Development of a three-dimensional finite element model of a human tibia using experimental modal analysis.

The modal analysis of a human tibia consisted of characterizing its dynamic behavior by determining natural frequency, damping ratio and mode shapes. Two methods were used to perform the modal analysis: (1) a finite element method (structural model); (2) an experimental modal analysis (modal model). The experimental modal model was used to optimize the structural model. After optimization, differences in results between the two models were found to be due only to mechanical properties and mass distribution. The influences of boundary conditions and geometric properties (such as inertia and length) were eliminated by the finite element model itself. The percent relative error between the two methods was approximately 3%, corresponding to the standard deviation of the measured frequencies. For the frequency range considered, the mode shapes were bending modes in two different vibration planes (latero-medial and sagittal), with a slight torsion effect due to the twisted geometry of the tibia.     

Dynamic analysis of olive trees in intensive orchards under forced vibration

The mechanical harvesting of fruit for oil production in an intensive olive tree orchard is generally accomplished by applying vibration to the tree’s trunk. This vibration is consequently transmitted to the branches, causing the fruit to detach. Although this practice is commonly used, the effects on tree behavior under forced vibration are not firmly established. Dynamic analysis was performed on 17 olive trees (Olea europaea L.) growing in an intensively-managed orchard using modal testing techniques. Modal parameter identification was focused inside the range excitation frequency used by the most commonly available trunk shakers on the market. The olive trees featuring a low morphological variability and modal parameters were obtained for a representative olive tree. The first two modes of vibration of the main tree frame were identified with damping ratios of 26.9 and 17.1% and natural frequencies of 20.2 and 37.7 Hz, respectively. A third mode of vibration of less importance was found at a higher frequency. Therefore, many local modes of vibration were detected near these natural frequencies, primarily located on secondary branches. During the testing, the olive trees behaved like a damped harmonic oscillator with predominantly mass damping in these modes.     

The feasibility of modal testing for measurement of the dynamic characteristics of goat vertebral motion segments

Structural vibration testing might be a promising method to study the mechanical properties of spinal motion segments as an alternative to imaging and spinal manipulation techniques. Structural vibration testing is a non-destructive measurement technique that measures the response of a system to an applied vibration as a function of frequency, and allows determination of modal parameters such as resonance frequencies (ratio between stiffness and mass), vibration modes (pattern of motion) and damping. The objective of this study was to determine if structural vibration testing can reveal the resonance frequencies that correspond to the mode shapes flexion-extension, lateroflexion and axial rotation of lumbar motion segments, and to establish whether resonance frequencies can discriminate specific structural alterations of the motion segment. Therefore, a shaker was used to vibrate the upper vertebra of 16 goat lumbar motion segments, while the response was obtained from accelerometers on the transverse and spinous processes and the anterior side of the upper vertebra. Measurements were performed in three conditions: intact, after dissection of the ligaments and after puncturing the annulus fibrosus. The results showed clear resonance peaks for flexion-extension, lateral bending and axial rotation for all segments. Dissection of the ligaments did not affect the resonance frequencies, but puncturing the annulus reduced the resonance frequency of axial rotation. These results indicate that vibration testing can be utilised to assess the modal parameters of lumbar motion segments, and might eventually be used to study the mechanical properties of spinal motion segments in vivo.     

Assessment of tibial stiffness by vibration testing in situ--I. Identification of mode shapes in different supporting conditions

Vibrational methods to monitor fracture healing, the BRA and the IFR, are compared under different supporting conditions, excitation technique and signal processing. Mode shapes are identified by modal analysis. A wet excised human tibia and an amputation specimen are investigated. Excitation technique and signal processing caused only minor differences in the resonance frequencies. The supporting conditions had an important influence on the single bending modes changing both mode-shapes and frequencies. Thus the BRA-splint imposed a node at the malleolus. Modal analysis revealed the following modes in the two supporting conditions: BRA-splint: A 'rigid body' mode of 165 Hz in the sagittal plane. A single bending mode of 315 Hz close to the sagittal plane. IFR-hanging leg: A 'rigid-body' mode of 167 Hz close to the sagittal plane. Two single bending modes ('free-free'), a mode of 303 Hz close to the frontal plane and a mode of 470 Hz in the sagittal plane.     

