Hierarchical analysis and multi-scale modelling of rat cortical and trabecular bone

A Novel Computational Biomechanics Framework to Model Vascular Mechanopropagation in Deep Bone Marrow

The mechanical stimuli generated by body exercise can be transmitted from cortical bone into the deep bone marrow (mechanopropagation). Excitingly, a mechanosensitive perivascular stem cell niche is recently identified within the bone marrow for osteogenesis and lymphopoiesis. Although it is long known that they are maintained by exercise-induced mechanical stimulation, the mechanopropagation from compact bone to deep bone marrow vasculature remains elusive of this fundamental mechanobiology field. No experimental system is available yet to directly understand such exercise-induced mechanopropagation at the bone-vessel interface. To this end, taking advantage of the revolutionary in vivo 3D deep bone imaging, an integrated computational biomechanics framework to quantitatively evaluate the mechanopropagation capabilities for bone marrow arterioles, arteries, and sinusoids is devised. As a highlight, the 3D geometries of blood vessels are smoothly reconstructed in the presence of vessel wall thickness and intravascular pulse pressure. By implementing the 5-parameter Mooney-Rivlin model that simulates the hyperelastic vessel properties, finite element analysis to thoroughly investigate the mechanical effects of exercise-induced intravascular vibratory stretching on bone marrow vasculature is performed. In addition, the blood pressure and cortical bone bending effects on vascular mechanoproperties are examined. For the first time, movement-induced mechanopropagation from the hard cortical bone to the soft vasculature in the bone marrow is numerically simulated. It is concluded that arterioles and arteries are much more efficient in propagating mechanical force than sinusoids due to their stiffness. In the future, this in-silico approach can be combined with other clinical imaging modalities for subject/patient-specific vascular reconstruction and biomechanical analysis, providing large-scale phenotypic data for personalized mechanobiology discovery.

The effect of Staphylococcus aureus exposure on white-tailed deer trabecular bone stiffness and yield

With a growing number of osteomyelitis diagnoses, many of which are linked to Staphylococcus aureus (S. aureus), it is imperative to understand the pathology of S. aureus in relation to bone to provide better diagnostics and patient care. While the cellular mechanisms of S. aureus and osteomyelitis have been studied, little information exists on the biomechanical effects of such infections. The aim of this study was to determine the effect of S. aureus exposure on the stiffness and yield of trabecular bone tissue. S. aureus-ATCC-12600, a confirmed biofilm producer, along with one hundred and three trabecular cubes (5 × 5 × 5 mm) from the proximal tibiae of Odocoileus virginianus (white-tailed deer) were used in this experiment. Bone cubes were disinfected and then swabbed to confirm no residual living microbes or endospore contamination before inoculation with S. aureus (test group) or sterile nutrient broth (control group) for 72 h. All cubes were then tested in compression until yield using an Instron 5942 Single-Column machine. Structural stiffness (N/mm) and yield (MPa) were calculated and compared between the two groups. Our results revealed that acute exposure to S. aureus, within the context of our deer tibia model, does not significantly decrease trabecular bone stiffness or yield. The results of this study may be of value clinically when assessing fracture risks for osteomyelitis or other patients whose cultures test positive for S. aureus.

Multiscale modeling of bone tissue mechanobiology

Mechanical environment has a crucial role in our organism at the different levels, ranging from cells to tissues and our own organs. This regulatory role is especially relevant for bones, given their importance as load-transmitting elements that allow the movement of our body as well as the protection of vital organs from load impacts. Therefore bone, as living tissue, is continuously adapting its properties, shape and repairing itself, being the mechanical loads one of the main regulatory stimuli that modulate this adaptive behavior. Here we review some key results of bone mechanobiology from computational models, describing the effect that changes associated to the mechanical environment induce in bone response, implant design and scaffold-driven bone regeneration.

