Yoshitaka Kameo

Trabecular bone remodelling simulation considering osteocytic response to fluid-induced shear stress

In bone functional adaptation by remodelling, osteocytes in the lacuno-canalicular system are believed to play important roles in the mechanosensory system. Under dynamic loading, bone matrix deformation generates an interstitial fluid flow in the lacuno-canalicular system; this flow induces shear stress on the osteocytic process membrane that is known to stimulate the osteocytes. In this sense, the osteocytes behave as mechanosensors and deliver mechanical information to neighbouring cells through the intercellular communication network. In this study, bone remodelling is assumed to be regulated by the mechanical signals collected by the osteocytes. From the viewpoint of multi-scale biomechanics, we propose a mathematical model of trabecular bone remodelling that takes into account the osteocytic mechanosensory network system. Based on this model, a computational simulation of trabecular bone remodelling was conducted for a single trabecula under cyclic uniaxial loading, demonstrating functional adaptation to the applied mechanical loading as a load-bearing construct.

Estimation of bone permeability considering the morphology of lacuno-canalicular porosity

Load-induced interstitial fluid flow in lacuno-canalicular porosity is believed to play an important role in cellular activities regulating adaptive bone remodeling. To investigate interstitial fluid behavior based on poroelasticity, it is important to determine the anisotropic permeability tensor reflecting the morphological features of the lacuno-canalicular porosity as fluid channels. In this study, we presented an estimation method of trabecular permeability by describing the analytical relationship between the volume orientation (VO) fabric tensor, which represents the canalicular orientation, and the permeability tensor. The relationship showed that the trabecular permeability tensor is proportional to the product of the volume fraction of the interstitial fluid and the VO fabric tensor of the canaliculi. We applied the proposed method to a two-dimensional fluorescent image of a trabecular cross section to quantify the canalicular anisotropy and the trabecular permeability tensor. The results indicated that the canaliculi are predominantly oriented in the radial direction of the trabecula, and the permeability depends strongly on the canalicular morphology.

Effects of loading frequency on the functional adaptation of trabeculae predicted by bone remodeling simulation.

The process of bone remodeling is regulated by metabolic activities of many bone cells. While osteoclasts and osteoblasts are responsible for bone resorption and formation, respectively, activities of these cells are believed to be controlled by a mechanosensory system of osteocytes embedded in the extracellular bone matrix. Several experimental and theoretical studies have suggested that the strain-derived interstitial fluid flow in lacuno-canalicular porosity serves as the prime mover for bone remodeling. Previously, we constructed a mathematical model for trabecular bone remodeling that interconnects the microscopic cellular activities with the macroscopic morphological changes in trabeculae through the mechanical hierarchy. This model assumes that fluid-induced shear stress acting on osteocyte processes is a driving force for bone remodeling. The validity of this model has been demonstrated with a remodeling simulation using a two-dimensional trabecular model. In this study, to investigate the effects of loading frequency, which is thought to be a significant mechanical factor in bone remodeling, we simulated morphological changes of a three-dimensional single trabecula under cyclic uniaxial loading with various frequencies. The results of the simulation show the trabecula reoriented to the loading direction with the progress of bone remodeling. Furthermore, as the imposed loading frequency increased, the diameter of the trabecula in the equilibrium state was enlarged by remodeling. These results indicate that our simulation model can successfully evaluate the relationship between loading frequency and trabecular bone remodeling.

Interstitial fluid flow in canaliculi as a mechanical stimulus for cancellous bone remodeling: in silico validation

Cancellous bone has a dynamic 3-dimensional architecture of trabeculae, the arrangement of which is continually reorganized via bone remodeling to adapt to the mechanical environment. Osteocytes are currently believed to be the major mechanosensory cells and to regulate osteoclastic bone resorption and osteoblastic bone formation in response to mechanical stimuli. We previously developed a mathematical model of trabecular bone remodeling incorporating the possible mechanisms of cellular mechanosensing and intercellular communication in which we assumed that interstitial fluid flow activates the osteocytes to regulate bone remodeling. While the proposed model has been validated by the simulation of remodeling of a single trabecula, it remains unclear whether it can successfully represent in silico the functional adaptation of cancellous bone with its multiple trabeculae. In the present study, we demonstrated the response of cancellous bone morphology to uniaxial or bending loads using a combination of our remodeling model with the voxel finite element method. In this simulation, cancellous bone with randomly arranged trabeculae remodeled to form a well-organized architecture oriented parallel to the direction of loading, in agreement with the previous simulation results and experimental findings. These results suggested that our mathematical model for trabecular bone remodeling enables us to predict the reorganization of cancellous bone architecture from cellular activities. Furthermore, our remodeling model can represent the phenomenological law of bone transformation toward a locally uniform state of stress or strain at the trabecular level.

Analytical technique for electroelastic field in piezoelectric bodies belonging to point group D

To elucidate the electroelastic field in woods, which are piezoelectric bodies belonging to point group D∞, we construct an analytical technique for general solutions to electroelastic problems in these bodies. First, the constitutive equations are derived considering the microstructures and their combined behaviors. Then, the displacement and electric field are expressed in terms of two types of displacement potential functions and the electric potential function, and their governing equations are obtained using the fundamental equations for the electroelastic field. As a result, the electroelastic field quantities are found to be expressed in terms of four functions, namely two elastic displacement potential functions and two piezoelastic displacement potential functions, each of which satisfies a Laplace equation with respect to the appropriately transformed spatial coordinates. As an application of the technique, the electroelastic field in a semi-infinite body subjected to a prescribed electric potential on its surface is analyzed, and the numerical results are illustrated. This novel technique serves to investigate the electroelastic field inside wooden materials.

