Model of mechanical alternans in the mammalian myocardium

A model is proposed to elucidate the cause and mechanism of mechanical alternans in cardiac muscle in terms of discrete calcium movements. Mechanical alternans, the cause of which lies within the borders of excitation-contraction-coupling (ECC), is analyzed. In this case, the "input" of the ECC system (the action potentials and intervals) is constant while the "output" (contractile force) oscillates between two constant values, indicating that the system has a "memory" with two "internal states". It is proposed that these two "states" are associated with a part of the sarcoplasmic reticulum ("releasable terminal") containing the readily releasable calcium. A mechanism of "calcium-concentration-dependent threshold" is suggested to govern the "release function", i.e. the release of calcium from the "releasable terminal" to the myofilaments. The "release function" is analyzed in both the linear and the non-linear cases and its implication on the initiation of sustained and transient mechanical alternans are described. The dependence of mechanical alternans on a disturbance is also explained. The model response resembles the experimental observations of mechanical alternans in mammalian myocardium in the following manners: abrupt transition from low to high heart rates, slow progressive acceleration of rate, variations in persistence at subthreshold rates, effect of premature and delayed beat following the small and large beats, restitution curves, and transient mechanical alternans initiated by a delayed beat.     

Effects of myocardial constraint on the passive mechanical behaviors of the coronary vessel wall

The large epicardial coronary arteries and veins span the surface of the heart and gradually penetrate into the myocardium. It has recently been shown that remodeling of the epicardial veins in response to pressure overload strongly depends on the degree of myocardial support. The nontethered regions of the vessel wall show significant intimal hyperplasia compared with the tethered regions. Our hypothesis is that such circumferentially nonuniform structural adaptation in the vessel wall is due to nonuniform wall stress and strain. Transmural stress and strain are significantly influenced by the support of the surrounding myocardial tissue, which significantly limits distension of the vessel. In this finite-element study, we modeled the nonuniform support by embedding the left anterior descending artery into the myocardium to different depths and analyzed deformation and strain in the vessel wall. Circumferential wall strain was much higher in the untethered than tethered region at physiological pressure. On the basis of the hypothesis that elevated wall strain is the stimulus for remodeling, the simulation results suggest that large epicardial coronary vessels have a greater tendency to become thicker in the absence of myocardial constraint. This study provides a mechanical basis for understanding the local growth and remodeling of vessels subjected to various degrees of surrounding tissue.     

The effect of strain rate on the mechanical properties of human cortical bone

Bone mechanical properties are typically evaluated at relatively low strain rates. However, the strain rate related to traumatic failure is likely to be orders of magnitude higher and this higher strain rate is likely to affect the mechanical properties. Previous work reporting on the effect of strain rate on the mechanical properties of bone predominantly used nonhuman bone. In the work reported here, the effect of strain rate on the tensile and compressive properties of human bone was investigated. Human femoral cortical bone was tested longitudinally at strain rates ranging between 0.14-29.1 s(-1) in compression and 0.08-17 s(-1) in tension. Young's modulus generally increased, across this strain rate range, for both tension and compression. Strength and strain (at maximum load) increased slightly in compression and decreased (for strain rates beyond 1 s(-1)) in tension. Stress and strain at yield decreased (for strain rates beyond 1 s(-1)) for both tension and compression. In general, there seemed to be a relatively simple linear relationship between yield properties and strain rate, but the relationships between postyield properties and strain rate were more complicated and indicated that strain rate has a stronger effect on postyield deformation than on initiation of yielding. The behavior seen in compression is broadly in agreement with past literature, while the behavior observed in tension may be explained by a ductile to brittle transition of bone at moderate to high strain rates.     

