local and global dose normalization to avoid overly permissive results in high-dose regions. These recommendations reinforce the need to track actual Gy values, linking gamma reports to SI dose definitions.
Concepts and Variants
Global vs Local Normalisation
Global gamma divides ΔD by a single reference value (often the maximum plan dose), while local gamma scales ΔD by the dose at each evaluated point. Local normalisation penalises small absolute errors in low-dose regions, improving sensitivity to leakage and shielding.
Thresholding and Analysis Volume
Analysts typically ignore points below 10 percent of the prescription to avoid noisy low-dose areas. However, emerging protocols for stereotactic treatments tighten thresholds to capture peripheral dose falloff, aligning gamma checks with DVH requirements.
3D and Time-Resolved Gamma
Log-file reconstructions and four-dimensional dose calculations extend gamma into volumetric and time-resolved domains, enabling motion-inclusive QA. These variants demand robust interpolation and uncertainty analysis, often leveraging confidence-interval planning to communicate reliability.
Applications
Patient-Specific QA
Before delivering IMRT, VMAT, or proton plans, physicists compare measured detector arrays against the treatment planning system. Gamma pass rates become a gating criterion for releasing plans to treatment.
Commissioning and Change Management
New beam models, MLC calibrations, or algorithm versions must demonstrate equivalent gamma performance compared with baselines. Z-scores of pass fractions help flag drifts after hardware upgrades.
In Vivo and Log-File Monitoring
EPID images or linac log files can reconstruct actual doses per fraction. Online gamma checks identify systematic trends before they trigger clinical deviations, complementing biological metrics like equivalent uniform dose.
Importance
Gamma indexing remains the lingua franca of external-beam QA because it unifies spatial and dosimetric tolerances in one interpretable number. While complementary tools such as DVH-based comparisons and machine learning classifiers are emerging, regulators still expect well-documented gamma statistics.
Communicating gamma results in relatable units—via outreach tools like the banana dose converter—helps clinicians explain QA margins to stakeholders while maintaining rigorous SI traceability.