Myocardial function defined by strain rate and strain during alterations in inotropic states and heart rate

For porcine myocardium, ultrasonic regional deformation parameters, systolic strain (epsilon(sys)) and peak systolic strain rate (SR(sys)), were compared with stroke volume (SV) and contractility [contractility index (CI)] measured as the ratio of end-systolic strain to end-systolic wall stress. Heart rate (HR) and contractility were varied by atrial pacing (AP = 120-180 beats/min, n = 7), incremental dobutamine infusion (DI = 2.5-20 microg. kg(-1). min(-1), n = 7), or continuous esmolol infusion (0.5 mg. kg(-1). min(-1)) + subsequent pacing (120-180 beats/min) (EI group, n = 6). Baseline SR(sys) and epsilon(sys) averaged 5.0 +/- 0.4 s(-1) and 60 +/- 4%. SR(sys) and CI increased linearly with DI (20 microg. kg(-1). min(-1); SR(sys) = 9.9 +/- 0.7 s(-1), P < 0.0001) and decreased with EI (SR(sys) = 3.4 +/- 0.1 s(-1), P < 0.01). During pacing, SR(sys) and CI remained unchanged in the AP and EI groups. During DI, epsilon(sys) and SV initially increased (5 microg. kg(-1). min(-1); epsilon(sys) = 77 +/- 6%, P < 0.01) and then progressively returned to baseline. During EI, SV and epsilon(sys) decreased (epsilon(sys) = 38 +/- 2%, P < 0.001). Pacing also decreased SV and epsilon(sys) in the AP (180 beats/min; epsilon(sys) = 36 +/- 2%, P < 0.001) and EI groups (180 beats/min; epsilon(sys) = 25 +/- 3%, P < 0.001). Thus, for normal myocardium, SR(sys) reflects regional contractile function (being relatively independent of HR), whereas epsilon(sys) reflects changes in SV.     

Gradients of strain and strain rate in the hollow muscular organs of soft-bodied animals

The cylindrical shape of soft-bodied invertebrates is well suited to functions in skeletal support and locomotion, but may result in a previously unrecognized cost—large non-uniformities in muscle strain and strain rate among the circular muscle fibres of the body wall. We investigated such gradients of strain and strain rate in the mantle of eight long-finned squid Doryteuthis pealeii and two oval squid Sepioteuthis lessoniana. Transmural gradients of circumferential strain were present during all jets (n = 312); i.e. for a given change in the circumference of the outer surface of the mantle, the inner surface experienced a greater proportional change. The magnitude of the difference increased with the amplitude of the mantle movement, with circular muscle fibres at the inner surface of the mantle experiencing a total range of strains up to 1.45 times greater than fibres at the outer surface during vigorous jets. Differences in strain rate between the circular fibres near the inner versus the outer surface of the mantle were also present in all jets, with the greatest differences occurring during vigorous jetting. The transmural gradients of circumferential strain and strain rate we describe probably apply not only to squids and other coleoid cephalopods, but also to diverse soft-bodied invertebrates with hollow cylindrical or conical bodies and muscular organs.     

Compressive strain rate sensitivity of ballistic gelatin

Gelatin is a popular tissue simulant used in biomedical applications. The uniaxial compressive stress–strain response of gelatin was determined at a range of strain rates. In the quasistatic regime, gelatin strength remained relatively constant. With increase in loading rate, the compressive strength increased from 3 kPa at a strain rate of around 0.0013/s to 6 MPa at a strain rate of around 3200/s. This dramatic increase in strength of gelatin at high rates is attributed to its shear-thickening behavior and is argued on the basis of hydrocluster formation mechanism and differences in internal energy dissipation mechanism under static and dynamic loading.     

Effect of strain rate on the fracture behaviour of skin

The effect of strain rate on the stress-strain behaviour of skin is studied. It is observed that the plastic set in the skin is dependent on strain rate. The scanning electron micrographs of the fractured skin sample shows thicker fibrils and thinner one at low strain rates. The plastic flow is clearly brought out in the stress-strain curves at different strain rates. The stress relaxation behaviour at any given strain is clearly brought out in the 3-dimensional plot.     