Inhomogeneity in the response to mechanical stimulation: cardiac muscle function and gene expression

Mechanical stimulation has important consequences for myocardial function. However, this stimulation and the response to it, is not uniform. The right ventricle is thinner walled and operates at lower pressure than the left ventricle. Within the ventricles, differences in the orientation of myocardial fibres exist. These differences produce inhomogeneity in the stress and strain between and across the ventricles. Possibly as a result of these variations in mechanical stimulation, there are well characterised inhomogeneities in gene expression and protein function within the ventricular myocardium, for example in the transient outward K+ current and its associated Kv channels. Perhaps not surprisingly, it is becoming apparent that gradients of expression and function exist for proteins that are intimately involved in the response to mechanical stimulation in the heart, for example in the left ventricle of the rat there is a transmural gradient in mRNA and current density of the mechanosensitive two-pore domain K+ channel TREK-1 (ENDO>EPI). In healthy hearts it is assumed that these gradients are important for normal function and therefore that their disruption in diseased myocardium is involved in the dysfunction that occurs.     

Molecular dynamics simulation studies of mechanical properties of different carbon nanotube systems

Various mechanical properties of single-walled carbon nanotubes (SWCNT) and double-walled carbon nanotubes (DWCNT) are evaluated using molecular dynamics (MD) simulations. A tensioning process was first performed on a SWCNT whose interaction is based on the Brenner’s ‘second generation’ potential under varying length–diameter ratios and strain rates, in order to understand the SWCNT’s behaviour under axial tension. The results showed an increase in the SWCNT’s ultimate tensile strength and a decrease in critical strain given the conditions of increasing strain rate and a decreasing length–diameter ratio. Comparison was done with previous studies on axial tensioning of SWCNT to validate the results obtained from the set-up, based on the general stress–strain relationship and key mechanical properties such as the strain at failure and the Young’s modulus. A DWCNT was then constructed, and Lennard-Jones ‘12-6’ potential was used to describe the energy present between the nanotube layers. Extraction of the inner tube in a DWCNT was performed using two inner wall tubings of different diameters to draw comparison to the energies needed to separate fully the outer and inner tubing. Finally, a bending test was performed on two DWCNTs with different intertube separations. Insights into the entire bending process were obtained through analyses of the variations in the strain energy characteristic of the surface atoms near the bending site, as the DWCNT is gradually bent until failure.     

Novel approach to studying relationship of 3D structure and mechanical properties of biological tissue

We present here a novel approach to studying the relationship of three-dimensional structural organization of myocardial tissue as an example of biological tissue and its mechanical properties. The approach consists in correlation of image series of the preparation internal structure obtained with a confocal laser scanning microscope LSM-710 and registration of tension-deformation properties of the preparation. The spatial structure images of the segment of rat right ventricular wall at different stretching levels have been obtained. It is shown that the proposed approach allows one to study in more detail the mechanisms of tension and strain development in living biological tissues.     

Action potential duration dispersion and alternans in simulated heterogeneous cardiac tissue with a structural barrier

Structural barriers to wave propagation in cardiac tissue are associated with a decreased threshold for repolarization alternans both experimentally and clinically. Using computer simulations, we investigated the effects of a structural barrier on the onset of spatially concordant and discordant alternans. We used two-dimensional tissue geometry with heterogeneity in selected potassium conductances to mimic known apex-base gradients. Although we found that the actual onset of alternans was similar with and without the structural barrier, the increase in alternans magnitude with faster pacing was steeper with the barrier--giving the appearance of an earlier alternans onset in its presence. This is consistent with both experimental structural barrier findings and the clinical observation of T-wave alternans occurring at slower pacing rates in patients with structural heart disease. In ionically homogeneous tissue, discordant alternans induced by the presence of the structural barrier arose at intermediate pacing rates due to a source-sink mismatch behind the barrier. In heterogeneous tissue, discordant alternans occurred during fast pacing due to a barrier-induced decoupling of tissue with different restitution properties. Our results demonstrate a causal relationship between the presence of a structural barrier and increased alternans magnitude and action potential duration dispersion, which may contribute to why patients with structural heart disease are at higher risk for ventricular tachyarrhythmias.     

