A graph model to describe the network connectivity of trabecular plates and rods.

Introduction: The trabecular network is perceived as a collection of interconnected plate- (P) and rod-like (R) elements. Previous research has highlighted how these elements and their connectivity influence the mechanical properties of bone, yet further work is required to elucidate better the deeply interconnected nature of the trabecular network with distinct element formations conducting forces per their mechanical boundary conditions. Within this network, forces act through elements: a rod or plate with force applied to one end will transmit this force to a component connected to the other end, defining the boundary conditions for the loading of each element. To that end, this study has two aims: First, to investigate the connectivity of individually segmented elements of trabecular bone with respect to their local boundary conditions as defined by the surrounding trabecular network and linking them directly to the bone's overall mechanical response during loading using a mathematical graph model of the plate and rod (PR) Network. Second, we use this model to quantify side artifacts, a known artifact when testing an excised specimen of trabecular bone, where vertical trabeculae lose their load-bearing capacity due to a loss of connectivity, ultimately resulting in a change of the trabecular network topology. Resuts: Connected elements derived from our model predicted apparent elastic modulus by fitting a linear regression (R 2 = 0.81). In comparison, prediction using conventional bone volume fraction results in a lower accuracy (R 2 = 0.72), demonstrating the ability of the PR Network to estimate compressive elastic modulus independent of specimen size or loading boundary condition. Discussion: PR Network models are a novel approach to describing connectivity within the trabecular network and incorporating mechanical boundary conditions within the morphological analysis, thus enabling the study of intrinsic material properties of trabecular bone. Ultimately, PR Network models may be an early predictor or provide further insights into osteo-degenerative diseases.

Poroelastic behavior and water permeability of human skin at the nanoscale.

Topical skin care products and hydrating compositions (moisturizers or injectable fillers) have been used for years to improve the appearance of, for example facial wrinkles, or to increase "plumpness". Most of the studies have addressed these changes based on the overall mechanical changes associated with an increase in hydration state. However, little is known about the water mobility contribution to these changes as well as the consequences to the specific skin layers. This is important as the biophysical properties and the biochemical composition of normal stratum corneum, epithelium, and dermis vary tremendously from one another. Our current studies and results reported here have focused on a novel approach (dynamic atomic force microscopy-based nanoindentation) to quantify biophysical characteristics of individual layers of ex vivo human skin. We have discovered that our new methods are highly sensitive to the mechanical properties of individual skin layers, as well as their hydration properties. Furthermore, our methods can assess the ability of these individual layers to respond to both compressive and shear deformations. In addition, since human skin is mechanically loaded over a wide range of deformation rates (frequencies), we studied the biophysical properties of skin over a wide frequency range. The poroelasticity model used helps to quantify the hydraulic permeability of the skin layers, providing an innovative method to evaluate and interpret the impact of hydrating compositions on water mobility of these different skin layers.

Evaluation of musculoskeletal phenotype of the G608G progeria mouse model with lonafarnib, pravastatin, and zoledronic acid as treatment groups.

Hutchinson-Gilford progeria syndrome (HGPS) is a uniformly fatal condition that is especially prevalent in skin, cardiovascular, and musculoskeletal systems. A wide gap exists between our knowledge of the disease and a promising treatment or cure. The aim of this study was to first characterize the musculoskeletal phenotype of the homozygous G608G BAC-transgenic progeria mouse model, and to determine the phenotype changes of HGPS mice after a five-arm preclinical trial of different treatment combinations with lonafarnib, pravastatin, and zoledronic acid. Microcomputed tomography and CT-based rigidity analyses were performed to assess cortical and trabecular bone structure, density, and rigidity. Bones were loaded to failure with three-point bending to assess strength. Contrast-enhanced µCT imaging of mouse femurs was performed to measure glycosaminoglycan content, thickness, and volume of the femoral head articular cartilage. Advanced glycation end products were assessed with a fluorometric assay. The changes demonstrated in the cortical bone structure, rigidity, stiffness, and modulus of the HGPS G608G mouse model may increase the risk for bending and deformation, which could result in the skeletal dysplasia characteristic of HGPS. Cartilage abnormalities seen in this HGPS model resemble changes observed in the age-matched WT controls, including early loss of glycosaminoglycans, and decreased cartilage thickness and volume. Such changes might mimic prevalent degenerative joint diseases in the elderly. Lonafarnib monotherapy did not improve bone or cartilage parameters, but treatment combinations with pravastatin and zoledronic acid significantly improved bone structure and mechanical properties and cartilage structural parameters, which ameliorate the musculoskeletal phenotype of the disease.

