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Differential DVH of “ideal point source”

The values of the differential DVH for an ideal point source can be calculated

directly because the isodose surfaces are spheres with the source as center,

The Natural Dose Volume Histogram (NDVH)

of which the volumes are easily calculated: V = (4/3)

π

r

3

.

For an ideal point

source with D = S / r

2

, V can be written as a function of D:

V = (4/3)

π

S

3/2

D

–3/2

But, if we define

u = D

-3/2

we have:

dV / du = (4/3)

π

S

3/2

dV / du becomes

a constant

propotional to the source strength S

3/2

.