Determination of the parameters of cancellous bone using high frequency acoustic measurements

The Biot model is widely used to model poroelastic media. Several authors have tested its applicability to cancellous bone, but to do so requires a priori estimation of the parameters of the Biot model, which is an uncertain and expensive endeavor. A method of computing acoustic pressure in the low 100 kHz range is developed.     

Effective parameters of cancellous bone

Cancellous bone is a two–component structure consisting of the bone frame and interstitial blood marrow. In the scope of this presentation, the multiscale finite element method is used for its modeling. This method results from a combination of homogenization theory and the theory of finite elements and is based on the calculation of effective material parameters by investigating representative volume elements (RVEs). For the particular kind of material considered here, a cubic two–phase RVE is assumed where the dry skeleton is modeled in different ways. Apart from the variations of the geometry, the influence of the usage of different types of finite elements is studied in this context. Note that the presence of a liquid phase requires dynamic investigation including the viscous phenomena. To this end, acoustic excitation and an analysis in the complex domain are chosen. The method permits calculation of the effective material parameters such as Young's modulus, bulk modulus and Poisson's ratio and furthermore the simulation of the behaviour of the complete bone or of its parts. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Estimation of material properties of cancellous bone using multiscale FEM

Cancellous bone is a spongy type of bone with voids filled by blood marrow. Without much loss of generality it can be modeled as a material with periodic microstructure where overall parameters can be calculated using homogenization methods. Here the multiscale finite element method is applied and the assumed representative volume element (RVE) is a cube with solid frame and fluid core. From the point of view of the finite element method the RVE is a combination of solid and shell elements. As the acoustic excitation is considered, a complex stiffness matrix and complex displacements appear in the solution of the problem. Calculation of overall properties is repeated for different geometries of the solid frame. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stable determination of an inhomogeneous inclusion by local boundary measurements

We deal with the problem of determining an inclusion within an electrostatic conductor from boundary measurements. Under mild a priori assumptions we establish optimal stability estimates. Measurements are performed on a portion of the boundary of the conductor.     

Deformability and strength of compact bone tissue during tensioning

The deformability and strength characteristics of compact bone tissue of human tibia during tensioning along all three main anisotropy axes was determined experimentally. The character of change in the secant moduli of elasticity and specific energies of deformation during the loading process were studied. A correlation was established between the mechanical characteristics and the biochemical composition of the bone tissue.     

Age aspects of the torsional strength of compact bone tissue

The variation of the strength of specimens of human tibial compact bone tissue with age has been investigated. It is shown that the torsional strength _i ^* increases sharply in childhood, reaches a maximum at age 25–35, and then gradually falls. There is a correlation between _i ^* and the porosity of the bone tissue. The mode of fracture of the bone tissue has been studied in relation to its orientation with respect to the principal axes of anisotropy.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 493–503, May–June, 1975.     

Degree of deformation and strength of compact bone tissue during torsion

This paper discusses the variation in the deformation and strength properties of compact bone tissue during torsion in various zones of the cross section of human tibia. A correlation has been found between the specific energy of deformation consumed during the loading process and the level of stress attained. The degree of correlation between the deformation and strength properties of the bone tissue has been studied as a function of the concentration of certain biochemical substances in its composition.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No.5, pp. 911–918, September–October, 1973.     

Bearing of geometric and material properties to bone strength in bending

Osteoporosis is characterized by decreasing of bone mass and bone strength with advanced age. For characterization of material properties of bone the volumetric bone mineral density is one of the most important contributing factors to bone strength. Often bending tests of whole bone are used to get information about the state of osteoporosis. From an uniaxial test of a bone specimen it is assumed that an elastic region exists up to initial yield stress and a following hardening region. In bending tests beside material properties geometric properties like shape and cortical thickness appropriate the non-linear moment-curvature curve. The aim of this contribution is to show how an elastic-plastic material law including tensile damage influences the global bending behavior. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Determining conductivity by boundary measurements

In [2], A. P. Caldéron posed the following question: can one determine the heat conductivity of an object from static temperature and heat flux measurements at the boundary? We show that such measurements uniquely determine the conductivity and all of its derivatives at the boundary.     

Reducing the consistency strength of an indestructibility theorem

Using an idea of Sargsyan, we show how to reduce the consistency strength of the assumptions employed to establish a theorem concerning a uniform level of indestructibility for both strong and supercompact cardinals. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Uniqueness for the determination of sound-soft defects in an inhomogeneous planar medium by acoustic boundary measurements

We consider the inverse problem of determining shape and location of sound-soft defects inside a known planar inhomogeneous and anisotropic medium through acoustic imaging at low frequency. In order to determine the defects, we perform acoustic boundary measurements, with prescribed boundary conditions of different types. We prove that at most two, suitably chosen, measurements allow us to uniquely determine multiple defects under minimal regularity assumptions on the defects and the medium containing them. Finally, we treat applications of these results to the case of inverse scattering.

     

Strength of fresh bone and bone preserved by freezing

The bending strength of 85 plates obtained from the tibias of human cadavers has been determined and compared with the strength of plates of bone tissue from the same bone stored at temperatures from ?25 to ?30°C for 3 months (44 cases), 6.5 months (32 cases), and 9.5 months (32 cases). It is found that the strength of the deep-frozen bone decreases with time.     

Stable determination of conductivity by boundary measurements

We consider the problem of determining the scalar coefficient γ in the elliptic equation div(γ grad u) = 0 in ω when, for every Dirichlet datum u = ? on ?ω , the Neumann datum γ(?/ ? n)u = ∧._γ? is known. We prove a continuous dependence result     

Predicting measurements at unobserved locations in an electrical transmission system

Electrical transmission systems consist of a huge number of locations (nodes) with different types of measurements available. Our aim is to derive a subset of nodes which contains almost sufficient information to describe the whole energy network. We derive a parameter set which characterises every single measuring location or node, respectively. Via analysing the behaviour of each node with respect to its neighbours, we construct a feasible random field metamodel over the whole transmission system. The metamodel is used to smooth the measurements across the network. In the next step we work with a subset of locations to predict the unobserved ones. We derive different graph kernels to define the missing covariance matrix from the neighbourhood structures of the network. This results in a metamodel that is able to smooth observed and predict unobserved locations in a spatial domain with non-isotropic distance functions.     

Flexure of beams with low shear strength on an elastic foundation

The deflection of a beam on an elastic foundation is determined with allowance for shears and without postulating a law of shear-stress distribution. The accuracy of approximating this law with a quadratic parabola is estimated. The effect of shears on deflection is investigated in relation to beams of different length made of materials of the oriented glass-reinforced plastic type with low shear strength.Mekhanika Polimerov, Vol. 3, No. 5, pp. 881–887, 1967