Flexural and torsional stiffness in multi-jointed biological beams

Flexibility, the ability to deform in response to loads, is a common property of biological beams. This paper investigates the mechanical behavior of multi-jointed beams, which are characterized by a linear series of morphologically similar joints. Flexural stiffness and torsional stiffness were measured in two structurally distinct beams, crinoid arms (Echinodermata, Comatulida) and crustacean antennae (Arthropoda, Decapoda). Morphological data from these beams were used to determine the relative contributions of beam diameter and joint density (number of joints per millimeter of beam length) to the flexural and torsional stiffness of these two structures. As predicted by beam theory, beam diameter influenced stiffness in both crinoid arms and crustacean antennae. In crinoid arms, increases in joint density were associated with decreases in stiffness, but joint density had no significant influence on stiffness in crustacean antennae. In both crinoid arms and crustacean antennae, the magnitudes of flexural and torsional stiffness, as well as the ratio of these two variables, were similar to previously reported values for non-jointed biological beams. These results suggest that the structural design of a biological beam is not a limiting factor determining its mechanical properties.     

A comparison of forefoot stiffness in running and running shoe bending stiffness

This study characterizes the stiffness of the human forefoot during running. The forefoot stiffness, defined as the ratio of ground reaction moment to angular deflection of the metatarsophalangeal joint, is measured for subjects running barefoot. The joint deflection is obtained from video data, while the ground reaction moment is obtained from force plate and video data. The experiments show that during push-off, the forefoot stiffness rises sharply and then decreases steadily, showing that the forefoot behaves not as a simple spring, but rather as an active mechanism that exhibits a highly time-dependent stiffness. The forefoot stiffness is compared with the bending stiffness of running shoes. For each of four shoes tested, the shoe stiffness is relatively constant and generally much lower than the mean human forefoot stiffness. Since forefoot stiffness and shoe bending stiffness act in parallel (i.e., are additive), the total forefoot stiffness of the shod foot is dominated by that of the human foot.     

In vivo measurement of bending stiffness in fracture healing

Background  

Measurement of the bending stiffness a healing fracture represents a valid variable in the assessment of fracture healing. However, currently available methods typically have high measurement errors, even for mild pin loosening. Furthermore, these methods cannot provide actual values of bending stiffness, which precludes comparisons among individual fractures. Thus, even today, little information is available with regards to the fracture healing pattern with respect to actual values of bending stiffness. Our goals were, therefore: to develop a measurement device that would allow accurate and sensitive measurement of bending stiffness, even in the presence of mild pin loosening; to describe the course of healing in individual fractures; and help to evaluate whether the individual pattern of bending stiffness can be predicted at an early stage of healing.     

Binding of tropomyosin-troponin to actin increases filament bending stiffness

Rheologic measurements show that the association of tropomyosin-troponin with actin filaments is responsible for the reduction of the internal chain dynamic and increase in the mechanical rigidity of actin filaments. Basing calculations on the linear relation between the plateau modulus, G(N)('), and bending modulus, kappa, I find that tropomyosin-troponin at r(AT) = 7 increases actin filament stiffness by approximately 50%. This is confirmed by dynamic light scattering. Further increases are observed at rising F-actin and constant tropomyosin-troponin concentrations. Tropomyosin-troponin also delays actin assembly and subsequent network formation and increases filament stiffness over time.     

