Muscle sound frequencies of the frog are modulated by skeletal muscle tension.

The purpose of this study was to determine the relationships among muscle sound frequencies, muscle tension, and stiffness. Time-frequency transformations of nonstationary acoustic signals provided measures of resonant frequency during isometric contractions of frog (Rana pipiens) semitendinosus and gastrocnemius muscles. A mathematical expression for muscle transverse resonant frequency, elastic modulus and tension, based on elastic beam theory, was formulated by the Rayleigh method adapted for muscles. For thin muscles, the elastic modulus was found to have negligible influence on transverse muscle resonant frequency. Changes in muscle tension were the major determinants of changes in transverse resonant frequency. Consequently, for thin muscles, the time course of muscle tension, but not elastic modulus, can be monitored acoustically during the early phase of contraction when muscles give rise to sounds. Muscles were found to be anisotropic with a modulus of elasticity, EL, measured via length perturbations near 0.1% muscle length peak-to-peak, that was much larger than the modulus of elasticity, Eb, that resists the lateral bending that causes sound production. The elastic and resonant behavior of a thin muscle is similar to a tensioned fibrous cable with distributed mass.     

Frequency tuning in animal locomotion

In locomotion that involves repetitive motion of propulsive structures (arms, legs, fins, wings) there are resonant frequencies f(*) at which the energy consumption is a minimum. As animals need to change their speed, they can maintain this energy minimum by tuning their body resonances. We discuss the physical principles of frequency tuning, and how it relates to forces, damping, and oscillation amplitude. The resonant frequency of pendulum-type oscillators (e.g. swinging arms and legs) may be changed by varying the mass moment of inertia, or the vertical acceleration of the pendulum pivot. The frequency of elastic vibrations (e.g. the bell of a jellyfish) can be tuned with a non-linear modulus of elasticity: soft for low deflection amplitudes (low resonant frequency), and stiff for large displacements (high resonant frequency). Tuning of elastic oscillations can also be achieved by changing the effective length or cross-sectional area of the elastic members, or by allowing springs in parallel or in series to become active. We propose that swimming and flying animals generate oscillating propulsive forces from precisely placed shed vortices and that these tuned motions can only occur when vortex shedding and the simple harmonic motion of the elastic elements of the propulsive structures are in resonance.     

Active Prestress Leads to an Apparent Stiffening of Cells through Geometrical Effects

Tuning of active prestress, e.g., through activity of molecular motors, constitutes a powerful cellular tool to adjust cellular stiffness through nonlinear material properties. Understanding this tool is an important prerequisite for our comprehension of cellular force response, cell shape dynamics, and tissue organization. Experimental data obtained from cell-mechanical measurements often show a simple linear dependence between mechanical prestress and measured differential elastic moduli. Although these experimental findings could point to stress-induced structural changes in the material, we propose a surprisingly simple alternative explanation in a theoretical study. We show how geometrical effects can give rise to increased cellular force response of cells in the presence of active prestress. The associated effective stress-stiffening is disconnected from actual stress-induced changes of the elastic modulus, and should therefore be regarded as an apparent stiffening of the material. We argue that new approaches in experimental design are necessary to separate this apparent stress-stiffening due to geometrical effects from actual nonlinearities of the elastic modulus in prestressed cellular material.     

Dynamic mechanical properties of body-wall dermis in various mechanical states and their implications for the behavior of sea cucumbers

