Micromechanical modelling of cortical bone

Cortical bone is a heterogeneous material with a complex hierarchical microstructure. In this work, unit cell finite element models were developed to investigate the effect of microstructural morphology on the macroscopic properties of cortical bone. The effect of lacunar and vascular porosities, percentage of osteonal bone and orientation of the Haversian system on the macroscopic elastic moduli and Poisson's ratios was investigated. The results presented provide relationships for applying more locally accurate material properties to larger scale and whole bone models of varying porosity. Analysis of the effect of the orientation of the Haversian system showed that its effects should not be neglected in larger scale models. This study also provides insight into how microstructural features effect local distributions and cause a strain magnification effect. Limitations in applying the unit cell methodology approach to bone are also discussed.     

The multiscale meso-mechanics model of viscoelastic cortical bone

Biomechanics and Modeling in Mechanobiology - Cortical bone is a complex hierarchical structure consisting of biological fiber composites with transversely isotropic constituents, whose...     

Transversely isotropic elasticity imaging of cancellous bone

To measure spatial variations in mechanical properties of biological materials, prior studies have typically performed mechanical tests on excised specimens of tissue. Less invasive measurements, however, are preferable in many applications, such as patient-specific modeling, disease diagnosis, and tracking of age- or damage-related degradation of mechanical properties. Elasticity imaging (elastography) is a nondestructive imaging method in which the distribution of elastic properties throughout a specimen can be reconstructed from measured strain or displacement fields. To date, most work in elasticity imaging has concerned incompressible, isotropic materials. This study presents an extension of elasticity imaging to three-dimensional, compressible, transversely isotropic materials. The formulation and solution of an inverse problem for an anisotropic tissue subjected to a combination of quasi-static loads is described, and an optimization and regularization strategy that indirectly obtains the solution to the inverse problem is presented. Several applications of transversely isotropic elasticity imaging to cancellous bone from the human vertebra are then considered. The feasibility of using isotropic elasticity imaging to obtain meaningful reconstructions of the distribution of material properties for vertebral cancellous bone from experiment is established. However, using simulation, it is shown that an isotropic reconstruction is not appropriate for anisotropic materials. It is further shown that the transversely isotropic method identifies a solution that predicts the measured displacements, reveals regions of low stiffness, and recovers all five elastic parameters with approximately 10% error. The recovery of a given elastic parameter is found to require the presence of its corresponding strain (e.g., a deformation that generates ??? is necessary to reconstruct C????), and the application of regularization is shown to improve accuracy. Finally, the effects of noise on reconstruction quality is demonstrated and a signal-to-noise ratio (SNR) of 40 dB is identified as a reasonable threshold for obtaining accurate reconstructions from experimental data. This study demonstrates that given an appropriate set of displacement fields, level of regularization, and signal strength, the transversely isotropic method can recover the relative magnitudes of all five elastic parameters without an independent measurement of stress. The quality of the reconstructions improves with increasing contrast, magnitude of deformation, and asymmetry in the distributions of material properties, indicating that elasticity imaging of cancellous bone could be a useful tool in laboratory studies to monitor the progression of damage and disease in this tissue.     

Nonlinear hierarchical multiscale modeling of cortical bone considering its nanoscale microstructure

We have used a hierarchical multiscale modeling scheme for the analysis of cortical bone considering it as a nanocomposite. This scheme consists of definition of two boundary value problems, one for macroscale, and another for microscale. The coupling between these scales is done by using the homogenization technique. At every material point in which the constitutive model is needed, a microscale boundary value problem is defined using a macroscopic kinematical quantity and solved. Using the described scheme, we have studied elastic properties of cortical bone considering its nanoscale microstructural constituents with various mineral volume fractions. Since the microstructure of bone consists of mineral platelet with nanometer size embedded in a protein matrix, it is similar to the microstructure of soft matrix nanocomposites reinforced with hard nanostructures. Considering a representative volume element (RVE) of the microstructure of bone as the microscale problem in our hierarchical multiscale modeling scheme, the global behavior of bone is obtained under various macroscopic loading conditions. This scheme may be suitable for modeling arbitrary bone geometries subjected to a variety of loading conditions. Using the presented method, mechanical properties of cortical bone including elastic moduli and Poisson's ratios in two major directions and shear modulus is obtained for different mineral volume fractions.     

The dependence of transversely isotropic elasticity of human femoral cortical bone on porosity

The objective of this study was to examine the dependence of the elastic properties of cortical bone as a transversely isotropic material on its porosity. The longitudinal Young's modulus, transverse Young's modulus, longitudinal shear modulus, transverse shear modulus, and longitudinal Poisson's ratio of cortical bone were determined from eighteen groups of longitudinal and transverse specimens using tensile and torsional tests on a servo-hydraulic material testing system. These cylindrical waisted specimens of cortical bone were harvested from the middle diaphysis of three pairs of human femora. The porosity of these specimens was assessed by means of histology. Our study demonstrated that the longitudinal Young's and shear moduli of human femoral cortical bone were significantly (p<0.01) negatively correlated with the porosity of cortical bone. Conversely, the elastic properties in the transverse direction did not have statistically significant correlations with the porosity of cortical bone. As a result, the transverse elastic properties of cortical bone were less sensitive to changes in porosity than those in the longitudinal direction. Additionally, the anisotropic ratios of cortical bone elasticity were found to be significantly (p<0.01) negatively correlated with its porosity, indicating that cortical bone tended to become more isotropic when its porosity increased. These results may help a number of researchers develop more accurate micromechanics models of cortical bone.     

