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EN
The aim of this research was to verify to what extent the shape of an indenter tip influences the final form of the constitutive equation for the trabecular bone. Methods: Trabecular bone was formulated as a non-linear viscoelastic material with Mooney–Rivlin hyperelastic model to describe the purely elastic response of the bone tissue. Tests of the mechanical properties of the trabecular bone, resected from the femoral head of a 56-year-old patient, were carried out with two types of indenter: the spherical tip of a diameter of 200 μm and pyramid Vickers tip with 136° between plane faces. Tests with both indenters included loading and unloading phases with no hold at peak force and with hold time t = 20 s and were conducted with a maximum load Pmax = 500 mN and loading/unloading rate V = 500 mN/min. Results: The formulated constitutive model describes the trabecula behaviour very well. The model curves match the experimental results in the loading phase, holding period and most of the unloading ramp. The purely viscoelastic material constants are very close in value for both considered tips, but purely elastic constants differ. Conclusions: The results indicate that the constitutive model based on the indentation with the Vickers tip does not cover the plastic residual deformation. When a viscoelastic response of bone is expected, a model with constants calibrated for the spherical tip should be used, and the other set of parameters values (Vickers tip) when trabeculae may undergo plastic deformation.
EN
Purpose: The purpose of the study was to evaluate the effects of different methods of trabecular bone storage on changes in its elastic properties. Methods: 186 porcine trabecular bone samples were divided into 6 groups, approximately 30 samples each. Five groups were stored using the following methods: in buffered 10% formalin solution at room temperature, frozen at –21 C, in the open air at room temperature, in 96% alcohol solution and in 50% alcohol solution at room temperature. The samples were subjected to compression test to measure the elastic modulus. The samples after the first measurement were subjected to further measurements for 14 weeks, every 2 weeks. The sixth group was used to determine the effects of 10 freeze-thaw cycles on changes in the elastic modulus. A Kolmogorov–Smirnov test at significance level p = 0.05 was used to determine the significance of changes in time. Results: The changes in elastic properties caused by the different storage methods were statistically insignificant, except for the group of samples stored in the open air. The changes in elastic modulus after 10 freeze-thaw cycles were also statistically insignificant. Conclusions: Except for the storage method in the open air, other storage methods did not significantly affect changes in elastic properties of the trabecular bones after 14 weeks. No effects of 10 freeze-thaw cycles on changes in elastic modulus were observed.
EN
Purpose: The goal of the study was to determine the influence of DSI test conditions, i.e. loading/ unloading rates, hold time, the value of the maximum loading force on selected mechanical properties of trabecular bone tissue. Methods: The test samples were resected from a femoral head of a patient qualified for a hip replacement surgery. During the DSI tests hardness (HV, HM, HIT) and elastic modulus (EIT) of trabecular bone tissue were measured using the Micro Hardness Tester (MHT, CSEM). Results: The analysis of the results of measurements and the calculations of total energy, i.e. elastic and inelastic (Wtotal,Welastic,Winelastic) and those of the parameters of hardness and elasticity made it possible to assess the impact of the process parameters (loading velocity, force and hold time) on mechanical properties of bone structures at a microscopic level. Conclusions: The coefficient k dependent on the ratio EIT / HIT and on the stored energy (ΔW = Wtotal- Welastic) is a measure of the material reaction to the loading and the deformation of tissue.
EN
Purpose: The study aimed to investigate a relationship between the mineral content of the human trabecular bone and parameters determined from compression fatigue tests at stepwiseincreasing amplitude. Methods: Mineral content of the trabecular bone was estimated as ash density and bone mineral density values. The relationship between the ash density, bone mineral density and factors obtained from fatigue test: fatigue life, cumulative elastic energy and cumulative energy of dissipation was determined. Results: The results from the measurements of ash density and bone mineral density show good correlation with the fatigue test results. The relationship was estimated based on the correlation coefficient R within 0.74-0.79 for the particular pairs of factors. Conclusions: The study shows that the ash density and the bone mineral density are good predictors to estimate the fatigue life of trabecular bone. The study also validates the applicability of the tests at stepwise-increasing amplitude in determining the mechanical properties of trabecular bone.
