A three-dimensional finite element model for arterial clamping

Clamp induced injuries of the arterial wall may determine the outcome of surgical procedures. Thus, it is important to investigate the underlying mechanical effects. We present a three-dimensional finite element model, which allows the study of the mechanical response of an artery-treated as a two-layer tube-during arterial clamping. The important residual stresses, which are associated with the load-free configuration of the artery, are also considered. In particular, the finite element analysis of the deformation process of a clamped artery and the associated stress distribution is presented. Within the clamping area a zone of axial tensile peak-stresses was identified, which (may) cause intimal and medial injury. This is an additional injury mechanism, which clearly differs from the commonly assumed wall damage occurring due to compression between the jaws of the clamp. The proposed numerical model provides essential insights into the mechanics of the clamping procedure and the associated injury mechanisms. It allows detailed parameter studies on a virtual clamped artery, which can not be performed with other methodologies. This approach has the potential to identify the most appropriate clamps for certain types of arteries and to guide optimal clamp design.     

Evaluation of liver tissue damage and grasp stability using finite element analysis

Minimizing tissue damage and maintaining grasp stability are essential considerations in surgical grasper design. Most past and current research analyzing graspers used for tissue manipulation in minimally invasive surgery is based on in vitro experiments. Most previous work assessed tissue injury and grasp security by visual inspection; only a few studies have quantified it. The goal of the present work is to develop a methodology with which to compute tissue damage magnitude and grasp quality that is appropriate for a wide range of grasper–tissue interaction. Using finite element analysis (FEA), four graspers with varying radii of curvature and four graspers with different tooth sizes were analyzed while squeezing and pulling liver tissue. All graspers were treated as surgical steel with linear elastic material properties. Nonlinear material properties of tissue used in the FEA as well as damage evaluation were derived from previously reported in vivo experiments. Computed peak stress, integrated stress, and tissue damage were compared. Applied displacement is vertical and then horizontal to the tissue surface to represent grasp and retraction. A close examination of the contact status of each node within the grasper–tissue interaction surface was carried out to investigate grasp stability. The results indicate less tissue damage with increasing radius of curvature. A smooth wave pattern reduced tissue damage at the cost of inducing higher percentage of slipping area. This methodology may be useful for researchers to develop and test various designs of graspers. Also it could improve surgical simulator performance by reflecting more realistic tissue material properties and predicting tissue damage for the student.     

In silico prediction of the mechanobiological response of arterial tissue: application to angioplasty and stenting

One way to restore physiological blood flow to occluded arteries involves the deformation of plaque using an intravascular balloon and preventing elastic recoil using a stent. Angioplasty and stent implantation cause unphysiological loading of the arterial tissue, which may lead to tissue in-growth and reblockage; termed "restenosis." In this paper, a computational methodology for predicting the time-course of restenosis is presented. Stress-induced damage, computed using a remaining life approach, stimulates inflammation (production of matrix degrading factors and growth stimuli). This, in turn, induces a change in smooth muscle cell phenotype from contractile (as exists in the quiescent tissue) to synthetic (as exists in the growing tissue). In this paper, smooth muscle cell activity (migration, proliferation, and differentiation) is simulated in a lattice using a stochastic approach to model individual cell activity. The inflammation equations are examined under simplified loading cases. The mechanobiological parameters of the model were estimated by calibrating the model response to the results of a balloon angioplasty study in humans. The simulation method was then used to simulate restenosis in a two dimensional model of a stented artery. Cell activity predictions were similar to those observed during neointimal hyperplasia, culminating in the growth of restenosis. Similar to experiment, the amount of neointima produced increased with the degree of expansion of the stent, and this relationship was found to be highly dependant on the prescribed inflammatory response. It was found that the duration of inflammation affected the amount of restenosis produced, and that this effect was most pronounced with large stent expansions. In conclusion, the paper shows that the arterial tissue response to mechanical stimulation can be predicted using a stochastic cell modeling approach, and that the simulation captures features of restenosis development observed with real stents. The modeling approach is proposed for application in three dimensional models of cardiovascular stenting procedures.     