Compressive and tensile mechanical properties of the porcine nasal septum

The expanding nasal septal cartilage is believed to create a force that powers midfacial growth. In addition, the nasal septum is postulated to act as a mechanical strut that prevents the structural collapse of the face under masticatory loads. Both roles imply that the septum is subject to complex biomechanical loads during growth and mastication. The purpose of this study was to measure the mechanical properties of the nasal septum to determine (1) whether the cartilage is mechanically capable of playing an active role in midfacial growth and in maintaining facial structural integrity and (2) if regional variation in mechanical properties is present that could support any of the postulated loading regimens. Porcine septal samples were loaded along the horizontal or vertical axes in compression and tension, using different loading rates that approximate the in vivo situation. Samples were loaded in random order to predefined strain points (2–10%) and strain was held for 30 or 120 seconds while relaxation stress was measured. Subsequently, samples were loaded until failure. Stiffness, relaxation stress and ultimate stress and strain were recorded. Results showed that the septum was stiffer, stronger and displayed a greater drop in relaxation stress in compression compared to tension. Under compression, the septum displayed non-linear behavior with greater stiffness and stress relaxation under faster loading rates and higher strain levels. Under tension, stiffness was not affected by strain level. Although regional variation was present, it did not strongly support any of the suggested loading patterns. Overall, results suggest that the septum might be mechanically capable of playing an active role in midfacial growth as evidenced by increased compressive residual stress with decreased loading rates. However, the low stiffness of the septum compared to surrounding bone does not support a strut role. The relatively low stiffness combined with high stress relaxation under fast loading rates suggests that the nasal septum is a stress dampener, helping to absorb and dissipate loads generated during mastication.     

Electrical and mechanical activity of isoproterenol-damaged frog heart

The electrical and mechanical activities of myocardial strips from Rana pipiens were studied in the steady state at various stimulation frequencies and after a period of rest. The temperature of the bath was varied between + 12 and 35 degrees C. Normal myocardium was compared with that damaged by isoproterenol (ISO). The percentage change of action potential durations (APD50) and isometric force (P) was similar in ISO-damaged and control hearts at various bath temperatures with steady state stimulation rates between 20 and 100/min. At low stimulation rates (3-6/min) the prolongation of the action potential (AP) was more pronounced and the P-decrease was less in ISO-damaged myocardium compared to controls. These differences became more apparent at low bath temperatures. After 10 min of rest, APD50-90 was significantly prolonged in ISO-damaged heart and P was increased by a factor of 2 compared to controls (stimulation rate 20/min). Steady state values, on the other hand, were nearly the same in both groups. These findings are interpreted as indicating a temperature or ISO-dependent increase of electrogenic trans-sarcolemmal Ca2+-uptake during low frequency, or post-rest stimulation, either directly by an increase of the slow inward current (Isi), or indirectly by decreased K+-permeabilities.     

Use of the chicken heart in a Langendorff preparation

Hearts isolated from healthy chickens were perfused with oxygenated Krebs-Henseleit buffer. Balloons were inserted into the left ventricle, filled with saline and attached to a pressure transducer for measuring left ventricular pressures. A bipolar electrogram was obtained between the atria and ventricles. Hearts so perfused manifested mechanical alternans for approximately 15 minutes, after which they sustained a regular sinus rhythm without mechanical alternans for at least 60 minutes. By infusing 0.1 ml increments of saline into the balloon located within the ventricle, Frank-Starling curves could be generated. This preparation has potential for use in pharmacologic evaluations.     

Influence of temperature and cyanide on electrical and mechanical activities of isoproterenol-damaged frog heart

The electrical and mechanical activities of myocardial strips from Rana pipiens treated with isoproterenol (ISO) were studied during cyanide hypoxia at different bath temperatures (12, 25 and 35 degrees C). In normal myocardium at 12 degrees C, the action potential duration (APD) was almost unchanged but the isometric force (P) was reduced to about 60% after 30 min in 3 mmol/l NaCN. At 25 degrees C, APD and P decreased to about 80 and 60%, respectively, after exposure to cyanide for 30 min. At 35 degrees C, a fast decrease of APD (to about 30%) and P (to about 10%) was seen within 30 min. In all cases, washout of cyanide interactions was possible. Large effects occurred when ISO-damaged myocardium was exposed to cyanide. During the initial 30 min of CN-treatment, APD and P were significantly reduced in the whole temperature range between 12 and 35 degrees C, when compared with controls. When the cyanide exposure times were long enough, all preparations developed contracture. Increase of the temperature and/or ISO-pretreatment shortened the time-course for resting tension increase. The effects of cyanide on APD and resting tension (RT) were strongly correlated and presumably a result of a cyanide-induced rise of the intracellular free calcium concentration (Ca2+i).     