Decorin Regulates the Aggrecan Network Integrity and Biomechanical Functions of Cartilage Extracellular Matrix.

Joint biomechanical functions rely on the integrity of cartilage extracellular matrix. Understanding the molecular activities that govern cartilage matrix assembly is critical for developing effective cartilage regeneration strategies. This study elucidated the role of decorin, a small leucine-rich proteoglycan, in the structure and biomechanical functions of cartilage. In decorin-null cartilage, we discovered a substantial reduction of aggrecan content, the major proteoglycan of cartilage matrix, and mild changes in collagen fibril nanostructure. This loss of aggrecan resulted in significantly impaired biomechanical properties of cartilage, including decreased modulus, elevated hydraulic permeability, and reduced energy dissipation capabilities. At the cellular level, we found that decorin functions to increase the retention of aggrecan in the neo-matrix of chondrocytes, rather than to directly influence the biosynthesis of aggrecan. At the molecular level, we demonstrated that decorin significantly increases the adhesion between aggrecan and aggrecan molecules and between aggrecan molecules and collagen II fibrils. We hypothesize that decorin plays a crucial structural role in mediating the matrix integrity and biomechanical functions of cartilage by providing physical linkages to increase the adhesion and assembly of aggrecan molecules at the nanoscale.

Nanoscale Poroelasticity of the Tectorial Membrane Determines Hair Bundle Deflections.

Stereociliary imprints in the tectorial membrane (TM) have been taken as evidence that outer hair cells are sensitive to shearing displacements of the TM, which plays a key role in shaping cochlear sensitivity and frequency selectivity via resonance and traveling wave mechanisms. However, the TM is highly hydrated (97% water by weight), suggesting that the TM may be flexible even at the level of single hair cells. Here we show that nanoscale oscillatory displacements of microscale spherical probes in contact with the TM are resisted by frequency-dependent forces that are in phase with TM displacement at low and high frequencies, but are in phase with TM velocity at transition frequencies. The phase lead can be as much as a quarter of a cycle, thereby contributing to frequency selectivity and stability of cochlear amplification.

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.

The effect of the rotator interval on glenohumeral kinematics during abduction.

BACKGROUND: The rotator interval (RI) has been exploited as a potentially benign point of entry into the glenohumeral (GH) joint. Bounded by the supraspinatus, subscapularis and coracoid process of the scapula, the RI is believed to be important in the shoulder's soft tissue balancing and function. However, the role of the RI in shoulder kinematics is not fully understood. The purpose of this study is to describe the effect of the RI on GH motion during abduction of the arm. METHODS: Six shoulders from three cadaveric torsos were studied to assess the impact of changes in the RI during abduction under four conditions: Intact (Baseline), Opened, Repaired (repaired with side-to-side tissue approximation, no overlap) and Tightened (repaired with 1 cm overlap). For each group, the GH translation and area under the Curve (AUC) were measured during abduction using an intact cadaveric shoulder (intact torso). RESULTS: GH kinematics varied in response to each intervention and throughout the entire abduction arc. Opening the RI caused a significant change in GH translation. The Repair and Tightened groups behaved similarly along all axes of GH motion. CONCLUSIONS: The RI is central to normal GH kinematics. Any insult to the tissue's integrity alters the shoulder's motion throughout abduction. In this model, closing the RI side-to-side has the same effect as tightening the RI. Since suture closure may offer the same benefit as tightening the RI, clinicians should consider this effect when treating patients with shoulder laxity. This investigation provides an improved perspective on the role of the RI on GH kinematics during abduction. When managing shoulder pathology, surgeons should consider how these different methods of RI closure affect the joint's motion. In different circumstances, the surgical approach to the RI can be tailored to address each patient's specific needs.

