CS-Cal - Fractionation

In cancer radiation therapy, treatment is mostly administered in several fractions.

Instead of giving e.g. a single dose of 30 Gy, the sample gets irradiated 15 times with 2 Gy on 15 days.
This allows normal cells to recover between the fractions, but not the tumor cells, which are less efficient in repairing radiation induced damages.

Sometimes it might be useful to modify the fractionation scheme: instead of 2 Gy fractions, 3 Gy fractions should be used.
Due to the varying radio sensitivity of different tissues / tumors, different fractionation schemes may result in different biological equivalent doses.

To compute the equivalent dose for a modified fractionation scheme the formula may be used:

(1)

With:

D_konv	= original full dose (e.g. 30 Gy)
d_o	= original dose per fraction (e.g. 2 Gy)
d₁	= new required dose per fraction (e.g. 3 Gy)
α / β	= tissue dependent sensitivity factor (e.g. 3 for heart tissue) This α / β -value is the one, derived from the linear-quadratic model fit to clonogenic survival data
D	= resulting biological equivalent dose ( for the example: D=25)

For details about linear-quadratic model and fractionation visit e.g. Wikipedia.

A default set of α / β - values is taken from:

	Emami B, Graham MV, 1997. Lung. In : Principles and Practice of Radiation Oncology, Parez CA & Brady LW, eds, 3rd edition, Philadelphia, pp. 1181-1220. Tolerance of normal tissue to therapeutic radiation. Int. J. Radiat. Oncol. Biol. Phys. 21: 109–122.
	T. S. KEHWAR, Ph. D., D. Sc. & *S. C. SHARMA, M.D. USE OF NORMAL TISSUE TOLERANCE DOSES INTO LINEAR QUADRATIC EQUATION TO ESTIMATE NORMAL TISSUE COMPLICATION PROBABILITY. http://www.rooj.com/Radiation%20Tissue%20Tolerance.htm

	SFJRO - eLQ eLQ - Radiation therapy dose calculator - Linear quadratic model SFRA - Societe Francaise de Radiotherapie Oncoloquiqe http://www.sfjro.fr/ilq/en/

On the Preferences page of the dialog you can freely edit the list of α / β -values according to your needs.

In CS-Cal select Main Menu | Fractionation.
A dialogs shows up:

Enter your input parameter into the respective fields (D_konv, d_o, d₁).
Select a α / β - value from the drop down list, or enter the value directly.
Click the Compute button.
The result is automatically copied to clipboard.

Important:

Take care you know about limitations of the model

CS-Cal is not a certified medical product.
Therefore, it should NOT be used in CLINICAL applications !!!

BED - EQD₂

Similarly you can compute the Biological Efficient Dose (BED).
Jones et al., The role of biologically effective dose (BED) in clinical oncology, Clinical Oncology, 13(2), 2001, 71-81.
It indicates quantitatively the biological effect of radiotherapy treatment, taking into account changes in dose-per-fraction or dose rate, total dose - and in extended model time.

	with:
	D	= total dose [Gy](= n*d)
	d	= dose per fraction [Gy]
	n	= number of fractions
	α/β	= tissue dependent sensitivity factor

Taking into account tumor repopulation:

	with:
	T	= total treatment time [days]
	T_k	= kick off time [days], period between radiation start and onset of tumor repopulation
	T_eff	= effective tumor doubling time [days]
	α	= linear coefficient of Linear quadratic model
		Fowler at al. 21 years of Biologically Effective Dose. Br J Radiol. 2010 July; 83(991): 554 – 568

BED - RBE

In case you want to compute BED for radiation qualities with different Radio Biological Effectiveness (RBE), i.e. different Line Energy Transfer (LET) compared to x-ray, formula (1) may be modified:

	with:
	RBE_max	= respective RBE Jones et al., The role of biologically effective dose (BED) in clinical oncology, Clinical Oncology, 13(2), 2001, 71-81.

EQD₂

EQD₂ = dose in 2 Gy fractions biologically equivalent to dose D given in fractions of size d, in units of Gray.

Use formula (1) from above and set d₁ = new required dose per fraction to a fixed value of = 2 Gy

In CS-Cal select Main Menu | BED - EQD2.

A dialogs shows up:

fill in the respective parameters in any suitable combination.
CS-Cal will compute the resulting others

To use additional parameters to compute BED with high LET radiation or to compensate for tumor repopulation, check the Advanced check box:

Preferences

On the Preferences page of the Fractionation dialog, you may freely edit the list of selectable α / β - values.

In the Edit alpha / beta list text field, the present list is shown.
Edit the list according to your requirements:

edit descriptioon / values
remove lines
add new lines

To recall the original default list, click the Reset to default button.
When done with editing, click the Apply button. Now the edited list is available for new calculations.

NB: Like any other program parameter, the edited list is saved in your MS Windows user profile.
If you want to use the modified list with another user profile (other MS Windows account, completely different computer) you have to modify the list there again.