The relative value of strain and strain rate for defining intrinsic myocardial function

It is well accepted that strain and strain rate deformation parameters are not only a measure of intrinsic myocardial contractility but are also influenced by changes in cardiac load and structure. To date, no information is available on the relative importance of these confounders. This study was designed to investigate how strain and strain rate, measured by Doppler echocardiography, relate to the individual factors that determine cardiac performance. Echocardiographic and conductance measurements were simultaneously performed in mice in which individual determinants of cardiac performance were mechanically and/or pharmacologically modulated. A multivariable analysis was performed with radial and circumferential strains and peak systolic radial and circumferential strain rates as dependent parameters and preload recruitable stroke work (PRSW), arterial elastance (E(a)), end-diastolic pressure, and left ventricular myocardial volume (LVMV) as independent factors representing myocardial contractility, afterload, preload, and myocardial volume, respectively. Radial strain was most influenced by E(a) (β = -0.58, R(2) = 0.34), whereas circumferential strain was strongly associated with E(a) and moderately with LVMV (β = 0.79 and -0.52, respectively, R(2) = 0.54). Radial strain rate was related to both PRSW and LVMV (β = 0.79 and -0.62, respectively, R(2) = 0.50), whereas circumferential strain rate showed a prominent correlation only with PRSW (β = -0.61, R(2) = 0.51). In conclusion, strain (both radial and circumferential) is not a good surrogate measure of intrinsic myocardial contractility unless the strong confounding influence of afterload is considered. Strain rate is a more robust measure of contractility that is less influenced by changes in cardiac load and structure. Thus, peak systolic strain rate is the more relevant parameter to assess myocardial contractile function noninvasively.     

High strain rate response of rabbit femur bones

Strain rate dependence of the mechanical response of hard tissues has led to a keen interest in their dynamic properties. The current study attempts to understand the high strain rate characteristics of rabbit femur bones. The testing was conducted using a split-Hopkinson pressure bar equipped with a high speed imaging system to capture the fracture patterns. The bones were also characterized under quasi-static compression to enable comparison with the high strain rate results. The quasi-static compressive moduli of the epiphyseal and diaphyseal regions were measured to be in the range of 2–3 and 5–7 GPa, respectively. Under high strain rate loading conditions the modulus is observed to increase with strain rate and attains values as high as 15 GPa for epiphyseal and 30 GPa for diaphyseal regions of the femur. The strength at high strain rate was measured to be about twice the quasi-static strength value. A large number of small cracks initiated on the specimen surface close to the incident bar. Coalescence of crack branches leading to fewer large cracks resulted in specimen fragmentation. In comparison, the quasi-static failure was due to shear cracking.     

Evaluation of the influence of strain rate on Colles' fracture load

Colles' fracture, a transverse fracture of the distal radius bone, is one of the most frequently observed osteoporotic fractures resulting from low energy or traumatic events, associated with low and high strain rates, respectively. Although experimental studies on Colles' fracture were carried out at various loading rates ranging from static to impact loadings, there is no systematic study in the literature that isolates the influence of strain rate on Colles' fracture load. In order to provide a better understanding of fracture risk, the current study combines experimental material property measurements under varying strain rates with computational modeling and presents new information on the effect of strain rate on Colles' fracture. The simulation results showed that Colles' fracture load decreased with increasing strain rate with a steeper change in lower strain rates. Specifically, strain rate values (0.29s(-1)) associated with controlled falling without fracture corresponded to a 3.7% reduction in the fracture load. On the other hand, the reduction in the fracture load was 34% for strain rate of 3.7s(-1) reported in fracture inducing impact cadaver experiments. Further increase in the strain rate up to 18s(-1) led to an additional 22% reduction. The most drastic reduction in fracture load occurs at strain rates corresponding to the transition from controlled to impact falling. These results are particularly important for the improvement of fracture risk assessment in the elderly because they identify a critical range of loading rates (10-50mm/s) that can dramatically increase the risk of Colles' fracture.     

