Analysis of tracheal mechanics and applications.

We have developed a mathematical model for a tracheal ring that consists of a "horseshoe" of cartilage with its tips joined by a membrane. The ring is subjected to a uniform transmural pressure (Ptm) difference. The model was used to calculate the cross-sectional area (A) of the trachea. Whereas the mechanics of the deformation of the cartilage were analyzed using elastica theory, the posterior membrane was treated as a simple membrane that is inextensible under changes in Ptm. The membrane can be specified to be of any length less than baseline and thus can represent a posterior membrane under tension. The cartilage can have specifiable nonuniform unstressed curvature as well as nonuniform bending stiffness. We have investigated the effect on the tracheal A-Ptm curve of posterior membrane length and tensile force in the membrane, cartilage shape and elasticity, and localized weakening of the cartilage. The model predictions are in good agreement with magnetic resonance imaging data from rabbit tracheas and show that the shape of the horseshoe as well as the posterior membrane force are important determinants of tracheal compliance.     

Relationship between transmural potential difference and smooth muscle slow waves and contractility in the rabbit small intestine in vitro

The relationship between transmural potential difference (PD) and smooth muscle electrical and mechanical activity was investigated in the rabbit ileum in vitro. Transmural PD was monitored using agar salt bridge electrodes connected via calomel half cells to an electrometer. Force displacement transducers recorded predominantly longitudinal smooth muscle activity. Concurrently, predominantly circular muscle activity was recorded at three sites using intraluminal pressure probes. At the same sites, suction electrodes monitored electrical activity of the smooth muscle. In all experiments, fluctuations in transmural PD were temporally linked to smooth muscle mechanical and electrical activity. The frequency of PD oscillations, electrical slow waves, and cyclic pressure changes were identical within each segment. Adrenaline abolished smooth muscle electrical spiking, all mechanical activity, and transmural fluctuations in PD. However, the slow waves were not abolished, though their frequency was increased. Phentolamine but not propranolol reversed the effects of adrenaline, thus slow wave frequency is influenced by alpha-adrenergic stimulation in the rabbit ileum. In conclusion, oscillations in transmural PD are unrelated to the ionic processes associated with the slow wave. However, they are in some way linked to smooth muscle contractile activity, possibly via an intrinsic neural mechanism as observed in the guinea pig.     

A model of NaCl and water flow through paracellular pathways of renal proximal tubules.

To explain how hydrostatic pressure differences between tubule lumen and interstitium modulate isotonic reabsorption rates, we developed a model of NaCl and water flow through paracellular pathways of the proximal tubule. Structural elements of the model are a tight junction membrane, an intercellular channel whose walls transport NaCl actively at a constant rate, and a basement membrane. Equations of change were derived for the channel, boundary conditions were formulated from irreversible thermodynamics, and a pressure-area relationship typical of thin-walled tubing was assumed. The boundary value problem was solved numerically. The principal conclusions are: 1) channel NaCl concentration must remain within a few mOsm of isotonic values for reabsorption rates to be modulated by transtubular pressure differences known to affect this system: 2) basement membrane and channel wall parameters determine reabsorbate tonicity; tight junction parameters affect the sensitivity of reabsorption to transmural pressure; 3) channel NaCl concentration varies inversely with transmural pressure difference; this concentration variation controls NaCl diffusion through the tight junction; 4) modulation of NaCl diffusion through the tight junction controls the rate of isotonic reabsorption; modulation of water flow can increase sensitivity to transmural pressure; 5) no pressure-induced change in permeability of the tight junction or basement membrane is needed for pressure to modulate reabsorption; and 6) system performance is indifferent to the distribution of active transport sites, to the numerical value of the compliance function, and to the relationship between lumen and cell pressures.     

A novel surrogate lung material for impact studies: Development and testing procedures

This work focuses on the development of a surrogate lung material (SLM) that reproduces the dynamic response of a human lung under various loading conditions and also allows for the analysis of the extent and distribution of damage. The SLM consists of polyurethane foam used to mimic the spongy lung tissue and fluid-filled gelatine microcapsules used to simulate the damage of alveoli.The bursting pressure of the microcapsules was investigated by conducting low and high rate compression tests on single microcapsules. A bursting pressure of around 5 bar was measured which is comparable to the reported lung overpressure at injury level.Low and high rate compression tests were conducted on the SLMs. From the measured mechanical properties and mass density, the stress wave speed was calculated and found to be well in the range of the reported values for human lungs (16–70 m/s).In order to study the extent and distribution of damage in the SLMs, as represented by burst microcapsules, a CT scan analysis was carried out before and after the impacts. The CT scan results clearly demonstrated the magnitude and distribution of damage within the specimen. The results are then compared to the Bowen curves, the most often used criteria for predicting blast injuries in humans. An excellent agreement was found between the observed damage in the surrogate lungs and the expected damage in real human lungs.In general, the SLM showed similar stress wave speed, bursting pressure and damage to that of the real lungs.     

