# Contour Propagation for Radiotherapy Treatment Planning Using Nonrigid Registration and Parameter Optimization: Case Studies in Liver and Breast Cancer

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Image Registration

#### 2.2. Demon Algorithm

#### 2.3. Algorithm Based on B-Spline

#### 2.4. Performance Measures

#### 2.4.1. Dice Coefficient

#### 2.4.2. Correlation Coefficient (CC)

#### 2.5. Data Structure and Preprocessing

#### Breast CT Acquisition in 4-D Format

## 3. Results and Discussion of Computational Experiments

#### 3.1. Parametrization of the Demons Algorithm

#### 3.2. Contour-Propagation Algorithm

Algorithm 1: matRad-contourPropagation |

Input: CT scans for the n scenarios and SCT for the fixed scenario.Output: CT scans for the n scenarios and SCT for the m structures.for scenario $i=\{1,2,\dots ,n\}$ do Calculate DVF ${\mathbf{u}}_{i}$ end forfor structure $j=\{1,2,\dots ,m\}$ do Convert linear indices of SCT structure j for Scenario 1 into a cube ($x\times y\times z$) for scenario $i=\{2,\dots ,n\}$ do Apply ${\mathbf{u}}_{i}$ to the structure j for scenario 1 to estimate structure j for scenario i Convert the cube of structure j for Scenario i into linear indices Store the structure j in the SCT for Scenario i end forend for |

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CC | Correlation coefficient |

CT | Computerized tomography |

CTV | Clinical treatment volume |

DCS | Dice similarity coefficient |

DVF | Displacement vector field |

FFD | Free form deformation |

MRI | Magnetic resonance imaging |

MSE | Mean squared error |

OF | Optical flow |

SCT | Segmented computed tomography |

VOI | Volume of interest |

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**Figure 2.**The images (

**a**–

**d**) are the CT scans with their corresponding meshes of control points (intersection between lines) with the corresponding deformation.

**Figure 3.**Images (

**a**,

**c**) are CTs of contours of the heart for different time frames. By segmenting this structure, a binary image can be extracted, as seen in (

**b**,

**d**), and their similarity can be found using Equation (10).

**Figure 4.**Converting linear indices 3, 4, 5, and 6 to subscripts of a $2\times 2\times 2$ matrix. Source: MathWorks.

**Figure 5.**Comparison between correlation coefficients of the initial parameters and the default parameters in Matlab. Default values are: $N=100$, $\rho =3$ y $\sigma =$ 1.0.

**Figure 6.**Efficient frontier coefficients, correlation coefficient vs. computing time, using local search algorithm.

**Figure 7.**Contrast between contour propagation with different correlation coefficients. The green and magenta colors show areas where the images do not match.

**Figure 8.**The diagram shows how each of the parameters intervene in order to obtain the optimal transformation in the matRad-contourPropagation algorithm.

**Figure 9.**Comparison between registrations with demons and B-spline for the 6 breast CT structures, using the Dice coefficient.

**Figure 10.**Comparison between the manual registration done by the professional oncologist and the registration made by the demon algorithm, for Scenarios 2 to 5 of the breast CT scans.

Scenario | Initial Parameters | Local Optima |
---|---|---|

Parameters | ||

$\mathit{N}=200$, $\mathit{\rho}=3$, $\mathit{\sigma}=$ 2.5 | $\mathit{N}=300$, $\mathit{\rho}=2$, $\mathit{\sigma}=$ 2.9 | |

1 | 1.0000 | 1.0000 |

2 | 0.9562 | 0.9585 |

3 | 0.9538 | 0.9611 |

4 | 0.9540 | 0.9608 |

5 | 0.9495 | 0.9580 |

6 | 0.9430 | 0.9582 |

7 | 0.9629 | 0.9641 |

8 | 0.9575 | 0.9635 |

9 | 0.9619 | 0.9640 |

10 | 0.9576 | 0.9629 |

**Table 2.**Time increment ratio, correlation coefficient interval length, and center value correlation coefficient interval for Scenarios 2 through 10.

Scenario | Time Increment | Correlation Coefficient | Correlation Coefficient |
---|---|---|---|

Ratio | Interval Length | Center Value | |

2 | 3.5455 | 0.0061 | 0.9658 |

3 | 2.2114 | 0.0051 | 0.9635 |

4 | 1.5268 | 0.0050 | 0.9646 |

5 | 5.4101 | 0.0050 | 0.9667 |

6 | 16.7341 | 0.0084 | 0.9657 |

7 | 1.7081 | 0.0066 | 0.9657 |

8 | 24.2389 | 0.0083 | 0.9648 |

9 | 21.8860 | 0.0065 | 0.9645 |

10 | 3.3256 | 0.0079 | 0.9626 |

**Table 3.**Set of candidate parameters for contour estimation in the 5 scenarios using breast CT scans.

Scenario 1 | Scenario 2 | Scenario 3 | Scenario 4 | Scenario 5 | |
---|---|---|---|---|---|

$\rho $ | 1 | 1 | 1 | 1 | 1 |

N | 100 | 100 | 100 | 100 | 100 |

$\sigma $ | 1.5 | 1.5 | 2.6 | 1.8 | 2.9 |

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**MDPI and ACS Style**

Vargas-Bedoya, E.; Rivera, J.C.; Puerta, M.E.; Angulo, A.; Wahl, N.; Cabal, G.
Contour Propagation for Radiotherapy Treatment Planning Using Nonrigid Registration and Parameter Optimization: Case Studies in Liver and Breast Cancer. *Appl. Sci.* **2022**, *12*, 8523.
https://doi.org/10.3390/app12178523

**AMA Style**

Vargas-Bedoya E, Rivera JC, Puerta ME, Angulo A, Wahl N, Cabal G.
Contour Propagation for Radiotherapy Treatment Planning Using Nonrigid Registration and Parameter Optimization: Case Studies in Liver and Breast Cancer. *Applied Sciences*. 2022; 12(17):8523.
https://doi.org/10.3390/app12178523

**Chicago/Turabian Style**

Vargas-Bedoya, Eliseo, Juan Carlos Rivera, Maria Eugenia Puerta, Aurelio Angulo, Niklas Wahl, and Gonzalo Cabal.
2022. "Contour Propagation for Radiotherapy Treatment Planning Using Nonrigid Registration and Parameter Optimization: Case Studies in Liver and Breast Cancer" *Applied Sciences* 12, no. 17: 8523.
https://doi.org/10.3390/app12178523