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Proton Induced X-ray Emission (PIXE) method is used for the determination of elemental concentration in a cancellous bone of human femoral head from five autopsies and seven patients with femoral neck broken. Specimen preparation and experimental procedure are described in detail. Using t test, the results show that the concentrations of P, Ca, Fe, Cu, Sr in a control group are higher than those in a patient group, but the concentrations of S, K, Zn, Mn are not significantly different. The physiological functions of metal elements in human bone are also discussed.

The impact of crack–cocaine dependence on the quality and microarchitecture of the mandibular bone tissue requires further investigation. This cross-sectional study evaluated the fractal dimension and panoramic radiomorphometric indices in crack–cocaine-addicted men. Panoramic radiographs were obtained from 24 addicted and 24 nonaddicted men (control individuals) between the ages of 18 years and 60 years. The fractal dimensions of four different regions, along with the cortical mandibular, mental, and panoramic mandibular indices, were evaluated bilaterally. Significance level of 5% ($p=0.05$) was adopted in the statistical analysis. Mean fractal dimension value of all the four different regions of the jaw in the addict group ($1.27\pm 0.05$) was lower than that of the nonaddict group ($1.32\pm 0.03$; $p<0.001$). Furthermore, the inter-group panoramic radiomorphometric indices were not significantly different ($p\ge 0.16$). Mean fractal dimension value was associated with the duration of addiction ($R=0.47$; $p=0.01$), contrary to the indices ($p\ge 0.10$). Crack–cocaine addiction and longer duration of addiction were associated with lower fractal dimension values in the mandibular bone. Therefore, patients and dentists should be aware of this condition while planning periodontal, implant, and orthodontic therapies. Furthermore, crack–cocaine patients should be referred to a specialist for the evaluation of osteoporosis and osteopenia.

The Biot model is widely used to model poroelastic media. Several authors have studied its applicability to cancellous bone. In this article the feasibility of determining the Biot parameters of cancellous bone by acoustic interrogation using frequencies in the 5–15 kHz range is studied. It is found that the porosity of the specimen can be determined with a high degree of accuracy. The degree to which other parameters can be determined accurately depends upon porosity.

In this paper we present some results from our research on the interrogation of cancellous bone using ultrasound. Cancellous bone is known to be poroelastic in structure and, hence, Biot's equations may be applicable. In order to do the interrogation we consider using focused, ultrasonic, waves, symmetric about the axis of propagation. This suggests that we formulate the Biot equations using cylindrical coordinates. Our results provide relations involving the velocities of the transmitted waves and the Biot coefficients and these have clinical applications to the determination of osteoporosis of the cancellous bone.

In a precursor to this article the Biot model was used to model poroelastic media. The question this article addresses is whether the sort of experiments described by McKelvie and Palmer, Williams, and Hosokawa and Otani can be used to determine the parameters of the Biot model. A method of computing acoustic pressure in the low 100 kHz range was developed in Buchanan and Gilbert, "Determination of the parameters of cancellous bone using high frequency acoustic measurements," which appeared in Math. Comput. Modelling. In the present work a parameter recovery algorithm which uses parallel processing is developed and tested. It is found that when it is assumed that the agreement between calculated and measured data is about two digits, porosity can be determined to within about 1–2% and permeability, pore size and the bulk moduli to within about 40%, but in most cases less than 20%.

This paper deals with the application of the multiscale finite element method for simulating the cancellous bone. For this purpose, two types of biphasic representative volume elements are proposed. In the first one, the solid frame consists of thin walls simulated by shell elements. On the other hand, the solid phase of the second model is made up of columns consisting of eight-node brick elements. This choice of representative volume elements is motivated by experimental investigations reporting on the existence of plate-like and rode-like types of cancellous bone and possible conversions between them. The proposed representative volume elements are used to calculate effective material tensors and parameters and to investigate their change in terms of increasing porosity, which is typical for osteoporosis. As a first example, changes in the geometry of the representative volume elements are used to explore material anisotropy. In the end, the final example considers wave propagation through the bone treated as a homogenized medium.

In this paper we treat the cancellous bone as is done in mixture theory, i.e. each point in the material has both a fluid and a solid phase co-existing there. Each phase is weighted by the volume fraction of material in the composite structure. It is seen that in such a material attenuation of amplitude as frequency increases occurs as is observed in laboratory experiments^33,34 and as was observed in the finite element homogenization approach used by Hackl, Ilic and Gilbert.

The assessment of the stability of implants in cancellous bone remains a clinical problem. It has been shown that orthopaedic screw fixation depends on the microstructure and orientation of the trabeculae. In the current study we have investigated the possibility of using natural frequency analysis as a means of ranking screw fixation in cancellous bone. A dynamic modal analysis has been completed using the finite element method as a means of measuring implant frequency in a simple description of cancellous bone. A range of impulse excitation values have been examined which lead to implant resonance in different cancellous bone architectures. These values are reported in order that the eventual provision of a clinical diagnostic tool may correctly assess frequency values from the applied impulse.