Microplane constitutive model and computational framework for blood vessel tissue

This paper presents a nonlinearly elastic anisotropic microplane formulation in 3D for computational constitutive modeling of arterial soft tissue in the passive regime. The constitutive modeling of arterial (and other biological) soft tissue is crucial for accurate finite element calculations, which in turn are essential for design of implants, surgical procedures, bioartificial tissue, as well as determination of effect of progressive diseases on tissues and implants. The model presented is defined at a lower scale (mesoscale) than the conventional macroscale and it incorporates the effect of all the (collagen) fibers which are anisotropic structural components distributed in all directions within the tissue material in addition to that of isotropic bulk tissue. It is shown that the proposed model not only reproduces Holzapfel's recent model but also improves on it by accounting for the actual three-dimensional distribution of fiber orientation in the arterial wall, which endows the model with advanced capabilities in simulation of remodeling of soft tissue. The formulation is flexible so that its parameters could be adjusted to represent the arterial wall either as a single material or a material composed of several layers in finite element analyses of arteries. Explicit algorithms for both the material subroutine and the explicit integration with dynamic relaxation of equations of motion using finite element method are given. To circumvent the slow convergence of the standard dynamic relaxation and small time steps dictated by the stability of the explicit integrator, an adaptive dynamic relaxation technique that ensures stability and fastest possible convergence rates is developed. Incompressibility is enforced using penalty method with an updated penalty parameter. The model is used to simulate experimental data from the literature demonstrating that the model response is in excellent agreement with the data. An experimental procedure to determine the distribution of fiber directions in 3D for biological soft tissue is suggested in accordance with the microplane concept. It is also argued that this microplane formulation could be modified or extended to model many other phenomena of interest in biomechanics.     

Nonlinear incompressible finite element for simulating loading of cardiac tissue--Part I: Two dimensional formulation for thin myocardial strips

A two-dimensional incompressible plane-stress finite element is formulated for the simulation of the passive-state mechanics of thin myocardial strips. The formulation employs a total Lagrangian and materially nonlinear approach, being based on a recently proposed structural material law, which is derived from the histological composition of the tissue. The ensuing finite element allows to demonstrate the mechanical properties of a single myocardial layer containing uniformly directed fibers by simulating various loading cases such as tension, compression and shear. The results of these cases show that the fiber direction is considerably stiffer than the cross-fiber direction, that there is significant coupling between these two directions, and that the shear stiffness of the tissue is lower than its tensile and compressive stiffness.     

Constitutive model of brain tissue suitable for finite element analysis of surgical procedures.

Realistic finite element modelling and simulation of neurosurgical procedures present a formidable challenge. Appropriate, finite deformation, constitutive model of brain tissue is a prerequisite for such development. In this paper, a large deformation, linear, viscoelastic model, suitable for direct use with commercially available finite element software packages such as ABAQUS is constructed. The proposed constitutive equation is of polynomial form with time-dependent coefficients. The model requires four material constants to be identified. The material constants were evaluated based on unconfined compression experiment results. The analytical as well as numerical solutions to the unconfined compression problem are presented. The agreement between the proposed theoretical model and the experiment is good for compression levels reaching 30% and for loading velocities varying over five orders of magnitude. The numerical solution using the finite element method matched the analytical solution very closely.     

Sensitivity of damage predictions to tissue level yield properties and apparent loading conditions

