7.12. [ T-SED ] section

Calculation of the probability density of deposition energies in microscopic sites, called the lineal energy \(y\) or specific energy \(z\), is of great importance in the estimation of the relative biological effectiveness (RBE) of charged particles. However, such microscopic probability densities cannot be directly calculated by PHITS simulation using the [t-deposit] tally, as PHITS is designed to simulate particle motion on a macroscopic scale and employs a continuous-slowing-down approximation (CSDA) for calculating the energy loss of charged particles. We therefore introduced a special tally named [t-sed] for calculating the microscopic probability densities using a mathematical function that can instantaneously calculate quantities around trajectories of charged particles. The function was developed on the basis of track structure simulations considering productions of \(\delta\)-rays and Auger electrons. Note that the name ‘SED’ derives from ‘Specific Energy Distribution.’ Details of the calculation procedure are given elsewhere. [1] [2] The function of the [delta ray] section should not be used together with this tally. When you use [t-sed], you have to activate the EGS mode, negs=1 or 2, and set the cut-off energy of electrons and positrons to 10 keV or 100 keV, emin(12-13)=0.01 or 0.1.

Using this tally, information on the probability densities of \(y\) and \(z\) in water can be obtained. It is also possible to calculate probability densities in different materials, although the accuracy of doing so has not yet been checked. Similar to [t-let], the dose is only counted from the energy loss of charged particles and nuclei, and therefore the Event Generator mode, e-mode>=1, must be used to transport low-energy neutrons. The deposition energy in microscopic sites can be expressed as the deposit energy \(\varepsilon\) in MeV, the lineal energy \(y\) in keV/um, or the specific energy \(z\) in Gy. The definitions of these quantities are given in ICRU Report 36. Usage of [t-sed] is similar to that of [t-let].

Table 7.12.1 mesh

value	explanation
reg, r-z, xyz	Mesh type. A mesh type subsection is required below this option.

Table 7.12.2 volume

value	explanation
(optional)	This option defines the volume for each region for reg mesh. Volume definitions are required below this option. Default values are given in input echo in the case of no definition.
reg vol	Volume definition. For details see the [volume] section.

Table 7.12.3 iechrl

value	explanation
72 (default)	Maximum number of columns for volume input echo.

Table 7.12.4 model

value	explanation
0, 1 (D=0)	0: old model. 1: new model (paper under preparation).

Table 7.12.5 se-unit

value	explanation
0, 1, 2, 3	Unit of deposition energy in microscopic sites. 0: Number of ionizations and electronic excitations. Selectable only when model=1. 1: deposit energy \(\varepsilon\) in MeV. 2: lineal energy \(y\) in keV/um. 3: specific energy \(z\) in Gy.

Table 7.12.6 cdiam

value	explanation
(optional, D=1.0)	Diameter of the target site in um. A value from 0.001 to 2.0 can be specified. If cdiam is set to a negative value, the peak due to the production of Auger electron is ignored.

Table 7.12.7 se-type

value

explanation

1, 2, 3, 4, 5

\(\varepsilon\), \(y\), or \(z\) mesh, where the unit is defined by se-unit. See Section 6.6.1 for mesh subsection format. If a ‘Warning: Z bin is not enough!’ message occurs, the emin, emax, and ne parameters must be changed. This warning indicates that the microdosimetric function cannot calculate the \(y\) or \(z\) distribution because the range is too small or the mesh resolution is too poor. For example, set se-type=3, emin=0.01, emax=10000.0, ne=60 or higher for calculating the \(y\) distribution for site diameter = 1 um, cdiam=1.0 and se-unit=2.

Table 7.12.8 part

value	explanation
all (default), particle name	Tally particle.

Table 7.12.9 axis

value	explanation
sed, reg, x, y, z, r	x axis value of output data.
xy, yz, xz, rz	2-dimensional.

Table 7.12.10 samepage

value	explanation
(optional, D=part)	The type of data to be displayed on the same page of the image output file. Parameters that can be defined in axis can be specified.

Table 7.12.11 file

value	explanation
file name	Define output file names. This is required by each setting of axis.

Table 7.12.12 resfile

value	explanation
(optional, D=file)	Define a file name of the past tally in the restart calculation. Even if several axis parameters were defined, specify only one resfile.

Table 7.12.13 unit

value	explanation
1, 2, 3, 4, 5, 6	1: Track [cm/(keV/um)/source] 2: Dose [MeV/(keV/um)/source], proportional to \(y*f(y)\). 3: Track [cm/ln(keV/um)/source] 4: Dose [MeV/ln(keV/um)/source], proportional to \(y*d(y)\). 5: Track [cm/source] 6: Dose [MeV/source]
7, 8	7: \(y*f(y)\) [dimensionless], where \(\int f(y)dy=1\). 8: \(y*d(y)\) [keV/um], where \(\int d(y)dy=1\). These units are for the case of se-unit=2. For se-unit=1 and 3, [keV/um] is replaced by [MeV] and [Gy], respectively.

Table 7.12.14 factor

value	explanation
(optional, D=1.0)	Normalization factor.

From version 3.02, new options, unit=7 and 8, were implemented. Using them, the frequency and dose probability densities of \(y\), \(f(y)\), and \(d(y)\), respectively, can be easily calculated. The results obtained from unit=7 and 8 are proportional to those obtained from unit=2 and 4, respectively, but their absolute values are different because the integral of the probability densities are normalized to 1 in the cases of the new options. In place of sum over, the frequency mean is output when unit=7, and the dose mean is output when unit=8, though their statistical errors are not calculated and are always shown as 0.000. Note that unit=7 and 8 can be set only when axis=sed.

