Diameter-dependent axial prestretch of porcine coronary arteries and veins

The pressure-diameter relation (PDR) and the wall strain of coronary blood vessels have important implications for coronary blood flow and arthrosclerosis, respectively. Previous studies have shown that these mechanical quantities are significantly affected by the axial stretch of the vessels. The objective of this study was to measure the physiological axial stretch in the coronary vasculature; i.e., from left anterior descending (LAD) artery tree to coronary sinus vein and to determine its effect on the PDR and hence wall stiffness. Silicone elastomer was perfused through the LAD artery and coronary sinus trees to cast the vessels at the physiologic pressure. The results show that the physiological axial stretch exists for orders 4 to 11 (> 24 μm in diameter) arteries and orders -4 to -12 (>38 μm in diameter) veins but vanishes for the smaller vessels. Statistically, the axial stretch is higher for larger vessels and is higher for arteries than veins. The axial stretch λ(z) shows a linear variation with the order number (n) as: λ(z) = 0.062n + 0.75 (R(2) = 0.99) for artery and λ(z) = -0.029n + 0.89 (R(2) = 0.99) for vein. The mechanical analysis shows that the axial stretch significantly affects the PDR of the larger vessels. The circumferential stretch/strain was found to be significantly higher for the epicardial arteries (orders 9-11), which are free of myocardium constraint, than the intramyocardial arteries (orders 4-8). These findings have fundamental implications for coronary blood vessel mechanics.     

Axial stretching of extremity artery induces reversible hyperpolarization of smooth muscle cell membrane in vivo

Circumferential stretch due to increases in pressure induces vascular smooth muscle cell depolarization and contraction known as the myogenic response. The aim of this study was to determine the in vivo effects of axial-longitudinal stretch of the rat saphenous artery (SA) on smooth muscle membrane potential (Em) and on external diameter. Consecutive elongations of the SA were carried out from resting length (L0) in 10% increments up to 140% L0 while changes in membrane potential and diameter were determined in intact and de-endothelized vessels. Axial stretching resulted in a small initial depolarization at 120% of L0 followed by a progressive 20 to 33% hyperpolarizaion of vascular smooth muscle between 130% and 140% of L0. At 140%, an average maximal 10.6 mV reversible hyperpolarization was measured compared to -41.2 +/- 0.49 mV Em at 100% L0. De-endothelialization completely eliminated the hyperpolarization to axial stretching and augmented the reduction of diameter beyond 120% L0. These results indicate that arteries have a mechanism to protect them from vasospasm that could otherwise occur with movements of the extremities.     

Dependence of cyclic stretch-induced stress fiber reorientation on stretch waveform

Cyclic uniaxial stretching of adherent nonmuscle cells induces the gradual reorientation of their actin stress fibers perpendicular to the stretch direction to an extent dependent on stretch frequency. By subjecting cells to various temporal waveforms of cyclic stretch, we revealed that stress fibers are much more sensitive to strain rate than strain frequency. By applying asymmetric waveforms, stress fibers were clearly much more responsive to the rate of lengthening than the rate of shortening during the stretch cycle. These observations were interpreted using a theoretical model of networks of stress fibers with sarcomeric structure. The model predicts that stretch waveforms with fast lengthening rates generate greater average stress fiber tension than that generated by fast shortening. This integrated approach of experiment and theory provides new insight into the mechanisms by which cells respond to matrix stretching to maintain tensional homeostasis.     

In Vitro Experimental Study for the Determination of Cellular Axial Strain Threshold and Preferential Axial Strain from Cell Orientation Behavior in a Non-uniform Deformation Field