Identification of in-vivo vibration modes of human tibiae by modal analysis

When attempting to evaluate the mechanical properties of human bones in vivo by mechanical vibration analysis, some essential requirements must be met. A quantitative relation between measured vibration parameters (e.g., natural frequency) and mechanical bone properties must be available, in-vivo vibration modes should correctly be identified and the associated natural frequencies reproducibly and accurately measured, the influence of joints and soft tissues must be known. These problems were addressed by modal analysis (i.e., experimental determination of natural frequencies, mode shapes and damping ratios) of human tibiae in the following situations: 1) dry excised tibiae, 2) fresh excised tibiae, 3) in-vivo tibiae, 4) tibiae in an amputated leg, in different steps of dissection. In the in-vivo measuring conditions used by the authors, the tibia vibration is practically free-free. Two single bending modes (at +/- 270 Hz and +/- 340 Hz, respectively), each of them corresponding with one principal direction for bending, were identified. The difference between the natural frequencies observed in vivo and those of fresh excised tibiae is almost completely caused by the effect of muscles (added mass and damping), whereas joints and skin play only a minor role. Frequency differences between fresh and dry excised tibiae are largely accounted for by the absence of bone marrow in the latter.     

Vibration of DNA polymer in viscous solvent

The problem of viscous damping of vibrating DNA polymer in solution is solved in the low-amplitude limit for all acoustic branches of the spectrum. The acoustic spectrum covers the microwave region of frequencies. Analytic solutions are obtained for a model describing the DNA polymer as a smooth circular cylinder. Numerical solutions are presented for a model describing the DNA polymer as a twisted cylinder of elliptical cross section. The amount of mass loading is determined for both models and the damped spectrum for the mass-loaded oscillator is calculated. The viscous damping is found to be a strong function of frequency, singular at very low frequencies for all modes except the torsional mode of the circular cylinder. All acoustic modes are overdamped, implying that the observation of well-defined resonances in DNA requires either highly structured water on the molecular level or very dry material.     

Natural sway frequencies and damping ratios of trees: concepts,review and synthesis of previous studies

Previous studies that measured the natural frequencies and damping ratios of conifer trees were reviewed and results synthesized. Analysis of natural frequency measurements from 602 trees, belonging to eight different species, showed that natural frequency was strongly and linearly related to the ratio of diameter at breast height to total tree height squared (i.e., DBH/H ²). After accounting for their size, pines (Pinus spp.) were found to have a significantly lower natural frequency than both spruce (Picea spp.) and Douglas-fir (Pseudotsuga spp.). Natural sway frequencies of de-branched trees were significantly higher than those of the same trees with the branches intact, and the difference increased with an increasing ratio of DBH/H ². Damping mechanisms were discussed and methods for measuring damping ratio were presented. Analysis of available data suggested that internal damping ratios were typically less than 0.05 and were not related to tree diameter. External damping was mainly due to aerodynamic drag on the foliage and contact between the crowns of adjacent trees. Analysis of data from previous wind-tunnel studies indicated that damping due to aerodynamic drag is a nonlinear function of velocity. Damping due to crown contact has been suggested by a previous author to be a function of both the distance to and the size of adjacent trees. Therefore, in uniformly spaced stands it may be possible to model crown contact damping as a function of stand density index (SDI), a common forestry measure which incorporates both of these variables.     

