Micromechanics of bone tissue-engineering scaffolds, based on resolution error-cleared computer tomography Stefan Scheiner a,1 , Raffaele Sinibaldi b,1 , Bernhard Pichler a , Vladimir Komlev b, c , Chiara Renghini b , Chiara Vitale-Brovarone d , Franco Rustichelli b , Christian Hellmich a, * a Vienna University of Technology, Institute for Mechanics of Materials and Structures, Karlsplatz 13/202, A-1040 Vienna, Austria b Polytechnic University of Marche, Department SAIFET, INBB – Istituto Nazionale Biostrutture e Biosistemi, CNISM – MATEC (Ancona) via Brecce Bianche, I-60131 Ancona, Italy c Russian Academy of Sciences, A.A. Baikov Institute of Metallurgy and Materials Science, Leninsky pr. 49,119991 Moscow, Russia d Politecnico di Torino, Department of Materials Science and Chemical Engineering, Corso Duca Degli Abruzzi 24, I-10129 Torino, Italy article info Article history: Received 12 November 2008 Accepted 19 December 2008 Available online 9 January 2009 Keywords: CEL2 glass–ceramic Scaffold Bone tissue engineering Continuum micromechanics Microtomography Finite element method abstract Synchrotron radiation micro-computed tomography (SRmCT) revealed the microstructure of a CEL2 glass–ceramic scaffold with macropores of several hundred microns characteristic length, in terms of the voxel-by-voxel 3D distribution of the attenuation coefficients throughout the scanned space. The probability density function of all attenuation coefficients related to the macroporous space inside the scaffold gives access to the tomograph-specific machine error included in the SRmCT measurements (also referred to as instrumental resolution function). After Lorentz function-based clearing of the measured CT data from the systematic resolution error, the voxel-specific attenuation information of the voxels representing the solid skeleton is translated into the composition of the material inside one voxel, in terms of the nanoporosity embedded in a dense CEL2 glass–ceramic matrix. Based on voxel-invariant elastic properties of dense CEL2 glass–ceramic, continuum micromechanics allows for translation of the voxel-specific nanoporosity into voxel-specific elastic properties. They serve as input for Finite Element analyses of the scaffold structure. Young’s modulus of a specific CT-scanned macroporous scaffold sample, predicted from a Finite Element simulation of a uniaxial compression test, agrees well with the experimental value obtained from an ultrasonic test on the same sample. This highlights the satisfactory predictive capabilities of the presented approach. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction Computed tomography (CT), the mathematical basis for which was established in 1917 by Radon [1], and for the first time successfully applied in 1972 [2], is a powerful non-destructive evaluation technique for producing three-dimensional (3D) images, revealing the microstructure of objects [3–10]. For this purpose, X-rays are sent through the investigated object, and the trans- mitted intensity is recorded as a 2D image [3]. If this transmission is repeated under different angles in the 3D space, all corresponding images can be transformed into one 3D distribution of X-ray attenuation coefficients, giving access to a 3D image of the object. Numerically, the latter is defined through values related to small volume units, called voxels. Over recent years, CT has become a widely applied tool in science, technology, industry, and medi- cine, with a particularly strong position in the latter field [6,11–16]. There, it supports the clinical practice, but also fundamental research devoted e.g. to development of novel biomaterials or tissue engineering [17–24] (regenerative medicine). The latter endeavors have motivated the striving for an even finer resolution, in order to reveal, in a 3D fashion, more and more of the micro- structures and nanostructures found in biological and biomimetic materials. Evaluation of the obtained data by means of appropriate visualization tools allows for definition of topology and geometry of the investigated objects. This information allows for further data processing and understanding, such as mechanical simulations (e.g. based on Finite Elements) of biostructures [25–29]. These analyses can serve as basis to quantify mechanical properties of the inves- tigated objects, which helps (i) to replace (or at least to decrease the amount of) additional, often expensive laboratory testing on a large number of specimens, and (ii) to learn about implications of different alternatives to a specific implantation strategy, as well as to support the corresponding decision-making process. * Corresponding author. Tel.: þ43 1 58801 20220; fax: þ43 1 58801 20299. E-mail address: christian.hellmich@tuwien.ac.at (C. Hellmich). 1 Both authors contributed equally to this work. Contents lists available at ScienceDirect Biomaterials journal homepage: www.elsevier.com/locate/biomaterials 0142-9612/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.biomaterials.2008.12.048 Biomaterials 30 (2009) 2411–2419