Gamma Analysis

Reference

Low DA, Harms WB, Mutic S, Purdy JA. "A technique for the quantitative evaluation of dose distributions." Med. Phys. 1998;25(5):656-61.

Theory

The gamma index at each reference point is:

\[\gamma(\mathbf{r}_r) = \min_{\mathbf{r}_e} \sqrt{ \frac{|\mathbf{r}_r - \mathbf{r}_e|^2}{\Delta d_M^2} + \frac{(D_r - D_e)^2}{\Delta D^2} }\]

Where \(\Delta d_M\) is the distance-to-agreement criterion (mm) and \(\Delta D\) is the dose-difference criterion.

Points with \(\gamma \leq 1\) pass the criteria.

Usage

from chromadose.analysis import gamma_2d

result = gamma_2d(
    reference=tps_dose,
    evaluated=film_dose,
    dose_criteria=3.0,           # 3%
    distance_criteria_mm=3.0,    # 3mm
    pixel_size_mm=0.353,         # e.g., 72 DPI film
    dose_threshold_pct=10.0,     # exclude < 10% of max
    dose_criteria_is_global=True,
)

print(f"Pass rate: {result.pass_rate * 100:.1f}%")
print(f"Points: {result.points_passed}/{result.points_evaluated}")

Parameters

Parameter	Default	Description
dose_criteria	3.0	Dose difference criterion (%)
distance_criteria_mm	3.0	DTA criterion (mm)
pixel_size_mm	1.0	Pixel size in mm
dose_threshold_pct	10.0	Exclude below this % of max
dose_criteria_is_global	True	Global (max dose) or local (per-point)
max_gamma	2.0	Cap gamma values

Output

GammaResult contains:

• gamma_map — 2D gamma index array (NaN below threshold)
• pass_rate — fraction of points with \(\gamma \leq 1\)
• criteria — human-readable string, e.g. "3%/3mm global"
• points_evaluated, points_passed — counts