Homogenization of cortical bone reveals that the organization and shape of pores marginally affect elasticity

With ageing and various diseases, the vascular pore volume fraction (porosity) in cortical bone increases, and the morphology of the pore network is altered. Cortical bone elasticity is known to decrease with increasing porosity, but the effect of the microstructure is largely unknown, while it has been thoroughly studied for trabecular bone. Also, popular micromechanical models have disregarded several micro-architectural features, idealizing pores as cylinders aligned with the axis of the diaphysis. The aim of this paper is to quantify the relative effects on cortical bone anisotropic elasticity of porosity and other descriptors of the pore network micro-architecture associated with pore number, size and shape. The five stiffness constants of bone assumed to be a transversely isotropic material were measured with resonant ultrasound spectroscopy in 55 specimens from the femoral diaphysis of 29 donors. The pore network, imaged with synchrotron radiation X-ray micro-computed tomography, was used to derive the pore descriptors and to build a homogenization model using the fast Fourier transform (FFT) method. The model was calibrated using experimental elasticity. A detailed analysis of the computed effective elasticity revealed in particular that porosity explains most of the variations of the five stiffness constants and that the effects of other micro-architectural features are small compared to usual experimental errors. We also have evidence that modelling the pore network as an ensemble of cylinders yields biased elasticity values compared to predictions based on the real micro-architecture. The FFT homogenization method is shown to be particularly efficient to model cortical bone.

Physicochemical and biochemical spatiotemporal maps of a mouse penis

Spatiotemporal mechanobiology resulting in penile pathologies continues to be investigated using small scale animals models such as mice. However, species-dependent functional biomechanics of a mouse penis, is not known. In this study, spatial mapping of a mechanosensitive transcription factor, scleraxis (Scx), at ages 4, 5, 6 weeks, and 1 year were generated to identify mechanoactive regions within penile tissues. Reconstructed volumes of baculum collected using micro X-ray computed tomography illustrated significantly increased baculum length with decreased porosity, and increased mineral density (p < 0.05) with age. The bony-baculum was held centrally in the Scx positive corpus cavernosum glandis (CCG), indicating mechanoactivity within the struts in a 6 week old mouse. The struts also were stained positive for fibrillar proteins including collagen and elastin, and globular proteins including protein gene product 9.5, and α-smooth muscle actin. The corpus cavernosum penis (CCP) contained significantly (p < 0.05) more collagen than CCG within the same penis, and both regions contained blood vessels with equivalent innervation at any given age. Comparison of volumes of flaccid and erect penile forms revealed functional characteristics of the CCP. Results of this study provided insights into biomechanical function of the CCG; in that, it is a high-pressure chamber that stiffens the penis and is similar to the human corpus cavernosum.

Extrafibrillar matrix yield stress and failure envelopes for mineralised collagen fibril arrays

Bone metabolic diseases such as osteoporosis constitute a major socio-economic challenge. A detailed understanding of the structure-property relationships of bone's underlying hierarchical levels has the potential to improve diagnosis and the ability to treat those diseases, especially with regards to the onset of failure. Therefore, elastic and yield properties of mineralised turkey leg tendon (MTLT), a mineralised tissue that is similar to bone but has a simpler multiscale structure, were investigated. Elastic properties were identified using a multiscale micromechanical model. The input parameters include constituent mechanical properties, volume fractions and inclusion aspect ratios and these were obtained from a wide variety of literature sources. The determined elastic properties were used to formulate micromechanically informed yield surfaces and to identify yield properties of MTLT at the nanometre length scale where failure is first reported to occur. This was done in conjunction with experimental results from the compression of micropillars extracted from individual mineralised collagen fibres. This data was then used to identify micromechanically informed failure envelopes. The shear yield stress of the extrafibrillar matrix, associated with interfibrillar sliding, was identified as 137.65 MPa. The ratio between tensile and compressive yield stress in the Drucker-Prager yield criterion was 0.65. For both criteria apparent yield stress of the mineralised collagen fibril decreased to 25.3-31.4% when varying fibril orientation from 0° to 90°. This study identified yield properties of extrafibrillar matrix using an aligned mineralised tissue. The ability to obtain yield stress data and unloading stiffness from micropillar compression tests of MTLT at the level of the mineralised collagen fibril array and downscaling these into the EM mitigates against possible errors associated with macroscopic stiffness predictions and proved to be an invaluable advantage compared to similar modelling approaches. Results may help to improve computational models that may then be used in pre-clinical testing or development of personalised treatment strategies.