Age-related changes in chest geometry during cardiopulmonary resuscitation

We studied alterations of chest geometry during conventional cardiopulmonary resuscitation in anesthetized immature swine. Pulsatile force was applied to the sternum in increments to determine the effects of increasing compression on chest geometry and intrathoracic vascular pressures. In 2-wk- and 1-mo-old piglets, permanent changes in chest shape developed due to incomplete recoil of the chest along the anteroposterior axis, and large intrathoracic vascular pressures were generated. In 3-mo-old animals, permanent chest deformity did not develop, and large intrathoracic vascular pressures were not produced. We propose a theoretical model of the chest as an elliptic cylinder. Pulsatile displacement along the minor axis of an ellipse produces a greater decrease in cross-sectional area than displacement of a circular cross section. As thoracic cross section became less circular due to deformity, greater changes in thoracic volume, and hence pressure, were produced. With extreme deformity at high force, pulsatile displacement became limited, diminishing pressure generation. We conclude that changes in chest geometry are important in producing intrathoracic intravascular pressure during conventional cardiopulmonary resuscitation in piglets.     

Compression of biocompatible liquid-filled HSA-alginate capsules: determination of the membrane mechanical properties

Compression experiments between two parallel plates are performed on a series of biocompatible HSA-alginate capsules with two different membrane thicknesses. The capsule geometry and size as well as the average membrane thickness are first measured. The compression set-up is fitted with a sensitive force transducer that allows measurement of the compression force as a function of plate separation. The response of the capsule is analyzed by assuming different constitutive models for the membrane, where the shear and surface dilatation effects are accounted. An apparent area dilatation modulus is then computed for different values of the plate separation and required to remain constant as the capsule deformation increases. This allows identification of plausible constitutive laws for the membrane material.     

Influence of microenvironmental conditions on hybridoma cell growth inside the alginate-poly-l-lysine microcapsule

A mathematical model was formulated to describe hybridoma cell growth within the alginate-poly-l-lysine (alginate-PLL) microcapsules during air-lift bioreactor cultivation. Model development was based on experimentally obtained data concerning the hybridoma cell counts, monoclonal antibody (mAb) production and the distribution of hybridoma cell growth within the microcapsules. The cell growth was modeled using a mean field approach expressed as Langevin class of equations for two different regions of alginate-PLL microcapsules, the alginate microcapsule core and the annular region between microcapsule core and membrane. In this paper we propose an influence of microenvironmental conditions on cell growth. The osmotic pressure changes in the Na-alginate liquefied annular region, as well as, the resistance effects of Ca-alginate hydrogel in the core region during the cell growth were incorporated into the model. Good agreement between the experimental data and model prediction values was obtained. The proposed model successfully predicted the impact of various microenvironmental restriction effects on the dynamics of cell growth and appears useful for further optimization of microcapsule design in order to achieve higher intra-capsule cell concentrations resulting in higher amounts of mAb produced.     

Dynamic unconfined compression of articular cartilage under a cyclic compressive load

To study the effect of dynamic mechanical force on cartilage metabolism, many investigators have applied a cyclic compressive load to cartilage disc explants in vitro. The most frequently used in vitro testing protocol has been the cyclic unconfined compression of articular cartilage in a bath of culture medium. Cyclic compression has been achieved by applying either a prescribed cyclic displacement or a prescribed cyclic force on a loading platen placed on the top surface of a cylindrical cartilage disc. It was found that the separation of the loading platen from the tissue surface was likely when a prescribed cyclic displacement was applied at a high frequency.The purpose of the present study was to simulate mathematically the dynamic behavior of a cylindrical cartilage disc subjected to cyclic unconfined compression under a dynamic force boundary condition protocol, and to provide a parametric analysis of mechanical deformations within the extracellular matrix. The frequency-dependent dynamic characteristics of dilatation, hydrostatic pressure and interstitial fluid velocity were analyzed over a wide range of loading frequencies without the separation of the loading platen. The result predicted that a cyclic compressive force created an oscillating positive-negative hydrostatic pressure together with a forced circulation of interstitial fluid within the tissue matrix. It was also found that the load partitioning mechanism between the solid and fluid phases was a function of loading frequency. At a relatively high loading frequency, a localized dynamic zone was developed near the peripheral free surface of the cartilage disc, where a large dynamic pressure gradient exists, causing vigorous interstitial fluid flow.     