Alterations in trunk bending stiffness following changes in stability and equilibrium demands of a load holding task

The contribution of the trunk neuromuscular system (TNS) to spine stability has been shown in earlier studies by characterizing changes in antagonistic activity of trunk muscles following alterations in stability demands of a task. Whether and/or how much such changes in the response of TNS to alteration in stability demand of the task alter spinal stiffness remains unclear. To address this research gap, a repeated measure study was conducted on twenty gender-balanced asymptomatic individuals to evaluate changes in trunk bending stiffness throughout the lumbar spine’s range of flexion following alterations in both stability and equilibrium demands of a load holding task. Trunk bending stiffness was determined using trunk stiffness tests in upright posture on a rigid metal frame under different equilibrium and stability demands on the lower back. Increasing the stability demand by increasing the height of lifted load ∼30 cm only increased trunk bending stiffness (∼39%) over the lower range of lumbar flexion and under the low equilibrium demand condition. Similarly, increasing the equilibrium demand of the task by increasing the weight of lifted load by 3.5 kg only increased trunk bending stiffness (55%) over the low range of lumbar flexion and under the low stability demand condition. Our results suggest a non-linear relationship between changes in stability and equilibrium demands of a task and the contribution of TNS to trunk bending stiffness. Specifically, alterations in TNS response to changes in stability and equilibrium demand of a given task will increase stiffness of the trunk only if the background stiffness is low.     

Prediction of bending stiffness and deformed shape of non-axially compressed microtubule by a semi-analytical approach

The bending stiffness of a microtubule is one of the most important parameters needed in the analysis of microtubule deformation. In this study, a semi-analytical approach is developed to predict the bending stiffness and deformed shape of a non-axially compressed microtubule in an explicit closed form. By using the solution presented in this paper and the experimentally observed values given in the literature, both the deformed configuration and bending stiffness of a single microtubule are determined. The proposed method is validated by comparing the obtained results with available data in the literature. The comparison shows that the present semi-analytical formulation provides the same accuracy with reduced numerical effort.     

Analysis of the bending behaviour of porcine xenograft leaflets and of neutral aortic valve material: bending stiffness, neutral axis and shear measurements

Flexibility of the materials used in the construction of bioprosthetic heart valves is essential for proper valve operation. We therefore examined the bending behaviour of glutaraldehyde treated porcine aortic valve cusps in comparison with fresh aortic valve tissue. We repeatedly bent a total of 35 strips of fresh and treated tissue to curvatures ranging from 0.2 to 2.2 mm-1. We compared the stiffness of the two materials between circumferential and radial bending, natural and reverse curvatures and constant or variable tensile stress (0.8-40 kPa). Our results showed a weak positive relationship between bending stiffness and applied tensile stress and a strong positive dependance of stiffness on tissue thickness (t). For the fresh tissue, the bending stiffness increased in proportion to t1.14 while for the glutaraldehyde treated tissue it increased with t2.18. Fourteen strips of fresh and treated tissue were also histologically processed, sectioned and examined with polarized light microscopy. Collagen fiber wavelengths and shear deformations were measured utilizing the tissue banding patterns produced by polarized light microscopy. The neutral axis of bending was found to lie very close to the outer surface of the tissue, suggesting that aortic leaflets have a very low compressive elastic modulus. The shear strains measured in fresh tissue were 10 +/- 2.7% vs 3 +/- 4.4% for the treated, indicating a stiffening of the tissue following glutaraldehyde fixation. We conclude that both natural and bioprosthetic valve cusps have a complex flexural behaviour that cannot be modeled using simple bending principles, although the bioprosthetic material more closely approximates the simple beam than does the fresh. The non-linear elastic modulus, high compressibility and shearing between fiber layers are likely responsible for the observed behaviour of the fresh tissue, while the cross-linking and dehydrating effects of glutaraldehyde are believed to be responsible for the alteration in bending properties observed in the treated tissue. Our study suggests that bioprosthetic valve material does not adequately mimic the mechanics of the natural valve tissue, and that the current glutaraldehyde fixation process eliminates many of the beneficial, stress-reducing properties of the aortic leaflet.     

