Ali M. Sadegh

An Evolutionary Wolff’s Law for Trabecular Architecture

A continuum model is proposed to describe the temporal evolution of both the density changes and the reorientation of the trabecular architecture given the applied stress state in the bone and certain material parameters of the bone. The data upon which the proposed model is to be based consist of experimentally determined remodeling rate coefficients and quantitative stereological and anisotropic elastic constant measurements of cancellous bone. The model shows that the system of differential equations governing the temporal changes in architecture is necessarily nonlinear. This nonlinearity is fundamental in that it stems from the fact that, during remodeling, the relationship between stress and strain is changing as the stress and strain variables themselves are changing. In order to preserve the remodeling property of the model, terms that are of the order strain times the changes in density and/or microstructural properties must be retained. If these terms were dropped, there would be no feedback mechanism for architectural adaptation and no adaptation of the trabecular architecture. There is, therefore, no linearized version of the model of the temporal evolution of trabecular architecture. An application of the model is illustrated by an example problem in which the temporal evolution of homogeneous trabecular architecture is predicted. A limitation of the proposed continuum model is the length scale below which it cannot be applied. The model cannot be applied in regions of cancellous bone where the trabecular bone architecture is relatively inhomogeneous or at a bone-implant interface.

Modular wall climbing robots with transition capability

This paper introduces two wall climbing robots based on different adhesive mechanisms: vortex attraction technique and the vacuum rotor package. The robots adopt modular design with each module can move on various smooth/rough surfaces independently while a combination of two modules can achieve wall-to-wall transition. Detailed description of the novel mechanical and electrical design is presented. Simulation is conducted to reveal aerodynamic behavior of the adhesive mechanism. Several robot prototypes are built to verify the design concepts. Future directions to improve the climbing robots are elaborated

Mechanics of plain-woven fabrics for inflated structures

Pressurized fabric tubes, pressure-stabilized beams (known as air beams) and air-inflated structures are considered to be valuable technologies for lightweight, rapidly deployable structures. Design optimization of an inflated structure depends on a thorough understanding of woven fabric mechanics. In this paper the bending response of woven pressure-stabilized beams have been experimentally tested and analytically investigated. Additionally, the micromechanical effects of interacting tows have been studied through finite element models containing contact surfaces and nonlinear slip/stick conditions. Local unit cell models consisting of pairs of woven tows were created to characterize the effective constitutive relations. The material properties from the unit cell models were then used for the global continuum model subjected to 4-point flexure. An experimental set-up was designed and manufactured for testing of Vectran and PEN air beams. The air beam mid-span deflections were measured as functions of inflation pressure and bending load. Plots of the elastic and shear moduli with respect to the pressure and coefficient of friction have been generated. It was determined that the effective elastic and shear moduli were functions of inflation pressure, the material used and the geometry of the weave. It was shown that pneumatic or pressurized tube structures differ fundamentally from conventional metal structures.

Implementation of strain rate as a bone remodeling stimulus

Strain rate is implemented as a stimulus for surface bone remodeling. Using idealized models for trabecular bone structures, the surface remodeling predictions using the strain rate as the stimulus are compared with the predictions using the peak strain magnitude as the stimulus. For a uniaxially loaded cruciform shape, the comparison shows that the two surface remodeling stimuli predict the same final shape under a periodic compressive load, but the two evolutionary paths to final shapes are different. Two biaxially loaded regular grid models of trabecular structure were considered, one a grid of square diamond shaped elements and the other a brick wall patterned grid. For both of these idealized trabecular structures, the comparison shows that the two surface remodeling stimuli predict the same final shape under a periodic compressive load, even from these distinctly different initial grid patterns, and the evolutionary paths to final shapes are quite different. In general the two stimuli do not predict the same remodeling and the conditions under which they do are derived. The models developed are also applied to the data from the animal experiments reported in Goldstein et al. (1991), and it is shown that the strain rate stimulus predicts bone remodeling similar to what was experimentally observed.

BONE INGROWTH: AN APPLICATION OF THE BOUNDARY ELEMENT METHOD TO BONE REMODELING AT THE IMPLANT INTERFACE

Surface bone remodeling theory and the boundary element method are employed to investigate the microstructural remodeling of bone at the bone-implant interface. Three situations are considered: remodeling-induced penetration between the screw threads of an implanted screw, penetration of bone tissue into a slot or cavity in an implant, and the interaction of individual trabeculae in the remodeling processes near an implant. For each case the bone ingrowth is determined as a function of the geometry and the applied load.

