Three-dimensional finite element simulations of the mechanical response of the fingertip to static and dynamic compressions

The analysis of the mechanics of the contact interactions of fingers/handle and the stress/strain distributions in the soft tissues in the fingertip is essential to optimize design of tools to reduce many occupation-related hand disorders. In the present study, a three-dimensional (3D) finite element (FE) model for the fingertip is proposed to simulate the nonlinear and time-dependent responses of a fingertip to static and dynamic loadings. The proposed FE model incorporates the essential anatomical structures of a finger: skin layers (outer and inner skins), subcutaneous tissue, bone and nail. The soft tissues (inner skin and subcutaneous tissue) are considered to be nonlinearly viscoelastic, while the hard tissues (outer skin, bone and nail) are considered to be linearly elastic. The proposed model has been used to simulate two loading scenarios: (a) the contact interactions between the fingertip and a flat surface and (b) the indentation of the fingerpad via a sharp wedge. For case (a), the predicted force/displacement relationships and time-dependent force responses are compared with the published experimental data; for case (b), the skin surface deflection profiles were predicted and compared with the published experimental observations. Furthermore, for both cases, the time-dependent stress/strain distributions within the tissues of the fingertip were calculated. The good agreement between the model predictions and the experimental observations indicates that the present model is capable of predicting realistic time-dependent force/displacement responses and stress/strain distributions in the soft tissues for dynamic loading conditions.     

Analysis of the dynamic strains in a fingertip exposed to vibrations: Correlation to the mechanical stimuli on mechanoreceptors

The reduction in vibrotactile sensitivity in the fingertip is assumed to be associated with the exposure of the tissues to repetitive, non-physiological strains during dynamic loading. Experimental results demonstrated that the magnitude of a vibration-induced temporary threshold shift is dependent upon the vibration frequency of both the exposure and testing stimuli. In the present study, the frequency-dependent strain imposed on cutaneous and subcutaneous tissues of the fingertip is analyzed theoretically using a finite element model. The proposed fingertip model is two-dimensional and includes major anatomical substructures: skin, subcutaneous tissue, bone, and nail. The soft tissues (skin and subcutaneous tissues) were assumed to be nonlinearly elastic and viscoelastic, while the bone and nail were considered as linearly elastic. Simulations were performed for the contact between the fingertip and a flat surface for four different pre-compressions (0.5, 1.0, 1.5, and 2.0 mm). The frequency-dependent distributions of the dynamic strain magnitudes in the soft tissues were investigated. The model predictions indicated that the vibration exposure at a frequency range from 63 to 250 Hz will induce excessive dynamic strain in the deep zone of the finger tissues, effectively inhibiting the high-frequency mechanoreceptors; while the vibration exposure at low frequency (less than 31.5 Hz) tends to induce excessive dynamic strain in superficial layer in the tissues, inhibiting the low-frequency mechanoreceptors. These theoretical predictions are consistent with the experimental observations in literature. The proposed model can be used to predict the responses of the soft tissues in different depths to vibration exposures, providing valuable information and data that are essential for improving vibrotactile perception tests.     

Modeling of time-dependent force response of fingertip to dynamic loading

An extended exposure to repeated loading on fingertip has been associated to many vascular, sensorineural, and musculoskeletal disorders in the fingers, such as carpal tunnel syndrome, hand-arm vibration syndrome, and flexor tenosynovitis. A better understanding of the pathomechanics of these sensorineural and vascular diseases in fingers requires a formulation of a biomechanical model of the fingertips and analyses to predict the mechanical responses of the soft tissues to dynamic loading. In the present study, a model based on finite element techniques has been developed to simulate the mechanical responses of the fingertips to dynamic loading. The proposed model is two-dimensional and incorporates the essential anatomical structures of a finger: skin, subcutaneous tissue, bone, and nail. The skin tissue is assumed to be hyperelastic and viscoelastic. The subcutaneous tissue was considered to be a nonlinear, biphasic material composed of a hyperelastic solid and an invicid fluid, while its hydraulic permeability was considered to be deformation dependent. Two series of numerical tests were performed using the proposed finger tip model to: (a) simulate the responses of the fingertip to repeated loading, where the contact plate was assumed to be fixed, and the bone within the fingertip was subjected to a prescribed sinusoidal displacement in vertical direction; (b) simulate the force response of the fingertip in a single keystroke, where the keyboard was composed of a hard plastic keycap, a rigid support block, and a nonlinear spring. The time-dependent behavior of the fingertip under dynamic loading was derived. The model predictions of the time-histories of force response of the fingertip and the phenomenon of fingertip separation from the contacting plate during cyclic loading agree well with the reported experimental observations.     