Mandibular Bone Loss after Masticatory Muscles Intervention with Botulinum Toxin: An Approach from Basic Research to Clinical Findings

The injection of botulinum toxin type A (BoNT/A) in the masticatory muscles, to cause its temporary paralysis, is a widely used intervention for clinical disorders such as oromandibular dystonia, sleep bruxism, and aesthetics (i.e., masseteric hypertrophy). Considering that muscle contraction is required for mechano-transduction to maintain bone homeostasis, it is relevant to address the bone adverse effects associated with muscle condition after this intervention. Our aim is to condense the current and relevant literature about mandibular bone loss in fully mature mammals after BoNT/A intervention in the masticatory muscles. Here, we compile evidence from animal models (mice, rats, and rabbits) to clinical studies, demonstrating that BoNT/A-induced masticatory muscle atrophy promotes mandibular bone loss. Mandibular bone-related adverse effects involve cellular and metabolic changes, microstructure degradation, and morphological alterations. While bone loss has been detected at the mandibular condyle or alveolar bone, cellular and molecular mechanisms involved in this process must still be elucidated. Further basic research could provide evidence for designing strategies to control the undesired effects on bone during the therapeutic use of BoNT/A. However, in the meantime, we consider it essential that patients treated with BoNT/A in the masticatory muscles be warned about a putative collateral mandibular bone damage.

Monte Carlo type Simulations of Mineralized Collagen Fibril based on Two Scale Asymptotic Homogenization

A multi-scale model for mineralized collagen fibril is proposed by taking into account the uncertainties associated with the geometrical properties of mineral phase and its distribution in the organic matrix. The asymptotic homogenization approach along with periodic boundary conditions has been used to derive the effective elastic moduli at two hierarchical length scales, namely: microfibril and mineralized collagen fibril. The uncertainties associated with the mineral plates have been directly included in the finite element mesh by randomly varying their sizes. A total 100 realizations for mineralized collagen fibril model with random distribution have been generated using an in-house MATLAB® code and Monte-Carlo type simulations have been performed under tension load to obtain the statistical equivalent modulus. The deformation response has been studied in both small (= 10%) and large (= 10%) strain regimes. The stress transformation mechanism has also been explored in microfibril which showed stress relaxation in the organic phase upon different stages of mineralization. The elastic moduli for microfibril under small and large strain have been obtained as 1.88 and 6.102 GPa, respectively, and have been used as input for upper scale homogenization procedure. Finally, the characteristic longitudinal moduli of the mineralized collagen fibril in the small and large strain regimes are obtained as 4.08 ± 0.062 and 12.93 ± 0.148 GPa, respectively. All the results are in good agreement to those obtained from previous experiments and molecular dynamics simulations in the literature with a significant reduction in the computational cost.

The Calcaneal Crescent in Patients With and Without Plantar Fasciitis: An Ankle MRI Study

OBJECTIVE

The bundled, crescent-shaped trabeculae within the calcaneal tuberosity-which we term and refer to here as the "calcaneal crescent"-may represent a structural adaption to the prevailing forces. Given Wolff law, we hypothesized that the calcaneal crescent would be more robust in patients with plantar fasciitis, a syndrome in part characterized by overload of the Achilles tendon-calcaneal crescent-plantar fascia system, than in patients without plantar fasciitis.

MATERIALS AND METHODS

MR images of 37 patients (27 women and 10 men; mean age ± SD, 51 ± 13 years; mean body mass index [BMI, weight in kilograms divided by the square of height in meters], 26.8 ± 6.3) referred for workup of foot or ankle pain were retrospectively evaluated by two blinded readers in this study. Patients were assigned to two groups: group A, which was composed of 15 subjects without clinical signs or MRI findings of Achilles tendon-calcaneal crescent-plantar fascia system abnormalities, or group B, which was composed of 22 patients with findings of plantar fasciitis. The thickness and cross-sectional area (CSA) of the Achilles tendon, calcaneal crescent, and plantar fascia were measured on proton density (PD)-weighted MR images. The entire crescent volume was manually measured using OsiriX software on consecutive sagittal PD-weighted images. Additionally, contrast-to-noise ratio (CNR) as a surrogate marker for trabecular density and the mean thickness of the calcaneal crescent were determined on PD-weighted MR images. The groupwise difference in the morphologic measurements were evaluated using ANOVA with BMI as a covariate. Partial correlation was used to assess the relationships of measurements for the group with plantar fasciitis (group B). Intraclass correlation coefficient (ICC) statistics were performed.