The dermis of the sea cucumber body wall is a typical catch connective tissue that rapidly changes its mechanical properties in response to various stimuli. Dynamic mechanical properties were measured in stiff, standard, and soft states of the sea cucumber Actinopyga mauritiana. Sinusoidal deformations were applied, either at a constant frequency of 0.1 Hz with varying maximum strain of 2%-20% or at a fixed maximum strain of 1.8% with varying frequency of 0.0005-50 Hz. The dermis showed viscoelasticity with both strain and strain-rate dependence. The dermis in the standard state showed a J-shaped stress-strain curve with a stiffness of 1 MPa and a dissipation ratio of 60%; the curve of the stiff dermis was linear with high stiffness (3 MPa) and a low dissipation ratio (30%). Soft dermis showed a J-shaped curve with low stiffness (0.3 MPa) and a high dissipation ratio (80%). The strain-induced softening was observed in the soft state. Stiff samples had a higher storage modulus and a lower tangent delta than soft ones, implying a larger contribution of the elastic component in the stiff state. A simple molecular model was proposed that accounted for the mechanical behavior of the dermis. The model suggested that stiffening stimulation increased inter-molecular bonds, whereas softening stimulation affected intra-molecular bonds. The adaptive significance of each mechanical state in the behavior of sea cucumbers is discussed.     

Modelling primary and secondary growth processes in plants: a summary of the methodology and new data from an early lignophyte

A mathematical method, based on polar coordinates that allow modelling of primary and secondary growth processes in stems of extant and fossil plants, is summarized and its potential is discussed in comparison with numerical methods using digitizing tablets or electronic image analysing systems. As an example, the modelling of tissue distribution in the internode of an extant sphenopsid (Equisetum hyemale) is presented. In the second half of the paper we present new data of a functional analysis of stem structure and biomechanics of the early lignophyte Tetraxylopteris schmidtii (Middle Devonian) using the polar coordinate method for modelling the tissue distribution in stems of different ontogenetic age. Calculations of the mechanical properties of the stems, based on the modelling of the tissue arrangement, indicate that there is no increase in structural bending modulus throughout the entire development of the plant. The oldest ontogenetic stage has a significantly smaller bending elastic modulus than the intermediate ontogenetic stage, a 'mechanical signal', which is not consistent with a self-supporting growth form. These results, and the ontogenetic variations of the contributions of different stem tissues to the flexural stiffness of the entire stem, are discussed in the evolutionary context of cambial secondary growth.     

Effect of plant interaction on wind-induced crop motion

Plant motion due to wind affects plant growth, a phenomenon called thigmomorphogenesis. Despite intensive studies of the turbulence over plant canopies, the study of plant motion induced by wind has often been limited to individual trees or cereal plants. Few models of global canopy motions are available. Moreover the numerical analysis of models that are based on individual stems becomes time consuming when dealing with crops. A model of motion within the canopies is proposed here using a wave propagation equation within a homogenized continuous medium, and a forcing function representing turbulent gusts advected over the canopy. This model is derived from a discrete model of a set of plant shoots represented as individual oscillators, including elastic contacts between shoots. Such contacts induce nonlinearities into the wave equation. A new experimental method to measure stem dynamical properties and elastic collision properties is presented with an illustration on alfalfa stems. Results obtained modeling plant motions in an alfalfa crop are presented.     

Effects of Vibration on Mechanical Properties and Biomass Allocation Pattern ofCapsella bursa-pastoris(Cruciferae)

The herbaceous dicot speciesCapsella bursa-pastoris(Cruciferae)was used to determine the influence of chronic mechanical perturbationon the biomass allocation pattern (i.e. dry weight distributionamong roots, stems and reproductive structures) and the mechanicalproperties of roots and stems (i.e. tensile breaking stressand Young's modulus). It was hypothesized that mechanicallystimulated plants would allocate more of their total biomassto root systems and less to shoots compared to control plantsand that the breaking stress (a measure of strength) and Young'smodulus (a measure of material stiffness) would increase forroots and decrease for stems because these responses would adaptivelyreduce the bending moment at the base of shoots and increasethe anchorage strength of root systems. It was also hypothesizedthat mechanical perturbation would maladaptively reduce therelative fitness of individuals by reducing biomass allocationto their reproductive organs and the ability to broadcast seedsby means of elastic stem flexure. These hypotheses were testedby vibrating cultivated plants for 60 s every day during thecourse of growth to maturity and comparing their dry weightdistributions and the mechanical properties of their body parts(measured in tension) to those of undisturbed control plants.Based on a total of 51 experimentally manipulated and 44 controlplants for which mechanical properties were successfully tested,chronic organ flexure resulted in more massive root systemsand less massive vegetative shoots, increased the magnitudesof root breaking stress and Young's modulus and had the reverseeffect on stems, reduced the dry weight of reproductive structuresat maturity, delayed the formation of the first mature flowerand fruit, and accelerated the on-set of plant senescence comparedto control plants. These responses to chronic organ flexureare interpreted to be vegetatively adaptive, since they reducethe probability of stem and root failure as a consequence ofwind-pressure or foraging, and to be reproductively maladaptive,since they reduce reproductive effort and the ability to mechanicallydischarge seeds.Copyright 1998 Annals of Botany Company Adaptation, biomass allocation, biomechanics, elastic properties, roots, stems, thigmomorphogenesis.     

