Validation tool for traction force microscopy

Traction force microscopy (TFM) is commonly used to estimate cells’ traction forces from the deformation that they cause on their substrate. The accuracy of TFM highly depends on the computational methods used to measure the deformation of the substrate and estimate the forces, and also on the specifics of the experimental set-up. Computer simulations can be used to evaluate the effect of both the computational methods and the experimental set-up without the need to perform numerous experiments. Here, we present one such TFM simulator that addresses several limitations of the existing ones. As a proof of principle, we recreate a TFM experimental set-up, and apply a classic 2D TFM algorithm to recover the forces. In summary, our simulator provides a valuable tool to study the performance, refine experimentally, and guide the extraction of biological conclusions from TFM experiments.

Numerical estimation of 3D mechanical forces exerted by cells on non-linear materials

The exchange of physical forces in both cell-cell and cell-matrix interactions play a significant role in a variety of physiological and pathological processes, such as cell migration, cancer metastasis, inflammation and wound healing. Therefore, great interest exists in accurately quantifying the forces that cells exert on their substrate during migration. Traction Force Microscopy (TFM) is the most widely used method for measuring cell traction forces. Several mathematical techniques have been developed to estimate forces from TFM experiments. However, certain simplifications are commonly assumed, such as linear elasticity of the materials and/or free geometries, which in some cases may lead to inaccurate results. Here, cellular forces are numerically estimated by solving a minimization problem that combines multiple non-linear FEM solutions. Our simulations, free from constraints on the geometrical and the mechanical conditions, show that forces are predicted with higher accuracy than when using the standard approaches.

Exploration of mechanisms underlying the strain-rate-dependent mechanical property of single chondrocytes

Based on the characterization by Atomic Force Microscopy (AFM), we report that the mechanical property of single chondrocytes has dependency on the strain-rates. By comparing the mechanical deformation responses and the Young’s moduli of living and fixed chondrocytes at four different strain-rates, we explore the deformation mechanisms underlying this dependency property. We found that the strain-rate-dependent mechanical property of living cells is governed by both of the cellular cytoskeleton (CSK) and the intracellular fluid when the fixed chondrocytes is mainly governed by their intracellular fluid which is called the consolidation-dependent deformation behavior. Finally, we report that the porohyperelastic (PHE) constitutive material model which can capture the consolidation-dependent behavior of both living and fixed chondrocytes is a potential candidature to study living cell biomechanics.

Molecular sliding filament model for muscular contraction based on multiscale investigation

A multiscale approach that bridges the biophysics of the actin molecules at nanoscale and the biomechanics of actin filament at microscale level is developed and used to evaluate the mechanical performances of actin filament bundles. In order to investigate the contractile properties of skeletal muscle which is induced by the protein motor of myosin, a molecular model is proposed in the prediction of the dynamic behaviors of skeletal muscle based on classic sliding filament model. Randomly distributed myosin motors are applied on a 2.2 μm long sarcomere, whose principal components include actin and myosin filaments. It can be found that, the more myosin motors on the sarcomere, the faster the sarcomere contracts. The result demonstrates that the sarcomere shortening speed cannot increase infinitely by the modulation of myosin, thus providing insight into the self-protective properties of skeletal muscles. This molecular filament sliding model provides a theoretical way to evaluate the properties of skeletal muscles, and contributes to the understandings of the molecular mechanisms in the physiological phenomenon of muscular contraction.

Concurrent validity of accelerations measured using a tri-axial inertial measurement unit while walking on firm, compliant and uneven surfaces

