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.     

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.     

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.     

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.     

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 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.     

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.     

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.     

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.     

An eFTD-VP framework for efficiently generating patient-specific anatomically detailed facial soft tissue FE mesh for craniomaxillofacial surgery simulation

Accurate surgical planning and prediction of craniomaxillofacial surgery outcome requires simulation of soft tissue changes following osteotomy. This can only be achieved by using an anatomically detailed facial soft tissue model. The current state-of-the-art of model generation is not appropriate to clinical applications due to the time-intensive nature of manual segmentation and volumetric mesh generation. The conventional patient-specific finite element (FE) mesh generation methods are to deform a template FE mesh to match the shape of a patient based on registration. However, these methods commonly produce element distortion. Additionally, the mesh density for patients depends on that of the template model. It could not be adjusted to conduct mesh density sensitivity analysis. In this study, we propose a new framework of patient-specific facial soft tissue FE mesh generation. The goal of the developed method is to efficiently generate a high-quality patient-specific hexahedral FE mesh with adjustable mesh density while preserving the accuracy in anatomical structure correspondence. Our FE mesh is generated by eFace template deformation followed by volumetric parametrization. First, the patient-specific anatomically detailed facial soft tissue model (including skin, mucosa, and muscles) is generated by deforming an eFace template model. The adaptation of the eFace template model is achieved by using a hybrid landmark-based morphing and dense surface fitting approach followed by a thin-plate spline interpolation. Then, high-quality hexahedral mesh is constructed by using volumetric parameterization. The user can control the resolution of hexahedron mesh to best reflect clinicians’ need. Our approach was validated using 30 patient models and 4 visible human datasets. The generated patient-specific FE mesh showed high surface matching accuracy, element quality, and internal structure matching accuracy. They can be directly and effectively used for clinical simulation of facial soft tissue change.     

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.     

Modified Bilston nonlinear viscoelastic model for finite element head injury studies

This paper proposes a modified nonlinear viscoelastic Bilston model (Bilston et al., 2001, Biorheol., 38, pp. 335-345). for the modeling of brain tissue constitutive properties. The modified model can be readily implemented in a commercial explicit finite element (FE) code, PamCrash. Critical parameters of the model have been determined through a series of rheological tests on porcine brain tissue samples and the time-temperature superposition (TTS) principle has been used to extend the frequency to a high region. Simulations by using PamCrash are compared with the test results. Through the use of the TTS principle, the mechanical and rheological behavior at high frequencies up to 10(4) rads may be obtained. This is important because the properties of the brain tissue at high frequencies and impact rates are especially relevant to studies of traumatic head injury. The averaged dynamic modulus ranges from 130 Pa to 1500 Pa and loss modulus ranges from 35 Pa to 800 Pa in the frequency regime studied (0.01 rads to 3700 rads). The errors between theoretical predictions and averaged relaxation test results are within 20% for strains up to 20%. The FEM simulation results are in good agreement with experimental results. The proposed model will be especially useful for application to FE analysis of the head under impact loads. More realistic analysis of head injury can be carried out by incorporating the nonlinear viscoelastic constitutive law for brain tissue into a commercial FE code.