Equibiaxial strain and strain rate stimulate early activation of G proteins in cardiac fibroblasts

Cardiacfibroblasts are responsible for the production of the extracellularmatrix of the heart, with alterations of fibroblast function implicatedin myocardial infarction and cardiac hypertrophy. Here the role ofheterotrimeric GTP-binding proteins (G proteins) in themechanotransduction of strain in rat cardiac fibroblasts wasinvestigated. Cells in an equibiaxial stretch device were incubatedwith the photoreactive GTP analog azidoanalido[-³²P]GTP (AAGTP)and were subjected to various regimens of strain. Autoradiographicanalysis showed a 42-kDa protein labeled for cells exposed to 12 cyclesof 3% strain or 6 cycles of 6% strain over 60 s (strain rate of1.2%/s), whereas 6 cycles of 3% strain (0.6%/s) elicited nomeasurable response. To further investigate the role of strain rate, asingle 6% cycle over 10 or 60 s (1.2% and 0.2%/s, respectively) wasapplied, with the more rapid cycle stimulating AAGTP binding, whereasthe lower strain rate showed no response. In cells subjected to asingle 6% cycle/10 s, immunoprecipitation identified the AAGTP-labeled42-kDa band as the G protein subunits G_q andG_i1. These results demonstratethat G protein activation represents one of the earlymechanotransduction events in cardiac fibroblasts subjected tomechanical strain, with the rate at which the strain is appliedmodulating this response.

     

Method and strain rate dependence of Achilles tendon stiffness

Tendon stiffness is calculated by dividing changes in tendon force by tendon elongation. For this purpose, participants are commonly asked to perform a maximal muscle contraction (“active” method). Alternatively tendon elongation can be achieved by means of a passive joint rotation (“passive” method). The purpose of this study was to compare Achilles tendon stiffness obtained from both methods across different tendon strain rates. Twenty adults performed a series of ramped maximum isometric plantarflexions of different durations. Passive ankle rotations of different angular velocities were also performed. Achilles tendon stiffness was obtained from a combination of motion analysis, isokinetic dynamometry and ultrasonography and compared across methods at three strain rates. At all strain rates, tendon stiffness obtained from the active method was 6% greater compared to the passive method. In spite of this systematic bias, there was good agreement between the methods. Intraclass correlation coefficients were greater than 0.98, and more than 95% of data points fell into the 95% confidence intervals. This agreement will be acceptable in many research contexts. We also found a linear increase in tendon stiffness with increasing strain rate, which must be taken into consideration when interpreting or reporting tendon stiffness.     

MRI-based strain and strain rate analysis of left ventricle: a modified hierarchical transformation model

Background

Different from other indicators of cardiac function, such as ejection fraction and transmitral early diastolic velocity, myocardial strain is promising to capture subtle alterations that result from early diseases of the myocardium. In order to extract the left ventricle (LV) myocardial strain and strain rate from cardiac cine-MRI, a modified hierarchical transformation model was proposed.

Methods

A hierarchical transformation model including the global and local LV deformations was employed to analyze the strain and strain rate of the left ventricle by cine-MRI image registration. The endocardial and epicardial contour information was introduced to enhance the registration accuracy by combining the original hierarchical algorithm with an Iterative Closest Points using Invariant Features algorithm. The hierarchical model was validated by a normal volunteer first and then applied to two clinical cases (i.e., the normal volunteer and a diabetic patient) to evaluate their respective function.

Results

Based on the two clinical cases, by comparing the displacement fields of two selected landmarks in the normal volunteer, the proposed method showed a better performance than the original or unmodified model. Meanwhile, the comparison of the radial strain between the volunteer and patient demonstrated their apparent functional difference.

Conclusions

The present method could be used to estimate the LV myocardial strain and strain rate during a cardiac cycle and thus to quantify the analysis of the LV motion function.