Rate-independent characteristics of an arthroscopically implantable force probe in the human achilles tendon

The effect of loading rate on specimen calibration was investigated for an implantable force sensor of the two-point loading variety. This variety of sensor incorporates a strain gage to measure the compressive load applied to the sensor due to tensile loading in a soft tissue specimen. The Achilles tendon in each of four human cadaveric lower extremities was instrumented with a force sensor and then loaded in tension using a materials testing machine. Each specimen was tensile tested at three different displacement rates, 0.25, 2.5 and 12.7 cm s(-1), corresponding with mean loading rates of 33.8, 513.2, and 2838.6 N s(-1), respectively. A calibration curve relating the force sensor signal and applied tendon tension was generated for each specimen/ displacement rate combination. For each specimen, calibration curves were compared by calculating an RMS error for the entire data set (eRMS = 1.6% of the full load value) and a coefficient of determination, R2, of a curve fit through all of the data (R2 = 99.6%). Over the range of rates tested, no measurable change in sensor sensitivity due to loading rate was observed. Hysteresis for all displacement rates was on the order of 2.4%.     

The mechanical properties of rat spinal cord in vitro

Freshly excised rat spinal cords were tested in uniaxial tension, in vitro, at strain rates ranging from 0.002 to 0.2 s-1. Stress relaxation tests were performed for a range of strains from 2% to 5%, with the relaxation behaviour being recorded for a period of at least 30 min. Samples exhibited a characteristic "J" shaped non-linear stress-strain response, with stiffness increasing with applied strain. The cords were labelled with rows of small markers and the uniaxial tension tests were recorded via video. Subsequent image analysis enabled the distribution of strain on the cord surface to be determined. Viscoelastic models were developed to model the mechanical behaviour of the specimens and were found to adequately describe the material behaviour.     

An extensometer for global measurement of bone strain suitable for use in vivo in humans

An axial extensometer able to measure global bone strain magnitudes and rates encountered during physiological activity, and suitable for use in vivo in human subjects, is described. The extensometer uses paired capacitive sensors mounted to intraosseus pins and allows measurement of strain due to bending in the plane of the extensometer as well as uniaxial compression or tension. Data are presented for validation of the device against a surface-mounted strain gage in an acrylic specimen under dynamic four-point bending, with square wave and sinusoidal loading inputs up to 1500 mu epsilon and 20 Hz, representative of physiological strain magnitudes and frequencies. Pearson's correlation coefficient (r) between extensometer and strain gage ranged from 0.960 to 0.999. Mean differences between extensometer and strain gage ranged up to 15.3 mu epsilon. Errors in the extensometer output were directly proportional to the degree of bending that occurs in the specimen, however, these errors were predictable and less than 1 mu epsilon for the loading regime studied. The device is capable of tracking strain rates in excess of 90,000 mu epsilon/s.     

Disrupted Calcium Release as a Mechanism for Atrial Alternans Associated with Human Atrial Fibrillation

