Πειραματική και αριθμητική διερεύνηση της επιφανειακής παραμόρφωσης σε φυσικό σπογγώδες οστό και 3Δ εκτυπωμένα αντίγραφά του για την μελέτη της οστεοπόρωσης

Abstract

Trabecular bones have been extensively studied for the last 50 years and the studies of its morphology have been carried out by numerous researchers. From an engineering point of view, cancellous bone is an anisotropic, highly complex structure. It demonstrates different properties in compression, tension and shear as well as across anatomical sites. Trabecular bone is regarded as a composite material, with open porous cellular structure that demonstrates elastic-plastic behavior under stress-strain relationship. Owing to the microarchitectural properties, the trabecular bone exhibits anisotropic mechanical properties which are influenced in a great scale by its volume fraction (apparent density). Applied stress or strain rates alter the microstructure of the trabecular bone and strength thus it is said that trabecular bone might be anisotropic since it exhibits different stiffness and strength in different directions of loading (longitudinal or transverse).The mechanical properties of trabecular bone tissue can be distinguished from other biological materials (including compact bone) due to high heterogeneity of trabecular structure which leads to huge variation in apparent properties. The heterogeneity results from the underlying variation of bone volume fraction, microarchitecture and tissue properties. Furthermore, it is affected by the different levels of physiological activities in the daily routine (walking, running, climbing stairs etc.). All these factors affect the magnitudes of modulus and strength across anatomic sites and species which depend on their respective mechanical response. Loss of stiffness and permanent residual strains are often observed to occur upon compressive loading-unloading of the trabecular bone beyond its yielding point. Reduction in stiffness suggests damage in the bone and plasticity is indicated by the residual strain accumulation. Damage in the trabeculae induces the stiffness reduction with microcracking occurrences at very small scales which is influenced by the strains at apparent and tissue levels. In the first part of the study, the surface heterogeneity in mechanical compressive strain of cancellous bone was investigated with digital image correlation (DIC). Moreover, the onset and progression of failure was studied by acoustic emission (AE). Strain of cubic cancellous bone specimens was analyzed by measuring the change of distance between the platens (crosshead) and via an optical method. Simultaneously, AE monitoring was performed. The experiments showed that compressive Young’s modulus determined by crosshead strain is underestimated at 23% in comparison to optically determined strain. However, surface strain fields defined by DIC displayed steep strain gradients, which can be attributed to cancellous bone porosity and inhomogeneity. The cumulative number of events for the total AE activity recorded from the sensors showed that the activity started at a mean load level of 36% of the maximum load and indicated the initiation of micro-cracking phenomena. Sequentially, acoustic emission (AE) and three-dimensional digital image correlation (3D-DIC) were combined during compression and tension of cancellous bone samples. The inhomogeneity distribution of the longitudinal surface strain along with the visualization of the full-field surface strain map were assessed by 3D-DIC. Simultaneously, AE monitoring was performed to evaluate the time of crack initiation and to correlate the acoustic behavior of the samples with the local surface measurements of strain. The experiments revealed an onset of the crack formation adjacent but prior to yielding and a continuation of the AE activity at the post-yield region for both loading methods. For the same displacement rate, there was a greater number of emissions during compression than tension, but magnitude of amplitude was almost the same. The cumulative AE events correlated with a power-law relationship with the load, time and surface strain for both experiments. Finally, through 3D-DIC, an inhomogeneous strain pattern was calculated across the samples’ surfaces for both loading methods. Dividing the specimen’s surface into areas from the center up to near the platens’ edges, calculation of strain field values suggested homogeneity during compression of the specimen but small differences between specific areas during tension. Finally, diffuse damage was appeared at the surface of the samples almost prior to yielding as a result of microcracking accumulation. Further analysis, requiring finite element models of these samples, is necessary to investigate the 3D-full field strain development. In the third part of this study, the aim