Contributions to the Biomechanics of Plants. I. Stabilities of Plant Stems with Strengthening Elements of Different Cross-Sections Against Weight and Wind Forces*

Biophysical considerations allow estimates of the mechanical stresses on self-bearing vertical stems of plants. Even at moderate wind velocities the stresses induced by aerodynamic forces dominate over those induced by the own weight. Using polar coordinates, analytical expressions of cross-sectional area and axial second moment of area for centrisymmetric structures with symmetries threefold or higher are derived. Calculating the relative section modulus for various (centrisymmetric) arrangements of stabilizing structures leads to an estimate of the “mechanical effectivity” of these structures. If for plant stems, seen as composite materials, the second moments of area and the elastic moduli are known, the contribution of the different tissues to mechanical stability can be determined quantitatively. The mechanical design of early “vascular” land plants and of stems of (fossil) trees and lianas in different ontogenetic stages can be assessed.     

The allometry of saguaro height

The allometry of plant height H with respect to mean stem diameter D was determined based on 118 saguaro plants. The slope obtained for the reduced major axis regression analysis of the data was 2.36 ± 0.085, indicating that taller plants are disproportionately more slender than their shorter, presumably younger counterparts. The consequences of this positive, extremely anisometric relation on the elastic stability of stems were estimated by computing the critical buckling height H_crit for each of the 118 stems on the basis of the mean density-specific stiffness (i.e., the quotient of Young's elastic modulus E and bulk tissue density ρ) determined for a single section from a mature saguaro stem. E/ρ was nearly equivalent to that of tissue samples of sclerenchyma isolated from other plant species. Since the slope of H_crit vs. D equals ≈ 0.67 when E/ρ ≈ a constant, the safety-factor for saguaro stems (i.e., H_crit/H) appeared to be size-dependent such that it decreased with increasing plant height (i.e., H_crit/H ≈ D^-1.65). However, the mean safety-factor computed for the 118 saguaro specimens was 9.64, indicating that, on the average, plant height was well below H_crit. Additionally, circumstantial evidence suggests that saguaro stems become more stiff as they increase in size (and age) and that the rate of stem growth decelerates over time. The former would obtain a near size-independent safety-factor against elastic buckling while the latter protracts the time required to reach the critical buckling height. Comparisons among the allometries of H and H_crit for saguaro, other cacti, nonwoody, and highly branched tree species indicated that saguaro size overlaps with the lower size-range of the largest known dicot and gymnosperm tree specimens likely as a consequence of the high E/ρ of mature saguaro stems.     

Development and Growth Form of the Neotropical Liana <Emphasis Type="Italic">Croton nuntians</Emphasis>: The Effect of Light and Mode of Attachment on the Biomechanics of the Stem

