Physiological Loading Rates Research Articles

Unexpected Low Mechanical Stability of Titin I27 Domain at Physiologically Relevant Temperature.

The extensively studied immunoglobulin (Ig) domain I27 of the giant force-bearing protein titin has provided a basis for our current understanding of the structural stability, dynamics, and function of the numerous mechanically stretched Ig domains in the force-bearing I-band of titin. The current consensus is that titin I27 has a high mechanical stability characterized by very low unfolding rate (<10-3 s-1) in physiological force range and high unfolding forces (>100 pN) at typical physiological force loading rates from experiments at typical laboratory temperatures. Here, we report that when the temperature is increased from 23 to 37 °C, the unfolding rate of I27 drastically increases by ∼100-fold at the physiological level of forces, indicating a low mechanical stability of I27 at physiological conditions. The result provides new insights into the structural states and the associated functions of I27 and other similar titin I-band Ig domains.

Rate-dependent mechanical behaviour of semilunar valves under biaxial deformation: From quasi-static to physiological loading rates

In this study we investigate the rate-dependency of the mechanical behaviour of semilunar heart valves under biaxial deformation, from quasi-static to physiological loading rates. This work extends and complements our previous undertaking, where the rate-dependency in the mechanical behaviour of semilunar valve specimens was documented in sub-physiological rate domains (Acta Biomater. 2019; https://doi.org/10.1016/j.actbio.2019.02.008). For the first time we demonstrate herein that the stress-stretch curves obtained from specimens under physiological rates too are markedly different to those at sufficiently lower rates and at quasi-static conditions. The results importantly underline that the mechanical behaviour of semilunar heart valves is rate dependent, and the physiological mechanical behaviour of the valves may not be correctly obtained via material characterisation tests at arbitrary low deformation rates. Presented results in this work provide an inclusive dataset for material characterisation and modelling of semilunar heart valves across a 10,000 fold deformation rate, both under equi-biaxial and 1:3 ratio deformation rates. The important application of these results is to inform the development of appropriate mechanical testing protocols, as well as devising new models, for suitable determination of the rate-dependent constitutive mechanical behaviour of the semilunar valves.

Nucleolin mediates the binding of cancer cells to L-selectin under conditions of lymphodynamic shear stress.

Head and neck squamous cell carcinoma (HNSCC) cells bind to lymphocytes via L-selectin in a shear-dependent manner. This interaction takes place exclusively under low-shear stress conditions, such as those found within the lymph node parenchyma. This represents a novel functional role for L-selectin-selectin ligand interactions. Our previous work has characterized as-of-yet unidentified L-selectin ligands expressed by HNSCC cells that are specifically active under conditions of low shear stress consistent with lymph flow. Using an affinity purification approach, we now show that nucleolin expressed on the surface of HNSCC cells is an active ligand for L-selectin. Parallel plate chamber flow-based experiments and atomic force microscopy (AFM) experiments show that nucleolin is the main functional ligand under these low-force conditions. Furthermore, AFM shows a clear relationship between work of deadhesion and physiological loading rates. Our results reveal nucleolin as the first major ligand reported for L-selectin that operates under low-shear stress conditions.

Rate-Dependent Mechanical Behaviour of Semilunar Valves Under Biaxial Deformation: From Quasi-Static to Physiological Loading Rates

In this study we investigate the rate-dependency of the mechanical behaviour of semilunar heart valves under biaxial deformation, from quasi-static to physiological loading rates. This work extends and complements our previous undertaking, where the rate-dependency in the mechanical behaviour of semilunar valve specimens was documented in sub-physiological rate domains (Acta Biomater. 2019. For the first time we demonstrate herein that the stress-stretch curves obtained from specimens under physiological rates too are markedly different to those at sufficiently lower rates and at quasi-static conditions. The results importantly underline that the mechanical behaviour of semilunar heart valves is rate dependent, and the physiological mechanical behaviour of the valves may not be correctly obtained via material characterisation tests at arbitrary low deformation rates. Presented results in this work provide an inclusive dataset for material characterisation and modelling of semilunar heart valves across a 10,000 fold deformation rate, both under equi-biaxial and 1:3 ratio deformation rates. The important application of these results is to inform the development of appropriate mechanical testing protocols, as well as devising new models, for suitable determination of the rate-dependent constitutive mechanical behaviour of the semilunar valves.

Steered molecular dynamics characterization of the elastic modulus and deformation mechanisms of single natural tropocollagen molecules.

