01 Therapy

Co-60 source decay

Output correction for T½ = 5.271 y (~1.1% per month).

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Simulation

Co-60 source decay — Change the numbers; the scene follows.

Where it works

Linear accelerator

Treatment head

Inside the treatment head: monitor chambers measure output; wedges and leakage live here.

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Formula

\dot{D}(t)=\dot{D}_0\,e^{-(\ln 2)\,t/5.271}

Variables

Ḋ₀ · Initial outputcGy/mint · Elapsed timey

Results

Ḋ
Current output
131.5166cGy/min
DF
Decay factor
0.8768
per month
Monthly loss
1.09%

Curve

Explanation

\dot{D}(t)=\dot{D}_0\,e^{-(\ln 2)\,t/5.271}

What it means

Co-60 decays with T½ = 5.271 years, about 1.09% output loss per month. Source-output tables in cobalt units must be decay-corrected from the calibration date. Two photons (1.17 and 1.33 MeV, mean 1.25 MeV) accompany each decay. This is a working relation in Radiotherapy.

Where it is used

Clinically it sits on the Linear accelerator — Treatment head. Inside the treatment head: monitor chambers measure output; wedges and leakage live here. Radiotherapy equations sit at the console and in the bunker: output, depth dose, equivalent square, and the monitor units that treat the patient. Hand-calc them beside the TPS, never instead of a commissioned plan.

Linear accelerator · Open this machine

How to use it

Enter the calibrated output and elapsed years (decimals allowed: 3 months = 0.25 y). Use the monthly-loss figure to sanity-check a hand-updated chart. Change one input and watch the curve and the simulation follow.

Symbols

Ḋ₀Initial output150 cGy/min
tElapsed time1 y

Worked example

A typical case from the default values: Ḋ₀ = 150 cGy/min (Initial output); t = 1 y (Elapsed time). Substituting into the relation gives Ḋ = 131.5166 cGy/min; DF = 0.8768; per month = 1.09 %. These are teaching numbers — align them with your machine.

Typical values give

Ḋ = 131.5166cGy/min
DF = 0.8768
per month = 1.09%

Where it comes from

The displayed formula is the working relation. Output correction for T½ = 5.271 y (~1.1% per month). Usual reference: Khan / NNDC. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Khan / NNDC

Assumptions & limits

Pure exponential of Co-60; no Co-59 contamination or timer-error. Air-kerma rate constants and scatter in the head are not included.

Pitfalls

Never mix PDD from one SSD with TMR from another without converting. Field size at the surface is not the size at isocentre. A hand MU is a check, not a treatment. Pure exponential of Co-60; no Co-59 contamination or timer-error. Air-kerma rate constants and scatter in the head are not included.

Keep this

Name the SSD, energy, and field size with every PDD or TMR you quote. Pure exponential of Co-60; no Co-59 contamination or timer-error. Air-kerma rate constants and scatter in the head are not included.

In this specialty

Radiotherapy