Theory of acoustic mode vibrations of DNA fibers

A previous model for acoustic mode vibrations of a DNA molecule in water is extended to the case of an array of many DNA molecules, as occurs in the fibers studied in most experimental work on DNA. The acoustic modes of this system are found to consist of coupled modes of water sound vibrations and DNA acoustic modes. This model is used to study the electrostatic coupling of acoustic vibrations to the relaxational modes of the orientational degrees of freedom of the water molecules. It is found that the long-range or macroscopic electric field generated by the acoustic mode vibrations of the water-DNA system gives too small a damping and frequency shift of the acoustic modes to account for the observations on DNA fibers. Therefore, the observed damping and frequency shifts are most likely due to either friction between the surrounding water and the vibrating DNA, or coupling to the water orientation degrees of freedom resulting from the short range (i.e., screened) Coulomb interaction. The latter explanation (which is most likely the correct one) implies that the relaxation time of the hydration shell water is longer than the observed relaxation time by a factor of the static dielectric constant of the hydration water.     

Assessment of tibial stiffness by vibration testing in situ--II. Influence of soft tissues, joints and fibula

The influence of soft tissues and joints on the vibration of the human tibia was examined by modal analysis on amputated lower limbs, where the soft tissues and the fibula were dissected gradually. Measurements were made in two different set ups, IFR and BRA, which were both designed to monitor fracture healing. In IFR, vibrations are generated by hammer impact on a relaxed hanging lower leg, with the knee flexed. Resonant frequencies are determined by a computer Fourier transform procedure. In BRA, a steady state vibration is induced in a lower leg, supported near the ankle and the tibial tuberosity, using an electromagnetic shaker. Resonant frequencies are determined from the maxima in vibration amplitudes. In both set ups the soft tissues have a similar influence on the vibration of the tibia: the skin hardly influences the determined modal parameter. The mass of the muscles influences both the resonant frequency and the damping. The fibula has a stiffening effect on the tibia. The influence of the joints is small in the IFR-set up: the tibia vibrates in conditions close to those for the free-free vibration. In the BRA-set up, the supports determine the boundary conditions.     

One-dimensional computer analysis of oscillatory flow in rigid tubes.

The dynamic characteristics of catheter-transducer systems using rigid tubes with compliance lumped in the transducer and oscillatory flow of fluid in rigid tubes were analyzed. A digital computer model based on one dimensional laminar oscillatory flow was developed and verified by exact solution of the Navier-Stokes Equation. Experimental results indicated that the damping ratio and resistance is much higher at higher frequencies of oscillation than predicted by the one dimensional model. An empirical correction factor was developed and incorporated into the computer model to correct the model to the experimental data. Amplitude of oscillation was found to have no effect on damping ratio so it was concluded that the increased damping ratio and resistance at higher frequencies was not due to turbulence but to two dimensional flow effects. Graphs and equations were developed to calculate damping ratio and undamped natural frequency of a catheter-transducer system from system parameters. Graphs and equations were also developed to calculate resistance and inertance for oscillatory flow in rigid tubes from system parameters and frequency of oscillation.     

A scaling law for the effects of architecture and allometry on tree vibration modes suggests a biological tuning to modal compartmentalization

Wind is a major ecological factor for plants and a major economical factor for forestry. Mechanical analyses have revealed that the multimodal dynamic behavior of trees is central to wind-tree interactions. Moreover, the trunk and branches influence dynamic modes, both in frequency and location. Because of the complexity of tree architecture, finite element models (FEMs) have been used to analyze such dynamics. However, these models require detailed geometric and architectural data and are tree-specific-two major restraints for their use in most ecological or biological studies. In this work, closed-form scaling laws for modal characteristics were derived from the dimensional analysis of idealized fractal trees that sketched the major architectural and allometrical regularities of real trees. These scaling laws were compared to three-dimensional FEM modal analyses of two completely digitized trees with maximal architectural contrast. Despite their simplifying hypotheses, the models explained most of the spatiotemporal characteristics of modes that involved the trunk and branches, especially for sympodial trees. These scaling laws reduce the tree to (1) a fundamental frequency and (2) one architectural and three biometrical parameters. They also give quantitative insights into the possible biological control of wind excitability of trees through architecture and allometries.     