Cells within connective tissues are routinely subjected to a wide range of non-uniform mechanical loads that regulate many cell behaviors. In the present study, the relationship between cell orientation angle and strain value of the membrane was comprehensively investigated using an inhomogeneous strain field. Additionally, the cellular axial strain threshold, which corresponds to the launching of cell reorientation response, was elucidated. Human bone marrow mesenchymal stem cells were used for these experiments. In this study, an inhomogeneous strain distribution was easily created by removing one side holes of an elastic chamber in a commonly used uniaxial stretching device. The strains of 2D stretched membranes were quantified on a position-by-position basis using the digital image correlation method. The normal strain in the direction of stretch was changed continuously from 2.0 to 15.0 %. A 3D histogram of the cell frequency, which was correlated with the cell orientation angle and normal strain of the membrane, made it possible to determine the axial strain threshold accurately. The value of the axial strain threshold was 4.4 ± 0.3 %, which was reasonable compared with previous studies based on cyclic uniaxial stretch stimulation (homogeneous strain field). Additionally, preferential axial strain of cells, which was a cell property firstly introduced, was also achieved and the value was ?2.0 ± 0.1 %. This study is novel in three respects: (i) it precisely and easily determined the axial strain threshold of cells; (ii) it is the first to suggest preferential axial strain of cells; and (iii) it methodically investigated cell behavior in an inhomogeneous strain field.     

Bovine annulus fibrosus hydration affects rate-dependent failure mechanics in tension

The high water content of the intervertebral disc is essential to its load bearing function and viscoelastic mechanical behavior. One of the primary biochemical changes associated with disc degeneration is the loss of proteoglycans, which leads to tissue dehydration. While previous studies have reported the effects of in vivo degeneration on annulus fibrosus (AF) failure mechanics, the independent role of water remains unclear, as does the tissue’s rate-dependent failure response. Our first objective was to determine the effect of loading rate on AF failure properties in tension; our second objective was to quantify the effect of water content on failure properties. Water content was altered through enzymatic digestion of glycosaminoglycans (GAGs) and through osmotic loading. Bovine AF specimens were tested monotonically to failure along the circumferential direction at 0.00697%/s or 6.97%/s. Increased loading rate resulted in a ∼50% increase in linear-region modulus, failure stress, and strain energy density across all treatment groups (p < 0.001). Decreased GAG and water contents resulted in decreased modulus, failure stress, and strain energy density; however, these differences were only observed at the low loading rate (p < 0.05; no changes at high rate). Osmotic loading was used to evaluate the effect of hydration independently from GAG composition, resulting in similar decreases in water content, modulus, and strain energy density. This suggests that hydration is essential for maintaining tissue stiffness and energy absorption capacity, rather than strength, and that GAGs contribute to tissue strength independently from mediating water content.     

Effect of cyclic axial stretch of rat arteries on endothelial cytoskeletal morphology and vascular reactivity

Pulsatile fluid shear stress and circumferential stretch are responsible for the axial alignment of vascular endothelial cells and their actin stress fibers in vivo. We studied the effect of cyclic alterations in axial stretch independent of flow on endothelial cytoskeletal organization in intact arteries and determined if functional alterations accompanied morphologic alterations. Rat renal arteries were axially stretched (20%, 0.5 Hz) around their in vivo lengths, for up to 4h. Actin stress fibers were examined by immunofluorescent staining. We found that cyclic axial stretching of intact vessels under normal transmural pressure in the absence of shear stress induces within a few hours realignment of endothelial actin stress fibers toward the circumferential direction. Concomitant with this morphologic alteration, the sensitivity (log(EC(50))) to the endothelium-dependent vasodilator (acetylcholine) was significantly decreased in the stretched vessels (after stretching -5.15+/-0.79 and before stretching -6.71+/-0.78, resp.), while there was no difference in sodium nitroprusside (SNP) sensitivity. There was no difference in sensitivity to both acetylcholine and SNP in time control vessels. Similar to cultured cells, endothelial cells in intact vessels subjected to cyclic stretching reorganize their actin filaments almost perpendicular to the stretching direction. Accompanying this morphological alteration is a loss of endothelium-dependent vasodilation but not of smooth muscle responsiveness.     

