Inverse analysis and robustness evaluation for biological structure behaviour in FE simulation: application to the liver

To prevent traumas to abdominal organs, the selection of efficient safety devices should be based on a detailed knowledge of injury mechanisms and related injury criteria. In this sense, finite element (FE) simulation coupled with experiment could be a valuable tool to provide a better understanding of the behaviour of internal organs under crash conditions. This work proposes a methodology based on inverse analysis which combines exploration process optimisation and robustness study to obtain mechanical behaviour of the complex structure of the liver through FE simulation. The liver characterisation was based on Mooney-Rivlin hyperelastic behaviour law considering whole liver structure under uniform quasi-static compression. With the global method used, the model fits experimental data. The variability induced by modelling parameters is quantified within a reasonable time.     

Estimation of conditions evoking fracture in finger bones under pinch loading based on finite element analysis

A finger finite element (FE) model was created from CT images of a Japanese male in order to obtain a shape-biofidelic model. Material properties and articulation characteristics of the model were taken from the literature. To predict bone fracture and realistically represent the fracture pattern under various loading conditions, the ESI-Wilkins-Kamoulakos rupture model in PAM-CRASH (ESI Group S.A., Paris, France) was utilized in this study with parameter values of the rupture model determined by compression testing and simulation of porcine fibula. A finger pinch simulation was then conducted to validate the finger FE model. The force-displacement curve and fracture load from the pinch simulation was compared to the result of finger pinch test using cadavers. Simulation results are coincident with the test result, indicating that the finger FE model can be used in an analysis of finger bone fracture during pinch accident. With this model, several pinch simulations were conducted with different pinching object’s stiffness and pinching energy. Conditions for evoking finger bone fracture under pinch loading were then estimated based on these results. This study offers a novel method to predict possible hazards of manufactured goods during the design process, thus finger injury due to pinch loading can be avoided.     

Liver injuries in frontal crash situations a coupled numerical—experimental approach

From clinical knowledge, it has been established that hepatic traumas frequently lead to lethal injuries. In frontal or lateral crash situations, these injuries can be induced by pure deceleration effects or blunt trauma due to belt or steering wheel impact. Concerning the liver under frontal decelerations, how could one investigate organ behaviour leading to the injury mechanisms? This work couples experimental organ decelerations measurements (with 19 tests on cadaver trunks) and finite element simulation, provides a first analysis of the liver behaviour within the abdomen. It shows the influence of the liver attachment system that leads to liver trauma and also torsion effects between the two lobes of the liver. Injury mechanisms were evaluated through the four phases of the liver kinematics under frontal impact: (1) postero-anterior translation, (2) compression and sagittal rotation, (3) rotation in the transverse plane and (4) relaxation.     

Liver injuries in frontal crash situations a coupled numerical - experimental approach

From clinical knowledge, it has been established that hepatic traumas frequently lead to lethal injuries. In frontal or lateral crash situations, these injuries can be induced by pure deceleration effects or blunt trauma due to belt or steering wheel impact. Concerning the liver under frontal decelerations, how could one investigate organ behaviour leading to the injury mechanisms? This work couples experimental organ decelerations measurements (with 19 tests on cadaver trunks) and finite element simulation, provides a first analysis of the liver behaviour within the abdomen. It shows the influence of the liver attachment system that leads to liver trauma and also torsion effects between the two lobes of the liver. Injury mechanisms were evaluated through the four phases of the liver kinematics under frontal impact: (1) postero-anterior translation, (2) compression and sagittal rotation, (3) rotation in the transverse plane and (4) relaxation.     