Modal damping for monitoring bone integrity and osteoporosis

We applied a noninvasive method to assess bone structural integrity. The method is based on the measurement of the dynamic characteristics of the bone (quality factor and modal damping factor) by applying vibration excitation in the range of acoustic frequencies, in the form of an acoustic sweep signal. Excised sheep femora were tested to detect changes in modal damping, density (kg/m3), bone mineral density (kg/m2) and bone mineral (hydroxyapatite) percentage. The changes were recorded after each time of chemical treatment of the bones performed to gradually cause mineral removal, thus simulating osteoporosis. It was shown that the change in quality factor and damping was in all cases on average equal or greater to the change in all other measured characteristics, thus strengthening the potential of the proposed method to become a valuable assessment tool for monitoring bone integrity and osteoporosis.     

大鼠海马神经元对于高频脉冲刺激的暂态响应

闭环刺激是深部脑刺激(deep brain stimulation,DBS)的重要发展方向之一,有望用于治疗多种脑神经系统疾病.与常规开环的长时间持续刺激不同,闭环刺激通常采用短促的高频脉冲序列.而神经元对于高频刺激的响应存在暂态过程,在初期的短时间内会发生很大变化,从而影响闭环刺激的作用.为了研究这种暂态过程,在大鼠...     

Structural Characteristics of Allomyrina Dichotoma Beetle＇s Hind Wings for Flapping Wing Micro Air Vehicle

In this study, we present a complete structural analysis ofAllomyrina dichotoma beetle＇s hind wings by investigating their static and dynamic characteristics. The wing was subjected to the static loading to determine its overall flexural stiffness. Dy- namic characteristics such as natural frequency, mode shape, and damping ratio of vibration modes in the operating frequency range were determined using a Bruel ＆ Kjaer fast Fourier transform analyzer along with a laser sensor. The static and dynamic characteristics of natural Allomyrina dichotoma beetle＇s hind wings were compared to those of a fabricated artificial wing. The results indicate that natural frequencies of the natural wing were significantly correlated to the wing surface area density that was defined as the wing mass divided by the hind wing surface area. Moreover, the bending behaviors of the natural wing and artificial wing were similar to that of a cantilever beam. Furthermore, the flexural stiffness of the artificial wing was a little higher than that of the natural one whereas the natural frequency of the natural wing was close to that of the artificial wing. These results provide important information for the biomimetic design of insect-scale artificial wings, with which highly ma- neuverable and efficient micro air vehicles can be designed.     

面孔分类中空间高低频表征的神经机制：一个颅内脑电研究

来自多方面的研究表明,面孔的分类和识别位于特定脑区．同时,已有行为实验研究表明,图像的空间高低频特征在面孔分类的不同范畴中起不同的贡献,例如身份更多被低频信号传递,性别被高低频共同传递,而表情更多被高频传递．然而,空间频率在面孔分类中的贡献,其表征和神经机制目前相关研究很少．利用特定癫痫患者植入颅内电极的监控期,呈现不同类型面孔图像,同时记录其颅内脑电,用事件相关电位方法考察了据认为是面孔特定成分的相关电位的潜伏期在170 ms的波形(N170波形)的变化;用电极反应显著性分析考察了空间频率在不同分类特征上的贡献．结果表明,空间高频(HSF)图像的N170潜伏期显著延迟．只呈现空间低频(LSF)图像,N170的潜伏期对普通人面孔会延迟,而对熟悉的名人则没有这个差异．女性面孔诱发的N170在HSF条件下潜伏期明显晚于LSF条件,而男性面孔诱发的波形则不存在这个差异．表情在N170上没有体现出任何差异．但是基于电极的显著性分析表明,有更多的额叶电极参与了表情的加工;身份特征加工有更多电极在空间低频上表现出差异,而性别加工则空间高低频比较平衡．与以往行为结果不同的是,表情加工也有更多低频贡献,而且表情的差异可以在早达114 ms的时候就发生．这符合表情信息在颞枕区域有一个快速基本加工,再传递到其他脑区的认知模型．因此,空间高低频信息在身份和性别上的贡献,可能发生在经典的面孔加工脑区,由N170表达,表情信息不由N170表达,而是在颞枕较广泛的范围内快速加工再传递到别的脑区,如额叶．这是首次利用颅内脑电就空间频率在面孔分类中的贡献的神经机制进行研究,为深入理解脑内面孔各种特征加工的动态过程提供了一个新的切入点．     

