Homogeneity Metrics¶

Homogeneity metrics characterize uniformity within a target or dose falloff around the prescription isodose. The four homogeneity.compute_* functions are reference-free. Their named distances are reference-based.

Classification¶

Metric	API	Reference use	Ideal or direction
Homogeneity index	`homogeneity.compute_homogeneity_index`	Reference-free	Lower
Gradient index	`homogeneity.compute_gradient_index`	Reference-free	Lower
Dose coefficient of variation	`homogeneity.compute_dose_homogeneity`	Reference-free	Lower
Uniformity index	`homogeneity.compute_uniformity_index`	Reference-free	Higher
Homogeneity index distance	`compare_homogeneity_index`	Reference-based	Lower
Paddick gradient index distance	`compare_paddick_gradient_index`	Reference-based	Lower

Homogeneity index¶

For a target DVH, \(D_x\) is the dose received by at least \(x\%\) of the target volume. The implemented homogeneity index is:

\[ \mathrm{HI}=\frac{D_2-D_{98}}{D_{50}}. \]

It is dimensionless; zero represents a perfectly uniform target dose.

from dosemetrics.metrics import homogeneity

hi = homogeneity.compute_homogeneity_index(dose, ptv)

Homogeneity-index distance¶

Reference-based · compare_homogeneity_index · dimensionless · lower is better.

Homogeneity-index distance The same \(D_2\), \(D_{50}\), and \(D_{98}\) definition is evaluated for each target DVH.

\[ \mathrm{HID} =\left|\mathrm{HI}_{\mathrm{evaluated}} -\mathrm{HI}_{\mathrm{reference}}\right|. \]

from dosemetrics.metrics import compare_homogeneity_index

hid = compare_homogeneity_index(reference, evaluated, ptv_high)

Gradient index¶

The Paddick gradient index is the ratio of the volume receiving at least half the prescription dose to the volume receiving at least the full prescription dose:

\[ \mathrm{GI} =\frac{V_{D_{\mathrm{Rx}}/2}}{V_{D_{\mathrm{Rx}}}}. \]

gi = homogeneity.compute_gradient_index(
    dose, ptv, prescription_dose=70.0
)

The volume ratio is evaluated over the complete dose grid. The target argument is retained for a consistent clinical call signature but does not alter this implementation.

Paddick gradient-index distance¶

Reference-based · compare_paddick_gradient_index · dimensionless · lower is better.

Paddick gradient-index distance Full- and half-prescription isodose volumes are measured independently for each plan.

\[ \mathrm{PGID} =\left|\mathrm{GI}_{\mathrm{evaluated}} -\mathrm{GI}_{\mathrm{reference}}\right|. \]

from dosemetrics.metrics import compare_paddick_gradient_index

pgid = compare_paddick_gradient_index(
    reference,
    evaluated,
    prescription_dose=70.0,
)

Dose coefficient of variation¶

compute_dose_homogeneity reports the coefficient of variation inside the target:

\[ \mathrm{CV}_{D} =\frac{\sigma_D}{\overline{D}}. \]

dose_cv = homogeneity.compute_dose_homogeneity(dose, ptv)

Uniformity index¶

The implemented uniformity index uses the median target dose as its reference:

\[ \mathrm{UI} =1-\frac{D_{\max}-D_{\min}}{D_{\mathrm{median}}}. \]

ui = homogeneity.compute_uniformity_index(dose, ptv)

A perfectly uniform target has a value of 1. Large dose ranges can produce a negative value; the function does not clip the result.

Choosing a homogeneity measure¶

Use compute_homogeneity_index for a percentile-based target summary that is less sensitive to a single extreme voxel.
Use compute_dose_homogeneity for a distribution-wide coefficient of variation.
Use compute_uniformity_index when the full target minimum-to-maximum range is intentional.
Use compute_gradient_index for dose falloff outside the prescription isodose, not for within-target uniformity.