A finite element model for analyzing shear wave propagation observed in magnetic resonance elastography

Magnetic resonance elastography (MRE) is a novel non-invasive approach to determine material stiffness by using a conventional magnetic resonance imaging (MRI) system incorporated with an oscillating motion-sensitizing gradient to detect nodal displacements produced by a shear excitation wave. The effects of material properties, excitation frequency, boundary conditions, and applied tension on shear wavelength measurement must be examined before MRE can become a useful diagnostic tool. We propose finite element (FE) modeling as a robust method to systematically study the effects of these parameters. An axisymmetric FE model was generated with ABAQUS to simulate agarose gel phantoms. The effects of material stiffness, density, and excitation frequency on propagating shear wavelength were examined individually. The effect of the boundary conditions on shear wavelength was also demonstrated. Results of shear wavelength from MRE measurement were compared with the results of FE model, which showed good agreement between the methods.     

Identification process based on shear wave propagation within a phantom using finite element modelling and magnetic resonance elastography

Magnetic resonance elastography (MRE), based on shear wave propagation generated by a specific driver, is a non-invasive exam performed in clinical practice to improve the liver diagnosis. The purpose was to develop a finite element (FE) identification method for the mechanical characterisation of phantom mimicking soft tissues investigated with MRE technique. Thus, a 3D FE phantom model, composed of the realistic MRE liver boundary conditions, was developed to simulate the shear wave propagation with the software ABAQUS. The assumptions of homogeneity and elasticity were applied to the FE phantom model. Different ranges of mesh size, density and Poisson's ratio were tested in order to develop the most representative FE phantom model. The simulated wave displacement was visualised with a dynamic implicit analysis. Subsequently, an identification process was performed with a cost function and an optimisation loop provided the optimal elastic properties of the phantom. The present identification process was validated on a phantom model, and the perspective will be to apply this method on abdominal tissues for the set-up of new clinical MRE protocols that could be applied for the follow-up of the effects of treatments.     

Finite element modeling of impulsive excitation and shear wave propagation in an incompressible,transversely isotropic medium

Elastic properties of materials can be measured by observing shear wave propagation following localized, impulsive excitations and relating the propagation velocity to a model of the material. However, characterization of anisotropic materials is difficult because of the number of elasticity constants in the material model and the complex dependence of propagation velocity relative to the excitation axis, material symmetries, and propagation directions. In this study, we develop a model of wave propagation following impulsive excitation in an incompressible, transversely isotropic (TI) material such as muscle. Wave motion is described in terms of three propagation modes identified by their polarization relative to the material symmetry axis and propagation direction. Phase velocities for these propagation modes are expressed in terms of five elasticity constants needed to describe a general TI material, and also in terms of three constants after the application of two constraints that hold in the limit of an incompressible material. Group propagation velocities are derived from the phase velocities to describe the propagation of wave packets away from the excitation region following localized excitation. The theoretical model is compared to the results of finite element (FE) simulations performed using a nearly incompressible material model with the five elasticity constants chosen to preserve the essential properties of the material in the incompressible limit. Propagation velocities calculated from the FE displacement data show complex structure that agrees quantitatively with the theoretical model and demonstrates the possibility of measuring all three elasticity constants needed to characterize an incompressible, TI material.     

Consideration of multiple load cases is critical in modelling orthotropic bone adaptation in the femur

Functional adaptation of the femur has been investigated in several studies by embedding bone remodelling algorithms in finite element (FE) models, with simplifications often made to the representation of bone’s material symmetry and mechanical environment. An orthotropic strain-driven adaptation algorithm is proposed in order to predict the femur’s volumetric material property distribution and directionality of its internal structures within a continuum. The algorithm was applied to a FE model of the femur, with muscles, ligaments and joints included explicitly. Multiple load cases representing distinct frames of two activities of daily living (walking and stair climbing) were considered. It is hypothesised that low shear moduli occur in areas of bone that are simply loaded and high shear moduli in areas subjected to complex loading conditions. In addition, it is investigated whether material properties of different femoral regions are stimulated by different activities. The loading and boundary conditions were considered to provide a physiological mechanical environment. The resulting volumetric material property distribution and directionalities agreed with ex vivo imaging data for the whole femur. Regions where non-orthogonal trabecular crossing has been documented coincided with higher values of predicted shear moduli. The topological influence of the different activities modelled was analysed. The influence of stair climbing on the properties of the femoral neck region is highlighted. It is recommended that multiple load cases should be considered when modelling bone adaptation. The orthotropic model of the complete femur is released with this study.     

