Analysis of effects of friction on the deformation behavior of soft tissues in unconfined compression tests

Frictionless specimen/platen contact in unconfined compression tests has traditionally been assumed in determining material properties of soft tissues via an analytical solution. In the present study, the suitability of this assumption was examined using a finite element method. The effect of the specimen/platen friction on the mechanical characteristics of soft tissues in unconfined compression was analyzed based on the published experimental data of three different materials (pigskin, pig brain, and human calcaneal fat). The soft tissues were considered to be nonlinear and viscoelastic; the friction coefficient at the contact interface between the specimens and platens was assumed to vary from 0.0 to 0.5. Our numerical simulations show that the tissue specimens are, due to the specimen/platen friction, not compressed in a uniform stress/strain state, as has been traditionally assumed in analytical analysis. The stress of the specimens obtained with the specimen/platen friction can be greater than those with the frictionless specimen/platen contact by more than 50%, even in well-controlled test conditions.     

Methodology to determine failure characteristics of planar soft tissues using a dynamic tensile test

Predicting the injury risk in automotive collisions requires accurate knowledge of human tissues, more particularly their mechanical properties under dynamic loadings. The present methodology aims to determine the failure characteristics of planar soft tissues such as skin, hollow organs and large vessel walls. This consists of a dynamic tensile test, which implies high-testing velocities close to those in automotive collisions. To proceed, I-shaped tissue samples are subjected to dynamic tensile tests using a customized tensile device based on the drop test principle. Data acquisition has especially been adapted to heterogeneous and soft biological tissues given that standard measurement systems (considered to be global) have been completed with a non-contact and full-field strain measurement (considered to be local). This local measurement technique, called the Image Correlation Method (ICM) provides an accurate strain analysis by revealing strain concentrations and avoids damaging the tissue. The methodology has first been applied to human forehead skin and can be further expanded to other planar soft tissues. The failure characteristics for the skin in terms of ultimate stress are 3 MPa +/- 1.5 MPa. The ultimate global longitudinal strains are equal to 9.5%+/-1.9% (Green-Lagrange strain), which contrasts with the ultimate local longitudinal strain values of 24.0%+/-5.3% (Green-Lagrange strain). This difference is a consequence of the tissue heterogeneity, clearly illustrated by the heterogeneous distribution of the local strain field. All data will assist in developing the tissue constitutive law that will be implemented in finite element models.     

Method for characterizing viscoelasticity of human gluteal tissue

Characterizing compressive transient large deformation properties of biological tissue is becoming increasingly important in impact biomechanics and rehabilitation engineering, which includes devices interfacing with the human body and virtual surgical guidance simulation. Individual mechanical in vivo behaviour, specifically of human gluteal adipose and passive skeletal muscle tissue compressed with finite strain, has, however, been sparsely characterised. Employing a combined experimental and numerical approach, a method is presented to investigate the time-dependent properties of in vivo gluteal adipose and passive skeletal muscle tissue. Specifically, displacement-controlled ramp-and-hold indentation relaxation tests were performed and documented with magnetic resonance imaging. A time domain quasi-linear viscoelasticity (QLV) formulation with Prony series valid for finite strains was used in conjunction with a hyperelastic model formulation for soft tissue constitutive model parameter identification and calibration of the relaxation test data. A finite element model of the indentation region was employed. Strong non-linear elastic but linear viscoelastic tissue material behaviour at finite strains was apparent for both adipose and passive skeletal muscle mechanical properties with orthogonal skin and transversal muscle fibre loading. Using a force-equilibrium assumption, the employed material model was well suited to fit the experimental data and derive viscoelastic model parameters by inverse finite element parameter estimation. An individual characterisation of in vivo gluteal adipose and muscle tissue could thus be established. Initial shear moduli were calculated from the long-term parameters for human gluteal skin/fat: G(∞,S/F)=1850 Pa and for cross-fibre gluteal muscle tissue: G(∞,M)=881 Pa. Instantaneous shear moduli were found at the employed ramp speed: G(0,S/F)=1920 Pa and G(0,M)=1032 Pa.     

Can loaded interface characteristics influence strain distributions in muscle adjacent to bony prominences?