firstly was to verify by compressive tests that a 3D-printer is capable to produce precisely and repeatedly “bone replica models” of different size and density. Following, replicas of the original specimens with two different polymers and thinned trabeculae models were used to investigate their ultrasonic properties (speed of sound (SOS) and backscatter coefficient), aiming to deconvolute the influence of material properties on ultrasound characteristics. The results revealed that matrix material properties influence only the magnitude of the backscatter coefficient, whereas the characteristic undulated patterns are related to the trabecular structure. Simulation of perforation and thinning of cancellous bone, associated with bone loss, showed that SOS and mechanical properties were reduced perfectly linearly with apparent density, when structure deteriorated. 3D-printed bone replicas have the potential to enable systematic investigations of the influence of structure on both acoustical and mechanical properties and evaluate changes caused by bone loss. The development of replicas from materials with properties close to those of bone will permit quantitative conclusions for trabecular bone. Trabecular bone is a hard tissue with a complex internal porous structure having an interconnected network with trabeculae. At tissue level, the material properties of the trabeculae, in combination with their microarchitectures, determine the strength and stiffness of trabecular bone under loading which indicates the capacity to withstand load. Furthermore, the evaluation of quantity and quality of bone provide the basic elements for the diagnosis and prevention of different bone diseases. One way to evaluate the pathophysiology of those diseases is to analyse the trabecular structure. However, the analysis of trabecular bone has been challenging. To obtain the mechanical properties researchers have performed mechanical tests. However, this method may be subject to large errors unless specific experimental protocols are designed to minimize the artifact errors. Secondly, since the tests are destructive, the number of measurements that can be taken for each specimen is narrowed. Moreover, the local morphological characteristics of trabecular bone play a relevant role at the way the damage grows at the local trabeculae, propagates and then is followed by the development of the fracture. With the development of computation power, micro-tomography (microCT) came to the foreground. MicroCT imaging allows the visualization of the 3-dimensional internal structure and geometry of the trabecular bone along with the examination of its framework by performing non-destructive analysis. Furthermore, microCT data linked to Finite Element Analysis (FEA) could provide estimations about bone strength along with stress and strain distribution. μFEA has gained popularity since it can be used to quantify the tissue Young’s modulus of trabecular bone under different and complex loading conditions determine the mechanical behavior and predict the apparent yield properties and estimate the amount of tissue damage. In the literature, FEM represents a widely accepted method for studying the mechanical behavior of trabecular bone at tissue level. The most common approach of the μFEM simulation is a linear elastic constitutive law either to calculate the elastic modulus at tissue level or to estimate the strain distribution all over the internal framework. For such studies, linear elastic isotropic material properties were assigned to bone tissue along with the assumption of small deformations under loading. However, a number of non-linear models are reported in the literature since under large loading conditions, bone tissue material nonlinearity and large deformations that may be occurred due to buckling and bending of the trabeculae should be taken into consideration. Yet, there is still a lack of knowledge about which non-linear model is the most reliable in estimating the stress and strain distribution. Eventually, in the last part of this study, microCT was used to characterize the internal structure of bovine trabecular bone specimen. μfinite element models were developed from CT scan images for a healthy trabecular bone and two technically simulated osteoporotic samples were produced in order to investigate the mechanical behavior of models with and without bone resorption. Finite element analysis was performed with aim to simulate the mechanical performance of samples with different BV/TV (bone volume fraction), estimate the yield features during compression of the samples and determine the strain field of different surface sections in order to process the homogeneity of it due to trabeculae oriented in the outer parts of the external surface which may be subjected to other loading mode than the external one.