Surface deflection of primate fingertip under line load

A study of the biomechanics of the skin and the subcutaneous soft tissues is of fundamental importance in understanding the process of transduction at the mechanoreceptive nerve terminals responsible for the sense of touch. In the present investigation, the fingertips (distal phalanges) of three adult humans and four monkeys were indented in vivo using a line load delivered by a sharp wedge. The resulting skin surface deflection profile was photographed and used as a clue to infer the mechanical nature of the materials that make up the fingertip. It is shown that the modified Boussinesq solution used by Phillips and Johnson (1981), applicable when the fingertip is modeled as an elastic half-space in a state of plane strain, predicts a skin surface deflection profile that can only roughly approximate the empirically observed profiles. As an alternative, a simple model which views the fingertip as an elastic membrane filled with an incompressible fluid (like a 'waterbed') under plane strain conditions is proposed. It is shown that the predictions of this model, which takes into account the finite deformations that occur, agree very well with the photographed profiles in the region of interest (up to about 3 mm from the load).     

Real-time subject-specific monitoring of internal deformations and stresses in the soft tissues of the foot: a new approach in gait analysis

No technology is presently available to provide real-time information on internal deformations and stresses in plantar soft tissues of individuals during evaluation of the gait pattern. Because internal deformations and stresses in the plantar pad are critical factors in foot injuries such as diabetic foot ulceration, this severely limits evaluation of patients. To allow such real-time subject-specific analysis, we developed a hierarchal modeling system which integrates a two-dimensional gross structural model of the foot (high-order model) with local finite element (FE) models of the plantar tissue padding the calcaneus and medial metatarsal heads (low-order models). The high-order whole-foot model provides real-time analytical evaluations of the time-dependent plantar fascia tensile forces during the stance phase. These force evaluations are transferred, together with foot-shoe local reaction forces, also measured in real time (under the calcaneus, medial metatarsals and hallux), to the low-order FE models of the plantar pad, where they serve as boundary conditions for analyses of local deformations and stresses in the plantar pad. After careful verification of our custom-made FE solver and of our foot model system with respect to previous literature and against experimental results from a synthetic foot phantom, we conducted human studies in which plantar tissue loading was evaluated in real time during treadmill gait in healthy individuals (N = 4). We concluded that internal deformations and stresses in the plantar pad during gait cannot be predicted from merely measuring the foot-shoe force reactions. Internal loading of the plantar pad is constituted by a complex interaction between the anatomical structure and mechanical behavior of the foot skeleton and soft tissues, the body characteristics, the gait pattern and footwear. Real-time FE monitoring of internal deformations and stresses in the plantar pad is therefore required to identify elevated deformation/stress exposures toward utilizing it in gait laboratories to protect feet that are susceptible to injury.     

Explicit finite element modelling of heel pad mechanics in running: inclusion of body dynamics and application of physiological impact loads