Linear and nonlinear stiffness and friction in biological rhythmic movements

Biological rhythmic movements can be viewed as instances of self-sustained oscillators. Auto-oscillatory phenomena must involve a nonlinear friction function, and usually involve a nonlinear elastic function. With respect to rhythmic movements, the question is: What kinds of nonlinear friction and elastic functions are involved? The nonlinear friction functions of the kind identified by Rayleigh (involving terms such as $\dot \theta ^3 $ ) and van der Pol (involving terms such as $\theta ^2 \dot \theta $ ), and the nonlinear elastic functions identified by Duffing (involving terms such as $\theta ^3 $ ), constitute elementary nonlinear components for the assembling of self-sustained oscillators. Recently, additional elementary nonlinear friction and stiffness functions expressed, respectively, through terms such as $\theta ^2 \dot \theta ^3 $ and $\theta \dot \theta ^2 $ , and a methodology for evaluating the contribution of the elementary components to any given cyclic activity have been identified. The methodology uses a quantification of the continuous deviation of oscillatory motion from ideal (harmonic) motion. Multiple regression of this quantity on the elementary linear and nonlinear terms reveals the individual contribution of each term to the oscillator's non-harmonic behavior. In the present article the methodology was applied to the data from three experiments in which human subjects produced pendular rhythmic movements under manipulations of rotational inertia (experiment 1), rotational inertia and frequency (experiment 2), and rotational inertia and amplitude (experiment 3). The analysis revealed that the pendular oscillators assembled in the three experiments were compositionally rich, braiding linear and nonlinear friction and elastic functions in a manner that depended on the nature of the task.     

Accuracy and reproducibility of bending stiffness measurements by mechanical response tissue analysis in artificial human ulnas

Osteoporosis is characterized by reduced bone strength, but no FDA-approved medical device measures bone strength. Bone strength is strongly associated with bone stiffness, but no FDA-approved medical device measures bone stiffness either. Mechanical Response Tissue Analysis (MRTA) is a non-significant risk, non-invasive, radiation-free, vibration analysis technique for making immediate, direct functional measurements of the bending stiffness of long bones in humans in vivo. MRTA has been used for research purposes for more than 20 years, but little has been published about its accuracy. To begin to investigate its accuracy, we compared MRTA measurements of bending stiffness in 39 artificial human ulna bones to measurements made by Quasistatic Mechanical Testing (QMT). In the process, we also quantified the reproducibility (i.e., precision and repeatability) of both methods. MRTA precision (1.0±1.0%) and repeatability (3.1±3.1%) were not as high as those of QMT (0.2±0.2% and 1.3+1.7%, respectively; both p<10⁻⁴). The relationship between MRTA and QMT measurements of ulna bending stiffness was indistinguishable from the identity line (p=0.44) and paired measurements by the two methods agreed within a 95% confidence interval of ±5%. If such accuracy can be achieved on real human ulnas in situ, and if the ulna is representative of the appendicular skeleton, MRTA may prove clinically useful.     

Effect of salicylate on the elasticity, bending stiffness, and strength of SOPC membranes

Salicylate is a small amphiphilic molecule which has diverse effects on membranes and membrane-mediated processes. We have utilized micropipette aspiration of giant unilamellar vesicles to determine salicylate's effects on lecithin membrane elasticity, bending rigidity, and strength. Salicylate effectively reduces the apparent area compressibility modulus and bending modulus of membranes in a dose-dependent manner at concentrations above 1 mM, but does not greatly alter the actual elastic compressibility modulus at the maximal tested concentration of 10 mM. The effect of salicylate on membrane strength was investigated using dynamic tension spectroscopy, which revealed that salicylate increases the frequency of spontaneous defect formation and lowers the energy barrier for unstable hole formation. The mechanical and dynamic tension experiments are consistent and support a picture in which salicylate disrupts membrane stability by decreasing membrane stiffness and membrane thickness. The tension-dependent partitioning of salicylate was utilized to calculate the molecular volume of salicylate in the membrane. The free energy of transfer for salicylate insertion into the membrane and the corresponding partition coefficient were also estimated, and indicated favorable salicylate-membrane interactions. The mechanical changes induced by salicylate may affect several biological processes, especially those associated with membrane curvature and permeability.     