Electroelastic Response of Cylindrical Fiber with D∞ Symmetry Exposed to Local Electric Field Through Opposed Electrode Pair

ABSTRACT To obtain practical information on the electroelastic behavior of poly-l-lactic acid microtweezers or catheters, a previously constructed analytical technique is used to obtain the electroelastic field solution of a poly-l-lactic acid cylindrical fiber exposed to a local electric field, which is applied through an opposed pair of square-sectioned electrodes. The numerical representation of the solution reveals the detailed field quantity distributions, their importance in the design of microtweezers and catheters, the overall deformation of such devices, and the effects of the electrode dimensions on the deformation. GRAPHICAL ABSTRACT

A general solution technique for electroelastic fields in piezoelectric bodies with D∞ symmetry in cylindrical coordinates

To elucidate the electroelastic field in bodies with D∞ symmetry such as wooden materials, we constructed a general solution technique for electroelastic problems in such bodies in a cylindrical coordinate system. We introduced the displacement and electric potential functions to express the displacement and electric field in cylindrical coordinates; their governing equations were obtained using the fundamental equations for the electroelastic field. The electroelastic field quantities could be expressed in terms of two elastic displacement potential functions and two piezoelastic displacement potential functions, each of which satisfies a Laplace equation with respect to the appropriately transformed cylindrical coordinates. As an application of the technique, we analyzed the problem of an infinitely long cylinder subjected to a non-axisymmetrically distributed electric surface potential. Using numerical calculations, we elucidated the electroelastic field quantities within the cylinder and found unique electroelastic coupling behaviors, which clearly demonstrate the necessity for the analytical technique presented. Moreover, we confirmed the possibility of the nondestructive evaluation (NDE) techniques by use of the piezoelectric effects.

Poroelastic analysis of interstitial fluid flow in a single lamellar trabecula subjected to cyclic loading

Trabecula, an anatomical unit of the cancellous bone, is a porous material that consists of a lamellar bone matrix and interstitial fluid in a lacuno-canalicular porosity. The flow of interstitial fluid caused by deformation of the bone matrix is believed to initiate a mechanical response in osteocytes for bone remodeling. In order to clarify the effect of the lamellar structure of the bone matrix—i.e., variations in material properties—on the fluid flow stimuli to osteocytes embedded in trabeculae, we investigated the mechanical behavior of an individual trabecula subjected to cyclic loading based on poroelasticity. We focused on variations in the trabecular permeability and developed an analytical solution containing both transient and steady-state responses for interstitial fluid pressure in a single trabecular model represented by a multilayered two-dimensional poroelastic slab. Based on the obtained solution, we calculated the pressure and seepage velocity of the interstitial fluid in lacuno-canalicular porosity, within the single trabecula, under various permeability distributions. Poroelastic analysis showed that a heterogeneous distribution of permeability produces remarkable variations in the fluid pressure and seepage velocity in the cross section of the individual trabecula, and suggests that fluid flow stimuli to osteocytes are mostly governed by the value of permeability in the neighborhood of the trabecular surfaces if there is no difference in the average permeability in a single trabecula.

Hygrothermal Field Considering Nonlinear Coupling Between Heat and Binary Moisture Diffusion in Porous Media

The hygrothermal field in porous media exposed to heat and moisture considering nonlinear coupling was studied. Dissolved and gaseous phases with different diffusivities were used to model the moisture in solids and voids, respectively. Heat generated by the transformation of gaseous moisture into dissolved moisture was considered along with the transformation from dissolved moisture into gaseous moisture due to a change in temperature. The balance between dissolved and gaseous moistures is determined by the chemical equilibrium. A system of nonlinear coupling diffusion equations was derived, and a steady field for an infinite strip was demonstrated.

Capturing microscopic features of bone remodeling into a macroscopic model based on biological rationales of bone adaptation

To understand Wolff’s law, bone adaptation by remodeling at the cellular and tissue levels has been discussed extensively through experimental and simulation studies. For the clinical application of a bone remodeling simulation, it is significant to establish a macroscopic model that incorporates clarified microscopic mechanisms. In this study, we proposed novel macroscopic models based on the microscopic mechanism of osteocytic mechanosensing, in which the flow of fluid in the lacuno-canalicular porosity generated by fluid pressure gradients plays an important role, and theoretically evaluated the proposed models, taking biological rationales of bone adaptation into account. The proposed models were categorized into two groups according to whether the remodeling equilibrium state was defined globally or locally, i.e., the global or local uniformity models. Each remodeling stimulus in the proposed models was quantitatively evaluated through image-based finite element analyses of a swine cancellous bone, according to two introduced criteria associated with the trabecular volume and orientation at remodeling equilibrium based on biological rationales. The evaluation suggested that nonuniformity of the mean stress gradient in the local uniformity model, one of the proposed stimuli, has high validity. Furthermore, the adaptive potential of each stimulus was discussed based on spatial distribution of a remodeling stimulus on the trabecular surface. The theoretical consideration of a remodeling stimulus based on biological rationales of bone adaptation would contribute to the establishment of a clinically applicable and reliable simulation model of bone remodeling.