A Generation Methodology for Numerical Phantoms with Statistically Relevant Variability of Geometric and Physical Properties

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1 A Generation Methodology for Numerical Phantoms with Statistically Relevant Variability of Geometric and Physical Properties Steven Dolly 1, Eric Ehler 1, Yang Lou 2, Mark Anastasio 2, Hua Li 2 (1) University of Minnesota, Minneapolis, MN (2) Washington University in St. Louis, Saint Louis (3) Washington University School of Medicine, Saint Louis, MO

2 Introduction Numerical (i.e. digital) phantoms are useful for implementing computer-simulation studies by providing a known, ground-truth object Enables assessment of image quality, segmentation, registration, and radiotherapy efficacy Useful studies require realistic phantoms Realistic in terms of depth of detail and breadth of variability

3 Introduction Depth of detail can be accomplished by thorough segmentation of high-quality medical images Breadth of variability is accomplished by adequately modeling the statistics of organ variability Geometric (e.g. shape) and physical (e.g. photon attenuation) properties

4 Purpose 1) To develop a methodology of generating numerical phantoms that have both geometric and physical property variability, which is learned from actual patient data using attribute distribution models 2) The methodology was demonstrated by generating an ensemble of head-and-neck CT phantoms, with corresponding images

5 Attribute Distribution Models Quantify the statistical distribution of an attribute in terms of its principal components using principal component analysis (PCA): Covariance Eigenvectors (direction) Eigenvalues (magnitude) Three attribute models considered for this numerical phantom: 1) Shape attribute distribution model 2) Centroid attribute distribution model 3) Physical attribute distribution model

6 Workflow Phase 1: Model Training Phase 2: Phantom Generation Training Data Acquisition Attribute Distribution Model Construction Apply Models Mesh Creation & Post-processing Numerical Phantom(s)

7 Workflow Phase 1: Model Training Phase 2: Phantom Generation Training Data Acquisition Attribute Distribution Model Construction Apply Models Mesh Creation & Post-processing Numerical Phantom(s)

8 Training Data Acquisition Extracted and anonymized planning CT images and RT structure files from previously treated head-and-neck cancer patients CT Image RT Structure (Left Parotid) Process produced 20 patient data sets, with 23 organs per patient

9 Attribute Distribution Model Construction Model: Mean + Randomly-weighted variation Trained Using: Shape: Centroid: RT Structures Physical (CT): CT Images + RT Structures

10 Sample Shape Attribute Distribution Model a(p) s = -2σ Mean Shape a(p) s = +2σ 1 st Component 2 nd Component Left Parotid Shape Components 3 rd Component

11 Centroid Attribute Distribution Model Superior Left Anterior

12 Physical Attribute Distribution Model Left Parotid Brain Organ CT histograms

13 Workflow Phase 1: Model Training Phase 2: Phantom Generation Training Data Acquisition Attribute Distribution Model Construction Apply Models Mesh Creation & Post-processing Numerical Phantom(s)

14 Numerical Phantom Generation HU **Repeat for all n organs **Repeat for all n organs

15 Numerical Phantom Geometries Superior Left Mean Sample

16 CT Image Simulation Helical projection data was simulated by calculating photon exponential attenuation through the phantoms

17 CT Images Mean Sample

18 In this study: Conclusion 1) The statistical variability of physical and geometric properties for patient organs was learned from training data using PCA 2) The generated phantoms encapsulate the variability of the training data set, removing the bias of single-phantom studies 3) CT images of the phantoms were simulated as a demonstrated use

19 Future Work Incorporation of a priori knowledge as constraints in the post-processing step Example: spinal cord must smoothly connect to brain stem More realistic representation of background tissues (e.g. muscle) Multi-modality imaging simulation (e.g. MRI)

20 Thank You! Any questions or comments? Contact: Steven Dolly

21 Extra Slides

22 Shape Attribute Distribution Model Organ shapes were defined using implicit surface functions: One model per organ: intra-structural model

23 Shape Attribute Distribution Model 1) Preprocessing: Translate organ surfaces (polygons) so centroid origin 2) Calculate implicit surfaces 3) Calculate mean and covariance 4) Perform PCA to produce components and construct model

24 Centroid Attribute Distribution Model 1) Pre-processing: Procrustes analysis 2) Calculate organ centroids (mean of each organ s polygon points) 3) Calculate mean and covariance 4) Perform PCA and construct model (inter-structural)

25 Physical Attribute Distribution Model 1) Determine which CT voxels belong to each organ using contours 2) Calculate HU histograms for each organ 3) Use most probable HU as the mean value

26 Numerical Phantom CT Numbers Organ Mean CT Number (HU) Sample CT Number (HU) Left Parotid Right Parotid Brain Stem Spinal Cord Left Eye Left Lacrimal Gland

27 Mesh Creation & Post-processing Normal calculation and Poisson surface reconstruction utilized to convert to triangular meshes; quadric edge decimation used to simplify

28 Organ Overlap Challenge Two main approaches to handle organ overlap issues via post-processing: 1) Heuristic iterative shift approach 2) Crop out intersection of deformable organs In the future, the shape/centroid models could be constrained to limit organ overlap

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