Although accelerometers are extensively used for assessing gait, limited research has evaluated the concurrent validity of these devices on less predictable walking surfaces or the comparability of different methods used for gravitational acceleration compensation. This study evaluated the concurrent validity of trunk accelerations derived from a tri-axial inertial measurement unit while walking on firm, compliant and uneven surfaces and contrasted two methods used to remove gravitational accelerations: i) subtraction of the best linear fit from the data (detrending), and; ii) use of orientation information (quaternions) from the inertial measurement unit. Twelve older and twelve younger adults walked at their preferred speed along firm, compliant and uneven walkways. Accelerations were evaluated for the thoracic spine (T12) using a tri-axial inertial measurement unit and an eleven-camera Vicon system. The findings demonstrated excellent agreement between accelerations derived from the inertial measurement unit and motion analysis system, including while walking on uneven surfaces that better approximate a real-world setting (all differences <0.16 m.s−2). Detrending produced slightly better agreement between the inertial measurement unit and Vicon system on firm surfaces (delta range: −0.05 to 0.06 vs. 0.00 to 0.14 m.s−2), whereas the quaternion method performed better when walking on compliant and uneven walkways (delta range: −0.16 to −0.02 vs. −0.07 to 0.07 m.s−2). The technique used to compensate for gravitational accelerations requires consideration in future research, particularly when walking on compliant and uneven surfaces. These findings demonstrate trunk accelerations can be accurately measured using a wireless inertial measurement unit and are appropriate for research that evaluates healthy populations in complex environments.

Hip and knee kinematics display complex and time-varying sagittal kinematics during repetitive stepping: Implications for design of a functional fatigue model of the knee extensors and flexors

The validity of fatigue protocols involving multi-joint movements, such as stepping, has yet to be clearly defined. Although surface electromyography can monitor the fatigue state of individual muscles, the effects of joint angle and velocity variation on signal parameters are well established. Therefore, the aims of this study were to i) describe sagittal hip and knee kinematics during repetitive stepping ii) identify periods of high inter-trial variability and iii) determine within-test reliability of hip and knee kinematic profiles. A group of healthy men (N = 15) ascended and descended from a knee-high platform wearing a weighted vest (10%BW) for 50 consecutive trials. The hip and knee underwent rapid flexion and extension during step ascent and descent. Variability of hip and knee velocity peaked between 20-40% of the ascent phase and 80-100% of the descent. Significant (p<0.05) reductions in joint range of motion and peak velocity during step ascent were observed, while peak flexion velocity increased during descent. Healthy individuals use complex hip and knee motion to negotiate a knee-high step with kinematic patterns varying across multiple repetitions. These findings have important implications for future studies intending to use repetitive stepping as a fatigue model for the knee extensors and flexors.

Reactive stepping behaviour in response to forward loss of balance predicts future falls in community-dwelling older adults

Background: a fall occurs when an individual experiences a loss of balance from which they are unable to recover. Assessment of balance recovery ability in older adults may therefore help to identify individuals at risk of falls. The purpose of this 12-month prospective study was to assess whether the ability to recover from a forward loss of balance with a single step across a range of lean magnitudes was predictive of falls. Methods: two hundred and one community-dwelling older adults, aged 65–90 years, underwent baseline testing of sensorimotor function and balance recovery ability followed by 12-month prospective falls evaluation. Balance recovery ability was defined by whether participants required either single or multiple steps to recover from forward loss of balance from three lean magnitudes, as well as the maximum lean magnitude participants could recover from with a single step. Results: forty-four (22%) participants experienced one or more falls during the follow-up period. Maximal recoverable lean magnitude and use of multiple steps to recover at the 15% body weight (BW) and 25%BW lean magnitudes significantly predicted a future fall (odds ratios 1.08–1.26). The Physiological Profile Assessment, an established tool that assesses variety of sensori-motor aspects of falls risk, was also predictive of falls (Odds ratios 1.22 and 1.27, respectively), whereas age, sex, postural sway and timed up and go were not predictive. Conclusion: reactive stepping behaviour in response to forward loss of balance and physiological profile assessment are independent predictors of a future fall in community-dwelling older adults. Exercise interventions designed to improve reactive stepping behaviour may protect against future falls.

