@article{GowinKurthsSaparinetal.1997,
  author    = {Gowin, W. and Kurths, J{\"u}rgen and Saparin, Peter and Felsenberg, D.},
  title     = {Measures of complexity and processing of vertebral CT-images},
  isbn      = {0-7803-4262-3},
  year      = {1997},
  language  = {en}
}
@article{GowinSaparinKurths2001,
  author    = {Gowin, W. and Saparin, Peter and Kurths, J{\"u}rgen},
  title     = {Bone architecture quantification: Measures of complexity compared to failure lead results},
  year      = {2001},
  language  = {en}
}
@article{GowinSaparinKurthsetal.2001,
  author    = {Gowin, W. and Saparin, Peter and Kurths, J{\"u}rgen and Felsenberg, D.},
  title     = {Bone Architecture assessment with Measures of Complexity},
  year      = {2001},
  language  = {en}
}
@article{KopitzkiWarnkeSaparinetal.2002,
  author    = {Kopitzki, K. and Warnke, P. C. and Saparin, Peter and Kurths, J{\"u}rgen and Timmer, Jens},
  title     = {Comment on "Kullback-Leibler and renormalized entropies: Applications to electroencephalograms of epilepsy patients"},
  year      = {2002},
  language  = {en}
}
@article{MarwanBellerFelsenbergetal.2012,
  author    = {Marwan, Norbert and Beller, Gise and Felsenberg, Dieter and Saparin, Peter and Kurths, J{\"u}rgen},
  title     = {quantifying changes in the spatial structure of trabecular bone},
  series = {International journal of bifurcation and chaos : in applied sciences and engineering},
  volume    = {22},
  journal   = {International journal of bifurcation and chaos : in applied sciences and engineering},
  number    = {2},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0218-1274},
  doi       = {10.1142/S0218127412500277},
  pages     = {12},
  year      = {2012},
  abstract  = {We apply recently introduced measures of complexity for the structural quantification of distal tibial bone. For the first time, we are able to investigate the temporal structural alteration of trabecular bone. Based on four patients, we show how the bone may alter due to temporal immobilization.},
  language  = {en}
}
@article{MarwanKurthsThomsenetal.2009,
  author    = {Marwan, Norbert and Kurths, J{\"u}rgen and Thomsen, Jesper Skovhus and Felsenberg, Dieter and Saparin, Peter},
  title     = {Three-dimensional quantification of structures in trabecular bone using measures of complexity},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.79.021903},
  year      = {2009},
  abstract  = {The study of pathological changes of bone is an important task in diagnostic procedures of patients with metabolic bone diseases such as osteoporosis as well as in monitoring the health state of astronauts during long-term space flights. The recent availability of high-resolution three-dimensional (3D) imaging of bone challenges the development of data analysis techniques able to assess changes of the 3D microarchitecture of trabecular bone. We introduce an approach based on spatial geometrical properties and define structural measures of complexity for 3D image analysis. These measures evaluate different aspects of organization and complexity of 3D structures, such as complexity of its surface or shape variability. We apply these measures to 3D data acquired by high-resolution microcomputed tomography (mu CT) from human proximal tibiae and lumbar vertebrae at different stages of osteoporotic bone loss. The outcome is compared to the results of conventional static histomorphometry and exhibits clear relationships between the analyzed geometrical features of trabecular bone and loss of bone density, but also indicate that the measures reveal additional information about the structural composition of bone, which were not revealed by the static histomorphometry. Finally, we have studied the dependency of the developed measures of complexity on the spatial resolution of the mu CT data sets.},
  language  = {en}
}
@article{NeimanSaparinStone1997,
  author    = {Neiman, Alexander and Saparin, Peter and Stone, L.},
  title     = {Coherence resonance at noisy precursors of bifurcation in nonlinear dynamical systems},
  year      = {1997},
  language  = {en}
}
@article{SaparinHuppertStoneetal.1998,
  author    = {Saparin, Peter and Huppert, Amit and Stone, L. and Price, C.},
  title     = {El ni{\~n}o chaos : The role of noise and stochastic resonance on the ENSO cycle},
  year      = {1998},
  language  = {en}
}
@article{SaparinKurthsGowinetal.1997,
  author    = {Saparin, Peter and Kurths, J{\"u}rgen and Gowin, P. and Felsenberg, D.},
  title     = {Die quantitative Beurteilung trabecul{\"a}rer Knochenstrukturen der Lendenwirbelk{\"o}rper durch Meßmethoden der nicht-linearen Dynamik},
  year      = {1997},
  language  = {de}
}
@article{SchmahMarwanThomsenetal.2011,
  author    = {Schmah, Tanya and Marwan, Norbert and Thomsen, Jesper Skovhus and Saparin, Peter},
  title     = {Long range node-strut analysis of trabecular bone microarchitecture},
  series = {Medical physics : the international journal of medical physics research and practice},
  volume    = {38},
  journal   = {Medical physics : the international journal of medical physics research and practice},
  number    = {9},
  publisher = {American Association of Physicists in Medicine},
  address   = {Melville},
  issn      = {0094-2405},
  doi       = {10.1118/1.3622600},
  pages     = {5003 -- 5011},
  year      = {2011},
  abstract  = {Purpose: We present a new morphometric measure of trabecular bone microarchitecture, called mean node strength (NdStr), which is part of a newly developed approach called long range nodestrut analysis. Our general aim is to describe and quantify the apparent "latticelike" microarchitecture of the trabecular bone network. Methods: Similar in some ways to the topological node-strut analysis introduced by Garrahan et al. [J. Microsc. 142, 341-349 (1986)], our method is distinguished by an emphasis on long-range trabecular connectivity. Thus, while the topological classification of a pixel (after skeletonization) as a node, strut, or terminus, can be determined from the 3 x 3 neighborhood of that pixel, our method, which does not involve skeletonization, takes into account a much larger neighborhood. In addition, rather than giving a discrete classification of each pixel as a node, strut, or terminus, our method produces a continuous variable, node strength. The node strength is averaged over a region of interest to produce the mean node strength of the region. Results: We have applied our long range node-strut analysis to a set of 26 high-resolution peripheral quantitative computed tomography (pQCT) axial images of human proximal tibiae acquired 17 mm below the tibial plateau. We found that NdStr has a strong positive correlation with trabecular volumetric bone mineral density (BMD). After an exponential transformation, we obtain a Pearson's correlation coefficient of r - 0.97. Qualitative comparison of images with similar BMD but with very different NdStr values suggests that the latter measure has successfully quantified the prevalence of the "latticelike" microarchitecture apparent in the image. Moreover, we found a strong correlation (r - 0.62) between NdStr and the conventional node-terminus ratio (Nd/Tm) of Garrahan et al. The Nd/Tm ratios were computed using traditional histomorphometry performed on bone biopsies obtained at the same location as the pQCT scans. Conclusions: The newly introduced morphometric measure allows a quantitative assessment of the long-range connectivity of trabecular bone. One advantage of this method is that it is based on pQCT images that can be obtained noninvasively from patients, i.e., without having to obtain a bone biopsy from the patient.},
  language  = {en}
}