The neotropical liana Croton nuntians (Euphorbiaceae) can occur in a variety of different growth habits. Juvenile freestanding plants are mechanically stable without support and resemble morphologically young trees or shrubs, whereas adult plants are climbers. Ontogenetic variation of bending and torsion properties of different growth phases are analyzed by measurements of flexural stiffness, structural bending modulus, torsional stiffness and structural torsional modulus. Mechanical and anatomical data show two fundamentally different patterns for juvenile freestanding and adult climbing plants. In freestanding plants, mechanical properties and the contribution of cortex, wood, and pith to the stem cross-section vary only little during ontogeny as is typical for semi-self-supporting plants. In contrast, climbing plants become significantly more flexible during ontogeny, as is characteristic for lianas. This is accompanied by a transition to the formation of a less dense wood type with large diameter vessels and an increasing contribution of flexible tissues (less dense wood and cortex) to the cross-sectional area and the axial second moment of area of the stems. Depending on the environmental conditions, freestanding plants can differ considerably in their appearance due to differences in branching system or stem taper. Therefore the influence of light quantity, measured as percentage of canopy opening, on the mechanical properties and the stem anatomy was tested. Freestanding plants grown with strong shade are significantly more stiff in bending compared with plants grown with a moderate light environment.     

The influence of gravity and wind on land plant evolution

Aspects of the engineering theory treating the elastic stability of vertical stems and cantilevered leaves supporting their own weight and additional wind-induced forces (drag) are reviewed in light of biomechanical studies of living and fossil terrestrial plant species. The maximum height to which arborescent species can grow before their stems elastically buckle under their own weight is estimated by means of the Euler-Greenhill formula which states that the critical buckling height scales as the 1/3 power of plant tissue-stiffness normalized with respect to tissue bulk density and as the 2/3 power of stem diameter. Data drawn from living plants indicate that progressively taller plant species employ stiffer and lighter-weight plant tissues as the principal stiffening agent in their vertical stems. The elastic stability of plants subjected to high lateral wind-loadings is governed by the drag torque (the product of the drag force and the height above ground at which this force is applied), which cannot exceed the gravitational bending moment (the product of the weight of aerial organs and the lever arm measured at the base of the plant). Data from living plants indicate that the largest arborescent plant species rely on massive trunks and broad, horizontally expansive root crowns to resist drag torques. The drag on the canopies of these plants is also reduced by highly flexible stems and leaves composed of tissues that twist and bend more easily than tissues used to stiffen older, more proximal stems. A brief review of the fossil record suggests that modifications in stem, leaf, and root morphology and anatomy capable of simultaneously coping with self-weight and wind-induced drag forces evolved by Devonian times, suggesting that natural selection acting on the elastic stability of sporophytes occurred early in the history of terrestrial plants.     

Growth habit and mechanical architecture of the sand dune-adapted climber Clematis flammula var. maritima L

Clematis flammula var. maritima is a woody lianoid plant that grows on coastal sand dunes in the Mediterranean region. Older perennial stems are present as extensive underground axes. These generate surface growth of shorter-lived stems producing monospecific trellises above the surface of the sand. Despite its sand dune habitat and shortage of host support plants, this variety of Clematis shows mechanical characteristics during growth that are closely comparable with those of scandent woody lianas. A significant decrease in the value of structural Young's modulus is observed from the aerial trellis-forming shoots (1.619 +/- 0.492 GN m(-2)) to emergent axes (0.855 +/- 0.253 GN m(-2)) and underground woody stems (0.470 +/- 0.113 GN m(-2)). Biomechanical and developmental observations indicate that most emergent branches are optimized geometrically and mechanically in relation to their points of emergence from the sand, with increases in structural Young's modulus and the second moment of area around the surface of the sand. Lianoid plants, physiologically capable of withstanding sand dune environments, might represent acceptable natural or introduced species for dune stabilization and conservation.     