Pressure distributions at the interface between skin and supporting tissues are used in design of supporting surfaces like beds, wheel chairs, prostheses and in sales brochures to support commercial products. The reasoning behind this is, that equal pressure distributions in the absence of high pressure gradients is assumed to minimise the risk of developing pressure sores. Notwithstanding the difficulty in performing reproducible and accurate pressure measurements, the question arises if the interface pressure distribution is representative of the internal mechanical state of the soft tissues involved. The paper describes a study of the mechanical condition of a supported buttock contact, depending on cushion properties, relative properties of tissue layers and friction. Numerical, mechanical simulations of a buttock on a supporting cushion are described. The ischial tuberosity is modelled as a rigid body, whereas the overlying muscle, fat and skin layers are modelled as a non-linear Ogden material. Material parameters and thickness of the fat layer are varied. Coulomb friction between buttock and cushion is modelled with different values of the friction coefficient. Moreover, the thickness and properties of the cushion are varied. High shear strains are found in the muscle near the bony prominence and the fat layer near the symmetry line. The performed parameter variations lead to large differences in shear strain in the fat layer but relatively small variations in the skeletal muscle. Even with a soft cushion, leading to a high reduction of the interface pressure the deformation of the skeletal muscle near the bone is high enough to form a risk, which is a clear argument that interface pressures alone are not sufficient to evaluate supporting surfaces.     

Inertia effects on characterization of dynamic response of brain tissue

Modeling and simulation of traumatic brain injury (TBI) resulted from collision or blast loading requires characterization of mechanical response over a wide range of loading rates under valid testing conditions. In this study, mechanical response of fresh bovine brain tissue was studied using the two modified Kolsky bar techniques. Radial deformation behavior of annular specimens, which are typically used to characterize the dynamic uniaxial compressive response of biological tissues, was examined using a modified Kolsky bar and a high speed camera to collect images while the specimen deforms at an axial strain rate of 2000s(-1). The high-speed images revealed inhomogeneous specimen deformation possibly brought about by radial inertia and causing a multi-axial stress state. To acquire valid stress-strain results that can be used to produce constitutive behavior of the soft materials, a novel torsion technique was developed to obtain pure shear response at dynamic loading rates. Experimental results show clear differences in the material response using the two methods. These results indicate that the previously demonstrated annular specimen geometry aimed at reducing inertia induced stress components for high rate soft materials uniaxial-compressive testing may still possess a significant component of radial inertia induced radial stress which consequently caused the observed inhomogeneous deformation in brain tissue test samples.     

Thermal expansion measurements of frozen biological tissues at cryogenic temperatures.

Thermal expansion data are essential for analyses of cryodestruction associated with thermal stresses during cryopreservation protocols as well as during cryosurgery. The present study tests a commonly used hypothesis that the thermal expansion of frozen tissues is similar to that of pure water ice crystals. This study further provides insight into the potential effect of the presence of cryoprotectants on thermal expansion. A new apparatus for thermal strain measurements of frozen biological tissues within a cryogenic temperature range is presented. Results are presented for fresh tissue samples taken from beef muscle, chicken muscle, rabbit muscle, rabbit bone, and pig liver. Pilot studies of the effect of cryoprotectants on thermal expansion are further presented for rabbit muscle immersed in dimethyl sulphoxide (2 mols/l) and glycerol (2 mols/l), and for pig liver perfused with dimethyl sulphoxide (2 mols/l). Thermal expansion of frozen soft biological tissues was found to be similar to that of water ice crystals in the absence of cryoprotectant. Thermal expansion of the rabbit bone was found to be about one half of that of frozen soft tissues. A significant reduction in the thermal expansion at higher temperatures was observed in the presence of cryoprotectants. A rapid change of thermal strain near -100 degrees C was also observed, which is likely to be associated with the glass transition process of the cryoprotectant solutions.     

Assessment of mechanical conditions in sub-dermal tissues during sitting: a combined experimental-MRI and finite element approach