EN
The article presents the algorithm for geometric modelling of bone structures. The images obtained during a microtomography test (fiCT) and the specialist engineering software allow to make 3D models of these structures and their application in further studies using the finite element method. Conducting the appropriate treatment of the derived models it is possible to improve the quality of the finite element mesh and to reduce the number of elements of which it is composed. This simplifies and accelerates the further numerical analysis conducted on bone models.
PL
Artykuł przedstawia algorytm postępowania przy modelowaniu geometrycznym struktur kostnych. Obrazy uzyskane podczas badania mikrotomografem oraz specjalistyczne oprogramowanie inżynierskie umożliwiają wykonywanie modeli 3D tychże struktur oraz wykorzystanie ich w dalszych badaniach z użyciem metody elementów skończonych. Przeprowadzając odpowiednią obróbkę uzyskanych modeli możliwa jest poprawa jakości siatki elementów skończonych oraz zmniejszenie liczby elementów, z których się składa. Ułatwia to i przyśpiesza dalszą analizę numeryczną prowadzoną na modelach kości.
EN
Research of tissue structures at a micro-structural level belongs to the contemporary research in Biomechanics. In the paper a theoretical analysis from Oliver-Pharr’s perspective was presented forming the basis for the measurement methods of bone tissue mechanical properties such as hardness and elasticity modulus. The aim of the study was to emphasize the fundamental assumptions in the analysis which lead to the diversified notions of hardness called technical and normal ones. In the experimental part of the paper, using appropriately prepared trabecular and cortical bone tissues, the measurements of the depth of the indenter penetrating with the applied loadings were made. They enable particularly to determine the elasticity modulus. The aim of this research was the assessment of the material properties of bone structures, having in mind the energetic aspects of the curve (indenter loading-depth) obtained in the cycle: non-elastic (plastic, viscoelastic …) loading and elastic unloading.
PL
Badania struktur tkankowych na poziomie mikrostrukturalnym należą do wspołczesnych w Biomechanice. W pracy przedstawiono analizę teoretyczną w ujęciu Olivera-Pharra leżącą u podstaw metod pomiarów własności mechanicznych tkanek kostnych takich jak twardość oraz moduł sprężystości. Celem opracowania było uwypuklenie podstawowych założeń w analizie, które prowadzą do zróżnicowanych pojęć twardości zwanych techniczną i normalną. W części eksperymentalnej pracy przeprowadzono, na stosownie przygotowanych tkankach kości gąbczastej i zbitej, pomiary głębokości zagłębiania wgłębnika przy zadanych obciążeniach. Umożliwiają one w szczególności określenie modułu sprężystości. Celem tych badań była ocena własności materiałowych struktur kostnych z uwagi na energetyczne aspekty krzywej (obciążenie-głębokość wgłębnika) otrzymanej w cyklu: obciążenie niesprężyste (plastyczne, lepko-sprężyste…) i odciążenie sprężyste.
7
Content available remote Trabecular bone numerical homogenization with the use of buffer zone
EN
The paper is devoted to calculation of effective orthotropic material parameters for trabecular bone tissue. The finite element method (FEM) numerical model of bone sample was created on the basis of microcomputed tomography (µCT) data. The buffer zone surrounding the tissue was created to apply the periodic boundary conditions. Numerical homogenization algorithm was implemented in FEM software and used to calculate the elasticity matrix coefficients of the considered bone sample.
EN
In this paper The presents the relationship among the the mineral content of human trabecular bone and its elastic modulus measured by ultrasonic test. Examined two groups of samples - osteoporotic and coxarthrotic. Relationship between bone mineral content and elastic modulus described the correlation coefficient R. For both groups of samples obtained R-values in the range 0.71 ÷ 0.72 for osteoporotic samples and 0.70 ÷ 0.7 2 for coxarthrotic samples. R-values obtained for both groups of samples are similar and suggest that the content of the mineral phase of bone is a good indicator for the indirect estimation of elastic properties of bone measured by elastic modulus.
PL
W pracy przedstawiono zależności pomiędzy zawartością fazy mineralnej ludzkiej kości beleczkowej a jej modułem sprężystości pomierzonym metodą ultrasonograficzną. Badaniu poddano dwie grupy kości - osteoporotycznych i koksartrycznych. Siłę zależności pomiędzy zawartością minerałów w kości a modułem sprężystości opisano współczynnikiem korelacji R. Dla badanych grup próbek uzyskano wartości współczynnika R w zakresie 0,71÷0,72 dla próbek osteoprotycznych oraz 0,70÷0,72 dla próbek koksartrycznych. Warto ści współczynnika R otrzymane dla obu grup próbek są podobne i wskazują na to że zawartość fazy mineralnej w kościach jest dobrym wskaźnikiem do pośredniej oceny własności sprężystych kości mierzonej modułem sprężystości.