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

The aim of this study was to explore the hierarchical arrangement of structural properties in cortical and trabecular bone and to determine a mathematical model that accurately predicts the tissue's mechanical properties as a function of these indices. By using a variety of analytical techniques, we were able to characterize the structural and compositional properties of cortical and trabecular bones, as well as to determine the suitable mathematical model to predict the tissue's mechanical properties using a continuum micromechanics approach. Our hierarchical analysis demonstrated that the differences between cortical and trabecular bone reside mainly at the micro- and ultrastructural levels. By gaining a better appreciation of the similarities and differences between the two bone types, we would be able to provide a better assessment and understanding of their individual roles, as well as their contribution to bone health overall.

Biomechanics and mechanobiology of trabecular bone: a review.

Trabecular bone is a highly porous, heterogeneous, and anisotropic material which can be found at the epiphyses of long bones and in the vertebral bodies. Studying the mechanical properties of trabecular bone is important, since trabecular bone is the main load bearing bone in vertebral bodies and also transfers the load from joints to the compact bone of the cortex of long bones. This review article highlights the high dependency of the mechanical properties of trabecular bone on species, age, anatomic site, loading direction, and size of the sample under consideration. In recent years, high resolution micro finite element methods have been extensively used to specifically address the mechanical properties of the trabecular bone and provide unique tools to interpret and model the mechanical testing experiments. The aims of the current work are to first review the mechanobiology of trabecular bone and then present classical and new approaches for modeling and analyzing the trabecular bone microstructure and macrostructure and corresponding mechanical properties such as elastic properties and strength.

Effects of different loading patterns on the trabecular bone morphology of the proximal femur using adaptive bone remodeling.

In this study, the changes in the bone density of human femur model as a result of different loadings were investigated. The model initially consisted of a solid shell representing cortical bone encompassing a cubical network of interconnected rods representing trabecular bone. A computationally efficient program was developed that iteratively changed the structure of trabecular bone by keeping the local stress in the structure within a defined stress range. The stress was controlled by either enhancing existing beam elements or removing beams from the initial trabecular frame structure. Analyses were performed for two cases of homogenous isotropic and transversely isotropic beams.Trabecular bone structure was obtained for three load cases: walking, stair climbing and stumbling without falling. The results indicate that trabecular bone tissue material properties do not have a significant effect on the converged structure of trabecular bone. In addition, as the magnitude of the loads increase, the internal structure becomes denser in critical zones. Loading associated with the stumbling results in the highest density;whereas walking, considered as a routine daily activity, results in the least internal density in different regions. Furthermore, bone volume fraction at the critical regions of the converged structure is in good agreement with previously measured data obtained from combinations of dual X-ray absorptiometry (DXA) and computed tomography (CT). The results indicate that the converged bone architecture consisting of rods and plates are consistent with the natural bone morphology of the femur. The proposed model shows a promising means to understand the effects of different individual loading patterns on the bone density.

Optimal fractal-like hierarchical honeycombs.

Hexagonal honeycomb structures are known for their high strength and low weight. We construct a new class of fractal-appearing cellular metamaterials by replacing each three-edge vertex of a base hexagonal network with a smaller hexagon and iterating this process. The mechanical properties of the structure after different orders of the iteration are optimized. We find that the optimal structure (with highest in-plane stiffness for a given weight ratio) is self-similar but requires higher order hierarchy as the density vanishes. These results offer insights into how incorporating hierarchy in the material structure can create low-density metamaterials with desired properties and function.