A common but potentially severe malady afflicting permanent wheelchair users is pressure sores caused by elevated soft tissue strains and stresses over a critical prolonged period of time. Presently, there is paucity of information regarding deep soft tissue strains and stresses in the buttocks of humans during sitting. Strain and stress distributions in deep muscle and fat tissues were therefore calculated in six healthy subjects during sitting, in a double-donut Open-MR system, using a "reverse engineering" approach. Specifically, finite element (FE) models of the undeformed buttock were built for each subject using MR images taken at the coronal plane in a non-weight-bearing sitting posture. Using a second MR image taken from each subject during weight-bearing sitting we characterized the ischial tuberosity sagging toward the sitting surface in weight-bearing, and used these data as displacement boundary conditions for the FE models. These subject-specific FE analyses showed that maximal tissue strains and stresses occur in the gluteal muscles, not in fat or at the skin near the body-seat interface. Peak principal compressive strain and stress in the gluteus muscle were 74+/-7% and 32+/-9 kPa (mean+/-standard deviation), respectively. Peak principal compressive strain and stress in enveloping fat tissue were 46+/-7% and 18+/-4 kPa, respectively. Models were validated by comparing measured peak interface pressures under the ischial tuberosities (17+/-4 kPa) with those calculated by means of FE (18+/-3 kPa), for each subject. This is the first study to quantify sub-dermal tissue strain and stress distributions in sitting humans, in vivo. These data are essential for understanding the aetiology of pressure sores, particularly those that were recently termed "deep tissue injury" at the US National Pressure Ulcer Advisory Panel (NPUAP) 2005 Consensus Conference.     

Quantifying dynamic mechanical properties of human placenta tissue using optimization techniques with specimen-specific finite-element models

Motor-vehicle crashes are the leading cause of fetal deaths resulting from maternal trauma in the United States, and placental abruption is the most common cause of these deaths. To minimize this injury, new assessment tools, such as crash-test dummies and computational models of pregnant women, are needed to evaluate vehicle restraint systems with respect to reducing the risk of placental abruption. Developing these models requires accurate material properties for tissues in the pregnant abdomen under dynamic loading conditions that can occur in crashes. A method has been developed for determining dynamic material properties of human soft tissues that combines results from uniaxial tensile tests, specimen-specific finite-element models based on laser scans that accurately capture non-uniform tissue-specimen geometry, and optimization techniques. The current study applies this method to characterizing material properties of placental tissue. For 21 placenta specimens tested at a strain rate of 12/s, the mean failure strain is 0.472±0.097 and the mean failure stress is 34.80±12.62 kPa. A first-order Ogden material model with ground-state shear modulus (μ) of 23.97±5.52 kPa and exponent (α₁) of 3.66±1.90 best fits the test results. The new method provides a nearly 40% error reduction (p<0.001) compared to traditional curve-fitting methods by considering detailed specimen geometry, loading conditions, and dynamic effects from high-speed loading. The proposed method can be applied to determine mechanical properties of other soft biological tissues.     

The effect of sterilization on mechanical properties of soft tissue allografts

One major concern regarding soft tissue allograft use in surgical procedures is the risk of disease transmission. Current techniques of tissue sterilization, such as irradiation have been shown to adversely affect the mechanical properties of soft tissues. Grafts processed using Biocleanse processing (a proprietary technique developed by Regeneration Technologies to sterilize human tissues) will have better biomechanical characteristics than tissues that have been irradiated. Fifteen pairs of cadaveric Achilles tendon allografts were obtained and separated into three groups of 10 each. Three treatment groups were: Biocleanse, Irradiated, and Control (untreated). Each specimen was tested to determine the biomechanical properties of the tissue. Specimens were cyclically preloaded and then loaded to failure in tension. During testing, load, displacement, and optical strain data were captured. Following testing, the cross sectional area of the tendons was determined. Tendons in the control group were found to have a higher extrinsic stiffness (slope of the load–deformation curve, p = .005), have a higher ultimate stress (force/cross sectional area, p = .006) and higher ultimate failure load (p = .003) than irradiated grafts. Biocleanse grafts were also found to be stiffer than irradiated grafts (p = .014) yet were not found to be statistically different from either irradiated or non-irradiated grafts in terms of load to failure. Biocleanse processing seems to be a viable alternative to irradiation for Achilles tendon allografts sterilization in terms of their biomechanical properties.     

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%.     

Muscle-driven finite element simulation of human foot movements

This paper describes a finite element scheme for realistic muscle-driven simulation of human foot movements. The scheme is used to simulate human ankle plantar flexion. A three-dimensional anatomically detailed finite element model of human foot and lower leg is developed and the idea of generating natural foot movement based entirely on the contraction of the plantar flexor muscles is used. The bones, ligaments, articular cartilage, muscles, tendons, as well as the rest soft tissues of human foot and lower leg are included in the model. A realistic three-dimensional continuum constitutive model that describes the biomechanical behaviour of muscles and tendons is used. Both the active and passive properties of muscle tissue are accounted for. The materials for bones and ligaments are considered as homogeneous, isotropic and linearly elastic, whereas the articular cartilage and the rest soft tissues (mainly fat) are defined as hyperelastic materials. The model is used to estimate muscle tissue deformations as well as stresses and strains that develop in the lower leg muscles during plantar flexion of the ankle. Stresses and strains that develop in Achilles tendon during such a movement are also investigated.     

