### Article

## Conserving absorbed energy during accumulation of dose from a 4D geometry

### Search Medline for

### Authors

Published: | September 24, 2009 |
---|

### Outline

### Text

**Purpose: **The aim of this work is to account for changes in patient geometry by accumulating all dose to a single fixed geometry, *I*
*
_{f}
*, while preserving deposited energy in all moving geometries.

**Materials: ** We consider a single instance *I*
_{m}, from the set of moving geometries where *I*
*
_{m}
* is related to

*I*

*by deformable registration. It is assumed that the mass is preserved between*

_{f}*I*

*and*

_{m }*I*

*. The energy absorbed by*

_{f}*I*

*should then also be preserved which implies that the dose should not be the transferred quantity since a voxel in*

_{m }*I*

*may consist of several*

_{f}*I*

*voxels with different composition. Dose varies smoother than absorbed energy and may be a preferred subject for an interpolation scheme. The accumulated dose is by choice selected to be presented in*

_{m}*I*

*, therefore the mass in*

_{f}*I*

*should be preserved.*

_{f}To fulfil these requirements for the dose in the fixed geometry, *D*
*
_{f}
*, an energy conservation interpolation method (ECI) is proposed according to

*D*

*(*

_{f}*r*

*) =*

_{f}*D*

*(*

_{m}*r*

*) ρ*

_{m}*(*

_{m}*r*

*) / ρ*

_{m}*(*

_{f}*r*

*), (1)*

_{f}where

*D*

_{m}*(r*

_{m}*)*and ρ

_{m}*(r*

_{m}*)*are interpolated quantities in

*I*

*and the position*

_{m }*r*

*is related to*

_{f}*r*

*by the registration. The energy in*

_{m}*I*

*is approximately preserved and the interpolation is done in the smoother dose domain.*

_{m }A post energy transfer method (PETM) is also proposed where each voxel in *I*
*
_{m}
* is divided into eight subvoxels and the energy absorbed by each subvoxel is transferred to

*I*

*using the registration.*

_{f}*D*

*(*

_{f}*r*

*) is calculated as the sum of transferred energy divided by the mass in*

_{f}*I*

*. The aim of PETM is to more accurately conserve the absorbed energy in*

_{f}*I*

*into*

_{m}*I*

*.*

_{f}The ECI and PETM methods are applied to a lung case treated with a 6x6 cm^{2} proton field with a SOBP of 4 cm wed. *I*
*
_{m}
* has an artificial displacement of the target volume of ~9 mm compared to

*I*

*. The dose is calculated with Geant4 (Agostinelli, et al. Nucl Instrum Meth. 2003;A 506) in a 2x2x3 mm grid.*

_{f}The transfer of dose from *I*
*
_{m}
* to

*I*

*is done using ECI and PETM and is compared to an energy transfer method (Siebers, et al. Med Phys. 2008;35) (ETM), and direct dose mapping (Rosu, et al. Med Phys. 2005;32) (DM) in*

_{f}*Im*.

The ETM can be considered to be accurate but is only applicable to Monte Carlo dose calculation and requires the less commonly existing deformation field from *I*
*
_{m }
*to

*I*

*. DM is a simple interpolation scheme but is sensitive to redistribution of mass between voxels.*

_{f}
**Results: **Figure 1 [Fig. 1] shows the CTV DVH in *I*
*
_{f}
* for the calculation of the same plan in

*I*

*where the dose is transferred to*

_{m}*I*

*using ECI, PETM, DM and ETM. For the data set considered in this work, the ECI and PETM method shows a qualitatively better agreement with the ETM than the DM.*

_{f}
**Conclusions: **We present two new schemes for transferring a dose distribution from a moving to a fixed geometry. Both methods better preserve the energy absorbed by the moving geometry.