title: A new algorithm for estimating the rod volume fraction and the trabecular thickness from in vivo computed tomography.
abstract: OBJECTIVE
  Existing microstructure parameters are able to predict vertebral in vitro failure load, but for noisy in vivo data more complex algorithms are needed for a robust assessment.
  
  
  METHODS
  A new algorithm is proposed for the microstructural analysis of trabecular bone under in vivo quantitative computed tomography (QCT). Five fractal parameters are computed: (1) the average local fractal dimension FD, (2) its standard deviation FD.SD, (3) the fractal rod volume ratio fRV/BV, (4) the average fractal trabecular thickness fTb.Th, and (5) its coefficient of variation fTb.Th.CV. The algorithm requires neither an explicit skeletonization of the trabecular bone, nor a well-defined transition between bone and marrow phases. Two experiments were conducted to compare the fractal with established microstructural parameters. In the first, 20 volumes-of-interest of embedded vertebrae phantoms were scanned five times under QCT and high-resolution (HR-)QCT and once under peripheral HRQCT (HRpQCT), to derive accuracy and precision. In the second experiment, correlations between in vitro HRQCT structural parameters were obtained from 76 human T11, T12, or L1vertebrae. In vitro fracture data were available for a subset of 17 human T12vertebrae so that linear regression models between failure load and microstructural HRQCT parameters could be analyzed.
  
  
  RESULTS
  The results showed correlations of fTb.Th and fRV/BV with their nonfractal pendants trabecular thickness (Tb.Th) and respective structure model index (SMI) while higher precision and accuracy was observed on the fractal measures. Linear models of bone mineral density with two and three fractal microstructural HRQCT parameters explained 86% and 90% (adjusted R2) of the failure load and significantly improved the linear models based only on BMD and established standard microstructural parameters (68%-77% adjusted R2).
  
  
  CONCLUSIONS
  The application of fractal methods may grant further insight into the study of bone quality in vivo when image resolution and quality are less than optimal for current standard methods.
authors.affiliation: National Scientific and Technical Research Council (CONICET) and Department of Electrical Engineering and Computers, National University of the South, Bahía Blanca 8000, Argentina.
authors.forename: Felix Sebastian Leo
authors.initials: FS
authors.lastname: Thomsen
authors.affiliation: Section Biomedical Imaging, Department of Radiology and Neurology, University Hospital Schleswig-Holstein, Campus Kiel 24118, Germany.
authors.forename: Jaime Andrés
authors.initials: JA
authors.lastname: Peña
authors.affiliation: Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China and Institute of Biomechanics, Hamburg University of Technology, Hamburg 21073, Germany.
authors.forename: Yongtao
authors.initials: Y
authors.lastname: Lu
authors.affiliation: Institute of Biomechanics, Hamburg University of Technology, Hamburg 21073, Germany.
authors.forename: Gerd
authors.initials: G
authors.lastname: Huber
authors.affiliation: Institute of Biomechanics, Hamburg University of Technology, Hamburg 21073, Germany.
authors.forename: Michael
authors.initials: M
authors.lastname: Morlock
authors.affiliation: Section Biomedical Imaging, Department of Radiology and Neurology, University Hospital Schleswig-Holstein, Campus Kiel 24118, Germany.
authors.forename: Claus-Christian
authors.initials: CC
authors.lastname: Glüer
authors.affiliation: National Scientific and Technical Research Council (CONICET) and Department of Electrical Engineering and Computers, National University of the South, Bahía Blanca 8000, Argentina.
authors.forename: Claudio Augusto
authors.initials: CA
authors.lastname: Delrieux
mesh_terms: D000465:Algorithms; D015519:Bone Density; D000071556:Cancellous Bone / Q000033:anatomy & histology / Q000000981:diagnostic imaging* / Q000502:physiology; D017709:Fractals; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D012044:Regression Analysis; D013131:Spine / Q000033:anatomy & histology / Q000000981:diagnostic imaging / Q000502:physiology; D014057:Tomography, X-Ray Computed; D016474:Weight-Bearing