Recent in vitro studies have provided evidence of the propagation of two different longitudinal wave modes at ultrasonic frequencies in cancellous bone. The genesis of these two plane waves in fluid-saturated porous media is predicted by the poroelastic approach to wave propagation originally developed by Biot. However, wave velocity is usually analyzed as a function of bone mass density only; therefore, the influence of the cancellous bone microstructure over the wave velocity is not taken into account. In the present study, a descriptor of the microstructure is considered in Biot's theory. This model is used to evaluate the large experimental variability of both fast and slow wave velocities measured on randomly oriented human and bovine cancellous bone samples. The role of the anisotropic solid structure and fluid in the behavior of fast and slow wave velocities is examined. Experimental and theoretically predicted velocities are found in close agreement when analyzed as a function of both porosity and structural index. This model has the potential to be used to determine an acoustically derived structural index in cancellous bone.

In this study, the effects of threshold variation in image segmentation of micro CT images of cancellous bone in the determination of the architectural parameters and stiffness were investigated. A total of 42 samples of 6 × 6 × 6 mm³ cubes with threshold values set between 500–1100 greyscale in increment of 100 of CT images of six human C5 vertebral bodies were analyzed. Threshold value of 800, based on Otsu's method, was set for the control group. From various threshold values, the respective architectural parameters, and the corresponding stiffness in three orthotropic directions (Exx, Eyy, Ezz) of each cube were computed from the voxel-based micro-finite element models under compressive simulation. The results showed that 1% variation of threshold value resulted in a 3.4% variation in BV/TV, 2% in Tb.N, 3.1% in Tb.Th, 2.9% in BS/BV, 1.8% in Tb.Sp, 29.2% in Exx, 28.7% Eyy and 27.7% in Ezz. Statistical analysis showed that 2.9% threshold variation caused significant change in BV/TV, Tb.Th, Exx, Eyy and Ezz values. The study shows that with threshold variation of more than 2.9%, significant differences in the architectural parameters and stiffness compared to those based on Otsu's method.

Bone remodeling is defined as the coupling of bone formation and resorption on the bone surface. Numerical simulations of the remodeling in cancellous bone were performed to reproduce the change in the trabecular structure. Assuming that the formation/resorption in cancellous bone could be generated on the trabecular surface, where the local stress under the mechanical load was larger/smaller than the averaged stress on the surrounding surface, voxel trabecular elements in a numerical model of bovine cancellous bone were added/removed. An ultrasound continuous wave in the frequency range 0.1–1.0 MHz was applied as the mechanical load, and then, the local stress was analyzed using a finite-difference time-domain (FDTD) method. Using the remodeling simulations, both changes in the trabecular structure could be reproduced with decreasing and increasing porosity. In changes, the trabecular elements and the pore spaces became strongly oriented in the direction of ultrasound propagation. In addition, the remodeling simulations indicated that both bone formation and resorption lessened as the frequency increased.

The increase of patients with osteoporosis is becoming a social problem, thus it is an urgent issue to find its prevention and treatment methods. Since cancellous bone is metabolically more active than cortical bone, cancellous bone is often used for diagnosis of osteoporosis and has received much attention within the study of bone. Bone is a hierarchically structured material and its mechanical properties vary at different structural levels, therefore it is important to break down the mechanical testing of bone according to the various levels within bone material. Mechanical properties of cancellous bone is said to be depended on quantities and orientation of trabecular bone. It is supposed that mechanical properties of trabecular bone are constant without depending on any structural arrangement and parts. However, such assumption has not been established in studies of trabecular bone. Furthermore test results have a large margin of error caused by insufficient shape assessment. In this study, three point bending tests of single cancellous bone trabeculae extracted from bovine femur were conducted to evaluate the effects of directions to the femur major axis direction on the mechanical properties. X-ray μCT was used to obtain shape of trabecular bone specimens. Furthermore compression tests of cancellous bone specimens, which were extracted in 10mm cubic geometry, were conducted for evaluation of directional properties.There were small difference in the elastic modulus of the trabecular bones which were extracted in parallel and in perpendicular to the major axis of femur. Considering from the results that the cancellous bone specimens, which were extracted in 10mm cubic geometry, have different elastic properties depending on the tested directions; the bone structure has larger influence than bone material property on the mechanical properties of cancellous bone.

Image analysis using computational Fourier transforms is here applied to radiographs of vertical vertebral bone sections. Simple variables are derived that measure gross properties of the vertebral patterns and study of these using univariate statistical analyses indicates, as would be expected, that there are differences with age and in each sex. Complex variables that characterise the transforms more completely show, when analysed using multivariate statistical methods, increased detail of difference with age and sex. Thus, in the oldest individuals of both sexes, the transforms seem to recognise osteoporosis. In middle-aged individuals, though males seem fairly normal, females have features that look like those in the old individuals, though only the older middle-aged specimens show the overt condition. Whether or not this is osteoporosis, the structural features found in the entire vertebral body in the old individuals exist in the two anterior quadrants of the middle-aged females. Even in young individuals, there is a difference between males and females. This seems to relate to the same structural features as before, but they exist in only a single quadrant, the antero-superior. Though used here for the analysis of radiographs of sections, the technique is equally applicable to non-invasive images. It is easy and inexpensive to carry out. It seems to provide information of functional importance in terms of vertebral mechanics. It may be capable of development for clinical situations to reveal incipient change long before symptomatic disease is present.

The current paper is concerned with simulating the behavior of cancellous bone by using the multiscale finite element method. This approach belongs to the group of homogenization methods and is special in so far as it solves boundary value problems at two scales by using the finite element method. In order to activate the viscous effects in the fluid phase of the cancellous bone, a dynamic investigation and an analysis in the complex domain are necessary.