High-resolution finite element models of trabecular bone failure could be used to augment current techniques for measuring damage in trabecular bone. However, the sensitivity of such models to the assumed tissue yield properties and apparent loading conditions is unknown. The goal of this study was to assess the sensitivity of the amount and mode (tension vs. compression) of tissue level yielding in trabecular bone to these factors. Linear elastic, high-resolution finite element models of nine bovine tibial trabecular bone specimens were used to calculate the fraction of the total tissue volume that exceeded each criterion for apparent level loading to the reported elastic limit in both on-axis and transverse compression and tension, and in shear. Four candidate yield criteria were studied, based on values suggested in the literature. Both the amount and the failure mode of yielded tissue were sensitive to the magnitudes of the tissue yield strains, the degree of tension-compression asymmetry of the yield criterion, and the applied apparent loads. The amount of yielded tissue was most sensitive to the orientation of the applied apparent loading, with the most tissue yielding for loading along the principal trabecular orientation and the least for loading perpendicular to it, regardless of the assumed tissue level yield criterion. Small changes in the magnitudes and the degree of asymmetry of the tissue yield criterion resulted in much larger changes in the amount of yielded tissue in the model. The results indicate that damage predictions based on high-resolution finite element models are highly sensitive to the assumed tissue yield properties. As such, good estimates of these values are needed before high-resolution finite element models can be applied to the study of trabecular bone damage. Regardless of the assumed tissue yield properties, the amount and type of damage that occurs in trabecular bone depends on the relative orientations of the applied apparent loads to the trabecular architecture, and this parameter should be controlled for both experimental and computational damage studies.     

Mechanical properties of brain tissue in-vivo: experiment and computer simulation

Realistic computer simulation of neurosurgical procedures requires incorporation of the mechanical properties of brain tissue in the mathematical model. Possible applications of computer simulation of neurosurgery include non-rigid registration, virtual reality training and operation planning systems and robotic devices to perform minimally invasive brain surgery. A number of constitutive models of brain tissue, both single-phase and bi-phasic, have been proposed in recent years. The major deficiency of most of them, however, is the fact that they were identified using experimental data obtained in vitro and there is no certainty whether they can be applied in the realistic in vivo setting. In this paper we attempt to show that previously proposed by us hyper-viscoelastic constitutive model of brain tissue can be applied to simulating surgical procedures. An in vivo indentation experiment is described. The force-displacement curve for the loading speed typical for surgical procedures is concave upward containing no linear portion from which a meaningful elastic modulus might be determined. In order to properly analyse experimental data, a three-dimensional, non-linear finite element model of the brain was developed. Magnetic resonance imaging techniques were used to obtain geometric information needed for the model. The shape of the force-displacement curve obtained using the numerical solution was very similar to the experimental one. The predicted forces were about 31% lower than those recorded during the experiment. Having in mind that the coefficients in the model had been identified based on experimental data obtained in vitro, and large variability of mechanical properties of biological tissues, such agreement can be considered as very good. By appropriately increasing material parameters describing instantaneous stiffness of the tissue one is able, without changing the structure of the model, to reproduce experimental curve almost perfectly. Numerical studies showed also that the linear, viscoelastic model of brain tissue is not appropriate for the modelling brain tissue deformation even for moderate strains.     

Initiation and progression of mechanical damage in the intervertebral disc under cyclic loading using continuum damage mechanics methodology: A finite element study

It is difficult to study the breakdown of disc tissue over several years of exposure to bending and lifting by experimental methods. There is also no finite element model that elucidates the failure mechanism due to repetitive loading of the lumbar motion segment. The aim of this study was to refine an already validated poro-elastic finite element model of lumbar motion segment to investigate the initiation and progression of mechanical damage in the disc under simple and complex cyclic loading conditions. Continuum damage mechanics methodology was incorporated into the finite element model to track the damage accumulation in the annulus in response to the repetitive loading. The analyses showed that the damage initiated at the posterior inner annulus adjacent to the endplates and propagated outwards towards its periphery under all loading conditions simulated. The damage accumulated preferentially in the posterior region of the annulus. The analyses also showed that the disc failure is unlikely to happen with repetitive bending in the absence of compressive load. Compressive cyclic loading with low peak load magnitude also did not create the failure of the disc. The finite element model results were consistent with the experimental and clinical observations in terms of the region of failure, magnitude of applied loads and the number of load cycles survived.     