Cell orientation response to cyclically deformed substrates: Experimental validation of a cell model

We have developed a stochastic model that describes the orientation response of bipolar cells grown on a cyclically deformed substrate. The model was based on the following hypotheses regarding the behavior of individual cells: (a) the mechanical signal responsible for cell reorientation is the peak to peak surface strain along the cell's major axis (p-p axial strain); (b) each cell has an axial strain threshold and the threshold is normally distributed in the cell population; (c) the cell will avoid any direction where the p-p axial strain is above its threshold; and (d) the cell will randomly orient within the range of directions where the p-p axial strains are less than the cell's threshold. These hypotheses were tested by comparing model predictions with experimental observations from stretch experiments conducted with human melanocytes. The cells were grown on elastic rectangular culture dishes subjected to unidirectional cyclic (1 Hz) stretching with amplitudes of 0, 4, 8, and 12%. After 24 h of stimulation, the distribution of cell orientations was determined by measuring the orientations of 300–400 randomly selected cells. The 12% stretch experiment was used to determine the mean, 3.5%, and the standard deviation, 1.0%, of the strain threshold for the cell population. The Kolmogorov-Smirnov test was then used to determine if the orientation distributions predicted by the model were different from experimentally measured distributions for the 4 and 8% stretches. No significant differences were found between the predicted and experimental distributions (4%: p = 0.70; and 8%: p = 0.71). These results support the hypothesis that cells randomly orient, but avoid directions where the p-p axial strains are above their thresholds.     

Development of fibroblast-seeded collagen gels under planar biaxial mechanical constraints: a biomechanical study

Prior studies indicated that mechanical loading influences cell turnover and matrix remodeling in tissues, suggesting that mechanical stimuli can play an active role in engineering artificial tissues. While most tissue culture studies focus on influence of uniaxial loading or constraints, effects of multi-axial loading or constraints on tissue development are far from clear. In this study, we examined the biaxial mechanical properties of fibroblast-seeded collagen gels cultured under four different mechanical constraints for 6 days: free-floating, equibiaxial stretching (with three different stretch ratios), strip-biaxial stretching, and uniaxial stretching. Passive mechanical behavior of the cell-seeded gels was also examined after decellularization. A continuum-based two-dimensional Fung model was used to quantify the mechanical behavior of the gel. Based on the model, the value of stored strain energy and the ratio of stiffness in the stretching directions were calculated at prescribed strains for each gel, and statistical comparisons were made among the gels cultured under the various mechanical constraints. Results showed that gels cultured under the free-floating and equibiaxial stretching conditions exhibited a nearly isotropic mechanical behavior, while gels cultured under the strip-biaxial and uniaxial stretching conditions developed a significant degree of mechanical anisotropy. In particular, gels cultured under the equibiaxial stretching condition with a greater stretch ratio appeared to be stiffer than those with a smaller stretch ratio. Also, a decellularized gel was stiffer than its non-decellularized counterpart. Finally, the retained mechanical anisotropy in gels cultured under the strip-biaxial stretching and uniaxial stretching conditions after cell removal reflected an irreversible matrix remodeling.     

Pipette aspiration technique for the measurement of nonlinear and anisotropic mechanical properties of blood vessel walls under biaxial stretch

A pipette aspiration technique was proposed for the measurement of nonlinear mechanical properties of arteries under biaxial stretching. A cross-shaped specimen of porcine thoracic aorta whose principal axes corresponded with the axial and circumferential directions of the aortic walls was excised. The intraluminal surface of the specimen was aspirated with a circular cross-sectioned glass pipette while the specimen was stretching in the axial and circumferential directions in 10% increments. The elastic modulus agreed with the incremental elastic modulus obtained through a conventional pressure-diameter test of the same specimen to within an error of 30% at a circumferential stretch ratio below 1.3 and an axial stretch ratio of 1.0, 1.1 or 1.2, which represent lower range of physiological stretch ratios for the porcine aorta. A rectangular cross-sectioned pipette was utilized to measure anisotropic properties of the specimen under biaxial stretching. When aspirated with such a pipette, the specimens' elastic properties along the length of the rectangular pipette cross section can be neglected. The elastic modulus was found to increase rapidly when the specimen was stretched in the direction of the pipette's width. Thus, pipette aspiration should have many advantages such as well measurement of the local nonlinear and anisotropic mechanical properties of blood vessel walls.     