草原蜥两性的咬合力及头部形态特征比较

咬合力作为衡量动物生存能力的重要指标,可以在一定程度上反映动物捕食、反捕食和争夺配偶的能力。对于蜥蜴类动物而言,头部形态和咬合力大小之间常呈现显著线性关系。通过测量2018年7月采集于新疆霍城县图开沙漠的24号草原蜥(Trapelussanguinolenta)(雌13,雄11)的头部形态指标,并使用薄膜压力测试仪测定咬合力,采用单因素方差分析(ANOVA)、主成分分析、模型拟合及逐步回归4种方法探究草原蜥咬合力的两性差异及其与头部形态指标的关系。结果表明,草原蜥头体长、头长、头宽、头高、口宽和下颌长在两性个体间均无显著差异,草原蜥两性个体之间咬合力也没有显著差异。主成分分析及赤池信息模型拟合结果均显示,头长、头宽和下颌长是影响草原蜥咬合力的重要因素,逐步回归分析揭示草原蜥的咬合力主要受头宽影响。上述研究结果表明,草原蜥的咬合力受头部形态大小的影响,但两性个体之间咬合力却不存在显著差异,这与头部形态特征未表现出两性差异一致,这可能是草原蜥对灌丛生活的适应,具体而言,是头部大小与运动权衡的结果。     

Circumferential variations of mechanical behavior of the porcine thoracic aorta during the inflation test

We developed an extension-inflation experimental apparatus with a stereo vision system and a stress-strain analysis method to determine the regional mechanical properties of a blood vessel. Seven proximal descending thoracic aortas were investigated during the inflation test at a fixed longitudinal stretch ratio of 1.35 over a transmural pressure range from 1.33 to 21.33 kPa. Four circumferential regions of each aorta were designated as the anterior (A), left lateral (L), posterior (P), and right lateral (R) regions, and the inflation test was repeated for each region of the aortas. We used continuous functions to approximate the surfaces of the regional aortic wall in the reference configuration and the deformed configuration. Circumferential stretch and stress at the four circumferential regions of the aorta were computed. Circumferential stiffness, defined as the tangent of the stress-stretch curve, and physiological aortic stiffness, named pressure-strain elastic modulus, were also computed for each region. In the low pressure range, the stress increased linearly with increased stretch, but the mechanical response became progressively stiffer in the high-pressure range above a transition point. At a transmural pressure of 12.00 kPa, mean values of stiffness were 416±104 kPa (A), 523±99 kPa (L), 634±91 kPa (P), and 489±82 kPa (R). The stiffness of the posterior region was significantly higher than that of the anterior region, but no significant difference was found in pressure-strain elastic modulus.     

MECHANICAL PROPERTIES OF SEA URCHIN EGGS III. VISCO-ELASTICITY OF THE CELL SURFACE

When a sea urchin egg was compressed between two parallel plates, the force required to keep the distance between the plates constant gradually decreased with time. The contours of the compressed egg were different from the contours expected from the assumption that the surface forces are uniform over the entire surface. The surface forces of the egg without deformation computed from the area of the cell surface in contact with the substratum, the density of the egg and its size were 0.02–0.04 dynes/cm in Hemicentrotus pulcherrimus. Larger values were obtained in eggs during compression. Surface forces, which were computed from measurements of the form of the egg and the applied force when the egg was deformed by a rod and a plate supporting the egg, increased as the deformation increased.
From these results, it was concluded that the cell surface is visco-elastic in sea urchin eggs.     

Influence of left-ventricular shape on passive filling properties and end-diastolic fiber stress and strain

Passive filling is a major determinant for the pump performance of the left ventricle and is determined by the filling pressure and the ventricular compliance. In the quantification of the passive mechanical behaviour of the left ventricle and its compliance, focus has been mainly on fiber orientation and constitutive parameters. Although it has been shown that the left-ventricular shape plays an important role in cardiac (patho-)physiology, the dependency on left-ventricular shape has never been studied in detail. Therefore, we have quantified the influence of left-ventricular shape on the overall compliance and the intramyocardial distribution of passive fiber stress and strain during the passive filling period. Hereto, fiber stress and strain were calculated in a finite element analysis of passive inflation of left ventricles with different shapes, ranging from an elongated ellipsoid to a sphere, but keeping the initial cavity volume constant. For each shape, the wall volume was varied to obtain ventricles with different wall thickness. The passive myocardium was described by an incompressible hyperelastic material law with transverse isotropic symmetry along the muscle fiber directions. A realistic transmural distribution in fiber orientation was assumed. We found that compliance was not altered substantially, but the transmural distribution of both passive fiber stress and strain was highly dependent on regional wall curvature and thickness. A low curvature wall was characterized by a maximum in the transmural fiber stress and strain in the mid-wall region, while a steep subendocardial transmural gradient was present in a high curvature wall. The transmural fiber stress and strain gradients in a low and high curvature wall were, respectively, flattened and steepened by an increase in wall thickness.     