Atrial fibrillation (AF) is the most common cardiac arrhythmia, but our knowledge of the arrhythmogenic substrate is incomplete. Alternans, the beat-to-beat alternation in the shape of cardiac electrical signals, typically occurs at fast heart rates and leads to arrhythmia. However, atrial alternans have been observed at slower pacing rates in AF patients than in controls, suggesting that increased vulnerability to arrhythmia in AF patients may be due to the proarrythmic influence of alternans at these slower rates. As such, alternans may present a useful therapeutic target for the treatment and prevention of AF, but the mechanism underlying alternans occurrence in AF patients at heart rates near rest is unknown. The goal of this study was to determine how cellular changes that occur in human AF affect the appearance of alternans at heart rates near rest. To achieve this, we developed a computational model of human atrial tissue incorporating electrophysiological remodeling associated with chronic AF (cAF) and performed parameter sensitivity analysis of ionic model parameters to determine which cellular changes led to alternans. Of the 20 parameters tested, only decreasing the ryanodine receptor (RyR) inactivation rate constant (ki_Ca) produced action potential duration (APD) alternans seen clinically at slower pacing rates. Using single-cell clamps of voltage, fluxes, and state variables, we determined that alternans onset was Ca²⁺-driven rather than voltage-driven and occurred as a result of decreased RyR inactivation which led to increased steepness of the sarcoplasmic reticulum (SR) Ca²⁺ release slope. Iterated map analysis revealed that because SR Ca²⁺ uptake efficiency was much higher in control atrial cells than in cAF cells, drastic reductions in ki_Ca were required to produce alternans at comparable pacing rates in control atrial cells. These findings suggest that RyR kinetics may play a critical role in altered Ca²⁺ homeostasis which drives proarrhythmic APD alternans in patients with AF.     

Biaxial mechanical testing of posterior sclera using high-resolution ultrasound speckle tracking for strain measurements

This study aimed to characterize the mechanical responses of the sclera, the white outer coat of the eye, under equal-biaxial loading with unrestricted shear. An ultrasound speckle tracking technique was used to measure tissue deformation through sample thickness, expanding the capabilities of surface strain techniques. Eight porcine scleral samples were tested within 72 h postmortem  . High resolution ultrasound scans of scleral cross-sections along the two loading axes were acquired at 25 consecutive biaxial load levels. An additional repeat of the biaxial loading cycle was performed to measure a third normal strain emulating a strain gage rosette for calculating the in-plane shear. The repeatability of the strain measurements during identical biaxial ramps was evaluated. A correlation-based ultrasound speckle tracking algorithm was used to compute the displacement field and determine the distributive strains in the sample cross-sections. A Fung type constitutive model including a shear term was used to determine the material constants of each individual specimen by fitting the model parameters to the experimental stress–strain data. A non-linear stress–strain response was observed in all samples. The meridian direction had significantly larger strains than that of the circumferential direction during equal-biaxial loadings (P's<0.05$P\text{'}s<0.05$). The stiffness along the two directions was also significantly different (P=0.02) but highly correlated (R²=0.8). These results showed that the mechanical properties of the porcine sclera were nonlinear and anisotropic under biaxial loading. This work has also demonstrated the feasibility of using ultrasound speckle tracking for strain measurements during mechanical testing.     

On the biaxial mechanical properties of the layers of the aortic valve leaflet

All existing constitutive models for heart valve leaflet tissues either assume a uniform transmural stress distribution or utilize a membrane tension formulation. Both approaches ignore layer specific mechanical contributions and the implicit nonuniformity of the transmural stress distribution. To begin to address these limitations, we conducted novel studies to quantify the biaxial mechanical behavior of the two structurally distinct, load bearing aortic valve (AV) leaflet layers: the fibrosa and ventricularis. Strip biaxial tests, with extremely sensitive force sensing capabilities, were further utilized to determine the mechanical behavior of the separated ventricularis layer at very low stress levels. Results indicated that both layers exhibited very different nonlinear, highly anisotropic mechanical behaviors. While the leaflet tissue mechanical response was dominated by the fibrosa layer, the ventricularis contributed double the amount of the fibrosa to the total radial tension and experienced four times the stress level. The strip biaxial test results further indicated that the ventricularis exhibited substantial anisotropic mechanical properties at very low stress levels. This result suggested that for all strain levels, the ventricularis layer is dominated by circumferentially oriented collagen fibers, and the initial loading phase of this layer cannot be modeled as an isotropic material. Histological-based thickness measurements indicated that the fibrosa and ventricularis constitute 41% and 29% of the total layer thickness, respectively. Moreover, the extensive network of interlayer connections and identical strains under biaxial loading in the intact state suggests that these layers are tightly bonded. In addition to advancing our knowledge of the subtle but important mechanical properties of the AV leaflet, this study provided a comprehensive database required for the development of a true 3D stress constitutive model for the native AV leaflet.     

