This tool is a specialized medical physics calculator used for quality assurance in radiation therapy. Its primary function is to compare two radiation dose distributions, typically the treatment plan created by a computer and the actual dose measured after being delivered by a treatment machine. You use the calculator to perform a Gamma Index analysis, which is a method that checks for both dose difference and spatial difference at the same time. The final result tells medical physicists whether the delivered radiation dose is sufficiently close to the intended plan, ensuring that the treatment is both safe and effective for the patient. It combines complex data into a simple pass or fail percentage, making it a critical tool for verifying the accuracy of cancer treatments.
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1. User-Defined Acceptance Criteria
Before any calculation, two criteria must be defined. These are the standards against which the comparison is made.
Dose Difference Criterion (ΔD): The maximum acceptable difference in dose, usually expressed as a percentage of the maximum or a prescribed dose.
Distance-to-Agreement Criterion (Δd): The maximum acceptable physical distance between two points, usually in millimeters.
2. The Gamma Function Formula
This formula calculates a composite “distance” value between a single point in a reference distribution and a single point in an evaluated distribution. It combines the spatial distance and the dose difference into one number.
Formula
Gamma Value = Square Root of [ (Spatial Distance^2 / Distance-to-Agreement Criterion^2) + (Dose Difference^2 / Dose Difference Criterion^2) ]
Explanation of Variables
Spatial Distance: The actual geometric distance between the reference point and the evaluated point.
Dose Difference: The difference in dose values between the reference point and the evaluated point.
Distance-to-Agreement Criterion (Δd): The user-defined value from step 1.
Dose Difference Criterion (ΔD): The user-defined value from step 1.
3. The Gamma Index Calculation for a Single Point
The Gamma Index for a specific point in the reference distribution is not just a single calculation. It is the minimum possible Gamma Value found by comparing that reference point to every point in the evaluated distribution.
Formula
Gamma Index for a Reference Point = Minimum { All Gamma Values calculated for this reference point }
Workflow
Select one point in the reference distribution.
Use the Gamma Function Formula to calculate a Gamma Value between that reference point and every single point in the evaluated distribution.
The smallest value from that entire set of calculations is the “Gamma Index” for that one reference point.
4. The Pass/Fail Condition
This is the test that determines if a reference point meets the criteria.
Condition
If the Gamma Index for a Reference Point is less than or equal to 1, the point passes.
If the Gamma Index for a Reference Point is greater than 1, the point fails.
5. Overall Gamma Passing Rate Calculation
The final result of a Gamma Index analysis is the percentage of points that passed the test.
Formula
Gamma Passing Rate = (Total Number of Points that Passed / Total Number of Points Evaluated) * 100
Common Clinical Gamma Index Criteria
This table shows some of the standard acceptance criteria used in clinical practice for radiation therapy quality assurance. The choice of criteria often depends on the complexity of the treatment technique and the specific area being treated.
| Criteria (Dose/Distance) | Common Clinical Application | Stringency Level |
| 3% / 3mm | Standard for IMRT (Intensity-Modulated Radiation Therapy) | Standard |
| 2% / 2mm | High-precision treatments like SRS/SBRT (Stereotactic Radiosurgery) | High |
| 5% / 3mm | Less critical regions or older treatment techniques | Lenient |
| 3% / 2mm | High-gradient regions, checking spatial accuracy | High (Spatial) |
| 2% / 3mm | High-dose, low-gradient regions, checking dose accuracy | High (Dose) |
Example
Let’s walk through a simplified calculation for a single reference point to see how the Gamma Index is determined.
Scenario and Criteria:
- We will use the common clinical criteria:
- Dose Difference Criterion (ΔD) = 3% of the maximum dose. Let’s say the max dose is 200 cGy, so ΔD = 6 cGy.
- Distance-to-Agreement Criterion (Δd) = 3 mm.
- Our Reference Point (from the treatment plan) has a dose of 150 cGy.
We measure two nearby points in the evaluated (delivered) dose distribution:
- Evaluated Point A: Is 2 mm away and has a dose of 152 cGy.
- Evaluated Point B: Is 4 mm away and has a dose of 148 cGy.
Calculation Steps:
- Calculate the Gamma Value for the Reference Point vs. Evaluated Point A:
- Spatial Distance = 2 mm
- Dose Difference = |152 cGy – 150 cGy| = 2 cGy
- Gamma Value (A) = Sqrt[ (2^2 / 3^2) + (2^2 / 6^2) ]
- Gamma Value (A) = Sqrt[ (4 / 9) + (4 / 36) ] = Sqrt[ 0.444 + 0.111 ] = Sqrt[0.555] = 0.745
- Calculate the Gamma Value for the Reference Point vs. Evaluated Point B:
- Spatial Distance = 4 mm
- Dose Difference = |148 cGy – 150 cGy| = 2 cGy
- Gamma Value (B) = Sqrt[ (4^2 / 3^2) + (2^2 / 6^2) ]
- Gamma Value (B) = Sqrt[ (16 / 9) + (4 / 36) ] = Sqrt[ 1.778 + 0.111 ] = Sqrt[1.889] = 1.374
- Determine the Gamma Index for the Reference Point:
- The calculator compares all gamma values. The minimum value is 0.745.
- Therefore, the Gamma Index for our reference point is 0.745.
- Apply the Pass/Fail Condition:
- Since 0.745 is less than 1, this reference point passes the test.
Most Common FAQs
A Gamma Index of 1 represents the exact boundary of your chosen acceptance criteria. If the calculation results in a value of 1, it means the measured dose point is exactly on the edge of what is considered acceptable, either in terms of its dose difference, its distance from the planned point, or a combination of both. A value less than 1 means the point is well within the acceptable limits. Conversely, a value greater than 1 means the point has failed to meet the combined criteria for agreement.
Radiation treatment plans contain areas with different characteristics. Some areas have a uniform, high dose, while others have a high dose gradient, meaning the dose level changes very quickly over a short distance. The dose difference criterion is most important for checking the accuracy in the uniform dose regions. The distance-to-agreement criterion is essential for checking the spatial accuracy in the high-gradient regions, where a small positioning error can lead to a very large dose difference. Using both ensures a comprehensive evaluation of the entire treatment area.
The difference lies in how the dose difference percentage is calculated. In a global gamma analysis, the dose difference is always calculated as a percentage of the single highest dose value found anywhere in the entire treatment plan. In a local gamma analysis, the dose difference is calculated as a percentage of the local dose at the specific point being evaluated. This makes local gamma a much stricter test, especially in low-dose areas, because a small absolute dose error can become a very large percentage error. Global gamma is more commonly used in clinical practice as it focuses on accuracy in the high-dose target regions.