     

Age-dependent influence of strain rate on the tensile failure of rat-tail tendon

Sensitivity of tensile strength, failure strain, and failure energy density to strain rate was studied for rat-tail tendon (RTT), a collagen-rich connective tissue. Tendons from animals aged 1-27 months were stretched at a high (720 percent/s) and low (3.6 percent/s) strain rate. Each failure parameter increased with strain rate. However, the sensitivity of tendon failure to rate of strain decreased rapidly during growth and sexual maturation of the animal. The study provides basic data on the rate-sensitive strength of collagen fibers using RTT.     

Temporal development of hippocampal cell death is dependent on tissue strain but not strain rate

Deformation of brain tissue in response to mechanical loading of the head is the root-cause of traumatic brain injury (TBI). Even below ultimate failure limits, deformation activates pathophysiological cascades resulting in delayed cell death. Injury response of soft tissues, such as the chest and spinal cord, is dependent on the product of deformation and velocity, a parameter termed the viscous criterion. We set out to test if hippocampal cell death could be predicted by a similar combination of strain and strain rate and if the viscous criterion was valid for hippocampus. Quantitative prediction of the brain's biological response to mechanical stimuli is difficult to achieve in animal models of TBI, so we utilized an in vitro model of TBI based on hippocampal slice cultures. We quantified the temporal development of cell death after precisely controlled deformations for 30 combinations of strain (0.05-0.50) and strain rate (0.1-50s(-1)) relevant to TBI. Loading conditions for a subset of cultures were verified by analysis of high-speed video. Cell death was found to be significantly dependent on time-post injury, on strain magnitude, and to a lesser extent, on anatomical region by a repeated-measures, three-way ANOVA. The responses of the CA1 and CA3 regions of the hippocampus were not statistically different in contrast to some in vivo TBI studies. Surprisingly, cell death was not dependent on strain rate leading us to conclude that the viscous criterion is not a valid predictor for hippocampal tissue injury. Given the large data set and extensive combinations of biomechanical parameters, predictive mathematical functions relating independent variables (strain, region, and time post-injury) to the resultant cell death were defined. These functions can be used as tolerance criteria to equip finite element models of TBI with the added capability to predict biological consequences.     

Associating the mesoscale fiber organization of the tongue with local strain rate during swallowing

The tongue is an intricately configured muscular organ that undergoes a stereotypical set of deformations during the course of normal human swallowing. In order to demonstrate quantitatively the relationship between 3D aligned lingual fiber organization and mechanics during swallowing, the tissue's myoarchitecture and strain rate were imaged before and during the propulsive phase of a 3.0ml water bolus swallow. Mesoscale fiber organization was imaged with high-resolution diffusion tensor imaging (DTI) and multi-voxel myofiber tracts generated along maximum diffusion vectors. Tissue compression/expansion was obtained via lingual pressure-gated phase-contrast (PC) MRI, a method which determines local strain rate as a function of the phase shift occurring along an applied gradient vector. The co-alignment of myofiber tract direction and the localized principal strain rate vectors was obtained by translating the strain rate tensor into the reference frame with the primary axis parallel to the maximum diffusion vector using Mohr's circle, resulting in the generation of fiber-aligned strain rate (FASR). DTI tractography displayed the complete fiber anatomy of the tongue, consisting of a core region of orthogonally aligned fibers encased within a longitudinal sheath, which merge with the externally connected styloglossus, hyoglossus, and genioglossus fibers. FASR images obtained in the mid-sagittal plane demonstrated that bolus propulsion was associated with prominent compressive strain aligned with the genioglossus muscle combined with expansive strain aligned with the verticalis and geniohyoid muscles. These data demonstrate that lingual deformation during swallowing involves complex interactions involving intrinsic and extrinsic muscles, whose contractility is directed by the alignment of mesoscale fiber tracts.     

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.     