Many heel pathologies including plantar heel pain may result from micro tears/trauma in the subcutaneous tissues, in which internal tissue deformation/stresses within the heel pad play an important role. Previously, many finite element models have been proposed to evaluate stresses inside the heel pad, but the majority of these models only focus on static loading boundary conditions. This study explored a dynamics modelling approach to the heel pad subjected to realistic impact loads during running. In this model, the inertial property and action of the body are described by a lumped parameter model, while the heel/shoe interactions are modelled using a viscoelastic heel pad model with contact properties. The impact force pattern, dynamic heel pad deformation and stress states predicted by the model were compared with published experimental data. Further parametrical studies revealed the model responses, in terms of internal stresses in the skin and fatty tissue, change nonlinearly when body dynamics changes. A reduction in foot's touchdown velocity resulted in a less severe impact landing and stress relief inside the heel pad, for example peak von-Mises stress in fatty tissue, was reduced by 11.3%. Applications of the model may be extendable to perform iterative analyses to further understand the complex relationships between body dynamics and stress distributions in the soft tissue of heel pad during running. This may open new opportunities to study the mechanical aetiology of plantar heel pain in runners.     

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.     

Experimentally tested computer modeling of stress fractures in rats

The objective of this study was to develop a finite-element (FE) modeling methodology for studying the etiology of a stress fracture (SF). Several variants of three-dimensional FE models of a rat hindlimb, which differed in length or stiffness of tissues, enabling the analyses of mechanical strains and stress in the tibia, were created. We compared the occurrence of SFs in an animal model to validate locations of peak strains/stresses in the FE models. Four Sprague-Dawley male rats, age ~7 wk, were subjected to mechanical cyclic loads of 1.2 Hz and ~6 N, which were delivered to their hindlimb for 30 min, 3 times/wk, up to 12 wk, by using a specially designed apparatus. The results showed that 1) FE modeling predicted the maximal strains/stresses (~220,0 με and ~29 MPa, respectively) between the mid- and proximal thirds of the tibia; 2) in a longer shin, greater and more inhomogeneous tensile strains/stresses were evident, at the same location; 3) anatomical variants in shin length influenced the strain/stress distributions to a greater extent with respect to changes in mechanical properties of tissues; and 4) bone stiffness was more dominant than muscle stiffness in affecting the strain/stress distributions. In the animal study, 35,000 loading cycles were associated with the formation of a SF. The location of the identified SF in the rat limb verified the FE model. We find the suggested model a valuable tool in studying various aspects of SFs.     

Development of a dynamic index finger and thumb model to study impairment

Modeling of the human hand provides insight for explaining deficits and planning treatment following injury. Creation of a dynamic model, however, is complicated by the actions of multi-articular tendons and their complex interactions with other soft tissues in the hand. This study explores the creation of a musculoskeletal model, including the thumb and index finger, to explore the effects of muscle activation deficits. The OpenSim model utilizes physiological axes of rotation at all joints, passive joint torques, and appropriate moment arms. The model was validated through comparison with kinematic and kinetic experimental data. Simulated fingertip forces resulting from modeled musculotendon loading largely fell within one standard deviation of experimental ranges for most index finger and thumb muscles, although agreement in the sagittal plane was generally better than for the coronal plane. Input of experimentally obtained electromyography data produced the expected simulated finger and thumb motion. Use of the model to predict the effects of activation deficits on pinch force production revealed that the intrinsic muscles, especially first dorsal interosseous (FDI) and adductor pollicis (ADP), had a substantial impact on the resulting fingertip force. Reducing FDI activation, such as might occur following stroke, altered fingertip force direction by up to 83° for production of a dorsal fingertip force; reducing ADP activation reduced force production in the thumb by up to 62%. This validated model can provide a means for evaluating clinical interventions.     

Three dimensional patient-specific collagen architecture modulates cartilage responses in the knee joint during gait

Site-specific variation of collagen fibril orientations can affect cartilage stresses in knee joints. However, this has not been confirmed by 3-D analyses. Therefore, we present a novel method for evaluation of the effect of patient-specific collagen architecture on time-dependent mechanical responses of knee joint cartilage during gait. 3-D finite element (FE) models of a human knee joint were created with the collagen architectures obtained from T₂ mapped MRI (patient-specific model) and from literature (literature model). The effect of accuracy of the implementation of collagen fibril architecture into the model was examined by using a submodel with denser FE mesh. Compared to the literature model, fibril strains and maximum principal stresses were reduced especially in the superficial/middle regions of medial tibial cartilage in the patient-specific model after the loading response of gait (up to ?413 and ?26%, respectively). Compared to the more coarsely meshed joint model, the patient-specific submodel demonstrated similar strain and stress distributions but increased values particularly in the superficial cartilage regions (especially stresses increased >60%). The results demonstrate that implementation of subject-specific collagen architecture of cartilage in 3-D modulates location- and time-dependent mechanical responses of human knee joint cartilage. Submodeling with more accurate implementation of collagen fibril architecture alters cartilage stresses particularly in the superficial/middle tissue.     