Effect of boundary conditions,impact loading and hydraulic stiffening on femoral fracture strength

Patient specific quantitative CT (QCT) imaging data together with the finite element (FE) method may provide an accurate prediction of a patient's femoral strength and fracture risk. Although numerous FE models investigating femoral fracture strength have been published, there is little consent on the effect of boundary conditions, dynamic loading and hydraulic strengthening due to intra-medullary pressure on the predicted fracture strength. We developed a QCT-derived FE model of a proximal femur that included node-specific modulus assigned based on the local bone density. The effect of three commonly used boundary conditions published in literature were investigated by comparing the resulting strain field due to an applied fracture load. The models were also augmented with viscoelastic material properties and subject to a realistic impact load profile to determine the effect of dynamic loads on the strain field. Finally, the effect of hydraulic strengthening was investigated by including node specific permeability and performing a coupled pore diffusion and stress analysis of the FE model. Results showed that all boundary conditions yield the same strain field patterns, but peak strains were 22% lower and fracture load was 18% higher when loaded at the greater trochanter than when loaded at the femoral head. Comparison of the dynamic models showed that material viscoelasticity was important, but inertial effects (vibration and shock) were not. Finally, pore pressure changes did not cause significant hydraulic strengthening of bone under fall impact loading.     

Simulation of direct shear tests on rooted and non-rooted soil using finite element analysis

The finite element (FE) method has been used in recent years to simulate overturning processes in trees and to better comprehend plant anchorage mechanics. We aimed at understanding the fundamental mechanisms of root-soil reinforcement by simulating direct shear of rooted and non-rooted soil. Two- (2D) and three-dimensional (3D) FE simulations of direct shear box tests were carried out using readily available software for routine strength assessment of the root-soil composite. Both rooted and non-rooted blocks of soil were modelled using a simplified model of root distribution and root material properties representative of real roots. Linear elastic behaviour was assumed for roots and the soil was modelled as an ideally plastic medium. FE analysis showed that direct shear tests were dependent on the material properties specified for both the soil and roots. 2D and 3D simulations of direct shear of non-rooted soil produced similar results and any differences between 2D and 3D simulations could be explained with regard to the spatial complexity of roots used in the root distribution model. The application of FE methods was verified through direct shear tests on soil with analogue roots and the results compared to in situ tests on rooted soil in field conditions.     

Validation of an efficient method of assigning material properties in finite element analysis of pelvic bone

Bone in the pelvis is a composite material with a complex anatomical structure that is difficult to model computationally. Rather than assigning material properties to increasingly smaller elements to capture detail in three-dimensional finite element (FE) models, properties can be assigned to Gauss points within larger elements. As part of a validation process, we compared experimental and analytical results from a composite beam under four-point load to FE models with material properties assigned to refined elements and Gauss points within larger elements. Both FE models accurately predicted deformation and the analytical predictions of internal shear stress.     

Identification of the testing parameters in high frequency dynamic shear measurement on agarose gels

Dynamic mechanical analysis (DMA) on agarose gels can be used to validate magnetic resonance elastography (MRE) measurements as well as to provide better understanding for the biological responses of cells to the dynamic loadings in cell culture studies. Various parameters potentially affecting the repeatability and accuracy of the DMA shear modulus measurements were investigated systematically in the present study, including sample thickness, shear strain, testing frequency, and compressive clamping strain. The study showed that the thickness of the agarose gel sample must be sufficiently small (1 mm) to prevent the erroneous fluctuation in the measured modulus. The appropriate levels of shear strain (< or = 0.5%) and compressive clamping strain (5-10%) must be applied to overcome the slippage at the gel-clamp interface without causing significant boundary and stress non-uniformity or micro-cracks in the agarose gel sample.     

The use of preserved tissue in finite element modelling of fresh ovine vertebral behaviour

The aim of this study was to investigate whether the predicted finite element (FE) stiffness of vertebral bone is altered when using images of preserved rather than fresh tissue to generate specimen-specific FE models. Fresh ovine vertebrae were used to represent embalmed (n = 3) and macerated dry-bone (n = 3) specimens and treated accordingly. Specimens were scanned pre- and post-treatment using micro-computed tomography. A constant threshold level derived from these images was used to calculate the respective bone volume fraction (BV/TV) from which the conversion factor validated for fresh tissue was used to determine material properties that were assigned to corresponding FE models. Results showed a definite change in the BV/TV between the fresh and the preserved bone. However, the changes in the predicted FE stiffness were not generally greater than the variations expected from assignment of loading and boundary conditions. In conclusion, images of preserved tissue can be used to generate FE models that are representative of fresh tissue with a tolerable level of error.     