Collagen is a common structural protein, providing mechanical integrity for various vertebrate connective tissues such as cartilage and bone. The mechanical behaviours of these tissues under physical stimulations are controlled by the hierarchical structure of collagen and its interactions with other extracellular matrix molecules. However, the mechanical properties and deformation mechanisms of natural collagen under physiological loading rates at the molecular level are not fully understood. In this study, comprehensive steered molecular dynamics (SMD) simulations were performed on the 2nd intact overlap region (d2ol) and the 2nd intact D-period (d2olgp) of an in-situ characterized collagen molecule, under a large range of strain rates (6.5 × 106% s-1 to 1.3 × 1012% s-1). The results show that, depending on the applied strain rates, tropocollagen molecules unfold in different ways. Particularly, at high and intermediate strain rates, the number of inter-chain hydrogen bonds decreases rapidly even at small deformations, leading to a dramatic increase in the force. This results in an increase in the estimated Young's modulus of collagen triple helices as the deformation rate goes up, which, together with the nonlinear mechanical behaviour, explains the broad range of the Young's modulus for collagen model peptides reported in earlier SMD studies. Atomistic-level analyses indicate that the elastic modulus of single tropocollagen molecules decreases as the strain rate becomes smaller. However, for strain rates below 1.3 × 108% s-1, the tangent Young's modulus of d2ol (d2olgp) converges to approximately 3.2 GPa (3.4 GPa), at the strain of 10.5% (12%) when the segment is fully uncrimped. Furthermore, for strain rates under 1.3 × 108% s-1, d2ol and d2olgp show identical deformation mechanisms (unwinding, uncoiling and backbone stretching), but the corresponding strain ranges are different. This study will aid in future studies on characterizing the mechanical properties of collagen molecules and collagen-like peptides by indicating the proper pulling strain rates and how to determine the suitable strain range used for evaluating the elastic modulus.

On the Functional Role of Valve Interstitial Cell Stress Fibers: A Continuum Modeling Approach.

The function of the heart valve interstitial cells (VICs) is intimately connected to heart valve tissue remodeling and repair, as well as the onset and progression of valvular pathological processes. There is yet only very limited knowledge and extant models for the complex three-dimensional VIC internal stress-bearing structures, the associated cell-level biomechanical behaviors, and how they change under varying activation levels. Importantly, VICs are known to exist and function within the highly dynamic valve tissue environment, including very high physiological loading rates. Yet we have no knowledge on how these factors affect VIC function. To this end, we extended our previous VIC computational continuum mechanics model (Sakamoto, et al., 2016, "On Intrinsic Stress Fiber Contractile Forces in Semilunar Heart Valve Interstitial Cells Using a Continuum Mixture Model," J. Mech. Behav. Biomed. Mater., 54(244-258)). to incorporate realistic stress-fiber geometries, force-length relations (Hill model for active contraction), explicit α-smooth muscle actin (α-SMA) and F-actin expression levels, and strain rate. Novel micro-indentation measurements were then performed using cytochalasin D (CytoD), variable KCl molar concentrations, both alone and with transforming growth factor β1 (TGF-β1) (which emulates certain valvular pathological processes) to explore how α-SMA and F-actin expression levels influenced stress fiber responses under quasi-static and physiological loading rates. Simulation results indicated that both F-actin and α-SMA contributed substantially to stress fiber force generation, with the highest activation state (90 mM KCL + TGF-β1) inducing the largest α-SMA levels and associated force generation. Validation was performed by comparisons to traction force microscopy studies, which showed very good agreement. Interestingly, only in the highest activation state was strain rate sensitivity observed, which was captured successfully in the simulations. These unique findings demonstrated that only VICs with high levels of αSMA expression exhibited significant viscoelastic effects. Implications of this study include greater insight into the functional role of α-SMA and F-actin in VIC stress fiber function, and the potential for strain rate-dependent effects in pathological states where high levels of α-SMA occur, which appear to be unique to the valvular cellular in vivo microenvironment.

Adaptive velocity-based six degree of freedom load control for real-time unconstrained biomechanical testing

Robotic biomechanics is a powerful tool for further developing our understanding of biological joints, tissues and their repair. Both velocity-based and hybrid force control methods have been applied to biomechanics but the complex and non-linear properties of joints have limited these to slow or stepwise loading, which may not capture the real-time behaviour of joints. This paper presents a novel force control scheme combining stiffness and velocity based methods aimed at achieving six degree of freedom unconstrained force control at physiological loading rates.

