### Abstract

Purpose: It is desirable to compute polyenergetic digitally reconstructed radiographs (DRRs) in many radiotherapy tasks, especially when investigating beam hardening effects in CT/CBCT reconstruction and studying 2D‐3D registration. The standard polyenergetic DRR calculation performs ray‐tracing for each energy bin. The computation time scales with the number of bins in the spectrum and the ray tracing operation for each bin dominates the computation time. This work develops a novel algorithm to enhance the efficiency of polyenergetic DRR computation. Methods: The inputs of our algorithm are 3D density and material arrays along with the energy spectrum. We compute a modified projection by ray tracing through the density data and saving the results from each material into separate 2D arrays. For each energy bin, the product of each density projection and its corresponding energy dependent mass attenuation coefficient is summed over all materials. The exponential of the results from each energy bin are weighted and summed to create a final polyenergetic DRR. Our new algorithm is mathematically equivalent to the standard approach. We use our algorithm to simulate a 512×512 polyenergetic DRR of a 512×512×182 phantom comprised of 3 materials (air, tissue, bone). A realistic 120kVp energy spectrum with 114 bins was used. The computation times and results of the new algorithm are compared to those of the standard algorithm. Results: We successfully improved the efficiency of the polyenergetic DRR calculation by a factor of 63.85 in our testing case. The average error between the results from our algorithm and that from the standard algorithm is on the order of machine precision. Conclusion: We have substantially improved the efficiency of the standard polyenergetic DRR algorithm without sacrificing accuracy. This new approach enables fast and accurate DRR calculations that will facilitate many tasks in radiotherapy.

Original language | English (US) |
---|---|

Pages (from-to) | 426 |

Number of pages | 1 |

Journal | Medical Physics |

Volume | 40 |

Issue number | 6 |

DOIs | |

State | Published - 2013 |

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### ASJC Scopus subject areas

- Biophysics
- Radiology Nuclear Medicine and imaging

### Cite this

**TU‐A‐116‐02 : A Novel Algorithm for Highly Efficient Polyenergetic DRR Calculation.** / Folkerts, M.; Jia, X.; Jiang, S.

Research output: Contribution to journal › Article

*Medical Physics*, vol. 40, no. 6, pp. 426. https://doi.org/10.1118/1.4815349

}

TY - JOUR

T1 - TU‐A‐116‐02

T2 - A Novel Algorithm for Highly Efficient Polyenergetic DRR Calculation

AU - Folkerts, M.

AU - Jia, X.

AU - Jiang, S.

PY - 2013

Y1 - 2013

N2 - Purpose: It is desirable to compute polyenergetic digitally reconstructed radiographs (DRRs) in many radiotherapy tasks, especially when investigating beam hardening effects in CT/CBCT reconstruction and studying 2D‐3D registration. The standard polyenergetic DRR calculation performs ray‐tracing for each energy bin. The computation time scales with the number of bins in the spectrum and the ray tracing operation for each bin dominates the computation time. This work develops a novel algorithm to enhance the efficiency of polyenergetic DRR computation. Methods: The inputs of our algorithm are 3D density and material arrays along with the energy spectrum. We compute a modified projection by ray tracing through the density data and saving the results from each material into separate 2D arrays. For each energy bin, the product of each density projection and its corresponding energy dependent mass attenuation coefficient is summed over all materials. The exponential of the results from each energy bin are weighted and summed to create a final polyenergetic DRR. Our new algorithm is mathematically equivalent to the standard approach. We use our algorithm to simulate a 512×512 polyenergetic DRR of a 512×512×182 phantom comprised of 3 materials (air, tissue, bone). A realistic 120kVp energy spectrum with 114 bins was used. The computation times and results of the new algorithm are compared to those of the standard algorithm. Results: We successfully improved the efficiency of the polyenergetic DRR calculation by a factor of 63.85 in our testing case. The average error between the results from our algorithm and that from the standard algorithm is on the order of machine precision. Conclusion: We have substantially improved the efficiency of the standard polyenergetic DRR algorithm without sacrificing accuracy. This new approach enables fast and accurate DRR calculations that will facilitate many tasks in radiotherapy.

AB - Purpose: It is desirable to compute polyenergetic digitally reconstructed radiographs (DRRs) in many radiotherapy tasks, especially when investigating beam hardening effects in CT/CBCT reconstruction and studying 2D‐3D registration. The standard polyenergetic DRR calculation performs ray‐tracing for each energy bin. The computation time scales with the number of bins in the spectrum and the ray tracing operation for each bin dominates the computation time. This work develops a novel algorithm to enhance the efficiency of polyenergetic DRR computation. Methods: The inputs of our algorithm are 3D density and material arrays along with the energy spectrum. We compute a modified projection by ray tracing through the density data and saving the results from each material into separate 2D arrays. For each energy bin, the product of each density projection and its corresponding energy dependent mass attenuation coefficient is summed over all materials. The exponential of the results from each energy bin are weighted and summed to create a final polyenergetic DRR. Our new algorithm is mathematically equivalent to the standard approach. We use our algorithm to simulate a 512×512 polyenergetic DRR of a 512×512×182 phantom comprised of 3 materials (air, tissue, bone). A realistic 120kVp energy spectrum with 114 bins was used. The computation times and results of the new algorithm are compared to those of the standard algorithm. Results: We successfully improved the efficiency of the polyenergetic DRR calculation by a factor of 63.85 in our testing case. The average error between the results from our algorithm and that from the standard algorithm is on the order of machine precision. Conclusion: We have substantially improved the efficiency of the standard polyenergetic DRR algorithm without sacrificing accuracy. This new approach enables fast and accurate DRR calculations that will facilitate many tasks in radiotherapy.

UR - http://www.scopus.com/inward/record.url?scp=84907501261&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84907501261&partnerID=8YFLogxK

U2 - 10.1118/1.4815349

DO - 10.1118/1.4815349

M3 - Article

AN - SCOPUS:84907501261

VL - 40

SP - 426

JO - Medical Physics

JF - Medical Physics

SN - 0094-2405

IS - 6

ER -