Arterial elasticity imaging: comparison of finite-element analysis models with high-resolution ultrasound speckle tracking

Background

To resolve the current shortage of donor hearts, we established the Adonhers protocol. An upward shift of the donor age cut-off limit (from the present 55 to 65 years) is acceptable if a stress echo screening on the candidate donor heart is normal. This study aimed to verify feasibility of a "second opinion" of digitally transferred images of stress echo results to minimize technical variability in selection of aged donor hearts for heart transplant.

Methods

The informatics infrastructure was created for a core lab reading with a second opinion from the Pisa stress echo lab. To test the system, simulation standard stress echo cineloops were sent digitally from 5 peripheral labs to the central core lab. Starting January 2009, real marginal donor stress echos were sent via internet to the central core echo lab, Pisa, for a second opinion before heart transplant.

Results

In the simulation protocol, 30 dipyridamole stress echocardiograms were sent from the five peripheral echo labs to the central core lab in Pisa. Both the echo images and reports were correctly uploaded in the web system and sent to the core echo lab; the second opinion evaluation was obtained in all cases (100% feasibility). In the transplant protocol, eight donor cases were sent to the Pisa core lab for the second opinion protocol, and six of them were transplanted in marginal recipients.

Conclusions

Second-Opinion Stress Tele-Echocardiography can effectively be performed in a network aimed to safely expand the heart donor pool for heart transplant.     

X-ray microscopy enables multiscale high-resolution 3D imaging of plant cells,tissues, and organs

Capturing complete internal anatomies of plant organs and tissues within their relevant morphological context remains a key challenge in plant science. While plant growth and development are inherently multiscale, conventional light, fluorescence, and electron microscopy platforms are typically limited to imaging of plant microstructure from small flat samples that lack a direct spatial context to, and represent only a small portion of, the relevant plant macrostructures. We demonstrate technical advances with a lab-based X-ray microscope (XRM) that bridge the imaging gap by providing multiscale high-resolution three-dimensional (3D) volumes of intact plant samples from the cell to the whole plant level. Serial imaging of a single sample is shown to provide sub-micron 3D volumes co-registered with lower magnification scans for explicit contextual reference. High-quality 3D volume data from our enhanced methods facilitate sophisticated and effective computational segmentation. Advances in sample preparation make multimodal correlative imaging workflows possible, where a single resin-embedded plant sample is scanned via XRM to generate a 3D cell-level map, and then used to identify and zoom in on sub-cellular regions of interest for high-resolution scanning electron microscopy. In total, we present the methodologies for use of XRM in the multiscale and multimodal analysis of 3D plant features using numerous economically and scientifically important plant systems.

Lab-based X-ray microscopy allows high-resolution 3D imaging of intact plant samples over a wide range of sample types and sizes, filling the imaging gap between light and electron microscopy.     

Finite element modelling of implant designs and cortical bone thickness on stress distribution in maxillary type IV bone

The aims of this study were to examine the effect of implant neck design and cortical bone thickness using 3D finite element analysis and to analyse the stability of clinical evidence based on micromotion and principal stress. Four commercial dental implants for a type IV bone and maxillary segments were created. Various parameters were considered, including the osseointegration condition, loading direction and cortical bone thickness. Micromotion and principal stresses were used to evaluate the failure of osseointegration and bone overloading, respectively. It was found that the maximum stress of the peri-implant bone decreased as cortical bone thickness increased. The micromotion level in full osseointegration is less than that in non-osseointegration and it also decreases as cortical bone thickness increases. The cortical bone thickness should be measured before surgery to help select a proper implant. In the early stage of implantation, the horizontal loading component induces stress concentration in bone around the implant neck more easily than does the vertical loading component, and this may result in crestal bone loss.     

Stochastic modelling of apoptosis kinetics

Robust quantitative estimation of average whole cell mitochondrial dysfunction is a useful tool for assessing sensitivity to apoptotic stimuli induced either by novel agents, or following manipulation of apoptotic threshold by pharmacological or functional genomics approaches. We have mathematically modelled the kinetics of whole cell mitochondrial membrane potential depolarisation within a population of cells as a Bernouli transition. An exponential distribution enables the median latency preceding mitochondrial membrane potential disispation to be derived. The kinetic model can be fitted to in vitro single cell resolution data derived from kinetic flow cytometric studies by non-linear regression. We propose that kinetic determination of cumulative frequency distibutions provides a useful approach for estimating apoptosis sensitivity across cell populations over short time-frames.     