A Coupling Analysis of the Biomechanical Functions of Human Foot Complex during Locomotion

This study represents a functional analysis of the human foot complex based on in-vivo gait measurements, finite element (FE) modeling and biological coupling theory, with the objective of achieving a comprehensive understanding of the impact attenuation and energy absorption functions of the human foot complex. A simplified heel pad FE model comprising reticular fiber structure and fat cells was constructed based on the foot pad Magnetic Resonance (MR) images. The model was then used to investigate the foot pad behaviors under impact during locomotion. Three-dimensional (3D) gait measurement and a 3D FE foot model comprising 29 bones, 85 ligaments and the plantar soft tissues were used to investigate the foot arch and plantar fascia deformations in mid-stance phase. The heel pad simulation results show that the pad model with fat cells (coupling model) has much stronger capacity in impact attenuation and energy storage than the model without fat cells (structure model). Furthermore, the FE simulation reproduced the deformations of the foot arch structure and the plantar fascia extension observed in the gait measurements, which reinforces the postulation that the foot arch structure also plays an important role in energy absorption during locomotion. Finally, the coupling mechanism of the human foot functions in impact attenuation and energy absorption was proposed.     

Lumbar spine finite element model for healthy subjects: development and validation

Finite element (FE) method is a proven powerful and efficient tool to study the biomechanics of the human lumbar spine. However, due to the large inter-subject variability of geometries and material properties in human lumbar spines, concerns existed on the accuracy and predictive power of one single deterministic FE model with one set of spinal geometry and material properties. It was confirmed that the combined predictions (median or mean value) of several distinct FE models can be used as an improved prediction of behavior of human lumbar spine under identical loading and boundary conditions. In light of this improved prediction, five FE models (L1-L5 spinal levels) of the human lumbar spine were developed based on five healthy living subjects with identical modeling method. The five models were extensively validated through experimental and computational results in the literature. Mesh convergence and material sensitivity analysis were also conducted. We have shown that the results from the five FE models developed in this paper were consistent with the experimental data and simulation results from the existing literature. The validated modeling method introduced in this study can be used in modeling dysfunctional lumber spines such as disc degeneration and scoliosis in future work.     

Human shoulder response to side impacts: a finite element study

This study aimed at developing a shoulder finite element (FE) model able to simulate the dynamic behaviour and to predict injuries in case of side impacts. This model is an updated version of the initial Human Model for Safety (HUMOS) FE model of the human body. Simulations performed with the model have been compared to experimental results of side impact tests conducted previously at INRETS. The shoulder model response under lateral impact appears to be in good agreement with experimental data such as impact force and shoulder deflections for different impact speeds and impact directions. These results seem promising for future applications such as shoulder injury prediction in simulated car crashes.     

Development of structural and material clavicle response corridors under axial compression and three point bending loading for clavicle finite element model validation

Clavicle injuries were frequently observed in automotive side and frontal crashes. Finite element (FE) models have been developed to understand the injury mechanism, although no clavicle loading response corridors yet exist in the literature to ensure the model response biofidelity. Moreover, the typically developed structural level (e.g., force–deflection) response corridors were shown to be insufficient for verifying the injury prediction capacity of FE model, which usually is based on strain related injury criteria. Therefore, the purpose of this study is to develop both the structural (force vs deflection) and material level (strain vs force) clavicle response corridors for validating FE models for injury risk modeling. 20 Clavicles were loaded to failure under loading conditions representative of side and frontal crashes respectively, half of which in axial compression, and the other half in three point bending. Both structural and material response corridors were developed for each loading condition. FE model that can accurately predict structural response and strain level provides a more useful tool in injury risk modeling and prediction. The corridor development method in this study could also be extended to develop corridors for other components of the human body.     

Long-term study of bone remodelling after femoral stem: a comparison between dexa and finite element simulation

A hip replacement with a cemented or cementless femoral stem produces an effect on the bone called adaptive remodelling, attributable to mechanical and biological factors. The objective of all of cementless prostheses designs has been to achieve a perfect transfer of loads in order to avoid stress-shielding, which produces an osteopenia. In order to quantify this, the long term and mass-produced study with dual energy X-ray absorptiometry (DEXA) is necessary. Finite element (FE) simulation makes possible the explanation of the biomechanical changes which are produced in the femur after stem implantation. The good correlation obtained between the results of the FE simulation and the densitometric study allow, on one hand, to explain from the point of view of biomechanical performance the changes observed in bone density in the long-term, where it is clear that these are due to a different transfer of load in the implanted model compared to the healthy femur; on the other hand, it validates the simulation model, in a way that it can be used in different conditions and at different time periods, to carry out a sufficiently precise prediction of the evolution of the bone density from the biomechanical behaviour in the interaction between the prosthesis and femur.     

