A three-constituent damage model for arterial clamping in computer-assisted surgery

Robotic surgery is an attractive, minimally invasive and high precision alternative to conventional surgical procedures. However, it lacks the natural touch and force feedback that allows the surgeon to control safe tissue manipulation. This is an important problem in standard surgical procedures such as clamping, which might induce severe tissue damage. In complex, heterogeneous, large deformation scenarios, the limits of the safe loading regime beyond which tissue damage occurs are unknown. Here, we show that a continuum damage model for arteries, implemented in a finite element setting, can help to predict arterial stiffness degradation and to identify critical loading regimes. The model consists of the main mechanical constituents of arterial tissue: extracellular matrix, collagen fibres and smooth muscle cells. All constituents are allowed to degrade independently in response to mechanical overload. To demonstrate the modularity and portability of the proposed model, we implement it in a commercial finite element programme, which allows to keep track of damage progression via internal variables. The loading history during arterial clamping is simulated through four successive steps, incorporating residual strains. The results of our first prototype simulation demonstrate significant regional variations in smooth muscle cell damage. In three additional steps, this damage is evaluated by simulating an isometric contraction experiment. The entire finite element simulation is finally compared with actual in vivo experiments. In the short term, our computational simulation tool can be useful to optimise surgical tools with the goal to minimise tissue damage. In the long term, it can potentially be used to inform computer-assisted surgery and identify safe loading regimes, in real time, to minimise tissue damage during robotic tissue manipulation.     

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.     

Analytic analysis of the force sharing among synergistic muscles in one- and two-degree-of-freedom models

Mathematical optimization of specific cost functions has been used in theoretical models to calculate individual muscle forces. Measurements of individual muscle forces and force sharing among individual muscles show an intensity-dependent, non-linear behavior. It has been demonstrated that the force sharing between the cat Gastrocnemius, Plantaris and Soleus shows distinct loops that change orientation systematically depending on the intensity of the movement. The purpose of this study was to prove whether or not static, non-linear optimization could inherently predict force sharing loops between agonistic muscles. Using joint moment data from a step cycle of cat locomotion, the forces in three cat ankle plantar flexors (Gastrocnemius, Plantaris and Soleus) were calculated using two popular optimization algorithms and two musculo-skeletal models. The two musculo-skeletal models included a one-degree-of-freedom model that considered the ankle joint exclusively and a two-degree-of-freedom model that included the ankle and the knee joint. The main conclusion of this study was that solutions of the one-degree-of-freedom model do not guarantee force-sharing loops, but the two-degree-of-freedom model predicts force-sharing loops independent of the specific values of the input parameters for the muscles and the musculo-skeletal geometry. The predicted force-sharing loops were found to be a direct result of the loops formed by the knee and ankle moments in a moment-moment graph.     

Viscoelastic properties of bovine orbital connective tissue and fat: constitutive models

Reported mechanical properties of orbital connective tissue and fat have been too sparse to model strain–stress relationships underlying biomechanical interactions in strabismus. We performed rheological tests to develop a multi-mode upper convected Maxwell (UCM) model of these tissues under shear loading. From 20 fresh bovine orbits, 30 samples of connective tissue were taken from rectus pulley regions and 30 samples of fatty tissues from the posterior orbit. Additional samples were defatted to determine connective tissue weight proportion, which was verified histologically. Mechanical testing in shear employed a triborheometer to perform: strain sweeps at 0.5–2.0 Hz; shear stress relaxation with 1% strain; viscometry at 0.01−0.5 s⁻¹ strain rate; and shear oscillation at 1% strain. Average connective tissue weight proportion was 98% for predominantly connective tissue and 76% for fatty tissue. Connective tissue specimens reached a long-term relaxation modulus of 668 Pa after 1,500 s, while corresponding values for fatty tissue specimens were 290 Pa and 1,100 s. Shear stress magnitude for connective tissue exceeded that of fatty tissue by five-fold. Based on these data, we developed a multi-mode UCM model with variable viscosities and time constants, and a damped hyperelastic response that accurately described measured properties of both connective and fatty tissues. Model parameters differed significantly between the two tissues. Viscoelastic properties of predominantly connective orbital tissues under shear loading differ markedly from properties of orbital fat, but both are accurately reflected using UCM models. These viscoelastic models will facilitate realistic global modeling of EOM behavior in binocular alignment and strabismus.     