Segmental torso masses in adolescent idiopathic scoliosis

Background Adolescent Idiopathic Scoliosis is the most common type of spinal deformity whose aetiology remains unclear. Studies suggest that gravitational forces in the standing position play an important role in scoliosis progression, therefore anthropometric data are required to develop biomechanical models of the deformity. Few studies have analysed the trunk by vertebral level and none have performed investigations of the scoliotic trunk. The aim of this study was to determine the centroid, thickness, volume and estimated mass, for sections of the trunk in Adolescent Idiopathic Scoliosis patients. Methods Existing low-dose Computed Tomography scans were used to estimate vertebral level-by-level torso masses for 20 female Adolescent Idiopathic Scoliosis patients. ImageJ processing software was used to analyse the Computed Tomography images and enable estimation of the segmental torso mass corresponding to each vertebral level. Findings The patients’ mean age was 15.0 (SD 2.7) years with mean major Cobb Angle of 52° (SD 5.9) and mean patient weight of 58.2 (SD 11.6) kg. The magnitude of torso segment mass corresponding to each vertebral level increased by 150% from 0.6kg at T1 to 1.5kg at L5. Similarly, the segmental thickness corresponding to each vertebral level from T1-L5 increased inferiorly from a mean 18.5 (SD 2.2) mm at T1 to 32.8 (SD 3.4) mm at L5. The mean total trunk mass, as a percentage of total body mass, was 27.8 (SD 0.5) % which was close to values reported in previous literature. Interpretation This study provides new anthropometric reference data on segmental (vertebral level-by-level) torso mass in Adolescent Idiopathic Scoliosis patients, useful for biomechanical models of scoliosis progression and treatment.

Segmental torso masses and joint torques produced by gravity in the adolescent scoliotic spine

Introduction Calculating segmental torso masses in Adolescent Idiopathic Scoliosis (AIS) patients allows the gravitational loading on the scoliotic spine during relaxed standing to be estimated. Methods Low dose CT data was used to calculate vertebral level-by-level torso masses and spinal joint torques for 20 female AIS patients (mean age 15.0 ± 2.7 years, mean Cobb angle 53 ± 7.1°). ImageJ software (v1.45 NIH USA) was used to threshold the T1 to L5 CT images and calculate the segmental torso volume and mass for each vertebral level. Masses for the head, neck and arms were taken from published data. Intervertebral joint torques in the coronal and sagittal planes at each vertebral level were found from the position of the centroid of the segment masses relative to the joint centres (assumed to be at the centre of the intervertebral disc. The joint torque at each level was found by summing torque contributions for all segments above that joint. Results Segmental torso mass increased from 0.6kg at T1 to 1.5kg at L5. The coronal plane joint torques due to gravity were 5-7Nm at the apex of the curve; sagittal torques were 3-5.4Nm. Conclusion CT scans were in the supine position and curve magnitudes are known to be smaller than those in standing. Hence, this study has shown that gravity produces joint torques potentially of higher than 7Nm in the coronal plane and 5Nm in the sagittal plane during relaxed standing in scoliosis patients. The magnitude of these torques may help to explain the mechanics of AIS progression and the mechanics of bracing. This new data on torso segmental mass in AIS patients will assist biomechanical models of scoliosis.

Functional impairments characterising mild, moderate and severe hallux valgus

Objective Hallux valgus has been linked to functional disability and increased falls risk, but mechanisms underpinning functional disability are unclear. This study investigated functional performance, muscle strength and plantar pressures in adults with mild, moderate, and severe HV compared to controls, while considering the influence of foot pain. Methods Sixty adults with hallux valgus (classified as mild, moderate and severe on dorsalplantar radiographs) and 30 controls participated. Measures included: hallux plantarflexion and abduction strength, walking performance, postural sway and forefoot plantar pressures. Multiple analysis of covariance and pairwise comparisons (p<0.05, Bonferroni adjustment) were used to investigate differences between groups, adjusting for age, sex, body mass index and foot pain. Results Hallux plantarflexion and abduction strength was significantly reduced in those with moderate (mean differences: plantarflexion -45.8N, abduction -12.3N, p<0.001) and severe hallux valgus (plantarflexion -50.1N, p<0.001; abduction -11.2N, p=0.01) compared to controls. A significant reduction in hallux peak pressure and pressure-time integral was evident in moderate (peak pressure -90.8kPa, p<0.001) and severe hallux valgus (peak pressure -106.2kPa, p<0.001) compared to controls. Those with severe hallux valgus also demonstrated increased mediolateral postural sway in single leg stance compared to controls (3.5cm, p=0.01). Conclusion Moderate to severe hallux valgus is associated with reduced hallux plantar pressures and strength measures, while relatively normal function compared to controls was found in those with mild deformity. Greater understanding of specific functional deficits associated with different stages of hallux valgus will help inform clinical management and future research.