Table 7.12.15 title

value	explanation
(optional)	Title.

Table 7.12.16 angel

value	explanation
(optional)	ANGEL parameters.

Table 7.12.17 sangel

value	explanation
(optional)	Special format for ANGEL parameters.

Table 7.12.18 2d-type

value	explanation
1, 2, 3, 4, 5, 6, 7	Options for 2-dimensional plot.
(optional, D=3)

Table 7.12.19 gshow

value	explanation
0 (default), 1, 2, 3, 4, 5	When mesh=xyz and axis=xy,yz,xz, region border (1), material name (2), region name (3), and LAT number (4) are plotted using this option. gshow=5 outputs only material colors in pixel style when icntl=8.

Table 7.12.20 rshow

value	explanation
0 (default), 1, 2, 3	When mesh=xyz and axis=xy,yz,xz, region border (1), material name (2), and region name (3) are plotted using this option. A xyz mesh section must be added below this option.

Table 7.12.21 gslat

value	explanation
2 (default)	Option to draw lattice or tetrahedral geometry boundary lines when gshow or rshow is specified.
0	Not drawing.
1	Drawing. Note that the line of voxel phantoms may not be drawn clearly.
2	Not drawing the lines in the same cell.
3	Not drawing the lines in the same material. In this case, the boundary of two adjacent cells filled with the same material is not also drawn, even if not lattice or tetrahedral geometry. When gshow>=3, cell and lattice numbers are now shown.

Table 7.12.22 x-txt

value	explanation
(optional)	\(x\) axis title.

Table 7.12.23 y-txt

value	explanation
(optional)	\(y\) axis title.

Table 7.12.24 z-txt

value	explanation
(optional)	\(z\) axis title.

Table 7.12.25 resol

value	explanation
1 (default)	This option multiplies the region line resolution by a factor of resol with the gshow or rshow option set to define the line thickness.

Table 7.12.26 width

value	explanation
0.5 (default)	The option defines the line thickness.

Table 7.12.27 trcl

value	explanation
(optional)	Coordinate transformation number or definition for r-z or xyz mesh.

Table 7.12.28 material

value	explanation
(optional)	Specify materials for scoring.
all	all is the default, same as no definition.
number of materials	To set number of materials, define the material numbers in the next line. The number of materials can be set as a negative value, in which case the specified materials are not included for scoring.
(next line)	2 5 8 Material numbers.

Table 7.12.29 volmat

value	explanation
(optional, D=9)	This option corrects the volume value for each mesh when material is defined by the xyz mesh. 0 means no correction. Value of volmat is the number of scans per one xyz mesh side.

Table 7.12.30 letmat

value

explanation

(optional)

Material id for LET, \(dE/dx\). If not defined, a real material is assumed. If a material not used in the geometry is selected, its material density must be defined in [material]. To calculate LET in water, define water with 1 g/cm^3 in [material]. When letmat<0 is set, PHITS automatically calculates \(dE/dx\) for water with 1 g/cm^3 for electrons and positrons. Please see ParticleTherapy in the recommendation setting for more details.

Table 7.12.31 rhomat

value	explanation
(optional, D=1.0)	Density of the material, g/cm^3, specified by letmat. The definition of rhomat is required when the material specified by letmat is other than water, although [t-sed] was originally developed for water.

Table 7.12.32 epsout

value	explanation
0 (default), 1, 2	When epsout=1, results are plotted into eps files. The eps file is named by replacing the extension with .eps. When epsout=2, error bars are also displayed in the eps file, except for the 2-dimensional type, axis=xy, yz, xz, rz.

Table 7.12.33 maxangel

value	explanation
Number of part (default)	Specify the number of part shown in the eps file. This parameter limits the number of particles shown in a tally eps file, while it does not limit them in a numerical data file.

Table 7.12.34 ctmin(i)

value	explanation
(optional, D=-9999)	Minimum value for the i-th counter.

Table 7.12.35 ctmax(i)

value	explanation
(optional, D=9999)	Maximum value for the i-th counter.

Table 7.12.36 chmin(i)

value	explanation
(optional, D=-9999)	Minimum value for the i-th history-counter. This parameter cannot be specified in the batch variance mode, istdev=1.

Table 7.12.37 chmax(i)

value	explanation
(optional, D=9999)	Maximum value for the i-th history-counter. This parameter cannot be specified in the batch variance mode, istdev=1.

Table 7.12.38 stdcut

value	explanation
(optional, D=-1)	Threshold value of STD cut off.

When specifying stdcut, PHITS automatically stop the calculation depending on values of STD, standard deviation. This function is available when stdcut is positive and itall=0,1 is set in [parameters] section. When all relative values of STD of the tally result are larger than 0 and smaller than stdcut at the last of one batch, the calculation is stopped. If stdcut in two or more tally sections is set, all the results of the tally sections have to satisfy the conditions in order for the function to work.

[1]

20. Sato, R. Watanabe and K. Niita, “Development of a calculation method for estimating the specific energy distribution in complex radiation fields,” Radiat. Prot. Dosim. 122, 41-45 (2006).

[2]

20. Sato, Y. Kase, R. Watanabe, K. Niita and L. Sihver, “Biological dose estimation for charged-particle therapy using an improved PHITS code coupled with a microdosimetric kinetic model,” Radiat. Res. 171, 107-117 (2009).