@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{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{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{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{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{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{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} } @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{ZaikinKurthsSaparinetal.2005, author = {Zaikin, Alexei and Kurths, J{\"u}rgen and Saparin, Peter and Gowin, W. and Prohaska, Steffen}, title = {Modeling bone resorption in 2D CT and 3D mu CT images}, issn = {0218-1274}, year = {2005}, abstract = {We study several algorithms to simulate bone mass loss in two-dimensional and three-dimensional computed tomography bone images. The aim is to extrapolate and predict the bone loss, to provide test objects for newly developed structural measures, and to understand the physical mechanisms behind the bone alteration. Our bone model approach differs from those already reported in the literature by two features. First, we work with original bone images, obtained by computed tomography (CT); second, we use structural measures of complexity to evaluate bone resorption and to compare it with the data provided by CT. This gives us the possibility to test algorithms of bone resorption by comparing their results with experimentally found dependencies of structural measures of complexity, as well as to show efficiency of the complexity measures in the analysis of bone models. For two-dimensional images we suggest two algorithms, a threshold algorithm and a virtual slicing algorithm. The threshold algorithm simulates bone resorption on a boundary between bone and marrow, representing an activity of osteoclasts. The virtual slicing algorithm uses a distribution of the bone material between several virtually created slices to achieve statistically correct results, when the bone-marrow transition is not clearly defined. These algorithms have been tested for original CT 10 mm thick vertebral slices and for simulated 10 mm thick slices constructed from ten I mm thick slices. For three-dimensional data, we suggest a variation of the threshold algorithm and apply it to bone images. The results of modeling have been compared with CT images using structural measures of complexity in two- and three-dimensions. This comparison has confirmed credibility of a virtual slicing modeling algorithm for two-dimensional data and a threshold algorithm for three-dimensional data}, 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} }