Development of a finite element model of the tibia for short-duration high-force axial impact loading

Finite element (FE) models can allow computer simulations of impact loading, providing a useful companion to cadaveric testing. These models allow injury evaluations to be conducted under a variety of conditions, but must be validated against experimental data. An FE model of a cadaveric tibia was developed using geometry from CT scans, and the quality of the mesh was evaluated. Loading and boundary conditions from experimental tests were simulated, and the model was optimised to best represent the response of natural bone to impacts. The model was shown to have good agreement for impact force, duration, impulse and strain during simulation of three non-injurious and one injurious axial impact when compared with experimental test data for the specimen. Failure criteria were evaluated for their ability to predict fracture. This model of the tibia can be used for future injury prediction assessment studies.     

Application of neural networks for the prediction of cartilage stress in a musculoskeletal system

Traditional finite element (FE) analysis is computationally demanding. The computational time becomes prohibitively long when multiple loading and boundary conditions need to be considered such as in musculoskeletal movement simulations involving multiple joints and muscles. Presented in this study is an innovative approach that takes advantage of the computational efficiency of both the dynamic multibody (MB) method and neural network (NN) analysis. A NN model that captures the behavior of musculoskeletal tissue subjected to known loading situations is built, trained, and validated based on both MB and FE simulation data. It is found that nonlinear, dynamic NNs yield better predictions over their linear, static counterparts. The developed NN model is then capable of predicting stress values at regions of interest within the musculoskeletal system in only a fraction of the time required by FE simulation.     

A power-law rheology-based finite element model for single cell deformation

Physical forces can elicit complex time- and space-dependent deformations in living cells. These deformations at the subcellular level are difficult to measure but can be estimated using computational approaches such as finite element (FE) simulation. Existing FE models predominantly treat cells as spring-dashpot viscoelastic materials, while broad experimental data are now lending support to the power-law rheology (PLR) model. Here, we developed a large deformation FE model that incorporated PLR and experimentally verified this model by performing micropipette aspiration on fibroblasts under various mechanical loadings. With a single set of rheological properties, this model recapitulated the diverse micropipette aspiration data obtained using three protocols and with a range of micropipette sizes. More intriguingly, our analysis revealed that decreased pipette size leads to increased pressure gradient, potentially explaining our previous counterintuitive finding that decreased pipette size leads to increased incidence of cell blebbing and injury. Taken together, our work leads to more accurate rheological interpretation of micropipette aspiration experiments than previous models and suggests pressure gradient as a potential determinant of cell injury.     

Development and validation of subject-specific finite element models for blunt trauma study

This study developed and validated finite element (FE) models of swine and human thoraxes and abdomens that had subject-specific anatomies and could accurately and efficiently predict body responses to blunt impacts. Anatomies of the rib cage, torso walls, thoracic, and abdominal organs were reconstructed from X-ray computed tomography (CT) images and extracted into geometries to build FE meshes. The rib cage was modeled as an inhomogeneous beam structure with geometry and bone material parameters determined directly from CT images. Meshes of soft components were generated by mapping structured mesh templates representative of organ topologies onto the geometries. The swine models were developed from and validated by 30 animal tests in which blunt insults were applied to swine subjects and CT images, chest wall motions, lung pressures, and pathological data were acquired. A comparison of the FE calculations of animal responses and experimental measurements showed a good agreement. The errors in calculated response time traces were within 10% for most tests. Calculated peak responses showed strong correlations with the experimental values. The stress concentration inside the ribs, lungs, and livers produced by FE simulations also compared favorably to the injury locations. A human FE model was developed from CT images from the Visible Human project and was scaled to simulate historical frontal and side post mortem human subject (PMHS) impact tests. The calculated chest deformation also showed a good agreement with the measurements. The models developed in this study can be of great value for studying blunt thoracic and abdominal trauma and for designing injury prevention techniques, equipments, and devices.     

