# Spectral reconstruction for Megavoltage X-ray sources from attenuation measurements

#### Abstract

Megavoltage X-ray sources are widely use in radiation therapy for deep tumors, because of their penetration power. Recently, they also started to be used for imaging (in Image Guided Radiation Therapy), where a Cone Beam Computed Tomography is employed. For both applications, the knowledge of the spectral density is extremely important. In radiation therapy, an essential clinical parameter is the dose delivered to the patient. The calculation of this dose is usually done by a simple "averaging" approximation, in which it is assumed that the radiation is monoenergetic, with photon energy being 1/3 of the maximum energy of the spectrum. This type of approximation was shown to introduce errors of the order of 10%. [Manciu *et al.,* 2008] Also, in imaging, knowledge of the spectral density allows corrections for polyenergetic beam image artifacts.^ A typical procedure to determine the spectral density consists in measuring transmission intensities through filters of variable thicknesses and to calculate the spectral distributions that match the experiment. The iterative methods currently employed, such as Expectation Maximization [Sidky *et al., * 1997] and Waggener' iterative procedure [Waggener * et al.,* 1999], are working well only when a very good initial "guess" spectrum is known. On the other hand, *ab initio* methods, which don't need a "guess" solution, such as Singular Value Decomposition or Truncated Singular Value Decomposition, fail drastically when noise is present in experimental data [pmb].^ In this work, a novel method, base on Total Variation Regularization [Manciu *et al.,* 2008] is employed to reconstruct spectral density of a Megavoltage X-ray source from experimental attenuation data. As is demonstrated in this thesis, the solution obtained via Total Variation Regularization method is much closer to the spectrum predicted by Monte Carlo than vii any other solutions (based on Expectation Maximization or Truncated Singular Value Decomposition). Two additional tests have been devised to validate this affirmation.^ In the first test, the attenuation data from the first 20 depths have been considered for spectral reconstruction, and the spectrum obtained has been used to predict the attenuation data for the next 21 depths. The discrepancy between the predicted and experimentally obtained data provides an estimate of the quality of the spectral reconstruction, and implicitly, of the accuracy of the dose calculation in tissue. Furthermore, it is worth noting that the dose calculations based on the Monte-Carlo method has much lower accuracy than the solutions obtained via any of the methods employed (Total Variation Regularization, Truncated Singular Value Decomposition, and Expectation Maximization). ^ The second test consisted in obtaining attenuation data without and with a lead filter. Both set were independently used to reconstruct two spectra, and the attenuation due to the lead filter of the first spectrum was compared to the second spectrum. The discrepancies between the two spectra are a measure of the errors involved in the spectral reconstruction. Both, the numerical algorithm and the quality of the attenuation data contributes to these discrepancies. ^ Finally, it was investigated the relation between the number of attenuation data considered and the quality of the reconstruction. The results showed that more than 20 experimental points do not significantly increase the quality of the reconstruction, while less than 20 attenuation data rapidly deteriorate the reconstruction.^ In conclusion, the Total Variation Regularization method proves to be very good for determination of the spectral density of Megavoltage X-ray sources from attenuation measurement. The implementation of the method described here in clinical practices will decrease the error in dose calculation by at least an order of magnitude.^

#### Subject Area

Health Sciences, Radiology|Physics, Radiation|Biophysics, Medical

#### Recommended Citation

Huerta-Hernandez, Claudia I, "Spectral reconstruction for Megavoltage X-ray sources from attenuation measurements" (2008). *ETD Collection for University of Texas, El Paso*. AAI1456735.

https://digitalcommons.utep.edu/dissertations/AAI1456735