Torsional motion of the left ventricle does not affect ventricular fluid dynamics of both foetal and adult hearts

Left ventricular torsion is caused by shortening and relaxation of the helical fibres in the myocardium, and is thought to be an optimal configuration for minimizing myocardial tissue strains. Characteristics of torsional motion has also been proposed to be markers for cardiac dysfunction. However, its effects on fluid and energy dynamics in the left ventricle have not been comprehensively investigated. To investigate this, we performed image-based flow simulations on five healthy adult porcine and two healthy human foetal left ventricles (representing two different length scales) at different degrees of torsional motions. In the adult porcine ventricles, cardiac features such as papillary muscles and mitral valves, and cardiac conditions such as myocardial infarctions, were also included to investigate the effect of twist. The results showed that, for all conditions investigated, ventricular torsional motion caused minimal changes to flow patterns, and consistently accounted for less than 2% of the energy losses, wall shear stresses, and ejection momentum energy. In contrast, physiological characteristics such as chamber size, stroke volume and heart rate had a much greater influence on flow patterns and energy dynamics. The results thus suggested that it might not be necessary to model the torsional motion to study the flow and energy dynamics in left ventricles.     

Cardiac fibroblasts and the mechano-electric feedback mechanism in healthy and diseased hearts

Cardiac arrhythmia is a serious clinical condition, which is frequently associated with abnormalities of mechanical loading and changes in wall tension of the heart. Recent novel findings suggest that fibroblasts may function as mechano-electric transducers in healthy and diseased hearts. Cardiac fibroblasts are electrically non-excitable cells that respond to spontaneous contractions of the myocardium with rhythmical changes of their resting membrane potential. This phenomenon is referred to as mechanically induced potential (MIP) and has been implicated in the mechano-electric feedback mechanism of the heart. Mechano-electric feedback is thought to adjust the frequency of spontaneous myocardial contractions to changes in wall tension, which may result from variable filling pressure. Electrophysiological recordings of single atrial fibroblasts indicate that mechanical compression of the cells may activate a non-selective cation conductance leading to depolarisation of the membrane potential. Reduced amplitudes of MIPs due to pharmacological disruption of F-actin and tubulin suggest a role for the cytoskeleton in the mechano-electric signal transduction process. Enhanced sensitivity of the membrane potential of the fibroblasts to mechanical stretch after myocardial infarction correlates with depression of heart rates. It is assumed that altered electrical function of cardiac fibroblasts may contribute to the increased risk of post-infarct arrhythmia.     

Thermoelastic properties of uniaxially deformed lung strips

We examined the temperature dependence of small degassed hamster lung strip mechanics to develop insights into the molecular basis of lung elasticity. Quasi-static length-tension curves of adapted lung strips were generated at 10, 23, 37, 50, and 80 degrees C; quasi-static tension-temperature plots (QSTT) at strains of 0.5, 0.75, and 1.0 were then formulated. Static tension-temperature (STT) plots at strain 1 were independently generated from other strips. Stress relaxation was evaluated as a function of temperature at different strains; hysteresis ratio was calculated as a parameter of mechanical efficiency. Between 23 and 37 degrees C, the slopes of the QSTT plots at the different strains were close to zero. The slope of the STT plot was slightly positive, indicating that the tension developed by a stretched strip was primarily due to entropic changes with length, suggesting that strips behave like rubber polymers near physiological temperature. Between 10 and 23 degrees C, the slope of the QSTT curve was zero at the two lowest strains but was negative at strain 1; and slope of the STT curve was zero at strain 1. These data indicated that collagen fiber and possibly glycosaminoglycan function was abnormally affected at 10 degrees C. Between 50 and 80 degrees C at strain 1, the slopes of both the QSTT and STT plots at all strains were positive. These data suggested that elastic fiber function was altered between 50 and 80 degrees C such that both internal energetic and entropic contributions to the tension were changed. Stress relaxation and hysteresis data were consistent with these findings.(ABSTRACT TRUNCATED AT 250 WORDS)