Monte Carlo Simulations
The results comparing the effect produced by the bone ribs are presented on . Values of calculated absorbed energy and the respective composition simulated for chest wall structure in each case are presented.
Deposited energy for chest wall irradiation with different compositions.
Although the energy deposited in structures of different compositions presents different values, as expected since they have different densities and attenuation coefficients, the difference between values of absorbed energy for the structure in the presence and absence of magnetic material presents percentage variation less than 0.5%. It is important to highlight that this result is achieved even for the limit case considered, where the complete structure was represented as being constituted uniquely by bone. After this result, the ribs bones were removed from the irradiation geometry and the chest wall was considered as composed by only muscle tissue.
The evaluation of the energy deposited in the chest wall and breast tissue/skin for the three types of magnetic heterogeneities as function of the expander volume is presented in , to 0° and opposed beams of 90° and 270°, respectively. Irradiation simulation in the absence of any type of heterogeneity (only water) is represented by squares, heterogeneity type I (SmCo+ Ti) by circles, type II (NdBFe+Ti) by triangles and type III (NdBFe+AuNiCu) by stars.
Deposited energy curves calculated with MCNP for the three heterogeneity types studied on the structures representing chest wall and breast tissue and skin (A) 0°, (B) 90° and (C) for 270° irradiation, respectively.
As can be observed, variations in the expandeŕs volume leads to a gradual decrease of the deposited energy in the structure that is located under it, except to breast tissue/skin for 0° irradiation where the deposited energy increases steadily due to the backscattering. This effect is clearly caused by the increase of the water layer thickness, which attenuates photons from the incident beam. With respect to the presence of the heterogeneity, the energy deposited in the chest wall doesńt change significantly for any of the three magnetic heterogeneities types studied.
At the larger volume studied, differences in the deposited energy at breast tissue and skin structure is around 7% (0°) and 1% (90°) in comparison with the first studied volume. The deposited energy calculated for the structure that represents the chest wall does not seem to be affected significantly by the change in the expander volume. No significant difference was observed for both irradiation angles.
The second step was to perform the deposited energy calculations only for structurés parts (cells) that lie just above and below the artifact to verify the existence of hot or cold spots ().
Breast phantom where structures constructed above and below the heterogeneity can be visualized.
In order to quantify these effects a Heterogeneity Factor (HF) was defined as the ratio between the values of deposited energy with and without the presence of the artifact. Three sample volumes were chosen in order to assess each effect, for irradiations at 0°. For the evaluation of attenuation, small volumes were chosen due to the disk proximity to the structure below it, and for backscattering evaluation three arbitrary volumes were tested: 100 ml, 364 ml and 600 ml. To evaluate backscattering and attenuation effects for opposed beams irradiation, five sample volumes were used. The first three volumes (100 ml, 124 ml and 184 ml), an intermediary (364 ml) and the larger one (600 ml) were studied. and show the HF for these volumes.
HF values for irradiation at 0° for the three types of heterogeneity studied.
HF values for opposed pair irradiation for the three types of heterogeneity studied.
It can be observed that the attenuation effect is inversely linked with the expander volume for the irradiation at 0° and is clearly caused by photons that are attenuated by the disk high density material and don’t reach the structure as expected. Therefore this effect is valid only for volumes where the disk is close to the structure; otherwise it couldn’t be associated to the presence of the magnetic disk but to the rise in the water layer thickness. A maximum was observed for the heterogeneity Type III on the first volume studied (HF
0.89), and even for the last volume studied (184 ml) the attenuation is significant (HF
0.93). The smaller HF values obtained for heterogeneity type III, in both 0° and opposed beam irradiation, is probably due to the fact that it has materials with higher atomic number on its surface (Zgold
28 and Znickel
29) compared with the others (Ztitanium
22), despite to be geometric smaller. Backscattering effects are insignificant (none HF >1.02) for the volumes studied, with respect to the three heterogeneity types investigated for the two irradiation positions.
Evaluation of a Treatment Planning
The maps of isodose curves with and without heterogeneity correction, for each volume, were compared.
An underdose region on both sides of the magnetic disc appears when the correction for heterogeneity was applied and increases with the volume. This effect can be seen in which shows the planning for the two extremes volumes with and without the heterogeneity correction algorithm. This hall of underdose is clearly caused by the angulation of the magnetic disc with respect to the incidence angle of the radiation beam. For larger volumes the disc becomes parallel to the beam, increasing the thickness of high density material, defining the path of beam entry and exit in the breast phantom.
Treatment Planning isodose Curves for the two extremes volumes considered with and without heterogeneity correction algorithm applied.
In Despite of the observation of different patterns in the isodose curves to all studied volumes when the correction for heterogeneity is applied, numerically none of these alterations was higher than 5% of the prescribed dose and are, in most of cases, limited to the expander volume, not reaching significantly the treatment volume.