The effect of intervertebral staple insertion on bovine spine segment stiffness

Introduction There is growing interest in the biomechanics of ‘fusionless’ implant constructs used for deformity correction in the thoracic spine. Intervertebral stapling is a leading method of fusionless corrective surgery. Although used for a number of years, there is limited evidence as to the effect these staples have on the stiffness of the functional spinal unit. Materials and Methods Thoracic spines from 6-8 week old calves were dissected and divided into motion segments including levels T4-T11 (n=14). Each segment was potted in polymethylemethacrylate. An Instron Biaxial materials testing machine with a custom made jig was used for testing. The segments were tested in flexion/extension, lateral bending and axial rotation at 37⁰C and 100% humidity, using moment control to a maximum 1.75 Nm with a loading rate of 0.3 Nm per second. This torque was found sufficient to achieve physiologically representative ranges of movement. The segments were initially tested uninstrumented with data collected from the tenth load cycle. Next a left anterolateral Shape Memory Alloy (SMA) staple was inserted (Medtronic Sofamor Danek, USA). Biomechanical testing was repeated as before with data collected from the tenth load cycle. Results In flexion/extension there was an insignificant drop in stiffness of 3% (p=0.478). In lateral bending there was a significant drop in stiffness of 21% (p<0.001). This was mainly in lateral bending away from the staple, where the stiffness reduced by 30% (p<0.001). This was in contrast to lateral bending towards the staple where it dropped by 12% which was still statistically significant (p=0.036). In axial rotation there was an overall near significant drop in stiffness of 11% (p=0.076). However, this was more towards the side of the staple measuring a decrease of 14% as opposed to 8% away from the staple. In both cases it was a statistically insignificant drop (p=0.134 and p=0.352 respectively). Conclusion Insertion of intervertebral SMA staples results in a significant reduction in motion segment stiffness in lateral bending especially in the direction away from the staple. The staple had less effect on axial rotation stiffness and minimal effect on flexion/extension stiffness.

Gravity-induced coronal plane joint moments in the adolescent scoliotic spine

INTRODUCTION Calculating segmental (vertebral level-by-level) torso masses in Adolescent Idiopathic Scoliosis (AIS) patients allows the gravitational loading on the scoliotic spine during relaxed standing to be estimated. METHODS Existing low dose CT scans were used to calculate vertebral level-by-level torso masses and joint moments occurring in the spine for a group of female AIS patients with right-sided thoracic curves. Image processing software, ImageJ (v1.45 NIH USA) was used to reconstruct the torso segments and subsequently measure the torso volume and mass corresponding to each vertebral level. Body segment masses for the head, neck and arms were taken from published anthropometric data. Intervertebral joint moments at each vertebral level were found by summing each of the torso segment masses above the required joint and multiplying it by the perpendicular distance to the centre of the disc. RESULTS AND DISCUSSION Twenty patients were included in this study with a mean age of 15.0±2.7 years and a mean Cobb angle 52±5.9°. The mean total trunk mass, as a percentage of total body mass, was 27.8 (SD 0.5) %. Mean segmental torso mass increased inferiorly from 0.6kg at T1 to 1.5kg at L5. The coronal plane joint moments during relaxed standing were typically 5-7Nm at the apex of the curve (Figure 1), with the highest apex joint of 7Nm. CT scans were performed in the supine position and curve magnitudes are known to be 7-10° smaller than those measured in standing [1]. Therefore joint moments produced by gravity will be greater than those calculated here. CONCLUSIONS Coronal plane joint moments as high as 7Nm can occur during relaxed standing in scoliosis patients, which may help to explain the mechanics of AIS progression. The body mass distributions calculated in this study can be used to estimate joint moments derived using other imaging modalities such as MRI and subsequently determine if a relationship exists between joint moments and progressive vertebral deformity.