PL
W pracy podjęto próbę określenia parametrów materiałowych kości beleczkowej dla skali makroskopowej na podstawie symulacji w skali mikro. Pozyskaną próbkę tkanki gąbczastej zeskanowano z wykorzystaniem mikrotomografu komputerowego i poddano próbie ściskania, a następnie zasymulowano numerycznie. Na podstawie uzyskanych wyników przeprowadzono identyfikację modułu Younga materiału beleczek kostnych oraz obliczono makroskopowe parametry materiałowe kości beleczkowej.
EN
In this paper an attempt to determine material parameters of a trabecular bone for the macroscopic scalę based on simulations in micro scale is prestented. The cylindrical sample of spongy bone extracted from a femoral head was scanned with theuse of computed micro-tomography and subjected to the compression test with the useof material testing machine. Then, numerical simulation of compression test was performed. On the basis of the obtained results, the identification of the material parameters of bone trabeculaes was made and the macroscopic material parameters of trabecular bone were calculated.
PL
Celem niniejszej pracy była analiza zdjęć mikrotomograficznych kręgów L3. Wyznaczono parametry histomorfometryczne kości beleczkowych kręgów pochodzących od kobiet w różnym wieku, przed oraz po wykonaniu próby ściskania. Dokonano analizy porównawczej parametrów w celu wyłonienia elementów struktury najbardziej podatnych na degradację.
EN
Stressed state peculiarities of cortical and trabecular bones by two,point asymmetric screw fixation with implant for femoral neck fracture are studied. Layer construction mechanic methods are used for analysis of stresses in cortical and trabecular bones. Biomechanical conditions for non,opening of the junction of the bone parts being joined are determined. It has been found that the total tightness of the broken parts when they rest against each other is secured over the whole fracture section without junction opening under condition that fixing screws are positioned in the trabecular bone without penetration of the thread side surface into cortical bone.
EN
The paper presents the results of examination of relations between indicators describing trabecular bone structure and its static and cyclic compressive strength. Samples of human trabecular bone were subject to microtomographic tests in order to specify indicators describing its structure. Part of the samples was subject to static compression tests, part to cyclic compressing loads with stepwise increasing amplitude. Evaluation of a degree of applicability level of estimation of bone compressive strength properties was conducted based upon values of structure indicators. Evaluation was performed based upon values of obtained determination coefficients R2 for linear regression. Obtained R2 values were within the range of 0.30-0.51 for relations between examined indicators and static compressive strength within the range of 0.47-0.69 for relations with the results of cyclic test with stepwise increasing amplitude.
PL
W pracy przedstawiono wyniki pomiarów gęstości fizycznej oraz wartości parametrów mechanicznych wyznaczonych w próbie jednoosiowego ściskania dla próbek tkanki kostnej gąbczastej osteoartrotycznej, pochodzących z głów ludzkich kości udowych. W pracy podjęto także próbę określenia korelacji pomiędzy gęstością fizyczną, a parametrami mechanicznymi tkanki kostnej. Gęstość fizyczna oraz parametry mechaniczne tkanki kostnej charakteryzują się najwyższą wartością dla próbek wyciętych z plastra II. Znaleziono również wysoką korelację pomiędzy gęstością hydrostatyczną, a modułem Young'a (R² = 0,53).
EN
The puproses of this study were to evaluate the mechanical properties of human patological trabecular bone from adult human femoral heads removed during surgery for hip-joint replacement and to measure bone densities. The correlations between the mechanical properties and bone densities were also considered. The results showed that mechanical properties of the specimens from region II are higher than those obtained from region I. The correlation between the bone density and mechanical properties is high (R² = 0,53).
EN
Trabecular bone is one of components of human bone. It is a porous structure which strength has principal influence on strength whole bone. In the study has been presented results investigation relationship between fatigue life (loading with stepwise increasing amplitude) and structural indices of human trabecular bone. Dependencies were described by determination coefficient R2. Obtained values the coefficient were contained in range 0,50÷0,69.