Growing multiblock structures: a semi-automated approach to block placement for multiblock hexahedral meshing

Finite element (FE) analysis is a cornerstone of orthopaedic biomechanics research. Three-dimensional medical imaging provides sufficient resolution for the subject-specific FE models to be generated from these data-sets. FE model development requires discretisation of a three-dimensional domain, which can be the most time-consuming component of a FE study. Hexahedral meshing tools based on the multiblock method currently rely on the manual placement of building blocks for mesh generation. We hypothesise that angular analysis of the geometric centreline for a three-dimensional surface could be used to automatically generate building block structures for the multiblock hexahedral mesh generation. Our algorithm uses a set of user-defined points and parameters to automatically generate a multiblock structure based on a surface's geometric centreline. This significantly reduces the time required for model development. We have applied this algorithm to 47 bones of varying geometries and successfully generated a FE mesh in all cases. This work represents significant advancement in automatically generating multiblock structures for a wide range of geometries.     

A modified human head model for the study of impact head injury

A recently published finite element (FE) head model is modified to consider the viscoelasticity of the meninges, the spongy and compact bone in the skull. The cerebrospinal fluid (CSF) is simulated explicitly as a hydrostatic fluid by using a surface-based fluid modelling method, which allows fluid and structure interaction. It is found that the modified model yields smoother pressure responses in a head impact simulation. The baseline model underestimated the peak von Mises stress in the brain by 15% and the peak principal stress in the skull by 33%. The increase in the maximum principal stress in the skull is mainly caused by the updation of the material's viscoelasticity, and the change in the maximum von Mises stress in the brain is mainly caused by the improvement of the CSF simulation. The study shows that the viscoelasticity of the head tissue should be considered, and that the CSF should be modelled as a fluid, when using FE analysis to study head injury due to impact.     

A novel approach for extracting viscoelastic parameters of living cells through combination of inverse finite element simulation and Atomic Force Microscopy

Dynamic mechanical behaviour of living cells has been described by viscoelasticity. However, quantitation of the viscoelastic parameters for living cells is far from sophisticated. In this paper, combining inverse finite element (FE) simulation with Atomic Force Microscope characterization, we attempt to develop a new method to evaluate and acquire trustworthy viscoelastic index of living cells. First, influence of the experiment parameters on stress relaxation process is assessed using FE simulation. As suggested by the simulations, cell height has negligible impact on shape of the force–time curve, i.e. the characteristic relaxation time; and the effect originates from substrate can be totally eliminated when stiff substrate (Young’s modulus larger than 3 GPa) is used. Then, so as to develop an effective optimization strategy for the inverse FE simulation, the parameters sensitivity evaluation is performed for Young’s modulus, Poisson’s ratio, and characteristic relaxation time. With the experiment data obtained through typical stress relaxation measurement, viscoelastic parameters are extracted through the inverse FE simulation by comparing the simulation results and experimental measurements. Finally, reliability of the acquired mechanical parameters is verified with different load experiments performed on the same cell.     

A mathematical model for the freezing process in biological tissue

A mathematical model has been developed to study the process of freezing in biological organs. The model consists of a repetitive unit structure comprising a cylinder of tissue with an axial blood vessel (Krogh cylinder) and it is analysed by the methods of irreversible thermodynamics. The mathematical simulation of the freezing process in liver tissue compares remarkably well with experimental data on the structure of tissue frozen under controlled thermal conditions and the response of liver cells to changes in cooling rate. The study also supports the proposal that the damage mechanism responsible for the lack of success in attempts to preserve tissue in a frozen state, under conditions in which cells in suspension survive freezing, is direct mechanical damage caused by the formation of ice in the vascular system.     