RESULTS

Patients with plantar fasciitis had a greater CSA and volume of the calcaneal crescent and had lower CNR (i.e., denser trabeculae) than those without Achilles tendon-calcaneal crescent-plantar fascia system abnormalities (CSA, 100.2 vs 73.7 mm², p = 0.019; volume, 3.06 vs 1.99 cm³, p = 0.006; CNR, -28.40 vs -38.10, p = 0.009). Interreader agreement was excellent (ICC = 0.85-0.99).

CONCLUSION

In patients with plantar fasciitis, the calcaneal crescent is enlarged compared with those without abnormalities of the Achilles tendon-calcaneal crescent-plantar fascia system. An enlarged and trabeculae-rich calcaneal crescent may potentially indicate that abnormally increased forces are being exerted onto the Achilles tendon-calcaneal crescent-plantar fascia system.

Biological connective tissues exhibit viscoelastic and poroelastic behavior at different frequency regimes: Application to tendon and skin biophysics

In this study, a poroviscoelastic finite element model (FEM) was developed and used in conjunction with an AFM-based wide-bandwidth nanorheology system to predict the frequency-dependent mechanical behavior of tendon and dermis subjected to compression via nanoindentation. The aim was to distinguish between loading rates that are dominated by either poroelasticity, viscoelasticity, or the superposition of these processes. Using spherical probe tips having different radii, the force and tip displacement were measured and the magnitude, E^∗, and phase angle, ϕ, of the dynamic complex modulus were evaluated for mouse supraspinatus tendon and mouse dermis. The peak frequencies of the phase angle were associated with the characteristic time constants of poroelastic and viscoelastic material behavior. The developed FE model could predict the separate poroelastic and viscoelastic responses of these soft tissues over a 4 decade frequency range, showing good agreement with experimental results. We observed that poroelasticity was the dominant energy dissipation mechanism for mouse dermis and supraspinatus tendon at higher indentation frequencies (10² to 10⁴ Hz) whereas viscoelasticity was typically dominant at lower frequencies (<10² Hz). These findings show the underlying mechanical behavior of biological connective tissues and give insight into the role played by these different energy dissipation mechanisms in governing the function of these tissues at nanoscale.

STATEMENT OF SIGNIFICANCE

Soft biological tissues exhibit complex, load- and time-dependent mechanical behavior. Evaluating their mechanical behavior requires sophisticated experimental tools and numerical models that can capture the fundamental mechanisms governing tissue function. Using an Atomic-force-microscopy-based rheology system and finite element models, the roles of the two most dominant time-dependent mechanisms (poroelasticity and viscoelasticity) that govern the dynamic loading behavior of mouse skin and tendon have been investigated. FE models were able to predict and quantify the contribution of each mechanism to the overall dynamic response and confirming the presence of these two distinct mechanisms in the mechanical response. Overall, these results provide novel insight into the viscoelastic and poroelastic properties of mouse skin and tendon and promote better understanding of the underlying origins of each mechanism.

Curved Beam Computed Tomography based Structural Rigidity Analysis of Bones with Simulated Lytic Defect: A Comparative Study with Finite Element Analysis

In this paper, a CT based structural rigidity analysis (CTRA) method that incorporates bone intrinsic local curvature is introduced to assess the compressive failure load of human femur with simulated lytic defects. The proposed CTRA is based on a three dimensional curved beam theory to obtain critical stresses within the human femur model. To test the proposed method, ten human cadaveric femurs with and without simulated defects were mechanically tested under axial compression to failure. Quantitative computed tomography images were acquired from the samples, and CTRA and finite element analysis were performed to obtain the failure load as well as rigidities in both straight and curved cross sections. Experimental results were compared to the results obtained from FEA and CTRA. The failure loads predicated by curved beam CTRA and FEA are in agreement with experimental results. The results also show that the proposed method is an efficient and reliable method to find both the location and magnitude of failure load. Moreover, the results show that the proposed curved CTRA outperforms the regular straight beam CTRA, which ignores the bone intrinsic curvature and can be used as a useful tool in clinical practices.