Muscle-driven finite element simulation of human foot movements

This paper describes a finite element scheme for realistic muscle-driven simulation of human foot movements. The scheme is used to simulate human ankle plantar flexion. A three-dimensional anatomically detailed finite element model of human foot and lower leg is developed and the idea of generating natural foot movement based entirely on the contraction of the plantar flexor muscles is used. The bones, ligaments, articular cartilage, muscles, tendons, as well as the rest soft tissues of human foot and lower leg are included in the model. A realistic three-dimensional continuum constitutive model that describes the biomechanical behaviour of muscles and tendons is used. Both the active and passive properties of muscle tissue are accounted for. The materials for bones and ligaments are considered as homogeneous, isotropic and linearly elastic, whereas the articular cartilage and the rest soft tissues (mainly fat) are defined as hyperelastic materials. The model is used to estimate muscle tissue deformations as well as stresses and strains that develop in the lower leg muscles during plantar flexion of the ankle. Stresses and strains that develop in Achilles tendon during such a movement are also investigated.     

The measurement of the variation in the surface strains of Achilles tendon grafts using imaging techniques

Uniaxial tensile tests are commonly used to characterize the structural and material properties of tendons and ligaments. During these tests, the stress and strain distributions applied to the specimen are assumed to be uniform. However, few studies have investigated the strain distributions throughout the tissue. The purpose of this study was to use imaging techniques to measure the strains around the circumference of 11 mm wide Achilles tendon grafts during a uniaxial tensile test. Pairs of radiopaque beads with a diameter of 2mm were affixed around the mid-substance of the tendon in four different locations. The motion of the beads was recorded using a cine fluoroscope. This system was shown to measure the displacement of the beads with an accuracy of 0.02 mm. During the uniaxial tensile test, large variations in local tissue strains were observed. At 10 MPa of applied stress, the local tissue strain varied from an average of 2.5-8.7%, an increase in strain of more than three times. As a result of these large variations, the modulus calculated from the stress-strain data varied from an average of 217 to 897 MPa, an increase of approximately 4 times. Furthermore, these data suggest that underestimates of the elastic modulus may result if a uniform strain distribution is assumed. These results indicate that during uniaxial tensile tests, the assumption of uniform stress and strain distributions should be carefully considered and small, uniform specimens should be used when measuring the material properties of soft tissues.     

Is obesity a risk factor for deep tissue injury in patients with spinal cord injury?

Deep tissue injury (DTI) is a severe form of pressure ulcers that occur in subcutaneous tissue under intact skin by the prolonged compression of soft tissues overlying bony prominences. Pressure ulcers and DTI in particular are common in patients with impaired motosensory capacities, such as those with a spinal cord injury (SCI). Obesity is also common among subjects with SCI, yet there are contradicting indications regarding its potential influence as a risk factor for DTI in conditions where these patients sit in a wheelchair without changing posture for prolonged times. It has been argued that high body mass may lead to a greater risk for DTI due to increase in compressive forces from the bones on overlying deep soft tissues, whereas conversely, it has been argued that the extra body fat associated with obesity may reduce the risk by providing enhanced subcutaneous cushioning that redistributes high interface pressures. No biomechanical evaluation of this situation has been reported to date. In order to elucidate whether obesity can be considered a risk factor for DTI, we developed computational finite element (FE) models of the seated buttocks with 4° of obesity, quantified by body mass index (BMI) values of 25.5, 30, 35 and 40 kg/m². We found that peak principal strains, strain energy densities (SED) and von Mises stresses in internal soft tissues (muscle, fat) overlying the ischial tuberosities (ITs) all increased with BMI. With a rise in BMI from 25.5 to 40 kg/m², values of these parameters increased 1.5 times on average. Moreover, the FE simulations indicated that the bodyweight load transferred through the ITs has a greater effect in increasing internal tissue strains/stresses than the counteracting effect of thickening of the adipose layer which is concurrently associated with obesity. We saw that inducing some muscle atrophy (30% reduction in muscle volume, applied to the BMI=40 kg/m² model) which is also characteristic of chronic SCI resulted in further substantial increase in all biomechanical measures reflecting geometrical distortion of muscle tissue, that is, SED, tensile stress, shear stress and von Mises stress. This result highlights that obesity and muscle atrophy, which are both typical of the chronic phase of SCI, contribute together to the state of elevated tissue loads, which consequently increases the likelihood of DTI in this population.     