Concurrent musculoskeletal dynamics and finite element analysis predicts altered gait patterns to reduce foot tissue loading

Current computational methods for simulating locomotion have primarily used muscle-driven multibody dynamics, in which neuromuscular control is optimized. Such simulations generally represent joints and soft tissue as simple kinematic or elastic elements for computational efficiency. These assumptions limit application in studies such as ligament injury or osteoarthritis, where local tissue loading must be predicted. Conversely, tissue can be simulated using the finite element method with assumed or measured boundary conditions, but this does not represent the effects of whole body dynamics and neuromuscular control. Coupling the two domains would overcome these limitations and allow prediction of movement strategies guided by tissue stresses. Here we demonstrate this concept in a gait simulation where a musculoskeletal model is coupled to a finite element representation of the foot. Predictive simulations incorporated peak plantar tissue deformation into the objective of the movement optimization, as well as terms to track normative gait data and minimize fatigue. Two optimizations were performed, first without the strain minimization term and second with the term. Convergence to realistic gait patterns was achieved with the second optimization realizing a 44% reduction in peak tissue strain energy density. The study demonstrated that it is possible to alter computationally predicted neuromuscular control to minimize tissue strain while including desired kinematic and muscular behavior. Future work should include experimental validation before application of the methodology to patient care.     

An investigation into the role of different constituents in damage accumulation in arterial tissue and constitutive model development

Carotid atherosclerotic plaque rupture is one of the leading causes of stroke. Treatments for atherosclerosis can induce tissue damage during the deployment of an intravascular device or through external tissue clamping during surgery. In this paper, a constituent specific study was performed to investigate the role of the ground matrix and collagen fibres of arterial tissue in response to supra-physiological loads. Cyclic mechanical tests were conducted on intact and collagenase-digested strips of porcine common carotid arteries. Using these tests, four passive damage-relevant phenomena were studied, namely (i) Mullins effect, (ii) hysteresis, (iii) permanent set and (iv) matrix failure and fibre rupture. A constitutive model was also developed to capture all of these damage-relevant phenomena using a continuum damage mechanics approach. The implemented constitutive model was fit to experimental results for both intact and digested samples. The results of this work demonstrate the important role of the ground matrix in the permanent deformation of the arterial tissue under high loads. Supra-physiological load-induced tissue damage may play a key role in vascular remodelling in arteries with atherosclerosis or following interventional procedures.     

Finite element thermal analysis of bone cement for joint replacements

A finite element technique was developed to investigate the thermal behavior of bone cement in joint replacement procedures. Thermal tests were designed and performed to provide the parameters in a kinetic model of bone cement exothermic polymerization. The kinetic model was then coupled with an energy balance equation using a finite element formulation to predict the temperature history and polymerization development in the bone-cement-prosthesis system. Based on the temperature history, the possibility of the thermal bone necrosis was then evaluated. As a demonstration, the effect of cement mantle thickness on the thermal behavior of the system was investigated. The temperature profiles in the bone-cement-prosthesis system have shown that the thicker the cement, the higher the peak temperature in the bone. In the 7 mm thick cement case, a peak temperature of over 55 degrees C was predicted. These high temperatures occurred in a small region near the bone/cement interface. No damage was predicted in the 3 mm and 5 mm cement mantle thickness cases. Although thermal damage was predicted in the bone for the 7 mm mantle thickness case, the amount of thermal necrosis predicted was minimal. If more cement is used in the surgical procedure, more heat will be generated and the potential for thermal bone damage may rise. The systems should be carefully selected to reduce thermal tissue damage when more cement is used. The methodology developed in this paper provides a numerical tool for the quantitative simulation of the thermal behavior of bone-cement-prosthesis designs.     

How does muscle stiffness affect the internal deformations within the soft tissue layers of the buttocks under constant loading?