Hot spots were not found in the treatment region. But is important to mention that the treatment planning system does not consider electrons transport in the calculations, which could be responsible for this type of effect.
Even with the limitation of the treatment planning system in reproduce the geometry and real density of the magnetic disc, and the absence of electron transport calculations, the results found by this approach confirm what was found with Monte Carlo simulations, e.g, that the presence of the heterogeneity didn’t alter the deposited dose (energy) on treatment structures when a traditional pair of opposite tangent 6 MV photon beam is used.
The influence of the magnetic heterogeneity inside tissue expanders was studied at a first approach using Monte Carlo simulations. The study was performed through the evaluation of the deposited energy values in structures which have clinical importance for the treatment considering three types of magnetic disk and irradiation with a 6 MV photon beam in three different angles. Expansion of the prosthesis was also taken into account.
Underdosage of 7% was found for the larger volume of breast implant, in the case of frontal field irradiation for the chest wall, indicating that the change in breast expander volume alters the deposited energy to this angle of beam.
Variations in the energy deposited due to the presence of the heterogeneity in the radiation field were observed mainly for irradiation at 0°, as could be also seen in the literature. And the alterations show great values of attenuation mostly for the tissue expander manufactured by SILIMED, never studied before. These large differences are presumably due to the higher atomic numbers of materials that compose the magnetic disk. Insignificant variations were observed for irradiation with opposed pair beams.
It should be remembered that direct irradiations with a beam at 0° are not commonly used at clinical practice in order to avoid great lung doses, and it has been considered at this work in the Monte Carlo simulations with the intention of assessing the results found in the literature. But it is also worth remembering that anatomical expanders have the magnetic valve positioned in many different places, and depending where it is positioned the incident radiation beam could have an angle of interaction with the magnetic disk close to the presented by the 0° angle of irradiation showed by this work.
To contrary to the literature values for attenuation and dose enhancement did not match exactly with the results found at this work, it has to emphasize that this work was concerned only with deposited energy on structures with clinical importance, regardless of the dose distribution inside the expander aqueous volume. Most of differences found by other works were at points close to the valve, which have probable localization inside the aqueous volume of the expander.
Despite the fact that little differences were found for the irradiation with a opposed pair of beams, the results suggest that patients implanted with heterogeneity of type III could have a greater possibility of failure on delivered dose, mainly below the heterogeneity (inside the breast) during the irradiation treatment, since the treatment can be executed with a beam positioned in angles between the extremes angles considered in this work.
It should be remembered that direct irradiations with a beam at 0° are not commonly used at clinical practice in order to avoid great lung doses, and it has been considered at this work with the intention of assessing the results found in the literature.
Since deposited energy is not directly related to clinic use, and with the aim of verifying if the heterogeneity alters the dose distribution, a conventional breast treatment planning was performed for five different expander volumes using CT images acquired from a anatomic breast phantom containing the magnetic disk type (heterogeneity Type III), which lead major changes in the study performed by Monte Carlo simulations.
Isodose curves show an underdose area at both sides of the magnetic disk when the correction for heterogeneities is applied. The results presented by Chatzigiannis et al.
agree in the location of underdose areas although they described greater values of underdose (6–13%), compared with what was found here (below 5%). Thompson and Morgan 
also described affects of attenuation in the same region (in order of 23%) but to smaller distance from the artifact, inside the expander tissue. Both studies consider the real density of heterogeneity (to other type of tissue expander), what was not possible with the planning system used for this work for the type III of expander. It is important to take into account the heterogeneity position with respect to the incidence angle of radiation beam; the two studies previously mentioned, as well as this work, found high underdose effects for angles of incident irradiation beam parallel to the heterogeneity position. This effect is easily explained by the enhancement of high density material thickness that the beam crosses at this situation. Overdose effects were not observed.
Many difficulties were found in the planning stage, as the presence of artifacts in the image modify the CT numbers of the structures and alters the real information contained in the image, leading to the necessity of redesign the heterogeneity limits in each slice of the CT set images, and also the limitation of the system in defining the real density of the heterogeneity and ignore the generations of electrons.
The results found in this study shows little influence of the presence of the magnetic disk for radiotherapy breast treatment and suggests that the high rate of complications and reconstruction failure should be related to other relevant parameters, like the biological aspects related to the irradiated tissues during the reconstruction process, as discussed by Ozden et al 
No significant differences were found for the presence of the heterogeneity during the treatment planning of irradiation with an opposed pair of beams. Most of differences found by other works were at points close to the magnetic disk, which have probable localization inside the aqueous volume of the expander, not being important for the treatment because it is not a structure to be treated.