The effect of torque direction and cylindrical handle diameter on the coupling between the hand and a cylindrical handle

Pheasant and O'Neill's torque model (1975) was modified to account for grip force distributions. The modified model suggests that skin friction produced by twisting an object in the direction of fingertips causes flexion of the distal phalanges and increases grip force and, thus, torque. Twelve subjects grasped a cylindrical object with diameters of 45.1, 57.8, and 83.2 mm in a power grip, and performed maximum torque exertions about the long axis of the handle in two directions: the direction the thumb points and the direction the fingertips point. Normal force on the fingertips increased with torque toward the fingertips, as predicted by the model. Consequently, torque toward the fingertips was 22% greater than torque toward the thumb. Measured torque and fingertip forces were compared with model predictions. Torque could be predicted well by the model. Measured fingertip force and thumb force were, on average, 27% less than the predicted values. Consistent with previous studies, grip force decreased as the handle diameter increased from 45.1 to 83.2 mm. This may be due not only to the muscle length-strength relationship, but also to major active force locations on the hand: grip force distributions suggest that a small handle allows fingertip force and thumb force to work together against the palm, resulting in a high reaction force on the palm, and, therefore, a high grip force. For a large handle, fingertip force and thumb force act against each other, resulting in little reaction force on the palm and, thus, a low grip force.     

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.     

Finite element analysis of heel pad with insoles

To design optimal insoles for reduction of pedal tissue trauma, experimental measurements and computational analyses were performed. To characterize the mechanical properties of the tissues, indentation tests were performed. Pedal tissue geometry and morphology were obtained from magnetic resonance scan of the subject's foot. Axisymmetrical finite element models of the heel of the foot were created with 1/4 of body weight load applied. The stress, strain and strain energy density (SED) fields produced in the pedal tissues were computed. The effects of various insole designs and materials on the resulting stress, strain, and SED in the soft pedal tissues were analyzed. The results showed: (a) Flat insoles made of soft material provide some reductions in the maximum stress, strain and SED produced in the pedal tissues. These maximum values were computed near the calcaneus. (b) Flat insoles, with conical/cylindrical reliefs, provided more reductions in these maximum values than without reliefs. (c) Custom insoles, contoured to match the pedal geometry provide most reductions in the maximum stress, strain and SED. Also note, the maximum stress, strain and SED computed near the calcaneus were found to be about 10 times the corresponding peak values computed on the skin surface. Based on the FEA analysis, it can be concluded that changing insole design and using different material can significantly redistribute the stress/strain inside the heel pad as well as on the skin surface.     

Material characterization of the pig kidney in relation with the biomechanical analysis of renal trauma