MECHANICAL BEHAVIOR OF PLANT TISSUES AS INFERRED FROM THE THEORY OF PRESSURIZED CELLULAR SOLIDS

The mechanical behavior of plant tissues and its dependency on tissue geometry and turgor pressure are analytically dealt with in terms of the theory of cellular solids. A cellular solid is any material whose matter is distributed in the form of beamlike struts or complete “cell” walls. Therefore, its relative density is less than one and typically less than 0.3. Relative density is the ratio of the density of the cellular solid to the density of its constitutive (“cell wall”) material. Relative density depends upon cell shape and the density of cell wall material. It largely influences the mechanical behavior of cellular solids. Additional important parameters to mechanical behavior are the elastic modulus of “cell walls” and the magnitude of internal “cell” pressure. Analyses indicate that two “stiffening” agents operate in natural cellular solids (plant tissues): 1) cell wall infrastructure and 2) the hydrostatic influence of the protoplasm within each cellular compartment. The elastic modulus measured from a living tissue sample is the consequence of both agents. Therefore, the mechanical properties of living tissues are dependent upon the magnitude of turgor pressure. High turgor pressure places cell walls into axial tension, reduces the magnitude of cell wall deformations under an applied stress, and hence increases the apparent elastic modulus of the tissue. In the absence of turgid protoplasts or in the case of dead tissues, the cell wall infrastructure will respond as a linear elastic, nonlinear elastic, or “densifying” material (under compression) dependent upon the magnitude of externally applied stress. Accordingly, it is proposed that no single tangent (elastic) modulus from a stress-strain curve of a plant tissue is sufficient to characterize the material properties of a sample. It is also suggested that when a modulus is calculated that it be referred to as the tissue composite modulus to distinguish it from the elastic modulus of a noncellular solid material.     

The Growth Response of the Stems of Genetically Modified Tobacco Plants (Nicotiana tabacum'Samsun') to Flexural Stimulation

Genetically modified tobacco plants (Nicotiana tabacum‘Samsun’)with antisense cinnamyl alcohol dehydrogenase DNA, produce secondaryxylem of a reduced tensile stiffness. These plants were grownalongside control plants. The stems of the plants were flexedor protected from flexing over a period of several weeks. Thetensile moduli and second moments of areas of the differenttissues inside the stems were measured and used to calculatethe bending stiffness of the plants. In tobacco, the cylinderof xylem was found to be the most important tissue in determiningthe bending stiffness of the plants. The thickness of the xylemtissue cylinder increased when plants were subjected to flexuralstimulation. This increased the bending stiffness of the stems.The response to mechanical stimulation was found to be correlatedwith tissue strain and the genetically modified plants wereable to exactly compensate for the reduced modulus of theirxylem tissue by increasing the thickness of the xylem tissuecylinder more than in control plants.Copyright 1999 Annals ofBotany Company. Tobacco plants, stem bending, xylem tissue, second moment of area, thigmomorphogenesis, mechanical strain.     

A nonlinear finite element analysis of interface conditions in porous coated hip endoprostheses

We used a geometrically simplified finite element model to investigate load transfer between a porous coated hip endoprosthesis and a femur. Assuming both rigidly bonded and nonlinear interfaces, we analyzed fully and partially coated stems that had coatings of different elastic moduli. Our results indicate that maximum values for relative motion in the interface between bone and implant occur for implants with the same elastic modulus as compact bone. By comparison, interface motion is reduced by about half for Co-Cr-Mo alloy stems. We also showed that the elastic modulus of the porous coating had only a small influence on bone stresses.     

Ontogeny of material stiffness heterogeneity in the macaque mandibular corpus

Evidence is accumulating that bone material stiffness increases during ontogeny, and the role of elastic modulus in conditioning attributes of strength and toughness is therefore a focus of ongoing investigation. Developmental changes in structural properties of the primate mandible have been documented, but comparatively little is known about changes in material heterogeneity and their impact on biomechanical behavior. We examine a cross‐sectional sample of Macaca fascicularis (N = 14) to investigate a series of hypotheses that collectively evaluate whether the patterning of material stiffness (elastic modulus) heterogeneity in the mandible differs among juvenile, subadult and adult individuals. Because differences in age‐related activity patterns are known to influence bone stiffness and strength, these data are potentially useful for understanding the relationship between feeding behavior on the one hand and material and structural properties of the mandible on the other. Elastic modulus is shown to be spatially dependent regardless of age, with this dependence being explicable primarily by differences in alveolar versus basal cortical bone. Elastic modulus does not differ consistently between buccal and lingual cortical plates, despite likely differences in the biomechanical milieu of these regions. Since we found only weak support for the hypothesis that the spatial patterning of heterogeneity becomes more predictable with age, accumulated load history may not account for regional differences in bone material properties in mature individuals with respect to the mandibular corpus. Am J Phys Anthropol 153:297–304, 2014. © 2013 Wiley Periodicals, Inc.     