Mechanical loading of soft tissues covering bony prominences can cause skeletal muscle damage, ultimately resulting in a severe pressure ulcer termed deep tissue injury (DTI). Deformation plays an important role in the aetiology of DTI. Therefore, it is essential to minimise internal muscle deformations in subjects at risk of DTI. As an example, spinal cord-injured (SCI) individuals exhibit structural changes leading to a decrease in muscle thickness and stiffness, which subsequently increase the tissue deformations. In the present study, an animal-specific finite element model, where the geometry and boundary conditions were derived from magnetic resonance images, was developed. It was used to investigate the internal deformations in the muscle, fat and skin layers of the porcine buttocks during loading. The model indicated the presence of large deformations in both the muscle and the fat layers, with maximum shear strains up to 0.65 in muscle tissue and 0.63 in fat. Furthermore, a sensitivity analysis showed that the tissue deformations depend considerably on the relative stiffness values of the different tissues. For example, a change in muscle stiffness had a large effect on the muscle deformations. A 50% decrease in stiffness caused an increase in maximum shear strain from 0.65 to 0.99, whereas a 50% increase in stiffness resulted in a decrease in maximum shear strain from 0.65 to 0.49. These results indicate the importance of restoring tissue properties after SCI, with the use of, for example, electrical stimulation, to prevent the development of DTI.     

Contribution of tissue composition and structure to mechanical response of articular cartilage under different loading geometries and strain rates

Mechanical function of articular cartilage in joints between articulating bones is dependent on the composition and structure of the tissue. The mechanical properties of articular cartilage are traditionally tested in compression using one of the three loading geometries, i.e., confined compression, unconfined compression or indentation. The aim of this study was to utilize a composition-based finite element model in combination with a fractional factorial design to determine the importance of different cartilage constituents in the mechanical response of the tissue, and to compare the importance of the tissue constituents with different loading geometries and loading rates. The evaluated parameters included water and collagen fraction as well as fixed charge density on cartilage surface and their slope over the tissue thickness. The thicknesses of superficial and middle zones, as based on the collagen orientation, were also included in the evaluated parameters. A three-level resolution V fractional factorial design was used. The model results showed that inhomogeneous composition plays only a minor role in indentation, though that role becomes more significant in confined compression and unconfined compression. In contrast, the collagen architecture and content had a more profound role in indentation than with two other loading geometries. These differences in the mechanical role of composition and structure between the loading geometries were emphasized at higher loading rates. These findings highlight how the results from mechanical tests of articular cartilage under different loading conditions are dependent upon tissue composition and structure.     

Accumulation of loading damage and unloading reperfusion injury — Modeling of the propagation of deep tissue ulcers

Deep tissue injury (DTI) occurs in deep muscles around bony prominences due to excessive and prolonged mechanical loading acting on the skin surface. The condition is clinically challenging because it can escape being noticed till the damage propagates all the way to the skin. In this study, a semi-3D finite element model of a human buttock was used to simulate the process of ulcer evolution based on our recent damage accumulation and repair theory for DTI. The theory included not only the loading damage, but also further reperfusion and inflammatory injuries upon unloading. The results showed that depending on the model parameters and loading conditions, a deep tissue ulcer may initiate around a bony prominence and expand to affect the entire tissue thickness. The damage evolution can be affected by the tissue healing rate, the loading–unloading pattern and the cushion stiffness. The results may help clinical workers appreciate the importance of proper patient turning and the appropriate choice of cushion.     

Patient-specific non-linear finite element modelling for predicting soft organ deformation in real-time; Application to non-rigid neuroimage registration

Long computation times of non-linear (i.e. accounting for geometric and material non-linearity) biomechanical models have been regarded as one of the key factors preventing application of such models in predicting organ deformation for image-guided surgery. This contribution presents real-time patient-specific computation of the deformation field within the brain for six cases of brain shift induced by craniotomy (i.e. surgical opening of the skull) using specialised non-linear finite element procedures implemented on a graphics processing unit (GPU). In contrast to commercial finite element codes that rely on an updated Lagrangian formulation and implicit integration in time domain for steady state solutions, our procedures utilise the total Lagrangian formulation with explicit time stepping and dynamic relaxation. We used patient-specific finite element meshes consisting of hexahedral and non-locking tetrahedral elements, together with realistic material properties for the brain tissue and appropriate contact conditions at the boundaries. The loading was defined by prescribing deformations on the brain surface under the craniotomy. Application of the computed deformation fields to register (i.e. align) the preoperative and intraoperative images indicated that the models very accurately predict the intraoperative deformations within the brain. For each case, computing the brain deformation field took less than 4 s using an NVIDIA Tesla C870 GPU, which is two orders of magnitude reduction in computation time in comparison to our previous study in which the brain deformation was predicted using a commercial finite element solver executed on a personal computer.     