The effects of deformation, ischemia, and reperfusion on the development of muscle damage during prolonged loading

Deep tissue injury (DTI) is a severe form of pressure ulcer where tissue damage starts in deep tissues underneath intact skin. In the present study, the contributions of deformation, ischemia, and reperfusion to skeletal muscle damage development were examined in a rat model during a 6-h period. Magnetic resonance imaging (MRI) was used to study perfusion (contrast-enhanced MRI) and tissue integrity (T2-weighted MRI). The levels of tissue deformation were estimated using finite element models. Complete ischemia caused a gradual homogeneous increase in T2 (～20% during the 6-h period). The effect of reperfusion on T2 was highly variable, depending on the anatomical location. In experiments involving deformation, inevitably associated with partial ischemia, a variable T2 increase (17-66% during the 6-h period) was observed reflecting the significant variation in deformation (with two-dimensional strain energies of 0.60-1.51 J/mm) and ischemia (50.8-99.8% of the leg) between experiments. These results imply that deformation, ischemia, and reperfusion all contribute to the damage process during prolonged loading, although their importance varies with time. The critical deformation threshold and period of ischemia that cause muscle damage will certainly vary between individuals. These variations are related to intrinsic factors, such as pathological state, which partly explain the individual susceptibility to the development of DTI and highlight the need for regular assessments of individual subjects.     

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.     

A muscle controlled finite-element model of laryngeal abduction and adduction

A three-dimensional finite-element model was developed to simulate the complex movement of the laryngeal cartilages during vocal fold abduction and adduction. The model consists of cricoid and arytenoid cartilages, as well as the intralaryngeal muscles and vocal folds. The active and passive properties of the muscles were idealised by one-dimensional elements based on the Hill theory. Its controlling input value is a time dependent stimulation rate. Optimisation loops have been carried out for the arrangement of the individual stimulation rates. Since in vivo measurements are not feasible, the developed biomechanical model shall be used to analyse the force distribution within the laryngeal muscles during phonatory manoeuvres. Simulations of abduction and adduction in different pitches of voice lead to realistic tensions of the vocal folds. The model is a first step to analyse motional vocal fold diseases and to predict the consequences of phonosurgical interventions.     

A muscle controlled finite-element model of laryngeal abduction and adduction

A three-dimensional finite-element model was developed to simulate the complex movement of the laryngeal cartilages during vocal fold abduction and adduction. The model consists of cricoid and arytenoid cartilages, as well as the intralaryngeal muscles and vocal folds. The active and passive properties of the muscles were idealised by one-dimensional elements based on the Hill theory. Its controlling input value is a time dependent stimulation rate. Optimisation loops have been carried out for the arrangement of the individual stimulation rates. Since in vivo measurements are not feasible, the developed biomechanical model shall be used to analyse the force distribution within the laryngeal muscles during phonatory manoeuvres. Simulations of abduction and adduction in different pitches of voice lead to realistic tensions of the vocal folds. The model is a first step to analyse motional vocal fold diseases and to predict the consequences of phonosurgical interventions.     

Condensin extrudes DNA loops in steps up to hundreds of base pairs that are generated by ATP binding events

The condensin SMC protein complex organizes chromosomal structure by extruding loops of DNA. Its ATP-dependent motor mechanism remains unclear but likely involves steps associated with large conformational changes within the ∼50 nm protein complex. Here, using high-resolution magnetic tweezers, we resolve single steps in the loop extrusion process by individual yeast condensins. The measured median step sizes range between 20–40 nm at forces of 1.0–0.2 pN, respectively, comparable with the holocomplex size. These large steps show that, strikingly, condensin typically reels in DNA in very sizeable amounts with ∼200 bp on average per single extrusion step at low force, and occasionally even much larger, exceeding 500 bp per step. Using Molecular Dynamics simulations, we demonstrate that this is due to the structural flexibility of the DNA polymer at these low forces. Using ATP-binding-impaired and ATP-hydrolysis-deficient mutants, we find that ATP binding is the primary step-generating stage underlying DNA loop extrusion. We discuss our findings in terms of a scrunching model where a stepwise DNA loop extrusion is generated by an ATP-binding-induced engagement of the hinge and the globular domain of the SMC complex.     