Study of Biomechanical Response of Human Hand-Arm to Random Vibrations of Steering Wheel of Tractor

This paper reports a study on the biomechanical response of a human hand-arm model to random vibrations of the steering wheel of a tractor. An anatomically accurate bone-only hand-arm model from TurboSquidTM was used to obtain a finite element (FE) model to understand the Hand-arm vibration syndrome (HAVS), which is a neurological and vascular disorder caused by exposure of the human hand-arm to prolonged vibrations. Modal analysis has been done to find out the first few natural frequencies and mode shapes of the system. Coupling of degrees of freedom (DOF) had to be done in the FE idealization to do modal analysis, as the bones were not attached to each other in the TurboSquidTM model. The shoulder bone, scapula, has been constrained at one end for eigenvalue analysis. It was observed that the first five natural frequencies were in the range of 0-250 Hz, which is the range in which the effect of HAVS is the highest. Harmonic analysis was done by giving a swept sine excitation in the frequency range 0 to 200 Hz. For this, a force input of 25 N was imparted at nodes perpendicular to the hand, the force value chosen being the nominal force in most applications involving powered hand-held tools and steering wheels of tractors. The nodes chosen for force application were determined experimentally from observations made by gripping the steering wheel. The frequency response function (FRF) plots were obtained in the x, y and z directions. Random vibration analysis was done next by giving force power spectral densities (PSD) in the form of nodal excitation as input to the FE model of hand-arm, and computing the output acceleration PSDs. The input force PSDs were measured using FlexiForce® sensors along the three axes. The acceleration responses at the steering wheel were also measured using tri-axial accelerometers for validating the computed results. The output acceleration PSDs were then weighted using the frequency weighting curves for hand-arm vibration and the total daily exposure A(8), computed using ISO 5349-1 standards, was compared with the vibration action and limit values. The A(8) values obtained are found to be higher than the vibration limit values.     

Relationship between the shape and density distribution of the femur and its natural frequencies of vibration

It has been recently suggested that mechanical loads applied at frequencies close to the natural frequencies of bone could enhance bone apposition due to the resonance phenomenon. Other applications of bone modal analysis are also suggested. For the above-mentioned applications, it is important to understand how patient-specific bone shape and density distribution influence the natural frequencies of bones. We used finite element models to study the effects of bone shape and density distribution on the natural frequencies of the femur in free boundary conditions. A statistical shape and appearance model that describes shape and density distribution independently was created, based on a training set of 27 femora. The natural frequencies were then calculated for different shape modes varied around the mean shape while keeping the mean density distribution, for different appearance modes around the mean density distribution while keeping the mean bone shape, and for the 27 training femora. Single shape or appearance modes could cause up to 15% variations in the natural frequencies with certain modes having the greatest impact. For the actual femora, shape and density distribution changed the natural frequencies by up to 38%. First appearance mode that describes the general cortical bone thickness and trabecular bone density had one of the strongest impacts. The first appearance mode could therefore provide a sensitive measure of general bone health and disease progression. Since shape and density could cause large variations in the calculated natural frequencies, patient-specific FE models are needed for accurate estimation of bone natural frequencies.     