Statistical finite element method for real-time tissue mechanics analysis

The finite element (FE) method can accurately calculate tissue deformation. However, its low speed renders it ineffective for many biomedical applications involving real-time data processing. To accelerate FE analysis, we introduce a novel tissue mechanics simulation technique. This technique is suitable for real-time estimation of tissue deformation of specific organs, which is required in computer-aided diagnostic or therapeutic procedures. In this method, principal component analysis is used to describe each organ shape and its corresponding FE field for a pool of patients by a small number of weight factors. A mapping function is developed to relate the parameters of organ shape to their FE field counterpart. We show that irrespective of the complexity of the tissue's constitutive law or its loading conditions, the proposed technique is highly accurate and fast in estimating the FE field. Average deformation errors of less than 2% demonstrate the accuracy of the proposed technique.     

Finite element modelling of the common carotid artery in the elderly with physiological intimal thickening using layer-specific stress-released geometries and nonlinear elastic properties

To investigate the mechanical effects of tissue responses, such as remodelling, in the arteries of the elderly, it is important to evaluate stress in the intimal layer. In this study, we investigated a novel technique to evaluate the effect of layer-specific characteristics on stress in the arterial wall in an elderly subject. We used finite element analysis of a segment of carotid artery with intimal thickening, incorporating stress-released geometries and the stress–strain relationships for three separate wall layers. We correlated the stress–strain relationships and local curvatures of the layers with the stress on the arterial wall under physiological loading. The simulation results show that both the stress–strain relationship and the local curvature of the innermost stress-released layer influence the circumferential stress and its radial gradient. This indicates that intimal stress is influenced significantly by location-dependent intimal remodelling. However, further investigation is needed before conclusive inferences can be drawn.     

Frictional behaviour of bovine articular cartilage

The experimentally measured indentation displacement and friction of normal and degraded (treated with chondroitinase AC) bovine articular cartilage plugs against a smooth steel plate were compared with the predictions based on the biphasic theory using the finite element method. It was found that the measured indentation displacement of both cartilage specimens could be predicted from the biphasic theory and the permeability for the degraded cartilage specimen was increased approximately three times. However, the measured friction coefficient was much lower for short period of loading, and the difference in the finite element prediction of friction coefficient between the normal and degraded cartilage specimens was not observed in the experiment. Therefore, it was concluded that both biphasic and other mechanisms were important in controlling the frictional and lubricating characteristics of articular cartilage in mixed and boundary lubrication regimes.     

Fitted hyperelastic parameters for Human brain tissue from reported tension,compression, and shear tests

The mechanical properties of human brain tissue are the subject of interest because of their use in understanding brain trauma and in developing therapeutic treatments and procedures. To represent the behavior of the tissue, we have developed hyperelastic mechanical models whose parameters are fitted in accordance with experimental test results. However, most studies available in the literature have fitted parameters with data of a single type of loading, such as tension, compression, or shear. Recently, Jin et al. (Journal of Biomechanics 46:2795−2801, 2013) reported data from ex vivo tests of human brain tissue under tension, compression, and shear loading using four strain rates and four different brain regions. However, they do not report parameters of energy functions that can be readily used in finite element simulations. To represent the tissue behavior for the quasi-static loading conditions, we aimed to determine the best fit of the hyperelastic parameters of the hyperfoam, Ogden, and polynomial strain energy functions available in ABAQUS for the low strain rate data, while simultaneously considering all three loading modes. We used an optimization process conducted in MATLAB, calling iteratively three finite element models developed in ABAQUS that represent the three loadings. Results showed a relatively good fit to experimental data in all loading modes using two terms in the energy functions. Values for the shear modulus obtained in this analysis (897−1653 Pa) are in the range of those presented in other studies. These energy-function parameters can be used in brain tissue simulations using finite element models.