The modular hip revision stem made of titanium alloy--influence and optimisation of bending stiffness]

The MRP-Titan Revision stem has proved to be a highly successful implant system for revision arthroplasty of the hip. Good and excellent clinical and radiological results with spontaneous filling of bony defects have been reported, The observation of atrophy of the proximal femur associated with stem diameters > 17mm prompted us to examine the bending stiffness of stems of various diameters. To determine their static bending characteristics, the stems were tested under axial pressure loads in accordance with Euler's buckling case. Dynamic tests were performed with the mono-axial servohydraulic test equipment MTS 810. From a stem diameter of 18 mm upwards, deflection of the stem under loading decreased disproportionately, in direct correlation with the stem stiffness. By optimising the geometry and varying the alloy it is possible to obtain a constant ISD factor for the modular MRP-Titan revision stem CONCLUSION: The MRP-Titan revision stem is a reliable implant system for revision arthroplasty of the hip. Clinical findings of atrophy of the proximal femur associated with stem diameters > 17 mm was found to be correlated with a disproportionate increase in bending stiffness. The aim of further developments will be to reduce the stiffness of larger-diameter stems by making changes to the design and/or to the alloy (Ti15Mo, Ti13Nb13Zr, Ti12Mo6Zr2Fe2).     

Anisotropic stiffness and tensional homeostasis induce a natural anisotropy of volumetric growth and remodeling in soft biological tissues

Biomechanics and Modeling in Mechanobiology - Growth in soft biological tissues in general results in anisotropic changes of the tissue geometry. It remains a key challenge in biomechanics to...     

Calcitroic acid: biological activity and tissue distribution studies

Calcitroic acid was recently identified as a major metabolite of 1,25-dihydroxyvitamin D₃ (Esvelt, Schnoes, and DeLuca, Biochemistry 18, 3977, 1979). The metabolite was found to have little, although significant, activity in healing rickets, and causing bone mineral mobilization but elicited no significant elevation in intestinal calcium transport. The compound showed little affinity for either the serum 25-hydroxyvitamin D binding protein or the intestinal cytosol receptor for 1,25-dihydroxyvitamin D₃. Various tissues of the rat were examined for the presence of calcitroic acid following a 120-ng dose of 1,25-dihydroxy-[3α-³H]vitamin D₃. The metabolite was detected in liver, intestinal mucosa, kidneys, and blood with livers and mucosa containing the highest concentrations. In each of these tissues the calcitroic acid content increased during the period between 4 and 12 h after the dose. The presence of calcitroic acid in femurs was indicated but could not be confirmed. Bile duct cannulation reduced but did not abolish the intestinal calcitroic acid content. In addition to calcitroic acid, other polar metabolites of 1,25-dihydroxyvitamin D₃ were detected in these experiments.     

Application of an image-based weighted measure of skeletal bending stiffness to great ape mandibles

Traditional measures of structural stiffness in the primate skeleton do not consider the heterogeneous material stiffness distribution of bone. This assumption of homogeneity introduces an unknown degree of error in estimating stiffness in skeletal elements. Measures of weighted stiffness can be developed by including heterogeneous grayscale variations evident in computed tomographic (CT) images. Since gray scale correlates with material stiffness, the distribution of bone quality and quantity can be simultaneously considered. We developed weighted measures of bending resistance and applied these to CT images at three locations along the mandibular corpus in the hominoids Gorilla, Pongo, and Pan. We calculated the traditional (unweighted) moment of inertia for comparison to our weighted measure, which weighs each pixel by its gray-scale value. This weighing results in assignment of reduced moment of inertia values to sections of reduced density. Our weighted and unweighted moments differ by up to 22%. These differences are not consistent among sections, however, such that they cannot be calculated by simple correction of unweighted moments. The effect of this result is that the rank ordering of individual sections within species changes if weighted moments are considered. These results suggest that the use of weighted moments may spur different interpretations of comparative data sets that rely on stiffness measures as estimates of biomechanical competence.     

