# A Radiation-Free Classification Pipeline for Craniosynostosis Using Statistical Shape Modeling

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## Abstract

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## 1. Introduction

#### 1.1. Craniosynostosis

#### 1.2. Assessment and Classification of Craniosynostosis Using Statistical Shape Modeling

#### 1.3. Scope of This Work

- We present an alternative classification approach for craniosynostosis to distinguish between controls and three different types of craniosynostosis directly on the parameter vector of our ssm built from 3D photogrammetric surface scans. We test five different machine-learning-based classifiers on our database consisting of 367 subjects and achieve state-of-the-art results. To the best of our knowledge, we conducted the largest classification study of craniosynostosis to date.
- We propose the first publicly available ssm of craniosynostosis patients using 3D surface scans, including pathology-specific submodels, texture, and 100 synthetic instances of each class. It is the first publicly available model of children younger than 1.5 years and ssm of craniosynostosis patients including both full head and texture. Our model is compatible with the Liverpool-York head model [24], as it makes use of the same point identifiers for correspondence establishment. This enables combining the texture and shape of both models.
- We demonstrate two applications of our ssm, which can easily be performed with the publicly available model: First, with regard to patient counseling, we apply attribute regression as proposed by [19] to remove the scaphocephaly head shape of a patient. Second, for pathology specific data augmentation, we use a generalized eigenvalue problem to define fixed points on the cranium and maximize changes on face and ears as proposed by [28]. To the best of our knowledge, neither of these applications have been applied to patients using a craniosynostosis shape model before.

## 2. Materials and Methods

#### 2.1. Dataset and Preprocessing

#### 2.2. Correspondence Establishment

#### 2.3. Statistical Modeling

#### 2.4. Classification of Craniosynostosis

## 3. Results

#### 3.1. Classification Results

#### 3.2. Morphing and Shape Model Evaluation

#### 3.3. Publicly Available Shape Model

#### 3.4. Shape Model Applications

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Shape model creation and classification pipeline. Blue: data, yellow: statistical and preprocessing methods, red: classification. Each of the top-level blocks is described individually.

**Figure 2.**Age distribution among classes of the dataset. Parenthesis indicate number of samples per class.

**Figure 3.**Confusion matrix, sensitivity, and specificity for lda, nonrigid iterative closest points affine (N-ICP-A) and the optimal number of components (44) using stratified 10-fold cross-validation. Con = control, Cor = coronal, Sag = sagittal, Met = metopic.

**Figure 4.**Compactness, generalization, and specificity of the final model as a function of the number of principal components.

**Top left**: Compactness.

**Top right**: Zoom-In. Higher is better.

**Bottom left**: Generalization error.

**Bottom right**: Specificity error. Lower is better.

**Figure 5.**First three modes of the full model in front and top view. From left to right: $-3\sigma $, mean shape, and $+3\sigma $. Color bar indicates vector norm difference between principal component shape and mean shape (gray).

**Figure 6.**Shape model metrics for the control submodel and the pathology-specific submodels. From top to bottom: compactness, generalization, and specificity.

**Figure 7.**Mean shapes of pathology-specific submodels, front and top view. From left to right: control model, coronal suture fusion model, sagittal suture fusion model, and metopic suture fusion model. Color bar indicates vector norm difference between principal component shape and mean shape (gray).

**Figure 8.**Patient pathology assessment using pathology change. Left: the original head shape of the scaphocephaly patient. Right: the patient’s head with removed pathology using our full ssm.

**Figure 9.**The first three flexibility modes with fixed cranium, applied to a synthetic scaphocephaly patient. Changes are minimal for the cranium and maximal for the face, neck, and ears.

**Table 1.**Confusion matrix, sensitivity, and specificity for linear discriminant analysis (LDA), nonrigid iterative closest points affine (N-ICP-A) and the optimal number of components (44) using stratified 10-fold cross-validation. Con = control, Cor = coronal, Sag = sagittal, Met = metopic.

True Class | Predicted Class | Sensitivity | Specificity | |||
---|---|---|---|---|---|---|

Con | Cor | Met | Sag | |||

Con | 178 | 0 | 0 | 0 | 1.000 | 0.958 |

Cor | 5 | 17 | 0 | 0 | 0.773 | 1.000 |

Met | 0 | 0 | 56 | 0 | 1.000 | 1.000 |

Sag | 3 | 0 | 0 | 108 | 0.973 | 1.000 |

G-mean | 0.931 | |||||

Total accuracy | 0.978 |

Mean Landmark Error (mm) | Mean Vertex-to-Nearest-Neighbor Distance (mm) | Mean Surface Normals Deviations (Degree) |
---|---|---|

$6.533\pm 1.796$ | $0.007\pm 0.003$ | $33.488\pm 1.578$ |

**Table 3.**Number of principal components included in the publicly available shape model data under Creative Commons license CC-BY-NC 4.0.

Model | Included Principal Components |
---|---|

Full shape model | 100 |

Texture model | 100 |

Control model | 30 |

Sagittal model | 30 |

Metopic model | 25 |

Coronal model | 15 |

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## Share and Cite

**MDPI and ACS Style**

Schaufelberger, M.; Kühle, R.; Wachter, A.; Weichel, F.; Hagen, N.; Ringwald, F.; Eisenmann, U.; Hoffmann, J.; Engel, M.; Freudlsperger, C.;
et al. A Radiation-Free Classification Pipeline for Craniosynostosis Using Statistical Shape Modeling. *Diagnostics* **2022**, *12*, 1516.
https://doi.org/10.3390/diagnostics12071516

**AMA Style**

Schaufelberger M, Kühle R, Wachter A, Weichel F, Hagen N, Ringwald F, Eisenmann U, Hoffmann J, Engel M, Freudlsperger C,
et al. A Radiation-Free Classification Pipeline for Craniosynostosis Using Statistical Shape Modeling. *Diagnostics*. 2022; 12(7):1516.
https://doi.org/10.3390/diagnostics12071516

**Chicago/Turabian Style**

Schaufelberger, Matthias, Reinald Kühle, Andreas Wachter, Frederic Weichel, Niclas Hagen, Friedemann Ringwald, Urs Eisenmann, Jürgen Hoffmann, Michael Engel, Christian Freudlsperger,
and et al. 2022. "A Radiation-Free Classification Pipeline for Craniosynostosis Using Statistical Shape Modeling" *Diagnostics* 12, no. 7: 1516.
https://doi.org/10.3390/diagnostics12071516