Mechanics of the Formation,Interaction, and Evolution of Membrane Tubular Structures

Membrane nanotubes, also known as membrane tethers, play important functional roles in many cellular processes, such as trafficking and signaling. Although considerable progresses have been made in understanding the physics regulating the mechanical behaviors of individual membrane nanotubes, relatively little is known about the formation of multiple membrane nanotubes due to the rapid occurring process involving strong cooperative effects and complex configurational transitions. By exerting a pair of external extraction upon two separate membrane regions, here, we combine molecular dynamics simulations and theoretical analysis to investigate how the membrane nanotube formation and pulling behaviors are regulated by the separation between the pulling forces and how the membrane protrusions interact with each other. As the force separation increases, different membrane configurations are observed, including an individual tubular protrusion, a relatively less deformed protrusion with two nanotubes on its top forming a V shape, a Y-shaped configuration through nanotube coalescence via a zipper-like mechanism, and two weakly interacting tubular protrusions. The energy profile as a function of the separation is determined. Moreover, the directional flow of lipid molecules accompanying the membrane shape transition is analyzed. Our results provide new, to our knowledge, insights at a molecular level into the interaction between membrane protrusions and help in understanding the formation and evolution of intra- and intercellular membrane tubular networks involved in numerous cell activities.     

Endocytosis against high turgor pressure is made easier by partial coating and freely rotating base

During clathrin-mediated endocytosis, a patch of flat plasma membrane is deformed into a vesicle. In walled cells, such as plants and fungi, the turgor pressure is high and pushes the membrane against the cell wall, thus hindering membrane internalization. In this work, we study how a patch of membrane is deformed against turgor pressure by force and by curvature-generating proteins. We show that a large amount of force is needed to merely start deforming the membrane and an even larger force is needed to pull a membrane tube. The magnitude of these forces strongly depends on how the base of the membrane is constrained and how the membrane is coated with curvature-generating proteins. In particular, these forces can be reduced by partially, but not fully, coating the membrane patch with curvature-generating proteins. Our theoretical results show excellent agreement with experimental data.     

Dynamic geometry of the intact left ventricle

Knowledge of left ventricular chamber dynamics is central to our understanding of cardiac physiology. The complicated changes in left ventricular geometry observed in the dog during various phases of the cardiac cycle can be represented as distinct linear relationships between chamber eccentricity and intracavitary volume during diastole and ejection, and probably represent structural properties of the ventricular wall. Chamber geometry of the left ventricle is a major determinant of overall myocardial function. The slope of the radius of curvature (r) to wall thickness (h) relationship is a geometric constant that determines the mural force at any given transmural pressure. Chronic pressure and volume overload produce changes in this geometric relationship as a result of increased mural force resisting ejection. The adaptive mechanism of ventricular hypertrophy in this setting alters the r/h ratio and returns systolic mural force toward normal. Coronary occlusion induces acute changes in regional geometry characterized by holosystolic wall bulging and systolic wall thinning, which shift the r/h relationship upward and to the left. The geometric alteration during ischemia probably increases systolic mural force and could adversely affect myocardial function. Recent studies with patients have shown the r/h ratio to be of value in distinguishing between reversible and irreversible impairment of myocardial performance. Because most myocardial diseases produce major alterations in the structure of the ventricular wall, analysis of dynamic chamber geometry may prove of prognostic value in assessing patients with cardiac disorders.     

A finite-element model of tracheal collapse

The trachea has been approximated by an appropriate finite-element model. The three-dimensional equilibrium problems set by the tracheal deformation under various stresses have been solved using a convenient augmented Lagrangian functional. The dimensions were obtained from human tracheae. Mechanical constants for the anatomic components were calculated from the stress-strain relationships. The compressive narrowing is essentially due to the invagination of the posterior membrane in the tracheal lumen for transmural pressures down to -7 kPa. A surface of contact between the membranous wall and the lateral walls appears when the transmural pressure equals -6 kPa. The transmural pressure-area relationship is sigmoidal with a compliance equal to 0.08 kPa-1 for a transmural pressure of -2 kPa. The tracheal collapse is greater when the material constants of the membranous wall decrease or when the tracheal segment is subjected to a longitudinal tension. A slight flexion of the trachea induces an asymmetric deformation.     