Evaluation of an aortic valve prosthesis: Fluid-structure interaction or structural simulation?

Bio-inspired polymeric heart valves (PHVs) are excellent candidates to mimic the structural and the fluid dynamic features of the native valve. PHVs can be implanted as prosthetic alternative to currently clinically used mechanical and biological valves or as potential candidate for a minimally invasive treatment, like the transcatheter aortic valve implantation. Nevertheless, PHVs are not currently used for clinical applications due to their lack of reliability. In order to investigate the main features of this new class of prostheses, pulsatile tests in an in-house pulse duplicator were carried out and reproduced in silico with both structural Finite-Element (FE) and Fluid-Structure interaction (FSI) analyses. Valve kinematics and geometric orifice area (GOA) were evaluated to compare the in vitro and the in silico tests. Numerical results showed better similarity with experiments for the FSI than for the FE simulations. The maximum difference between experimental and FSI GOA at maximum opening time was only 5%, as compared to the 46.5% between experimental and structural FE GOA. The stress distribution on the valve leaflets clearly reflected the difference in valve kinematics. Higher stress values were found in the FSI simulations with respect to those obtained in the FE simulation. This study demonstrates that FSI simulations are more appropriate than FE simulations to describe the actual behaviour of PHVs as they can replicate the valve-fluid interaction while providing realistic fluid dynamic results.     

Concept and development of an orthotropic FE model of the proximal femur

PURPOSE: In contrast to many isotropic finite-element (FE) models of the femur in literature, it was the object of our study to develop an orthotropic FE "model femur" to realistically simulate three-dimensional bone remodelling. METHODS: The three-dimensional geometry of the proximal femur was reconstructed by CT scans of a pair of cadaveric femurs at equal distances of 2mm. These three-dimensional CT models were implemented into an FE simulation tool. Well-known "density-determined" bony material properties (Young's modulus; Poisson's ratio; ultimate strength in pressure, tension and torsion; shear modulus) were assigned to each FE of the same "CT-density-characterized" volumetric group.In order to fix the principal directions of stiffness in FE areas with the same "density characterization", the cadaveric femurs were cut in 2mm slices in frontal (left femur) and sagittal plane (right femur). Each femoral slice was scanned into a computer-based image processing system. On these images, the principal directions of stiffness of cancellous and cortical bone were determined manually using the orientation of the trabecular structures and the Haversian system. Finally, these geometric data were matched with the "CT-density characterized" three-dimensional femur model. In addition, the time and density-dependent adaptive behaviour of bone remodelling was taken into account by implementation of Carter's criterion. RESULTS: In the constructed "model femur", each FE is characterized by the principal directions of the stiffness and the "CT-density-determined" material properties of cortical and cancellous bone. Thus, on the basis of anatomic data a three-dimensional FE simulation reference model of the proximal femur was realized considering orthotropic conditions of bone behaviour. CONCLUSIONS: With the orthotropic "model femur", the fundamental basis has been formed to realize realistic simulations of the dynamical processes of bone remodelling under different loading conditions or operative procedures (osteotomies, total hip replacements, etc).     

Finite element model of the human neck during omni-directional impacts. Part II: relation between cervical curvature and risk of injury

A detailed 3D FE model of the human neck was used to assess a possible relationship between risk of injury and cervical spine curvature for various impacts. A FE model was previously developed, representing the head and neck of a 50th percentile human with a normal lordotic curvature. The model behaviour was omni-directionally validated for various impacts using published results. For the present study, the model was deformed in order to obtain a straight and a kyphotic curvature, and for each geometry, rear-end, frontal, lateral and oblique impact were simulated. Although results showed similar kinematic patterns, significant differences were found in the distribution and peak values of ligament elongations, forces and moments along the cervical spine for the three configurations. It was concluded that the variability observed on the curvature of the human cervical spine may have a significant influence both on the behaviour and on the risk of injury of the neck during impact.