A biomechanical analysis of growing rods used in the management of early onset scoliosis

INTRODUCTION Managing spinal deformities in young children is challenging, particularly early-onset scoliosis (EOS). Any progressive spinal deformity particularly in early life presents significant health risks for the child and a challenge for the treating surgeon. Surgical intervention is often required if EOS has been unresponsive to conservative treatment particularly with rapidly progressive curves. An emerging treatment option particularly for EOS is fusionless scoliosis surgery. Similar to bracing this surgical option potentially harnesses growth, motion and function of the spine along with correcting spinal deformity. Dual growing rods is one such fusionless treatment, which aims to modulate growth of the vertebrae. The aim of this study was to ascertain the extent to which semi-constrained growing rods (Medtronic, Memphis, TN) with a telescopic sleeve component, reduce rotational constraint on the spine compared with standard rigid rods and hence potentially provide a more physiological mechanical environment for the growing spine. METHODS Six 40-60kg English Large White porcine spines served as a model for the paediatric human spine. Each spine was dissected into 7 level thoracolumbar multi-segment unit (MSU) spines, removing all non-ligamentous soft tissues. Appropriately sized semi-constrained growing rods and rigid rods were secured by multi-axial screws (Medtronic) prior to testing in alternating sequences for each spine. Pure nondestructive moments of +/4Nm at a constant rotation rate of 8deg/s was applied to the mounted MSU spines. Displacement of each level was captured using an Optotrak (Northern Digital Inc, Waterloo, ON). The range of motion (ROM), neutral zone (NZ) size and stiffness (Nm/deg) were calculated from the Instron load-displacement data and intervertebral ROM was calculated through a MATLAB algorithm from Optotrak data. RESULTS Irrespective of sequence order rigid rods significantly reduced the total ROM (deg) than compared to semi-constrained rods (p<0.05) and resulted in a significantly stiffer (Nm/deg) spine for both left and right axial rotation testing (p<0.05). Analysing the intervertebral motion within the instrumented levels, rigid rods showed reduced ROM (Deg) than compared to semi-constrained growing rods and the un-instrumented (UN-IN) test sequences. CONCLUSION The semi-constrained growing rods maintained rotation similar to UN-IN spines while the rigid rods showed significantly reduced axial rotation across all instrumented levels. Clinically the effect of semi-constrained growing rods evaluated in this study is that they will allow growth via the telescopic rod components while maintaining the axial rotation ability of the spine, which may also reduce the occurrence of the crankshaft phenomenon.

Stress relaxation analysis of single chondrocytes using porohyperelastic model based on AFM experiments

The aim of this study is to investigate the stress relaxation behavior of single chondrocytes using the Porohyperelastic (PHE) model and inverse Finite Element Analysis (FEA). Firstly, based on Atomic Force Microscopy (AFM) technique, we have found that the chondrocytes exhibited stress relaxation behavior. We explored the mechanism of this stress relaxation behavior and concluded that the intracellular fluid exuding out from the cells during deformation plays the most important role in the stress relaxation. Next, we have applied the inverse FEA technique to determine necessary material parameters for PHE model to simulate this stress relaxation behavior as this model is proven capable of capturing the non-linear behavior and the fluid-solid interaction during the stress relaxation of the single chondrocytes. It is observed that this PHE model can precisely capture the stress relaxation behavior of single chondrocytes and would be a suitable model for cell biomechanics.

Determination of strain-rate-dependent mechanical behavior of living and fixed osteocytes and chondrocytes using atomic force microscopy and inverse finite element analysis

The aim of this paper is to determine the strain-rate-dependent mechanical behavior of living and fixed osteocytes and chondrocytes, in vitro. Firstly, Atomic Force Microscopy (AFM) was used to obtain the force-indentation curves of these single cells at four different strain-rates. These results were then employed in inverse finite element analysis (FEA) using Modified Standard neo-Hookean Solid (MSnHS) idealization of these cells to determine their mechanical properties. In addition, a FEA model with a newly developed spring element was employed to accurately simulate AFM evaluation in this study. We report that both cytoskeleton (CSK) and intracellular fluid govern the strain-rate-dependent mechanical property of living cells whereas intracellular fluid plays a predominant role on fixed cells’ behavior. In addition, through the comparisons, it can be concluded that osteocytes are stiffer than chondrocytes at all strain-rates tested indicating that the cells could be the biomarker of their tissue origin. Finally, we report that MSnHS is able to capture the strain-rate-dependent mechanical behavior of osteocyte and chondrocyte for both living and fixed cells. Therefore, we concluded that the MSnHS is a good model for exploration of mechanical deformation responses of single osteocytes and chondrocytes. This study could open a new avenue for analysis of mechanical behavior of osteocytes and chondrocytes as well as other similar types of cells.