Vibrational spectroscopy of biopolymers under mechanical stress: processing cellulose spectra using bandshift difference integrals

Mechanical stretching of covalent bonds, for example when a fibrous polymer is loaded in tension, results in their stretching vibrational bands in the infrared or Raman spectrum being shifted to lower frequency. Conversely stretching a hydrogen bond shifts the stretching vibrational mode of the donor covalent X-H bond to higher frequency. These band shifts are small and difficult to detect in complex regions of the spectrum where differently affected bands overlap. This paper describes a method of integrating the difference spectra (spectrum under tensile strain minus spectrum at zero tensile strain) to recover the shape of the bands that are shifted and the spectral variation in bandshift. The application of this method to two sets of vibrational spectra of cellulose under tension is described. In one example, C-O-C stretching bands of highly crystalline tunicate cellulose were observed to shift to lower frequency under axial strain. In the other example, a group of overlapping O-D stretching bands in partially deuterated cellulose showed varied bandshifts under axial strain, some bandshifts being positive as expected due to extension of axially oriented hydrogen bonds while others were negative. The possibility of constructing spectral plots of bandshift has the potential to clarify the interpretation of overlapped, shifting bands in the vibrational spectra of polymers under tension.     

Patient-Specific Artery Shrinkage and 3D Zero-Stress State in Multi-Component 3D FSI Models for Carotid Atherosclerotic Plaques Based on <i>In Vivo</i> MRI Data

Image-based computational models for atherosclerotic plaques have been developed to perform mechanical analysis to quantify critical flow and stress/strain conditions related to plaque rupture which often leads directly to heart attack or stroke. An important modeling issue is how to determine zero stress state from in vivo plaque geometries. This paper presents a method to quantify human carotid artery axial and inner circumferential shrinkages by using patient-specific ex vivo and in vivo MRI images. A shrink-stretch process based on patient-specific in vivo plaque morphology and shrinkage data was introduced to shrink the in vivo geometry first to find the zero-stress state (opening angle was ignored to reduce the complexity), and then stretch and pressurize to recover the in vivo plaque geometry with computed initial stress, strain, flow pressure and velocity conditions. Effects of the shrink-stretch process on plaque stress/strain distributions were demonstrated based on patient-specific data using 3D models with fluid-structure interactions (FSI). The average artery axial and inner circumferential shrinkages were 25% and 7.9%, respectively, based on a data set obtained from 10 patients. Maximum values of maximum principal stress and strain increased 349.8% and 249% respectively with 33% axial stretch. Influence of inner circumferential shrinkage (7.9%) was not very noticeable under 33% axial stretch, but became more noticeable under smaller axial stretch. Our results indicated that accurate knowledge of artery shrinkages and the shrink-stretch process will considerably improve the accuracy of computational predictions made based on results from those in vivo MRI-based FSI models.     

Micromanipulation of Chromosomes in Mitotic Vertebrate Tissue Cells: Tension Controls the State of Kinetochore Movement

In mitotic vertebrate tissue cells, chromosome congression to the spindle equator in prometaphase and segregation to the poles in anaphase depend on the movements of kinetochores at their kinetochore microtubule attachment sites. To test if kinetochores sense tension to control their states of movement poleward (P) and away from the pole (AP), we applied an external force to the spindle in preanaphase newt epithelial cells by stretching chromosome arms with microneedles. For monooriented chromosomes (only one kinetochore fiber), an abrupt stretch of an arm away from the attached pole induced the single attached kinetochore to persist in AP movement at about 2 μm/min velocity, resulting in chromosome movement away from the pole. When the stretch was reduced or the needle removed, the kinetochore switched to P movement at about 2 μm/min and pulled the chromosome back to near the premanipulation position within the spindle. For bioriented chromosomes (sister kinetochores attached to opposite poles) near the spindle equator, stretching one arm toward a pole placed the kinetochore facing away from the direction of stretch under tension and the sister facing toward the stretch under reduced tension or compression. Kinetochores under increased tension exhibited prolonged AP movement while kinetochores under reduced tension or compression exhibited prolonged P movement, moving the centromeres at about 2 μm/min velocities off the metaphase plate in the direction of stretch. Removing the needle resulted in centromere movement back to near the spindle equator at similar velocities. These results show that tension controls the direction of kinetochore movement and associated kinetochore microtubule assembly/disassembly to position centromeres within the spindle of vertebrate tissue cells. High tension induces persistent AP movement while low tension induces persistent P movement. The velocity of P and AP movement appears to be load independent and governed by the molecular mechanisms which attach kinetochores to the dynamic ends of kinetochore microtubules.     