Η παρούσα διατριβή αποτελεί μια συνεισφορά στον επιστημονικό χώρο της εμβιομηχανικής και πιο συγκεκριμένα της οστεομηχανικής. Κομμάτι του κλάδου αυτού αποτελεί η μελέτη του σπογγώδους οστού, ένα από τα δύο βασική είδη οστού που συναντώνται στους ζώντες οργανισμούς. Η ιδιαίτερη εσωτερική αρχιτεκτονική δομή που παρουσιάζει σε συνδυασμό με το φλέγον οικονομικό και ιατρικό ζήτημα της οστεοπόρωσης, την περισσότερο συνηθισμένη ασθένεια του σπογγώδους οστού, και τις μεταβολές που προκαλεί στη δομή του και κατ’ επέκταση στη μηχανική του συμπεριφορά, το καθιστά αντικείμενο έρευνας και μελέτης. Το έναυσμα για τη διατριβή δόθηκε εξαιτίας ενός ζητήματος που επικρατεί στον κλάδο της μηχανικής των οστών και αφορά δυσκολίες/περιορισμούς στο μηχανικό πείραμα της θλιπτικής καταπόνησης δοκιμίων σπογγώδους οστού και στις αλλοιώσεις που δύναται να προκληθούν στη μέτρηση των μηχανικών ιδιοτήτων (π.χ. εκτίμηση μέτρου ελαστικότητας). Ξεκινώντας από το ζήτημα αυτό, στην πορεία προέκυψαν περαιτέρω θέματα προς μελέτη, όπως τι μπορεί να προκαλεί τις μεταβολές στις μετρήσεις, γι’ αυτό και προσδιορίστηκε το πεδίο παραμορφώσεων στην επιφάνεια δοκιμίων σπογγώδους οστού κατά τη διάρκεια θλιπτικών και εφελκυστικών καταπονήσεων, μέσω οπτικής μεθόδου μέτρησης παραμορφώσεων ώστε να ελεγχθεί και η εγκυρότητα της χρήσης της ως εναλλακτικό μέσο εκτίμησης μηχανικών ιδιοτήτων καθώς και η καταγραφή υπερηχητικών σημάτων από το εσωτερικό των δοκιμίων για συσχέτιση τους με την επιφανειακή συμπεριφορά και τη μακροσκοπική διαρροή του υλικού με τη διάδοση και έναρξη μικρορωγμών.Επεκτείνοντας τη διατριβή, μελετήθηκε το ζήτημα της οστεοπόρωσης. Προσομοιώθηκαν δύο βαθμοί οστεοπόρωσης μέσω 3Δ εκτυπωμένων τεχνητών αντιγράφων φυσικών δοκιμίων σπογγώδους οστού. Στόχος ήταν η καταγραφή της μεταβολής των μηχανικών ιδιοτήτων του σπογγώδους οστού λόγω απώλειας ιστού και κατά πόσον εξαρτάται η μηχανική συμπεριφορά του από το υλικό του ιστού ή από την εσωτερική του δομή. Ολοκληρώνοντας τη διατριβή, πραγματοποιήθηκαν αριθμητικές αναλύσεις των αντίστοιχων μηχανικών πειραμάτων θλιπτικής καταπόνησης στα ψηφιακά μοντέλα των φυσικών δοκιμίων σπογγώδους οστού. Σκοπός ήταν η περαιτέρω διερεύνηση της κατανομής πεδίου επιφανειακών παραμορφώσεων και η μελέτη των μορφών καταπόνησης των στοιχείων (προσομοίωση δοκίδων) για τη σύγκριση και επαλήθευση των δεδομένων των αρχικών μηχανικών πειραμάτων και των αιτιών αλλοίωσης των μηχανικών ιδιοτήτων. Παράλληλοι στόχοι ήταν η επιβεβαίωση των υπολογιστικών αναλύσεων μέσω της ΑΕ με τη μέτρηση του ποσοστού των στοιχείων που ξεπερνούν το όριο διαρροής καθώς και η σύγκριση των αποτελεσμάτων των αριθμητικών προσομοιώσεων με τα αντίστοιχα ευρήματα της οπτικής μεθόδου προσδιορισμού επιφανειακών παραμορφώσεων ώστε να ελεγχθεί η εγκυρότητας της τεχνικής αυτής ως μέσο υπολογισμού μηχανικών ιδιοτήτων. Τα αποτελέσματα της διατριβής συμβάλλουν στην επέκταση του γνωστικού ορίζοντα σχετικά με την καταπόνηση των δοκίδων (βασική μονάδα του σπογγώδους οστού) και στη φύση και κατανομή των βαθμίδων παραμόρφωσης στην επιφάνεια με παράλληλη αντιστοίχησή τους με τη μηχανική συμπεριφορά δοκιμίων σπογγώδους οστού.