gms | German Medical Science

Introduction: Radiotherapy of thoracic and abdominal tumors has to cope with breathing-induced motion as a major source of localisation uncertainties. State-of-the-art problem-solving approaches like gating or tracking usually rely on external breathing signals [1]. Assuming a (linear) relation between these external surrogate signals and the internal motion, patient-specific correspondence models can be trained and used for prediction purposes. Since internal motion takes place in three dimensions, it is questionable if one-dimensional external signals (e.g. spirometry) offer a sufficiently precise prediction of the internal motion. This suggests the use of multi-dimensional breathing signals. In this work, a simulation framework is employed to study the prediction accuracy of multi-dimensional external signals acquired by common range-imaging (RI) devices, effects of different sampling patterns, and the influence of the signal dimensionality.

Material and Methods: Our study is based on thoracic 4D CT data sets of lung cancer patients. A multi-dimensional external signal is simulated from 4D CT data by tracking the lifting of the chest wall following the idea of RI-techniques. In our prediction framework, internal motion information is represented by non-linear diffeomorphic transformations. A multilinear model whose parameters are estimated by a multivariate linear regression describes the correspondence between the simulated external and the internal motion representation mathematically [2]. Simulated height maps enable us to investigate the influence of signal dimensionality and sampling patterns on the prediction accuracy: Signals containing only 1 point (sternum), 150 points on a line and 150/10000 equally spread points are considered in our study. The prediction precision of the different signals is measured using 4D CT data of 10 patients, each representing one breathing cycle consisting of 10-14 phases. Evaluation is performed by Leave-out-tests forming extrapolation scenarios: During the training of the correspondence models between external and internal motion data, the end-expiratory and its two adjacent phases are not considered. Subsequently, the internal motion between end-inspiration, being the models reference phase, and the end-expiratory phase is predicted by the different external signals. Prediction accuracy is quantitatively assessed by computing target registration errors (TRE; 70 manually defined corresponding landmarks per patient).

Results: In general, our results show that high-dimensional signals have significant advantage over 1D height signals (TRE: 1pt 4.21 +/- 1.87 mm; 150 eq. spread pts: 1.75 +/- 0.22 mm). However, a signal containing 10000 sampling points leads to a less precise prediction: (2.08 +/- 0.39 mm), suggesting an overfitting problem. Interestingly, no significant influence of the sampling pattern [line with 150pts or equally distributed points (150, 10000pts)] on the prediction accuracy could be observed. Furthermore, automatically determined "optimal" tracking positions on the patient's surface (low residual values during the training) were not superior in terms of prediction accuracy compared to positions selected based on anatomical criteria (sternum).

Discussion: The results show that the use of multi-dimensional external signals significantly improves the prediction accuracy compared to one-dimensional signals. Variations of sampling patterns do not lead to significant differences in prediction accuracy. The overfitting effect could be reduced by using dimensionality reduction techniques as described in [3].