Determination of mechanical stiffness of bone by pQCT measurements: correlation with non-destructive mechanical four-point bending test data

Mechanical tests of bone provide valuable information about material and structural properties important for understanding bone pathology in both clinical and research settings, but no previous studies have produced applicable non-invasive, quantitative estimates of bending stiffness. The goal of this study was to evaluate the effectiveness of using peripheral quantitative computed tomography (pQCT) data to accurately compute the bending stiffness of bone. Normal rabbit humeri (N=8) were scanned at their mid-diaphyses using pQCT. The average bone mineral densities and the cross-sectional moments of inertia were computed from the pQCT cross-sections. Bending stiffness was determined as a function of the elastic modulus of compact bone (based on the local bone mineral density), cross-sectional moment of inertia, and simulated quasistatic strain rate. The actual bending stiffness of the bones was determined using four-point bending tests. Comparison of the bending stiffness estimated from the pQCT data and the mechanical bending stiffness revealed excellent correlation (R2=0.96). The bending stiffness from the pQCT data was on average 103% of that obtained from the four-point bending tests. The results indicate that pQCT data can be used to accurately determine the bending stiffness of normal bone. Possible applications include temporal quantification of fracture healing and risk management of osteoporosis or other bone pathologies.     

Electric field distribution in biological systems

Electric field distribution in biological systems was investigated. In the analysis both the conductive and the dielectric properties of biological systems were considered. Making use of the complex dielectric coefficient, equations which describe the electric field behavior in such media, were formulated. These equations were solved numerically for a few biological systems. The solutions show that the macroscopic field distribution, for example, the refraction of the ECG wave upon passing from one tissue into another, is mainly determined by the tissue's conductive properties (in the frequency range of 0–10⁸ Hz). However, the microscopic field distribution around the individual cells is determined by the conductive, the dielectric or both properties, depending on the frequency. At frequencies below 10⁴ Hz the field configuration is determined largely by the system's conductive properties. At frequencies above 10⁷ – 10⁸ Hz, by the dielectric properties and in the range of 10⁴ – 10⁶ Hz both properties affect the field distribution. In this range the field direction may be shifted by as much as 90° by relatively small frequency changes.     

Hopanoids in marine cyanobacteria: probing their phylogenetic distribution and biological role

Cyanobacteria are key players in the global carbon and nitrogen cycles and are thought to have been responsible for the initial rise of atmospheric oxygen during the Neoarchean. There is evidence that a class of membrane lipids known as hopanoids serve as biomarkers for bacteria, including many cyanobacteria, in the environment and in the geologic record. However, the taxonomic distributions and physiological roles of hopanoids in marine cyanobacteria remain unclear. We examined the distribution of bacteriohopanepolyols (BHPs) in a collection of marine cyanobacterial enrichment and pure cultures and investigated the relationship between the cellular abundance of BHPs and nitrogen limitation in Crocosphaera watsonii, a globally significant nitrogen‐fixing cyanobacterium. In pure culture, BHPs were only detected in species capable of nitrogen fixation, implicating hopanoids as potential markers for diazotrophy in the oceans. The enrichment cultures we examined exhibited a higher degree of BHP diversity, demonstrating that there are presently unaccounted for marine bacteria, possibly cyanobacteria, associated with the production of a range of BHP structures. Crocosphaera watsonii exhibited high membrane hopanoid content consistent with the idea that hopanoids have an important effect on the bulk physical properties of the membrane. However, the abundance of BHPs in C. watsonii did not vary considerably when grown under nitrogen‐limiting and nitrogen‐replete conditions, suggesting that the role of hopanoids in this organism is not directly related to the physiology of nitrogen fixation. Alternatively, we propose that high hopanoid content in C. watsonii may serve to reduce membrane permeability to antimicrobial toxins in the environment.