Mortality rate and relative strain index in Buenos Aires city

Thermal stress may seriously affect human health to the extent of provoking death in those human groups at high risk such as little children and elderly persons. This research studies the climatology of the relative strain index (RSI) in the city of Buenos Aires (Argentina). It is observed that the conditions at 1400 hours local time on more than 75% of summer days cause discomfort, though only on 25% of days are physiological failure levels reached. The nocturnal RSI values show 75% of nights to be comfortable, bringing relief and allowing physiological recuperation. Comparison between the RSI frequency distributions of different decades by the application of the Kolmogorov-Smirnov test shows a possible urban heat-island effect that increases nocturnal RSI values. The relationship between the RSI and the daily number of interments is also analysed. Because of the large number of different causes of mortality, only about 10% of the variance of the daily number of interments can be explained by the RSI value at 1400 hours local time 1 or 2 days before. Comparison of mortality figures with these RSI values shows deaths to be at a minimum for the interval 0.0-0.1 (the RSI comfort range), slightly increasing for negative values that could represent unexpected Summer cold waves. For values of RSI over 0.2 the increment is more abrupt, indicating an impact of a thermal strain on mortality. The relationship between the joint occurrence of the 1400 hour and 0200 hour (local time) RSI values and mortality shows a clear impact of prolonged exposure to uncomfortable conditions.     

Bone strain magnitude is correlated with bone strain rate in tetrapods: implications for models of mechanotransduction

Hypotheses suggest that structural integrity of vertebrate bones is maintained by controlling bone strain magnitude via adaptive modelling in response to mechanical stimuli. Increased tissue-level strain magnitude and rate have both been identified as potent stimuli leading to increased bone formation. Mechanotransduction models hypothesize that osteocytes sense bone deformation by detecting fluid flow-induced drag in the bone''s lacunar–canalicular porosity. This model suggests that the osteocyte''s intracellular response depends on fluid-flow rate, a product of bone strain rate and gradient, but does not provide a mechanism for detection of strain magnitude. Such a mechanism is necessary for bone modelling to adapt to loads, because strain magnitude is an important determinant of skeletal fracture. Using strain gauge data from the limb bones of amphibians, reptiles, birds and mammals, we identified strong correlations between strain rate and magnitude across clades employing diverse locomotor styles and degrees of rhythmicity. The breadth of our sample suggests that this pattern is likely to be a common feature of tetrapod bone loading. Moreover, finding that bone strain magnitude is encoded in strain rate at the tissue level is consistent with the hypothesis that it might be encoded in fluid-flow rate at the cellular level, facilitating bone adaptation via mechanotransduction.     

Increasing strain and strain rate strengthen transient stiffness but weaken the response to subsequent compression for articular cartilage in unconfined compression

Strain amplitude and strain rate dependent nonlinear behavior and load-induced mechanical property alterations of full-thickness bovine articular cartilage attached to bone were investigated in unconfined compression. A sequence of test compressions of finite deformation (ranging from 0.9% to 34.5% nominal strain) was performed at strain rates ranging from approximately 0.053%/s to 5.8%/s. Peak and equilibrium loads were analyzed to determine strain amplitude and strain rate dependence of linear versus nonlinear responses. The test protocol was designed to reveal changes in mechanical properties due to these finite deformations by interspersing small-amplitude witness ramps of approximately 1.1% deformation and approximately 0.44%/s strain rate between the test ramps ("witness" meaning to assess any mechanical property changes). We found that peak loads displayed high nonlinearity, stiffening with both increasing compression amplitude and more so with increasing strain rate. The response to witness ramps suggested that mechanical weakening occurred when compression amplitude reached 1.9-2.9% strain and beyond, and that weakening was much more significant at higher strain rate. These findings delineate regimes of linear versus nonlinear behavior of cartilage, and indicate the types of loads which can cause mechanical property alterations. Biological implications of this study are that strain amplitude and strain rate dependent stiffening may be essential to bear physiological loads and to protect cells and matrix from mechanical damage. Structural changes reflected by mechanical weakening at small compression could also initiate remodeling or disease processes.