Human cervical spine ligaments exhibit fully nonlinear viscoelastic behavior

Spinal ligaments provide stability and contribute to spinal motion patterns. These hydrated tissues exhibit time-dependent behavior during both static and dynamic loading regimes. Therefore, accurate viscoelastic characterization of these ligaments is requisite for development of computational analogues that model and predict time-dependent spine behavior. The development of accurate viscoelastic models must be preceded by rigorous, empirical evidence of linear viscoelastic, quasi-linear viscoelastic (QLV) or fully nonlinear viscoelastic behavior. This study utilized multiple physiological loading rates (frequencies) and strain amplitudes via cyclic loading and stress relaxation experiments in order to determine the viscoelastic behavior of the human lower cervical spine anterior longitudinal ligament, the posterior longitudinal ligament and the ligamentum flavum. The results indicated that the cyclic material properties of these ligaments were dependent on both strain amplitude and frequency. This strain amplitude-dependent behavior cannot be described using a linear viscoelastic formulation. Stress relaxation experiments at multiple strain magnitudes indicated that the shape of the relaxation curve was strongly dependent on strain magnitude, suggesting that a QLV formulation cannot adequately describe the comprehensive viscoelastic response of these ligaments. Therefore, a fully nonlinear viscoelastic formulation is requisite to model these lower cervical spine ligaments during activities of daily living.

Limitation of Finite Element Analysis of Poroelastic Behavior of Biological Tissues Undergoing Rapid Loading

The finite element method is used in biomechanics to provide numerical solutions to simulations of structures having complex geometry and spatially differing material properties. Time-varying load deformation behaviors can result from solid viscoelasticity as well as viscous fluid flow through porous materials. Finite element poroelastic analysis of rapidly loaded slow-draining materials may be ill-conditioned, but this problem is not widely known in the biomechanics field. It appears as instabilities in the calculation of interstitial fluid pressures, especially near boundaries and between different materials. Accurate solutions can require impractical compromises between mesh size and time steps. This article investigates the constraints imposed by this problem on tissues representative of the intervertebral disc, subjected to moderate physiological rates of deformation. Two test cylindrical structures were found to require over 10(4) linear displacement-constant pressure elements to avoid serious oscillations in calculated fluid pressure. Fewer Taylor-Hood (quadratic displacement-linear pressure elements) were required, but with complementary increases in computational costs. The Vermeer-Verruijt criterion for 1D mesh size provided guidelines for 3D mesh sizes for given time steps. Pressure instabilities may impose limitations on the use of the finite element method for simulating fluid transport behaviors of biological soft tissues at moderately rapid physiological loading rates.

Compression data on bovine bone confirms that a “stressed volume” principle explains the variability of fatigue strength results

The literature contains many measurements of the fatigue properties of compact bone, but these experimental results have been difficult to interpret and use due to a large amount of apparent scatter: variation in the number of cycles to failure for a given cyclic stress or strain range. Recently Taylor (1998a, Journal of Orthopaedic Research, 16, 163–169) showed that much of this scatter could be explained using a statistical model which took into account specimen size, or more specifically stressed volume. The present paper describes an attempt to test this model by using it to predict some new data, for bovine bone tested in compressive loading at room temperature at physiological loading rates. Twenty specimens were tested at the same applied load range (100 MPa). The theory was able to predict the mean behaviour of the specimens very well, with an accuracy (expressed in terms of stress) of 2%. It was also able to predict the degree of scatter (i.e. the variation of N f), which was shown to be similar to that measured by other workers.

A technique for measuring the compressive modulus of articular cartilage under physiological loading rates with preliminary results.

This paper describes a technique and apparatus for measuring the compressive modulus of articular cartilage under physiological loading rates. The compressive modulus is the most relevant property to the primary function of articular cartilage i.e., load carriage. It has been determined previously from measurement of cartilage deformation under slow or almost static loading conditions. The modulus was based on deformations occurring 2 s after the initial application of load which greatly reduces its relevance since in physiological conditions joint loading occurs within 10-150 ms. Five human knee joints have been used to test the apparatus before a major study is undertaken. The preliminary results from these joints show that the compressive modulus of articular cartilage measured within physiological loading time intervals was much greater than previously reported. The compressive modulus at 20 ms was in the range 4.4-27 MPa and was between 32 and 75 per cent greater than its value obtained at 2 s after loading.

A Comparison of the Dynamic Force Transmitting Properties of Subchondral Bone and Articular Cartilage

Compression tests on plugs of bovine articular cartilage and of subchondral bone demonstrated that both are capable of deforming under pressure and thus attenuating peak dynamic forces applied to the plugs. Although cancellous bone is approximately ten times stiffer than articular cartilage per unit of thickness, subchondral bone in vivo is considerably thicker and would, therefore, seem capable of contributing to dynamic force attenuation as much as the cartilage does or more. Under physiological loads and loading rates, a film of synovial fluid on the cartilage added nothing to the ability of cartilage plugs to attenuate peak dynamic force; however, at very low load rates cartilage plugs coated with synovial fluid were consistently stiffer than specimens coated with veronate buffer. It is highly likely, from the evidence presented, that alterations in the quality of the subchondral bone could have a profound effect on the ability of a subchondral bone-articular cartilage system to withstand compressive dynamic forces.