Torsional Behavior of Axonal Microtubule Bundles

Axonal microtubule (MT) bundles crosslinked by microtubule-associated protein (MAP) tau are responsible for vital biological functions such as maintaining mechanical integrity and shape of the axon as well as facilitating axonal transport. Breaking and twisting of MTs have been previously observed in damaged undulated axons. Such breaking and twisting of MTs is suggested to cause axonal swellings that lead to axonal degeneration, which is known as “diffuse axonal injury”. In particular, overstretching and torsion of axons can potentially damage the axonal cytoskeleton. Following our previous studies on mechanical response of axonal MT bundles under uniaxial tension and compression, this work seeks to characterize the mechanical behavior of MT bundles under pure torsion as well as a combination of torsional and tensile loads using a coarse-grained computational model. In the case of pure torsion, a competition between MAP tau tensile and MT bending energies is observed. After three turns, a transition occurs in the mechanical behavior of the bundle that is characterized by its diameter shrinkage. Furthermore, crosslink spacing is shown to considerably influence the mechanical response, with larger MAP tau spacing resulting in a higher rate of turns. Therefore, MAP tau crosslinking of MT filaments protects the bundle from excessive deformation. Simultaneous application of torsion and tension on MT bundles is shown to accelerate bundle failure, compared to pure tension experiments. MAP tau proteins fail in clusters of 10–100 elements located at the discontinuities or the ends of MT filaments. This failure occurs in a stepwise fashion, implying gradual accumulation of elastic tensile energy in crosslinks followed by rupture. Failure of large groups of interconnecting MAP tau proteins leads to detachment of MT filaments from the bundle near discontinuities. This study highlights the importance of torsional loading in axonal damage after traumatic brain injury.     

Responses of single-ventricular myocytes to dynamic axial stretching

Mechano-electrical feedback (MEF) has mainly been studied in isolated single cardiomyocytes using the microelectrode and micropipette techniques, but information regarding its dynamic aspects at the cellular level is limited due to the technical difficulties associated with manipulating single cells and maintaining stable attachment of these devices. To overcome such difficulties, we have combined two experimental methods, namely a carbon fiber technique to hold single myocytes and a ratiometric fluorescence measurement technique to monitor Ca2+ transients or membrane potentials. Following an overview of the experimental technique for stretching myocytes, the results for single rat ventricular myocytes under axial stretching are presented. Ca2+ transients were influenced by the loading conditions and involvement of myofilaments was suspected in regulatory mechanism. Membrane potential measurements during dynamic axial stretching revealed that the action potential duration was prolonged when the stretch was applied during the late phase of twitch contraction, and that depolarization of the resting membrane potential depended on the phase, amplitude and speed of the applied stretch. The amplitude may also modulate the ion selectivity of stretch-activated channels. This combination of the carbon fiber technique with fluorescence measurement could represent a powerful tool for clarifying MEF at the cellular level.     

Mechanical unfolding of cardiac myosin binding protein-C by atomic force microscopy

Cardiac myosin-binding protein-C (cMyBP-C) is a thick-filament-associated protein that performs regulatory and structural roles within cardiac sarcomeres. It is a member of the immunoglobulin (Ig) superfamily of proteins consisting of eight Ig- and three fibronectin (FNIII)-like domains, along with a unique regulatory sequence referred to as the M-domain, whose structure is unknown. Domains near the C-terminus of cMyBP-C bind tightly to myosin and mediate the association of cMyBP-C with thick (myosin-containing) filaments, whereas N-terminal domains, including the regulatory M-domain, bind reversibly to myosin S2 and/or actin. The ability of MyBP-C to bind to both myosin and actin raises the possibility that cMyBP-C cross-links myosin molecules within the thick filament and/or cross-links myosin and thin (actin-containing) filaments together. In either scenario, cMyBP-C could be under mechanical strain. However, the physical properties of cMyBP-C and its behavior under load are completely unknown. Here, we investigated the mechanical properties of recombinant baculovirus-expressed cMyBP-C using atomic force microscopy to assess the stability of individual cMyBP-C molecules in response to stretch. Force-extension curves showed the presence of long extensible segment(s) that became stretched before the unfolding of individual Ig and FNIII domains, which were evident as sawtooth peaks in force spectra. The forces required to unfold the Ig/FNIII domains at a stretch rate of 500 nm/s increased monotonically from ∼30 to ∼150 pN, suggesting a mechanical hierarchy among the different Ig/FNIII domains. Additional experiments using smaller recombinant proteins showed that the regulatory M-domain lacks significant secondary or tertiary structure and is likely an intrinsically disordered region of cMyBP-C. Together, these data indicate that cMyBP-C exhibits complex mechanical behavior under load and contains multiple domains with distinct mechanical properties.     