Statistical study of rapid mechanodependent cell movements in deformed explants of african clawed frog <Emphasis Type="Italic">Xenopus laevis</Emphasis> embryonic tissues

Computer analysis of artificially deformed (stretched or compressed) double explants (sandwiches) of the blastocoel roof (BRs) and suprablastoporal region (SBRs) of African clawed frog Xenopus laevis early gastrula has been performed using frames of time-lapse microfilming. During the first 14 min after cutting off, the velocities and displacement angles of several hundreds of cells relative to one another, as well as to fixed points and the extension axis, were measured in the control and deformed samples. It has been found that the deformation of samples leads to a rapid reorientation of large cell masses and increase in the velocities of movements along the extension axes or perpendicularly to the compression axes. In addition, an increase in the velocities of mutual cell displacements in the stretched BRs and cell convergence to the extension axes have been observed. Comparison of different angular sectors demonstrates a statistically significant positive correlation between the mean velocities of cell movements and the number of cells moving within an individual sector. This suggests cooperativity of mechanodependent cell movements. In general, these results demonstrate an important role of mechanical factors in regulation of collective cell movements.     

Statistical study of rapid mechanodependent cell movements in deformed explants of African clawed frog Xenopus laevis embryonic tissues

Computer analysis of artificially deformed (stretched or compressed) double explants (sandwiches) of the blastocoel roof (BRs) and suprablastoporal region (SBRs) of African clawed frog Xenopus laevis early gastrula has been performed using frames of time-lapse microfilming. During the first 14 min after cutting off, the velocities and displacement angles of several hundreds of cells relative to one another, as well as to fixed points and the extension axis, were measured in the control and deformed samples. It has been found that the deformation of samples leads to a rapid reorientation of large cell masses and increase in the velocities of movements along the extension axes or perpendicularly to the compression axes. In addition, an increase in the velocities of mutual cell displacements in the stretched BRs and cell convergence to the extension axes have been observed. Comparison of different angular sectors demonstrates a statistically significant positive correlation between the mean velocities of cell movements and the number of cells moving within an individual sector. This suggests cooperativity of mechanodependent cell movements. In general, these results demonstrate an important role of mechanical factors in regulation of collective cell movements.     

Nonlinear material and ionic transport through membrane nanotubes

Membrane nanotubes (NTs) and their networks play an important role in intracellular membrane transport and intercellular communications. The transport characteristics of the NT lumen resemble those of conventional solid-state nanopores. However, unlike the rigid pores, the soft membrane wall of the NT can be deformed by forces driving the transport through the NT lumen. This intrinsic coupling between the NT geometry and transport properties remains poorly explored. Using synchronized fluorescence microscopy and conductance measurements, we revealed that the NT shape was changed by both electric and hydrostatic forces driving the ionic and solute fluxes through the NT lumen. Far from the shape instability, the strength of the force effect is determined by the lateral membrane tension and is scaled with membrane elasticity so that the NT can be operated as a linear elastic sensor. Near shape instabilities, the transport forces triggered large-scale shape transformations, both stochastic and periodic. The periodic oscillations were coupled to a vesicle passage along the NT axis, resembling peristaltic transport. The oscillations were parametrically controlled by the electric field, making NT a highly nonlinear nanofluidic circuitry element with biological and technological implications.     

Verification of Beam Models for Ionic Polymer-Metal Composite Actuator

Ionic Polymer-Metal Composite (IPMC) can work as an actuator by applying a few voltages.A thick IPMC actuator,whereNafion-117 membrane was synthesized with polypyrrole/alumina composite filler,was analyzed to verify the equivalent beamand equivalent bimorph beam models.The blocking force and tip displacement of the IPMC actuator were measured with a DCpower supply and Young’s modulus of the IPMC strip was measured by bending and tensile tests respectively.The calculatedmaximum tip displacement and the Young’s modulus by the equivalent beam model were almost identical to the correspondingmeasured data.Finite element analysis with thermal analogy technique was utilized in the equivalent bimorph beam model tonumerically reproduce the force-displacement relationship of the IPMC actuator.The results by the equivalent bimorph beammodel agreed well with the force-displacement relationship acquired by the measured data.It is confirmed that the equivalentbeam and equivalent bimorph beam models are practically and effectively suitable for predicting the tip displacement,blockingforce and Young’s modulus of IPMC actuators with different thickness and different composite of ionic polymer membrane.