The objective of this study was an investigation of the material properties of the fresh pig kidney and parametric characterization of its elastic and inelastic material behavior. The material investigation included density measurements, uniaxial as well as three-dimensional compression tests, tensile tests. and shear tests on the samples extracted from the fresh pig kidney. For comparison, density measurements on a number of soft synthetic materials were also performed. Compression tests on the radial and the tangential specimens from the cortex tissue were performed at various loading rates. Three-axial compression tests were performed on the cortex tissues placed in a compression chamber. Shear tests were performed by punching a cylinder into a slice of the cortex. Tensile tests were carried out on the outer capsule. For characterization of the material behavior, a non-linear theoretical simulation based on a two parameter Blatz model was used. For characterization of the time-dependent behavior of the pig kidney cortex, a four-parameter linear viscoelastic model was employed. From the present experimental and theoretical studies, a number of conclusions were derived: (1) The general behavior of the pig kidney cortex samples under compression showed the general non-linear features typical of the soft tissues; the stress strain diagram was composed of a very flat part at very low stress level to about 30% relative deformation which was followed by a steeply rising stiffening leading to the radial rupture of samples marked by a maximum nominal rupture strain of about 50%. (2) The uniaxial compression tests on the radial and the tangential samples from the cortex tissue showed an increase of the rupture stress with the increase in the loading rate, but a decrease in the related rupture strain. (3) The long-term uniaxial compression tests on the cortex specimens under sustained constant load showed an instantaneous deformation followed by a creep response which eventually approached an asymptote. (4) Simulation of the non-linear material behavior of the cortex tissue under uniaxial compression by the Blatz model gave two pairs of material parameters for the cortex in the radial and the tangential directions. Furthermore, fitting of the assumed four-parameter linear viscoelastic model with the experimental data resulted in the viscoelastic material parameters.     

Numerical study of tension and strain distribution around rat molars]

A knowledge of the mechanical processes triggered in the bone and periodontal ligament (PDL) by orthodontic forces applied to a tooth is of decisive importance for an understanding of the subsequent remodelling around the tooth. To investigate these mechanical relationships, three-dimensional finite element (FE) models of the first lower molar in the rat were established. On the basis of digitized serial histological sections, these FE models were generated semi-automatically. Using various simplified geometrical variations, an appropriate FE model for the analysis of the stress and strain distributions was established. The numerical analyses were carried out under a mesially directed force of 0.1 N. Stress distributions in the bone and PDL showed a similar pattern, while strains in the bone were lower than in the PDL by a factor of 10-5. The data confirm the assumption that strain patterns in the PDL may be the key stimulus of bone remodelling.     

A finite viscoelastic–plastic model for describing the uniaxial ratchetting of soft biological tissues

In this paper, a phenomenological constitutive model is constructed to describe the uniaxial ratchetting (i.e., the cyclic accumulation of inelastic deformation) of soft biological tissues in the framework of finite viscoelastic-plasticity. The model is derived from a polyconvex elastic free energy function and addresses the anisotropy of cyclic deformation of the tissues by means of structural tensors. Ratchetting is considered by the evolution of internal variables, and its time-dependence is described by introducing a pseudo-potential function. Accordingly, all the evolution equations are formulated from the dissipation inequality. In numerical examples, the uniaxial monotonic stress–strain responses and ratchetting of some soft biological tissues, such as porcine skin, coronary artery layers and human knee ligaments and tendons, are predicted by the proposed model in the range of finite deformation. It is seen that the predicted monotonic stress–strain responses and uniaxial ratchetting obtained at various loading rates and in various loading directions are in good agreement with the corresponding experimental results.     

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.     

Finite element implementation of a new model of slight compressibility for transversely isotropic materials

Modelling transversely isotropic materials in finite strain problems is a complex task in biomechanics, and is usually addressed by using finite element (FE) simulations. The standard method developed to account for the quasi-incompressible nature of soft tissues is to decompose the strain energy function (SEF) into volumetric and deviatoric parts. However, this decomposition is only valid for fully incompressible materials, and its use for slightly compressible materials yields an unphysical response during the simulation of hydrostatic tension/compression of a transversely isotropic material. This paper presents the FE implementation as subroutines of a new volumetric model solving this deficiency in two FE codes: Abaqus and FEBio. This model also has the specificity of restoring the compatibility with small strain theory. The stress and elasticity tensors are first derived for a general SEF. This is followed by a successful convergence check using a particular SEF and a suite of single-element tests showing that this new model does not only correct the hydrostatic deficiency but may also affect stresses during shear tests (Poynting effect) and lateral stretches during uniaxial tests (Poisson's effect). These FE subroutines have numerous applications including the modelling of tendons, ligaments, heart tissue, etc. The biomechanics community should be aware of specificities of the standard model, and the new model should be used when accurate FE results are desired in the case of compressible materials.