Exposure to internal muscle tissue loads under the ischial tuberosities during sitting is elevated at abnormally high or low body mass indices

Deep tissue injury (DTI) is a severe pressure ulcer characteristic of chairfast or bedfast individuals, such as those with impaired mobility or neurological disorders. A DTI differs from superficial pressure ulcers in that the onset of DTI occurs under intact skin, in skeletal muscle tissue overlying bony prominences, and progression of the wound continues subcutaneously until skin breakdown. Due to the nature of this silently progressing wound, it is highly important to screen potentially susceptible individuals for their risk of developing a DTI. Abnormally low and high values of the body mass index (BMI) have been proposed to be associated with pressure ulcers, but a clear mechanism is lacking. We hypothesize that during sitting, exposure to internal muscle tissue loads under the ischial tuberosities (IT) is elevated at abnormally high or low body mass indices. Our aims in this study were: (a) to develop biomechanical models of the IT region in the buttocks that represent an individual who is gaining or losing weight drastically. (b) To determine changes in internal tissue load measures: principal compression strain, strain energy density (SED), principal compression stress and von Mises stress versus the BMI. (c) To determine percentage volumes of muscle tissue exposed to critical levels of the above load measures, which were defined based on our previous animal and tissue engineered model experiments: strain≥50%, stress≥2 kPa, SED≥0.5 kPa. A set of 21 finite element models, which represented the same individual, but with different BMI values within the normal range, above it and below it, was solved for the outcome measures listed above. The models had the same IT shape, size, distance between the IT, and (non-linear) mechanical properties for all soft tissues, but different thicknesses of gluteus muscles and fat tissue layers, corresponding to the BMI level. The resulted data indicated a trend of progressive increase in internal tissue loading, particularly in volumetric exposure to critical loading for BMI values outside the 17≤BMI≤22 kg/m² range, supporting our hypothesis for this study. We concluded that exposure to internal muscle tissue loads under the IT during sitting is optimally reduced at the low-normal BMI range, which is important not only in the context of DTI research, but also for understanding general sitting biomechanics.     

Quantification of strains in biaxially tested soft tissues

A technique for the quantification of the strain field in the central region of biaxially tested planar soft tissues is presented. A vidicon-based image analysis system interfaced to a PDP 11/34 minicomputer is employed to track particles affixed to the specimen surface in real-time, from which the strains are inferred. Illustrative results are given for tests on excised canine pleural specimens on which four particles were affixed. The technique is applicable, however, to any planar soft tissue and any number of tracking particles. This procedure is recommended over previously used methods when testing anisotropic tissues.     

Modeling mechanical strains and stresses in soft tissues of the shoulder during load carriage based on load-bearing open MRI

Shoulder strain is a major limiting factor associated with load carriage. Despite advances in backpack designs, there are still reports of shoulder discomfort, loss of sensorimotor functions, and brachial plexus syndrome. The current study is aimed at characterizing mechanical loading conditions (strains and stresses) that develop within the shoulder's soft tissues when carrying a backpack. Open MRI scans were used for reconstructing a three-dimensional geometrical model of an unloaded shoulder and for measuring the soft tissue deformations caused by a 25-kg backpack; subsequently, a subject-specific finite element (FE) model for nonlinear, large-deformation stress-strain analyses was developed. Skin pressure distributions under the backpack strap were used as reference data and for verifying the numerical solutions. The parameters of the model were adjusted to fit the calculated tissue deformations to those obtained by MRI. The MRI scans revealed significant compression of the soft tissues of the shoulder, with substantial deformations in the area of the subclavian muscle and the brachial plexus. The maximal pressure values exerted by a 25-kg load were substantial and reached ～90 kPa. In the muscle surrounding the brachial plexus, the model predicted maximal compressive strain of 0.14 and maximal tensile strain of 0.13, which might be injurious for the underlying neural tissue. In conclusion, the FE model provided some insights regarding the potential mechanisms underlying brachial plexus injuries related to load carriage. The large tissue deformations and pressure hotspots that were observed are likely to result in tissue damage, which may hamper neural function if sustained for long time exposures.