Failure modelling of trabecular bone using a non-linear combined damage and fracture voxel finite element approach

Trabecular bone tissue failure can be considered as consisting of two stages: damage and fracture; however, most failure analyses of 3D high-resolution trabecular bone samples are confined to damage mechanisms only, that is, without fracture. This study aims to develop a computational model of trabecular bone consisting of an explicit representation of complete failure, incorporating damage criteria, fracture criteria, cohesive forces, asymmetry and large deformation capabilities. Following parameter studies on a test specimen, and experimental testing of bone sample to complete failure, the asymmetric critical tissue damage and fracture strains of ovine vertebral trabecular bone were calibrated and validated to be compression damage ?1.16 %, tension damage 0.69 %, compression fracture ?2.91 % and tension fracture 1.98 %. Ultimate strength and post–ultimate strength softening were captured by the computational model, and the failure of individual struts in bending and shear was also predicted. This modelling approach incorporated a cohesive parameter that provided a facility to calibrate ductile–brittle behaviour of bone tissue in this non-linear geometric and non-linear constitutive property analyses tool. Finally, the full accumulation of tissue damage and tissue fracture has been monitored from range of small magnitude (normal daily loading) through to specimen yielding, ultimate strength and post–ultimate strength softening.     

Mechanical characterization of anisotropic planar biological soft tissues using finite indentation: experimental feasibility

Heart valve tissue engineering offers a promising alternative for current treatment and replacement strategies, e.g., synthetic or bioprosthetic heart valves. In vitro mechanical conditioning is an important tool for engineering strong, implantable heart valves. Detailed knowledge of the mechanical properties of the native tissue as well as the developing tissue construct is vital for a better understanding and control of the remodeling processes induced by mechanical conditioning. The nonlinear, anisotropic and inhomogeneous mechanical behavior of heart valve tissue necessitates a mechanical characterization method that is capable of dealing with these complexities. In a recent computational study we showed that one single indentation test, combining force and deformation gradient data, provides sufficient information for local characterization of nonlinear soft anisotropic tissue properties. In the current study this approach is validated in two steps. First, indentation tests with varying indenter sizes are performed on linear elastic PDMS rubbers and compared to tensile tests on the same specimen. For the second step, tissue constructs are engineered using uniaxial or equibiaxial static constrained culture conditions. Digital image correlation (DIC) is used to quantify the anisotropy in the tissue constructs. For both validation steps, material parameters are estimated by inverse fitting of a computational model to the experimental results.     

Virtual models of the HLA class I antigen processing pathway

Antigen recognition by cytotoxic CD8 T cells is dependent upon a number of critical steps in MHC class I antigen processing including proteosomal cleavage, TAP transport into the endoplasmic reticulum, and MHC class I binding. Based on extensive experimental data relating to each of these steps there is now the capacity to model individual antigen processing steps with a high degree of accuracy. This paper demonstrates the potential to bring together models of individual antigen processing steps, for example proteosome cleavage, TAP transport, and MHC binding, to build highly informative models of functional pathways. In particular, we demonstrate how an artificial neural network model of TAP transport was used to mine a HLA-binding database so as to identify HLA-binding peptides transported by TAP. This integrated model of antigen processing provided the unique insight that HLA class I alleles apparently constitute two separate classes: those that are TAP-efficient for peptide loading (HLA-B27, -A3, and -A24) and those that are TAP-inefficient (HLA-A2, -B7, and -B8). Hence, using this integrated model we were able to generate novel hypotheses regarding antigen processing, and these hypotheses are now capable of being tested experimentally. This model confirms the feasibility of constructing a virtual immune system, whereby each additional step in antigen processing is incorporated into a single modular model. Accurate models of antigen processing have implications for the study of basic immunology as well as for the design of peptide-based vaccines and other immunotherapies.     