EN
Trabecular bone is one of components of bone which quality is responsible for strength whole human bone. It is a porous structure, which change with age. In medical practise for estimation quality of bone the most often is used dual energy x-ray absorptiometry (DEXA). For scientific investigation of bones are often used apparent density and ash density. In the work presented results comparison values BMD, apparent and ash density obtained from measurement samples of human trabecular bone. Obtained values coefficient of determination R2 for relationship between this densities were in range 0,28÷0,62.
16
Content available remote Measurement of structural parameters of trabecular bone using fuzzy logic
EN
In this paper there was proposed the trabecular bone structure analysis using fuzzy logic. Theoretical and algorithmic basis method of measurement structural parameters there was presented. Application using FDT algorithm was adapted to analysis thickness of trabecular bone. Study methodics of measurements of gray level images allows using physical relation between mechanical and structural properties of images especially for limited resolution images, with data inaccuracies, graded object compositions and for structures having similar intensities for different parts.
PL
W artykule zaproponowano zastosowanie logiki rozmytej do analizy struktury kości beleczkowej. Przedstawione zostały teoretyczne i algorytmiczne podstawy metod pomiaru parametrów strukturalnych. Do analizy grubości beleczek zastosowano aplikację korzystającą z algorytmu FDT. Opracowanie metodyki pomiarów na obrazach w skali szarości pozwoli na wykorzystanie fizycznie uzasadnionych relacji wiążących własności mechaniczne i strukturalne obrazów w zastosowaniach medycznych, szczególnie w przypadku obrazów o niskiej rozdzielczości, z nieścisłymi danymi, stopniowanym układem obiektu oraz dla podobnej struktury różnych części.
EN
The paper considers the application of statistical properties of backscattered ultrasonic signal for assessment of the trabecular bone status. Computer simulations were conducted to investigate the properties of the ultrasound pulse-echo signal, as it is received on the transducer surface after scattering in trabecular bone. The micro-architecture of trabecular bone was modeled by a random distribution of long and thin cylindrical scatterers of randomly varying diameters and mechanical properties, oriented perpendicular to the ultrasound beam axis. The received echo signal was calculated as a superposition of echoes from all the scatterers present in the scattering volume. The simulated signal envelope was used for statistical processing to compute various parameters like the mean amplitude, the amplitude MSR defined as the ratio of the mean to the standard deviation and the amplitude histogram. Results indicated that while for the well-defined trabeculae properties within the simulated bone structure the signal envelope values are Rayleigh distributed the significant departures from Rayleigh statistics may be expected as the thickness of trabeculae become random. The influence of the variation of mechanical properties of the bone tissue building the trabeculae on the bone backscattered signal parameters was not observed.
EN
BMD density, fractal dimension and volume tissue in volume of sample can be used to estimate the strength of trabecular bone. In the paper, presented is the comparison relations between the indicators for two groups of human trabecular bones – osteoporotic and coxarthrotic. Dependencies between the indicators were described with the determination coefficient R. Achieved values of the coefficient are contained in range 0,2÷0,56.
PL
W pracy przedstawiono wyniki badań próbek kostnych mających na celu określenie wskaźników opisujących ich strukturę. Badania przeprowadzono na mikrotomografie komputerowym. Na podstawie analizy statystycznej stwierdzono, że różnice pomiędzy strukturą kości: osteoporotycznej i koksartrycznej najlepiej opisują dwa wskaźniki: średnia odległość pomiędzy beleczkami w kości Tb.Sp i gęstość prześwietleniowa BMD.
EN
Results of microtomographic investigation of human trabecular bonę samples arę presented in the paper. The aim of investigation was to describe bonę structure factors. On basis of statistical analysis it was found that such factors as trabecular separation Tb.Sp and X-ray den-sity BMD aro better for description of diffurences between the structure of osteoporotic and coxarthrotic bonę.
PL
W pracy przedstawiono wskaźniki struktury uzyskane z badań mikro- tomograficznych, kości beleczkowej osteoporotycznej i koksartrycznej. Zaprezentowano różnice w budowie kości w obu badanych grupach próbek. Przeprowadzono wstępną ocenę wyników i na tej podstawie określono wytyczne do dalszych analiz.
EN
In this study factors of structure, obtained from microtomographic investigation, of osteoporotic and coxarthrotic trabecular bonę arę presented. Differences in the bonę structure in both examined groups arę shown. Preliminary analysis of obtained results and defined direction for further studies arę displayed.
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