Stochastic modelling of tumour-induced angiogenesis

A major source of complexity in the mathematical modelling of an angiogenic process derives from the strong coupling of the kinetic parameters of the relevant stochastic branching-and-growth of the capillary network with a family of interacting underlying fields. The aim of this paper is to propose a novel mathematical approach for reducing complexity by (locally) averaging the stochastic cell, or vessel densities in the evolution equations of the underlying fields, at the mesoscale, while keeping stochasticity at lower scales, possibly at the level of individual cells or vessels. This method leads to models which are known as hybrid models. In this paper, as a working example, we apply our method to a simplified stochastic geometric model, inspired by the relevant literature, for a spatially distributed angiogenic process. The branching mechanism of blood vessels is modelled as a stochastic marked counting process describing the branching of new tips, while the network of vessels is modelled as the union of the trajectories developed by tips, according to a system of stochastic differential equations à la Langevin.     

Stochastic modelling of animal movement

Modern animal movement modelling derives from two traditions. Lagrangian models, based on random walk behaviour, are useful for multi-step trajectories of single animals. Continuous Eulerian models describe expected behaviour, averaged over stochastic realizations, and are usefully applied to ensembles of individuals. We illustrate three modern research arenas. (i) Models of home-range formation describe the process of an animal ‘settling down’, accomplished by including one or more focal points that attract the animal''s movements. (ii) Memory-based models are used to predict how accumulated experience translates into biased movement choices, employing reinforced random walk behaviour, with previous visitation increasing or decreasing the probability of repetition. (iii) Lévy movement involves a step-length distribution that is over-dispersed, relative to standard probability distributions, and adaptive in exploring new environments or searching for rare targets. Each of these modelling arenas implies more detail in the movement pattern than general models of movement can accommodate, but realistic empiric evaluation of their predictions requires dense locational data, both in time and space, only available with modern GPS telemetry.     

Dynamic statistical parametric mapping: combining fMRI and MEG for high-resolution imaging of cortical activity

Functional magnetic resonance imaging (fMRI) can provide maps of brain activation with millimeter spatial resolution but is limited in its temporal resolution to the order of seconds. Here, we describe a technique that combines structural and functional MRI with magnetoencephalography (MEG) to obtain spatiotemporal maps of human brain activity with millisecond temporal resolution. This new technique was used to obtain dynamic statistical parametric maps of cortical activity during semantic processing of visually presented words. An initial wave of activity was found to spread rapidly from occipital visual cortex to temporal, parietal, and frontal areas within 185 ms, with a high degree of temporal overlap between different areas. Repetition effects were observed in many of the same areas following this initial wave of activation, providing evidence for the involvement of feedback mechanisms in repetition priming.     

A multiscale optimisation method for bone growth scaffolds based on triply periodic minimal surfaces

Tissue engineered bone scaffolds are potential alternatives to bone allografts and autografts. Porous scaffolds based on triply periodic minimal surfaces (TPMS) are good candidates for tissue growth because they offer high surface-to-volume ratio, have tailorable stiffness, and can be easily fabricated by additive manufacturing. However, the range of TPMS scaffold types is extensive, and it is not yet clear which type provides the fastest cell or tissue growth while being sufficiently stiff to act as a bone graft. Nor is there currently an established methodology for TPMS bone scaffold design which can be quickly adopted by medical designers or biologists designing implants. In this study, we examine six TPMS scaffold types for use as tissue growth scaffolds and propose a general methodology to optimise their geometry. At the macro-scale, the optimisation routine ensures a scaffold stiffness within suitable limits for bone, while at the micro-scale it maximises the cell growth rate. The optimisation procedure also ensures the scaffold pores are of sufficient diameter to allow oxygen and nutrient delivery via capillaries. Of the examined TPMS structures, the Lidinoid and Split P cell types provide the greatest cell growth rates and are therefore the best candidates for bone scaffolds.

     

Opportunities for biomineralization research using multiscale computed X-ray tomography as exemplified by bone imaging

Biominerals typically have complex hierarchical structures traversing many length scales. This makes their structural characterization complicated, since it requires 3D techniques that can probe full specimens at down to nanometer-resolution, a combination that is difficult – if not impossible – to achieve simultaneously. One challenging example is bone, a mineralized tissue with a highly complex architecture that is replete with a network of cells. X-ray computed tomography techniques enable multiscale structural characterization through the combination of various equipment and emerge as promising tools for characterizing biominerals. Using bone as an example, we discuss how combining different X-ray imaging instruments allow characterizing bone structures from the nano- to the organ-scale. In particular, we compare and contrast human and rodent bone, emphasize the importance of the osteocyte lacuno-canalicular network in bone, and finally illustrate how combining synchrotron X-ray imaging with laboratory instrumentation for computed tomography is especially helpful for multiscale characterization of biominerals.