Natural frequencies and damping ratios of Norway spruce (<Emphasis Type="Italic">Picea abies</Emphasis> (L.) Karst) growing on subalpine forested slopes

We investigated the natural frequencies and damping ratios of 24 Norway spruce trees (Picea abies (L.) Karst) growing on subalpine forested slopes using swaying experiments. Trees were winched to the release position using a manually operated cable winch. Before release, the stem base rotation was approximately 2 degrees. All trees were tested in both fall-line and cross-slope direction if possible to reveal the difference between the two perpendicular directions. A new method based upon the Hilbert transformation for evaluating the damping ratio for trees was used. It enabled us to investigate the damping ratio for all excited modes of vibration in the tree structure during the swaying experiments and to study if velocity proportional damping (viscous damping) is a reasonable assumption when predicting the tree response to different external actions using mechanical models. No difference in first natural frequency and damping ratio was found between the fall-line and cross-slope direction for all tested trees. The first natural frequencies correlated best with the diameter at breast height and squared total tree height DBH/H ². For the damping ratio, no significant correlation with different tree characteristics could be found. A non-velocity proportional damping ratio was observed for two trees. This indicates that using a viscous damping for all frequencies is an appropriate simplification when modelling the wind-tree interaction.     

Non-Locus-Specific Polygenes Giving Responses to Selection for Gene Conversion Frequencies in Ascobolus Immersus

Selection for higher and lower meiotic conversion frequencies was investigated in the fungus Ascobolus immersus. Strains carrying the same known gene conversion control factors, which have major effects on conversion frequencies at their specific target locus, sometimes gave significant differences in conversion frequency. Selection for high or low conversion frequencies at the w1-78 site was practiced for five generations, giving significant responses in both directions. These responses were due to polygenes, or genes of minor effect, not to new conversion control factors of major effect. Crosses of selected strains to strains with other mutations showed that the genes' effects were not specific to w1-78, but could affect conversion frequencies of another mutation, w1-3C1, at that locus and of two other loci, w-BHj and w9, which are unlinked to w1 or to each other. The proportional changes in gene conversion frequency due to selection varied according to the locus and site involved and according to the conversion control factor alleles present. There were differences of >/=277% in conversion frequency between ``high' and ``low' strains. Selection for conversion frequency had little effect on other features of conversion, such as the frequency of postmeiotic segregation or the relative frequencies of conversion to mutant or wild type.     

Spatial distribution and dose-response relationship for different operation modes in a reaction-diffusion model of the MAPK cascade

The mitogen-activated protein kinase (MAPK) cascade plays a critical role in the control of cell growth. Deregulation of this pathway contributes to the development of many cancers. To better understand its signal transduction, we constructed a reaction-diffusion model for the MAPK pathway. We modeled the three layers of phosphorylation-dephosphorylation reactions and diffusion processes from the cell membrane to the nucleus. Based on different types of feedback in the MAPK cascade, four operation modes are introduced. For each of the four modes, spatial distributions and dose-response curves of active kinases (i.e. ppMAPK) are explored by numerical simulation. The effects of propagation length, diffusion coefficient and feedback strength on the pathway dynamics are investigated. We found that intrinsic bistability in the MAPK cascade can generate a traveling wave of ppMAPK with constant amplitude when the propagation length is short. ppMAPK in this mode of intrinsic bistability decays more slowly than it does in all other modes as the propagation length increases. Moreover, we examined the global and local responses to Ras-GTP of these four modes, and demonstrated how the shapes of these dose-response curves change as the propagation length increases. Also, we found that larger diffusion constant gives a higher response level on the zero-order regime and makes the ppMAPK profiles flatter under strong Ras-GTP stimulus. Furthermore, we observed that spatial responses of ppMAPK are more sensitive to negative feedback than to positive feedback in the broader signal range. Finally, we showed how oscillatory signals pass through the kinase cascade, and found that high frequency signals are damped faster than low frequency ones.