title: A method of surface marker location optimization for tumor motion estimation in lung stereotactic body radiation therapy.
abstract: OBJECTIVE
  Accurately localizing lung tumor localization is essential for high-precision radiation therapy techniques such as stereotactic body radiation therapy (SBRT). Since direct monitoring of tumor motion is not always achievable due to the limitation of imaging modalities for treatment guidance, placement of fiducial markers on the patient's body surface to act as a surrogate for tumor position prediction is a practical alternative for tracking lung tumor motion during SBRT treatments. In this work, the authors propose an innovative and robust model to solve the multimarker position optimization problem. The model is able to overcome the major drawbacks of the sparse optimization approach (SOA) model.
  
  
  METHODS
  The principle-component-analysis (PCA) method was employed as the framework to build the authors' statistical prediction model. The method can be divided into two stages. The first stage is to build the surrogate tumor matrix and calculate its eigenvalues and associated eigenvectors. The second stage is to determine the "best represented" columns of the eigenvector matrix obtained from stage one and subsequently acquire the optimal marker positions as well as numbers. Using 4-dimensional CT (4 DCT) and breath hold CT imaging data, the PCA method was compared to the SOA method with respect to calculation time, average prediction accuracy, prediction stability, noise resistance, marker position consistency, and marker distribution.
  
  
  RESULTS
  The PCA and SOA methods which were both tested were on all 11 patients for a total of 130 cases including 4 DCT and breath-hold CT scenarios. The maximum calculation time for the PCA method was less than 1 s with 64 752 surface points, whereas the average calculation time for the SOA method was over 12 min with 400 surface points. Overall, the tumor center position prediction errors were comparable between the two methods, and all were less than 1.5 mm. However, for the extreme scenarios (breath hold), the prediction errors for the PCA method were not only smaller, but were also more stable than for the SOA method. Results obtained by imposing a series of random noises to the surrogates indicated that the PCA method was much more noise resistant than the SOA method. The marker position consistency tests using various combinations of 4 DCT phases to construct the surrogates suggested that the marker position predictions of the PCA method were more consistent than those of the SOA method, in spite of surrogate construction. Marker distribution tests indicated that greater than 80% of the calculated marker positions fell into the high cross correlation and high motion magnitude regions for both of the algorithms.
  
  
  CONCLUSIONS
  The PCA model is an accurate, efficient, robust, and practical model for solving the multimarker position optimization problem to predict lung tumor motion during SBRT treatments. Due to its generality, PCA model can also be applied to other imaging guidance system whichever using surface motion as the surrogates.
authors.affiliation: Department of Radiation Oncology, University of Florida College of Medicine, Gainesville, Florida 32610.
authors.forename: Bo
authors.initials: B
authors.lastname: Lu
authors.affiliation: Department of Mathematics, University of Florida College of Liberal Arts and Sciences, Gainesville, Florida 32610.
authors.forename: Yunmei
authors.initials: Y
authors.lastname: Chen
authors.affiliation: Department of Radiation Oncology, University of Florida College of Medicine, Gainesville, Florida 32610.
authors.forename: Justin C
authors.initials: JC
authors.lastname: Park
authors.affiliation: Department of Radiation Oncology, University of Florida College of Medicine, Gainesville, Florida 32610.
authors.forename: Qiyong
authors.initials: Q
authors.lastname: Fan
authors.affiliation: Department of Radiation Oncology, University of Florida College of Medicine, Gainesville, Florida 32610.
authors.forename: Darren
authors.initials: D
authors.lastname: Kahler
authors.affiliation: Department of Radiation Oncology, University of Florida College of Medicine, Gainesville, Florida 32610.
authors.forename: Chihray
authors.initials: C
authors.lastname: Liu
mesh_terms: D000465:Algorithms; D062485:Breath Holding; D057918:Fiducial Markers; D006801:Humans; D008168:Lung / Q000000981:diagnostic imaging; D008175:Lung Neoplasms / Q000000981:diagnostic imaging / Q000532:radiotherapy* / Q000601:surgery; D008954:Models, Biological; D009038:Motion; D025341:Principal Component Analysis; D016634:Radiosurgery / Q000379:methods*; D012189:Retrospective Studies; D013997:Time Factors; D014057:Tomography, X-Ray Computed / Q000379:methods