RTH-10

Tissue–phantom ratio

TPR(d,dref) = D(d)/D(dref) at fixed SAD. TPR20,10 indexes beam quality.

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Beam dataIAEA TRS-398TPR20,10

Governing equation

\mathrm{TPR}(d,d_{\mathrm{ref}})=e^{-\mu(d-d_{\mathrm{ref}})}

$d \in \left[1, 30\right]$

where

\mu: Attenuation μ (1/cm)
d: Depth (cm)
d_{ref}: Reference depth (cm)
TPR: Tissue–phantom ratio (—)

The figure, part by part

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①

Governing law — red

\mathrm{TPR}(d,d_{\mathrm{ref}})=e^{-\mu(d-d_{\mathrm{ref}})}

$d \in \left[1, 30\right]$

$d = 1$ $TPR = 1.568$

Along the curve

②

Domain of the variable — blue

d_{\min} = 1,\quad d_{\max} = 30

$d \in \left[1, 30\right]$

$d = 1$ $d = 1$

Along the curve

③

Response curve — green

\mathrm{TPR}(d,d_{\mathrm{ref}})=e^{-\mu(d-d_{\mathrm{ref}})}

$d \in \left[1, 30\right]$

$d = 1$ $TPR = 1.568$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}TPR}{\mathrm{d}d}

$d \in \left[1, 30\right]$

$d = 1.182$ $TPR^{\prime} = -0.078$

Along the curve

Lecture brief

Historical brief

The linear-quadratic model, BED, tissue-maximum ratio and Clarkson scatter turned radiotherapy into fraction arithmetic. MU calculation on these sheets is that clinical closed form. This sheet (RTH-10 — Tissue–phantom ratio) is the form associated with IAEA TRS-398 · TPR20,10. Working symbols: $\mu$ , $d$ , $d_{ref}$ $\rightarrow$ $TPR$ . Unlike PDD there is no inverse-square change of SAD. TPR20,10 ≈ 0.67–0.80 for clinical x-rays.

Purpose

Purpose: compute

TPR

from

\mu

d

d_{ref}

in Radiotherapy via

\mathrm{TPR}(d,d_{\mathrm{ref}})=e^{-\mu(d-d_{\mathrm{ref}})}

TPR(d,dref) = D(d)/D(dref) at fixed SAD. TPR20,10 indexes beam quality. Use it when a real radiotherapy question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\mu = 0.050\,\mathrm{1/cm}

d = 20.000\,\mathrm{cm}

d_{ref} = 10.000\,\mathrm{cm}

, the governing relation

\mathrm{TPR}(d,d_{\mathrm{ref}})=e^{-\mu(d-d_{\mathrm{ref}})}

yields

TPR = 0.6065\,\mathrm{—}

. Two phantom depths at isocentre. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Attenuation μ \mu0.05 1/cmDepth d20 cmReference depth d_{ref}10 cm

Outputs

Tissue–phantom ratio TPR0.6065 —

Reading speed

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Narration of this film

Two phantom depths at isocentre.

Unlike PDD there is no inverse-square change of SAD. TPR20,10 ≈ 0.67–0.80 for clinical x-rays.

Reading speed

Watch on YouTube