The use of synchrotron radiation micro-computed tomography (SR-microCT) is becoming increasingly popular for studying the relationship between microstructure and bone mechanics subjected to in situ mechanical testing. However, it is well known that the effect of SR X-ray radiation can considerably alter the mechanical properties of bone tissue. Digital volume correlation (DVC) has been extensively used to compute full-field strain distributions in bone specimens subjected to step-wise mechanical loading, but tissue damage from sequential SR-microCT scans has not been previously addressed. Therefore, the aim of this study is to examine the influence of SR irradiation-induced microdamage on the apparent elastic properties of trabecular bone using DVC applied to in situ SR-microCT tomograms obtained with different exposure times. Results showed how DVC was able to identify high local strain levels (> 10,000 µε) corresponding to visible microcracks at high irradiation doses (~ 230 kGy), despite the apparent elastic properties remained unaltered. Microcracks were not detected and bone plasticity was preserved for low irradiation doses (~ 33 kGy), although image quality and consequently, DVC performance were reduced. DVC results suggested some local deterioration of tissue that might have resulted from mechanical strain concentration further enhanced by some level of local irradiation even for low accumulated dose.
Cortical bone is an example of a mineralized tissue containing a compositional distribution of hard and soft phases in 3-dimensional space for mechanical function. X-ray computed tomography (XCT) is able to describe this compositional and morphological complexity but methods to provide a physical output with sufficient fidelity to provide comparable mechanical function is lacking. A workflow is presented in this work to establish a method of using high contrast XCT to establish a virtual model of cortical bone that is manufactured using a multiple material capable 3D printer. Resultant 3D printed structures were produced based on more and less remodelled bone designs exhibiting a range of secondary osteon density. Variation in resultant mechanical properties of the 3D printed composite structures for each bone design was achieved using a combination of material components and reasonable prediction of elastic modulus provided using a Hashin-Shtrikman approach. The ability to 3D print composite structures using high contrast XCT to distinguish between compositional phases in a biological structure promises improved anatomical models as well as next-generation mechano-mimetic implants.
The complex geometry of cancellous bone tissue makes it difficult to generate finite element (FE) models. Only a few studies investigated the convergence behavior at the tissue scale using Cartesian meshes. However, these studies were not conducted according to an ideal patch test and the postelastic convergence behavior was not reported. In this study, the third principal strain and stress, and the displacement obtained from human micro finite element (microFE) models of lower resolutions were compared against the model of 19.5 μm as a reference, representing the original spatial resolution of microCT data. Uni-axial compression simulations using both linear-elastic and nonlinear constitutive equations were performed. The results showed a decrease in percentage difference in all three values as the element size decreased, with the displacement converging the fastest among the three. Simulations carried out using a nonlinear constitutive equation however, failed to show convergence for the third principal strains and stresses. It was concluded that at the tissue level, Cartesian meshes of human cancellous bone tissue were able to reach a converged solution in all three parameters investigated for linear simulation and only in displacement for nonlinear simulation. These parameters can be used as references in the future for studies in local biomechanical behavior of human cancellous bone tissues with linear simulation. The convergence behavior for human cancellous bone tissue using nonlinear constitutive equations needs further investigation.
A popular framework in continuum mechanics modeling of soft tissues is the use of an additive split of the total strain energy function (W) into the contribution of the isotropic matrix (Wiso) and the anisotropic collagen fiber networks (Waniso): W = Wiso + Waniso. This paper presents specialized strain energy functions for the Waniso part of this additive split, in the form of Waniso(I4) or Waniso(I4, I6) for one or two fiber families, respectively, accounting for the deformation and contribution of the collagen fibers’ network. The models have their origins in the statistical mechanics treatment of chains network based on a non-Gaussian, a Gaussian, and a modified Gaussian approach. The models are applied to extant experimental stress-stretch data, across multi-scales from a single collagen molecule to the network ensemble, demonstrating an excellent agreement. Due to the direct physical structural basis of the model parameters and therefore their objectivity and uniqueness, these models are proposed as advantageous options next to the existing phenomenological continuum-based strain energy functions in the literature. In addition, and while not exploited in this paper, since the model parameters are inherent structural properties of the collagen molecular chains, they may be established a priori via imaging or molecular techniques. Therefore, the proposed models allow the important possibility of precluding the need for destructive mechanical tests and calibration a posteriori, instead of paving the way for predicting the mechanical behavior of the collagen network from pre-established structural parameters. These features render the proposed models as attractive choices for application in continuum-based modeling of collagenous soft tissues.
Many biological phenomena are inherently multiscale, i.e. they are characterised by interactions involving different scales at the same time. This is the case of bone remodelling, where macroscopic behaviour (at organ and tissue scale) and microstructure (at cell scale) strongly influence each other. Consequently, several approaches have been defined to model such a process at different spatial and temporal levels and, in particular, in terms of continuum properties, abstracting in this way from a realistic - and more complex - cellular scenario. While a large amount of information is available to validate such models separately, more work is needed to integrate all levels fully in a faithful multiscale model.\ud
In this scenario, we propose the use of BioShape, a 3D particle-based, scale-independent, geometry and space oriented simulator. It is used to define and integrate a cell and tissue scale model for bone remodelling in terms of shapes equipped with perception, interaction and movement capabilities. Their in-silico simulation allows for tuning continuum-based tissutal and cellular models, as well as for better understanding - both in qualitative and in quantitative terms - the blurry synergy between mechanical and metabolic factors triggering bone remodelling
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