Decrimping Behavior of Uncoated Plain-woven Fabrics Subjected to Combined Biaxial Tension and Shear Stresses

Tension structures continue to be of increasing importance to military applications requiring minimal weight, small packaging volumes and enhanced deployment operations. Presently, design methods for inflated fabric structures are not well established. Analysis tools for their efficient design lag behind those for conventional structures, partly because woven fabrics do not behave as a continuum. Changes in fabric architecture occur with loading and lead to several sources of nonlinear response. In particular, effective constitutive relationships must be developed that institute the combined effects of biaxial tensile stresses from inflation and shear stresses from bending for use in structural models. Through analysis and experiment, this study addressed these architectural changes, such as crimp interchange, and their effects on the mechanical properties of uncoated plain-woven fabrics. This was accomplished through meso-scale finite element analyses and material tests using a recently developed experimental fixture. The fixture facilitated testing of a wide variety of fabrics (woven, braided, knitted, etc.) subjected to combined biaxial tensile and shear stresses. The meso-scale models and swatch-level test results confirmed that: (1) crimp interchange profoundly influenced the fabric elastic and shear stiffnesses, as changes in crimp heights occurred with increasing biaxial tensions, (2) the shear modulus was highly dependent upon the biaxial tensions and compaction of the tows at the crossover points and (3) the shear modulus was highly nonlinear and was not monotonic with rotation and shear force. This study also presents analytical and experimental methods to ascertain the elastic and shear moduli of woven fabrics for use in evaluating the performance of air beams.

The effect of surface roughness on the stress adaptation of trabecular architecture around a cylindrical implant.

The effect of implant-bone bonding and the effect of implant surface roughness on bone remodeling near the bone-implant interface were studied by using a surface remodeling theory and the boundary element method. The study has shown that implant attachment plays an important role in bone remodeling near the implant. It has been observed in animal experiments and in clinical situations that the remodeled trabecular bone architecture around a cylindrical implant could vary, on one hand, from a hub surrounding the implant with a set of external spokes to, on the other hand, a hubless situation in which a set of spokes attach directly to the implant. It is shown here that the difference in these structures may be attributed to differences in implant attachment. The results show that the bone with perfect bonding or roller boundary condition without a gap remodeled to a hubless spoke trabecular bone architecture. On the other hand, the roller boundary condition with a specified gap yielded a spoke trabecular architecture with a hub or ring surrounding the implant. These quantitative results mirror the experimental and clinical observations. It is concluded that the hub is a consequence of the gap and not a consequence of the lack of friction between the implant and the bone.

Boundary integral equation technique with application to freezing around a buried pipe

Abstract In this paper the use of the boundary integral equation method (BIEM) for multidimensional problems with a moving phase-change interface is explored. The method is shown to be suited to heat transfer problems where the field equations are linear in each region and the boundary or interface matching conditions are both highly irregular and non-linear. For moving interface problems the BIE technique both reduces the dimensions of the problem by one, thus decreasing storage requirements, and directly solves for the unknown normal temperature gradient on each side of the interface for the determination of the instantaneous interface velocity. To illustrate the versatility of this technique the BIEM is applied to a previously unsolved problem: the melting/freezing around a pipe buried in a semi-infinite domain where the melting/freezing is initiated at the free surface and the medium is initially not at the phase-change temperature. For simplicity quasi-steady heat conduction is assumed in both the thawed and frozen zones. Solutions are presented for various values of the governing parameters.

Non-interacting modes for stress, strain and energy in anisotropic hard tissue

The six non-interacting modes for stress, strain and energy in an orthotropic elastic model of human femoral cortical bone tissue are discussed and illustrated. The stress and strain modes are illustrated using the representation of the stress and strain fields around a circular hole in a flat plate of cortical bone subjected to a uniaxial field of tension as the example. The six modes play a role in the stress analysis of orthotropic elastic materials similar to the roles played by the hydrostatic and deviatoric non-interacting stress, strain and energy modes in isotropic elasticity. The biomechanical significance of the six non-interacting modes for stress, strain and energy in hard tissue is both practical and suggestive. The modes suggest a practical scheme for the representation of stress and strain fields in hard tissue. The existence of the modes suggests physical insights, for example, possible failure mechanisms or adaptation strategies possessed by the hard tissues.

Global/local head models to analyse cerebral blood vessel rupture leading to ASDH and SAH

Blunt and rotational head impacts due to vehicular collisions, falls and contact sports cause relative motion between the brain and skull. This increases the normal and shear stresses in the (skull/brain) interface region consisting of cerebrospinal fluid (CSF) and subarachnoid space (SAS) trabeculae. The relative motion between the brain and skull can explain many types of traumatic brain injuries (TBI) including acute subdural hematomas (ASDH) and subarachnoid hemorrhage (SAH) which is caused by the rupture of bridging veins that transverse from the deep brain tissue to the superficial meningeal coverings. The complicated geometry of the SAS trabeculae makes it impossible to model all the details of the region. Investigators have compromised this layer with solid elements, which may lead to inaccurate results. In this paper, the failure of the cerebral blood vessels due to the head impacts have been investigated. This is accomplished through a global/local modelling approach. Two global models, namely a global solid model (GSM) of the skull/brain and a global fluid model (GFM) of the SAS/CSF, were constructed and were validated. The global models were subjected to two sets of impact loads (head injury criterion, HIC = 740 and 1044). The relative displacements between the brain and skull were determined from GSM. The CSF equivalent fluid pressure due to the impact loads were determined by the GFM. To locally study the mechanism of the injury, the relative displacement between the brain and skull along with the equivalent fluid pressure were implemented into a new local solid model (LSM). The strains of the cerebral blood vessels were determined from LSM. These values were compared with their relevant experimental ultimate strain values. The results showed an agreement with the experimental values indicating that the second impact (HIC = 1044) was strong enough to lead to severe injury. The global/local approach provides a reliable tool to study the cerebral blood vessel ruptures leading to ASDH and/or SAH.