Temporal development of hippocampal cell death is dependent on tissue strain but not strain rate

Deformation of brain tissue in response to mechanical loading of the head is the root-cause of traumatic brain injury (TBI). Even below ultimate failure limits, deformation activates pathophysiological cascades resulting in delayed cell death. Injury response of soft tissues, such as the chest and spinal cord, is dependent on the product of deformation and velocity, a parameter termed the viscous criterion. We set out to test if hippocampal cell death could be predicted by a similar combination of strain and strain rate and if the viscous criterion was valid for hippocampus. Quantitative prediction of the brain's biological response to mechanical stimuli is difficult to achieve in animal models of TBI, so we utilized an in vitro model of TBI based on hippocampal slice cultures. We quantified the temporal development of cell death after precisely controlled deformations for 30 combinations of strain (0.05-0.50) and strain rate (0.1-50s(-1)) relevant to TBI. Loading conditions for a subset of cultures were verified by analysis of high-speed video. Cell death was found to be significantly dependent on time-post injury, on strain magnitude, and to a lesser extent, on anatomical region by a repeated-measures, three-way ANOVA. The responses of the CA1 and CA3 regions of the hippocampus were not statistically different in contrast to some in vivo TBI studies. Surprisingly, cell death was not dependent on strain rate leading us to conclude that the viscous criterion is not a valid predictor for hippocampal tissue injury. Given the large data set and extensive combinations of biomechanical parameters, predictive mathematical functions relating independent variables (strain, region, and time post-injury) to the resultant cell death were defined. These functions can be used as tolerance criteria to equip finite element models of TBI with the added capability to predict biological consequences.     

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.     

Mechanical properties of passive myocardium: experiment and mathematical model

We present here a 3D mathematical model of rheological properties of a morphofunctional unit of myocardium as example of biological tissue. The model consists of longitudinal and transverse elastic elements and inclined viscoelastic elements connected pivotally without friction. The parameters of viscosity and elasticity of the structural elements of the model do not depend on the magnitude of deformation. The model adequately describes nonlinear viscoelastic behavior of isolated samples of passive myocardium both in static condition and under dynamic loading. The simulation data fit the experiment very well both for intact rat papillary muscle and for a decellularized specimen.     

Constitutive modelling of brain tissue: Experiment and theory

Recent developments in computer-integrated and robot-aided surgery—in particular, the emergence of automatic surgical tools and robots—as well as advances in virtual reality techniques, call for closer examination of the mechanical properties of very soft tissues (such as brain, liver, kidney, etc.). The ultimate goal of our research into the biomechanics of these tissues is the development of corresponding, realistic mathematical models. This paper contains experimental results of in vitro, uniaxial, unconfined compression of swine brain tissue and discusses a single-phase, non-linear, viscoelastic tissue model. The experimental results obtained for three loading velocities, ranging over five orders of magnitude, are presented. The applied strain rates have been much lower than those applied in previous studies, focused on injury modelling. The stress-strain curves are concave upward for all compression rates containing no linear portion from which a meaningful elastic modulus might be determined. The tissue response stiffened as the loading speed increased, indicating a strong stress-strain rate dependence. The use of the single-phase model is recommended for applications in registration, surgical operation planning and training systems as well as a control system of an image-guided surgical robot. The material constants for the brain tissue are evaluated. Agreement between the proposed theoretical model and experiment is good for compression levels reaching 30% and for loading velocities varying over five orders of magnitude.     

Compression-induced deep tissue injury examined with magnetic resonance imaging and histology.

The underlying mechanisms leading to deep tissue injury after sustained compressive loading are not well understood. It is hypothesized that initial damage to muscle fibers is induced mechanically by local excessive deformation. Therefore, in this study, an animal model was used to study early damage after compressive loading to elucidate on the damage mechanisms leading to deep pressure ulcers. The tibialis anterior of Brown-Norway rats was loaded for 2 h by means of an indenter. Experiments were performed in a magnetic resonance (MR)-compatible loading device. Muscle tissue was evaluated with transverse relaxation time (T2)-weighted MRI both during loading and up to 20 h after load removal. In addition, a detailed examination of the histopathology was performed at several time points (1, 4, and 20 h) after unloading. Results demonstrated that, immediately after unloading, T2-weighted MR images showed localized areas with increased signal intensity. Histological examination at 1 and 4 h after unloading showed large necrotic regions with complete disorganization of the internal structure of the muscle fibers. Hypercontraction zones were found bilateral to the necrotic zone. Twenty hours after unloading, an extensive inflammatory response was observed. The proposed relevance of large deformation was demonstrated by the location of damage indicated by T2-weighted MRI and the histological appearance of the compressed tissues. Differences in damage development distal and proximal to the indenter position suggested a contribution of perfusion status in the measured tissue changes that, however, appeared be to reversible.     

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.     

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.