Materials

This page will list all the functions and classes related to the materials that are used in the code.

Functions

cross_section(Z, nrj)

Parameters:

• Z (1xN double) – An array of atomic numbers.

• nrj (Mx1 double) – The photon energy.

Given an array of atomic numbers and a set of photon energies, this function returns the Compton cross section for each element in the array. The method is taken from Geant4 Compton Scattering, has been translated to MATLAB, and extended to use arrays of atomic numbers. The photon energy does not need to be a column vector, and could be a row vector, but the array of atomic numbers must be a row vector.

Returns:

cs – an array containing the Compton cross section for each Z at each energy in nrj.

Return type:

Mx1 double

photon_attenuation(Z, fracs, density, nrj)

Parameters:

• Z (1xN double) – An array of atomic numbers.

• fracs (1xN double) – An array of mass fractions.

• density (double) – The density of the material.

• nrj (1xM double) – The photon energies.

The arrays Z and fracs must be the same size. This function is based on PhotonAttenuation package available on the MATLAB File Exchange, but has been heavily reduced in size and simplified for the purposes of this code. The function is not directly used in the code, but is converted to a MEX file using MATLAB Coder, which is then used in the code.

Returns:

att – The linear attenuation coefficient for the material at each energy in nrj.

Return type:

1xM double

get_photon_attenuation(Z)

Parameters:

Z (1xN double) – An array of atomic numbers.

Given an array of atomic numbers, this function returns a gridded interpolant of the attenuation coefficients for the elements in the array. This function is significantly faster than the photon_attenuation() function, when run in MATLAB, as it only needs to be run once for each element in the array. However, the gridded interpolant is a large object and so is not suitable for use in the MEX file, if parallel processing is to be used.

Returns:

att_fun – A gridded interpolant of the attenuation coefficients for the elements in the array. This gridded interpolant returns the mass attenuation coefficients for the elements when given a photon energy. These values can then be converted to linear attenuation coefficients using the atomic fractions and density of the material.

Return type:

griddedInterpolant

mat_consts

Purpose

This class is used to store the constants that are used in the materials functions. This is done to reduce the size of various classes that may be copied, and to make the code more readable.

Properties

known_materials

(1xN cell) This is a cell array of chars, containing the names of the materials that are known to the code. This is used to check that the user has entered a valid material name. The index of the material in this array is used to access the other properties of the material.

known_densities

(1xN double) This is a vector of the densities of the materials.

known_atomic_numbers

(1xN cell) This is a cell array of vectors, containing the atomic numbers of the elements in the materials.

known_mass_fractions

(1xN cell) This is a cell array of vectors, containing the mass fractions of the elements in the materials.

atomic_masses

(1x82 double) This is a vector of the atomic masses of every element in the periodic table, up to lead (Z = 82). The atomic masses are in \(g/mol\).

Potential Future Changes

It is expected that the known_materials, known_densities, known_atomic_numbers, and known_mass_fractions properties will be updated to include more materials. It is possible that these attributes could be merged together, introducing each material as a separate attribute instead of relying on the index of the material in the known_materials cell array.

material_attenuation

Purpose

This class is used to provide the user with a “material” object, which contains the properties of the material that are used in the code (linear attenuation coefficient and Compton mean free path).

Properties

name

(string) This is the name of the material.

atomic_numbers

(1xN double) This is a vector of the atomic numbers of the elements in the material.

mass_fractions

(1xN double) This is a vector of the mass fractions of the elements in the material (must be the same size as atomic_numbers).

density

(double) This is a scalar value of the density of the material in \(g/cm^3\).

mu_from_energy

(handle) This is a function handle that returns the linear attenuation coefficient of the material at a given energy. This attribute will only be defined if the photon_attenuation_mex function is available.

use_mex

(logical) This is a boolean value that is true if the photon_attenuation_mex function is available, and false otherwise.

Functions

material_attenuation(material_name, varargin)

Parameters:

• material_name (string) – The name of the material.

• varargin – The atomic numbers, mass fractions, and density of the material, or omitted if the material is known.

This function is used to create a “material_attenuation” object, which contains the properties of the material that are used in the code.

If only the material_name is given, the function will use the known_materials property of the mat_consts class to find the material properties, and will error if the material name is not found, otherwise it will return the material object.

If the material_name, atomic_numbers, mass_fractions, and density (in that order) are given, the function will create a material object using the given properties. The function will error if the atomic_numbers and mass_fractions are not vectors of the same size, or if the density is not a scalar value.

Returns:

material – a material object that contains the properties of the material that are used in the code.

Return type:

material_attenuation

Methods

get_mu(obj, nrj)

Parameters:

nrj (1xN double) – The photon energy.

This method returns the linear attenuation coefficient of the material at a given energy. If the photon_attenuation_mex() function is available, the method will use the mu_from_energy attribute (the result of get_photon_attenuation()) to return the linear attenuation coefficient. Otherwise, the method will use the MEX of the photon_attenuation() function to return the linear attenuation coefficient.

Returns:

mu – the linear attenuation coefficient of the material at each energy in nrj.

Return type:

1xN double

mean_free_path(obj, nrj)

Parameters:

nrj (double) – The photon energy.

This method returns the Compton mean free path of the material at a given energy. The method uses the cross_section() function to return the Compton mean free path.

Returns:

mfp – the Compton mean free path of the material at each energy in nrj.

Return type:

Nx1 double

Static Methods

static get_materials(filename)

Given a file that can be read using the readtable() function, this static method will return a cell array of material objects. In this file, the first column should contain the names of the materials, with the header “Name”. From the second column onwards, the first row should contain the atomic numbers of the elements in the material, while the following rows are the mass fractions of the elements in the material specified in the first column. The second to last row should contain the density of the material, with the header “Density”. The last row should contain an index of the material, with the header “Organ ID”, starting from 0. The returned cell array will contain the material objects in the order of the value contained in “Organ ID” column.

Returns:

materials – a cell array of material objects.

Return type:

1xN cell