**4.2 Computer simulation of the absorbed dose distribution in biological objects using GEANT4**

During computer simulation biological objects irradiated with electron beams are usually represented by water phantoms since water is close in its properties to the range of biological objects involved in irradiation processing. To calculate the

*Electron Beam Processing of Biological Objects and Materials DOI: http://dx.doi.org/10.5772/intechopen.112699*

absorbed dose distribution using GEANT4, it is necessary to describe the geometry of the object and determine the radiation source and the volume for detecting the absorbed energy.

GEANT4 contains more than 20 standard shapes that can be used to simulate the geometry of biological objects. To increase the accuracy of depth dose distributions in biological objects, it is necessary to determine the geometry of the object as a set of volumes of different densities and chemical compositions that correspond to the different parts of the object. Electron beam is determined by specifying its size and shape, the coordinates of its center, electron energy spectrum, spatial distribution, and number of electrons emitted per second to simulate the irradiation method used. Detection is performed using virtual volumes, which divide the water phantom with the linear dimensions of *X* � *Y* � *Z* into the number of *Nx* � *Ny* � *Nz* cubic cells. In each cell, the total energy absorbed during interactions of electrons with matter is recorded using the following formula:

$$E\_{i,j,k} = \sum\_{n=0}^{N\_{i,j,k}} \Delta \mathbf{E}\_{i,j,k,n},\tag{3}$$

where *i,j,k* is the cell index, ΔE*<sup>i</sup>*,*j*,*k*,*<sup>n</sup>* is the energy absorbed by the *i,j,k* cells during the *n* interaction, *Ni*,*j*,*<sup>k</sup>* is the number of interactions occurring in the *i,j,k* cell.

The standard deviation of absorbed energy *Si*,*j*,*<sup>k</sup>*in the *i,j,k* cell is determined by the sum of the squares of the absorbed energy P*Ni*,*j*,*<sup>k</sup> <sup>n</sup>*¼<sup>1</sup> *<sup>E</sup>*<sup>2</sup> *<sup>i</sup>*,*j*,*<sup>k</sup>* and is calculated using the formula:

$$S\_{i,j,k} = \sqrt{\frac{1}{N\_{i,j,k}} \sum\_{n=1}^{N\_{i,k}} E\_{i,j,k}^2 - \left(\frac{1}{N\_{i,j,k}} \sum\_{n=1}^{N\_{i,j,k}} E\_{i,j,k}\right)^2}. \tag{4}$$

Then, knowing the mass of the *i,j,k* cell *mi,j,k*, the absorbed dose is determined by the formula

$$D\_{i,j,k} = \frac{E\_{i,j,k}}{m\_{i,j,k}}.\tag{5}$$

To calculate a 3D-color map representing the relative absorbed dose distribution throughout the biological object the dose absorbed by each *i,j,k* cell of water phantom is color-coded, and each cell is marked with the color corresponding to the value *Drel <sup>i</sup>*,*j*,*<sup>k</sup>*, which is the ratio between *Di*,*j*,*<sup>k</sup>* and the maximum dose value in the water phantom.