How should the optical tweezers experiment be used to characterize the red blood cell membrane mechanics?

Stretching red blood cells using optical tweezers is a way to characterize the mechanical properties of their membrane by measuring the size of the cell in the direction of the stretching (axial diameter) and perpendicularly (transverse diameter). Recently, such data have been used in numerous publications to validate solvers dedicated to the computation of red blood cell dynamics under flow. In the present study, different mechanical models are used to simulate the stretching of red blood cells by optical tweezers. Results first show that the mechanical moduli of the membranes have to be adjusted as a function of the model used. In addition, by assessing the area dilation of the cells, the axial and transverse diameters measured in optical tweezers experiments are found to be insufficient to discriminate between models relevant to red blood cells or not. At last, it is shown that other quantities such as the height or the profile of the cell should be preferred for validation purposes since they are more sensitive to the membrane model.     

Systolic axial artery length reduction: an overlooked phenomenon in vivo

To demonstrate axial artery motion during the cardiac cycle, the common carotid arteries (CCA) of 10 pigs were exposed and equipped with piezoelectric crystals sutured onto the artery as axial position detectors. An echo-tracking system was used to simultaneously measure the CCA diameter. For each animal, data for pressure, length, and diameter were collected at a frequency of 457 Hz. At a mean pulse pressure of 33 +/- 8 mmHg, the mean systolodiastolic length difference was 0.3 +/- 0.01 mm for a mean arterial segment of 11.35 +/- 1.25 mm. Systolic and diastolic diameters were 4.1 +/- 0.3 and 3.9 +/- 0.2 mm, respectively. The examined CCA segment displayed a mean axial systolic shortening of 2.7%. This study clearly demonstrates, for the first time, that the length of a segment of the CCA changes during the cardiac cycle and that this movement is inversely correlated with pulse pressure. It is also apparent that the segmental axial strain is significantly smaller than the diameter variation during the cardiac cycle and that the impact of the axial strain for compliance computation should be further evaluated.     

Mechanical anisotropy of inflated elastic tissue from the pig aorta

Uniaxial and biaxial mechanical properties of purified elastic tissue from the proximal thoracic aorta were studied to understand physiological load distributions within the arterial wall. Stress–strain behaviour was non-linear in uniaxial and inflation tests. Elastic tissue was 40% stiffer in the circumferential direction compared to axial in uniaxial tests and～100% stiffer in vessels at an axial stretch ratio of 1.2 or 1.3 and inflated to physiological pressure. Poisson’s ratio v_θz averaged 0.2 and v_zθ increased with circumferential stretch from ～0.2 to ～0.4. Axial stretch had little impact on circumferential behaviour. In intact (unpurified) vessels at constant length, axial forces decreased with pressure at low axial stretches but remained constant at higher stretches. Such a constant axial force is characteristic of incrementally isotropic arteries at their in vivo dimensions. In purified elastic tissue, force decreased with pressure at all axial strains, showing no trend towards isotropy. Analysis of the force–length–pressure data indicated a vessel with v_θz≈0.2 would stretch axially 2–4% with the cardiac pulse yet maintain constant axial force. We compared the ability of 4 mathematical models to predict the pressure-circumferential stretch behaviour of tethered, purified elastic tissue. Models that assumed isotropy could not predict the stretch at zero pressure. The neo-Hookean model overestimated the non-linearity of the response and two non-linear models underestimated it. A model incorporating contributions from orthogonal fibres captured the non-linearity but not the zero-pressure response. Models incorporating anisotropy and non-linearity should better predict the mechanical behaviour of elastic tissue of the proximal thoracic aorta.