Onset of neonatal locomotor behavior and the mechanical development of Achilles and tail tendons

Tendon tissue engineering approaches are challenged by a limited understanding of the role mechanical loading plays in normal tendon development. We propose that the increased loading that developing postnatal tendons experience with the onset of locomotor behavior impacts tendon formation. The objective of this study was to assess the onset of spontaneous weight-bearing locomotion in postnatal day (P) 1, 5, and 10 rats, and characterize the relationship between locomotion and the mechanical development of weight-bearing and non-weight-bearing tendons. Movement was video recorded and scored to determine non-weight-bearing, partial weight-bearing, and full weight-bearing locomotor behavior at P1, P5, and P10. Achilles tendons, as weight-bearing tendons, and tail tendons, as non-weight-bearing tendons, were mechanically evaluated. We observed a significant increase in locomotor behavior in P10 rats, compared to P1 and P5. We also found corresponding significant differences in the maximum force, stiffness, displacement at maximum force, and cross-sectional area in Achilles tendons, as a function of postnatal age. However, the maximum stress, strain at maximum stress, and elastic modulus remained constant. Tail tendons of P10 rats had significantly higher maximum force, maximum stress, elastic modulus, and stiffness compared to P5. Our results suggest that the onset of locomotor behavior may be providing the mechanical cues regulating postnatal tendon growth, and their mechanical development may proceed differently in weight-bearing and non-weight-bearing tendons. Further analysis of how this loading affects developing tendons in vivo may inform future engineering approaches aiming to apply such mechanical cues to regulate engineered tendon formation in vitro.     

Thigmomorphogenesis: On the mechanical properties of mechanically perturbed bean plants

The mechanical properties of control and mechanically perturbed (MP) bean stems ( Phaseolus vulgaris L., ev. Cherokee wax) were compared. The rubbed plants were greatly hardened against mechanical rupture by previous MP. This hardening was due to a dramatic increase in the flexibility of the stems, but not in their stiffness. The MP-plants were able lo bend more than 90° without breaking, whereas the control plants broke after just slight bending. A comparison with other work reveals that different species utilize different tactics for achieving similar resistance to rupture due to mechanical stress.     

The Growth Form of Croton pullei (Euphorbiaceae) - Functional Morphology and Biomechanics of a Neotropical Liana

Abstract: Croton pullei (Euphorbiaceae) is a woody climber of the lowland rainforest in French Guyana and Surinam. During ontogeny, a shift from a juvenile free-standing growth phase to an older supported growth phase is observed. The following biomechanical parameters were studied: structural Young's modulus, structural torsional modulus, flexural stiffness and bend to twist ratios. Changes in anatomical development were also analysed for different stages of development of C. pullei which differ significantly in their mechanical properties. Free-standing plants show a nearly constant structural Young's modulus and structural torsional modulus during ontogeny, with flexural stiffness increasing proportionally with the axial second moment of area. These patterns are typical for “semi-self-supporting plants". In contrast, supported plants show a significant decrease in structural Young's modulus in older stem parts, as well as a decrease in structural torsional modulus. Due to the decrease in structural Young's modulus, flexural stiffness does not increase proportionally with the axial second moment of area. These patterns are typical for non-self-supporting lianas. In all supported plants, a sudden transition occurs from early dense wood to a wood type with a much higher proportion of large diameter vessels. In contrast, only the dense wood type is present in all tested free-standing plants. The data are compared with results from other climbing species of the same study area and discussed with reference to observed features characterizing the growth form and life history of C. pullei.