Magnetic resonance elastography in nonlinear viscoelastic materials under load

Characterisation of soft tissue mechanical properties is a topic of increasing interest in translational and clinical research. Magnetic resonance elastography (MRE) has been used in this context to assess the mechanical properties of tissues in vivo noninvasively. Typically, these analyses rely on linear viscoelastic wave equations to assess material properties from measured wave dynamics. However, deformations that occur in some tissues (e.g. liver during respiration, heart during the cardiac cycle, or external compression during a breast exam) can yield loading bias, complicating the interpretation of tissue stiffness from MRE measurements. In this paper, it is shown how combined knowledge of a material’s rheology and loading state can be used to eliminate loading bias and enable interpretation of intrinsic (unloaded) stiffness properties. Equations are derived utilising perturbation theory and Cauchy’s equations of motion to demonstrate the impact of loading state on periodic steady-state wave behaviour in nonlinear viscoelastic materials. These equations demonstrate how loading bias yields apparent material stiffening, softening and anisotropy. MRE sensitivity to deformation is demonstrated in an experimental phantom, showing a loading bias of up to twofold. From an unbiased stiffness of \(4910.4 \pm 635.8\) Pa in unloaded state, the biased stiffness increases to 9767.5 \(\pm \,\)1949.9 Pa under a load of \(\approx \) 34% uniaxial compression. Integrating knowledge of phantom loading and rheology into a novel MRE reconstruction, it is shown that it is possible to characterise intrinsic material characteristics, eliminating the loading bias from MRE data. The framework introduced and demonstrated in phantoms illustrates a pathway that can be translated and applied to MRE in complex deforming tissues. This would contribute to a better assessment of material properties in soft tissues employing elastography.

     

Mechanical properties of porcine brain tissue in vivo and ex vivo estimated by MR elastography

The mechanical properties of brain tissue in vivo determine the response of the brain to rapid skull acceleration. These properties are thus of great interest to the developers of mathematical models of traumatic brain injury (TBI) or neurosurgical simulations. Animal models provide valuable insight that can improve TBI modeling. In this study we compare estimates of mechanical properties of the Yucatan mini-pig brain in vivo and ex vivo using magnetic resonance elastography (MRE) at multiple frequencies. MRE allows estimations of properties in soft tissue, either in vivo or ex vivo, by imaging harmonic shear wave propagation. Most direct measurements of brain mechanical properties have been performed using samples of brain tissue ex vivo. It has been observed that direct estimates of brain mechanical properties depend on the frequency and amplitude of loading, as well as the time post-mortem and condition of the sample. Using MRE in the same animals at overlapping frequencies, we observe that porcine brain tissue in vivo appears stiffer than porcine brain tissue samples ex vivo at frequencies of 100 Hz and 125 Hz, but measurements show closer agreement at lower frequencies.     

Experimental validation of a time-domain-based wave propagation model of blood flow in viscoelastic vessels

Time-domain-based one-dimensional wave propagation models of the arterial system are preferable over one-dimensional wave propagation models in the frequency domain since the latter neglect the non-linear convection forces present in the physiological situation, especially when the vessel is tapered. Moreover, one-dimensional wave propagation models of the arterial system can be used to provide boundary conditions for fully three-dimensional fluid-structure interaction computations that are usually defined in the time domain. In this study, a time-domain-based one-dimensional wave propagation model in a cross-sectional area, flow and pressure (A,q,p)-formulation is developed. Using this formulation, a constitutive law that includes viscoelasticity based on the mechanical behaviour of a Kelvin body, is introduced. The resulting pressure and flow waves travelling through a straight and tapered vessel are compared to experimental data obtained from measurements in an in vitro setup. The model presented shows to be well suited to predict wave propagation through these straight and tapered vessels with viscoelastic wall properties and hereto can serve as a time-domain-based method to model wave propagation in the human arterial system.     

Effects of vessel compliance on flow pattern in porcine epicardial right coronary arterial tree

The compliance of the vessel wall affects hemodynamic parameters which may alter the permeability of the vessel wall. Based on experimental measurements, the present study established a finite element (FE) model in the proximal elastic vessel segments of epicardial right coronary arterial (RCA) tree obtained from computed tomography. The motion of elastic vessel wall was measured by an impedance catheter and the inlet boundary condition was measured by an ultrasound flow probe. The Galerkin FE method was used to solve the Navier–Stokes and Continuity equations, where the convective term in the Navier–Stokes equation was changed in the arbitrary Lagrangian–Eulerian (ALE) framework to incorporate the motion due to vessel compliance. Various hemodynamic parameters (e.g., wall shear stress—WSS, WSS spatial gradient—WSSG, oscillatory shear index—OSI) were analyzed in the model. The motion due to vessel compliance affects the time-averaged WSSG more strongly than WSS at bifurcations. The decrease of WSSG at flow divider in elastic bifurcations, as compared to rigid bifurcations, implies that the vessel compliance decreases the permeability of vessel wall and may be atheroprotective. The model can be used to predict coronary flow pattern in subject-specific anatomy as determined by noninvasive imaging.     

A Study on the Finite Element Model for Head Injury in Facial Collision Accident

In order to predict and evaluate injury mechanism and biomechanical response of the facial impact on head injury in a crash accident. With the combined modern medical imaging technologies, namely computed tomography (CT) and magnetic resonance imaging (MRI), both geometric and finite element (FE) models for human head-neck with detailed cranio-facial structure were developed. The cadaveric head impact tests were conducted to validate the headneck finite element model. The intracranial pressure, skull dynamic response and skull-brain relative displacement of the whole head-neck model were compared with experimental data. Nine typical cases of facial traffic accidents were simulated, with the individual stress wave propagation paths to the intracranial contents through the facial and cranial skeleton being discussed thoroughly. Intracranial pressure, von Mises stress and shear stress distribution were achieved. It is proved that facial structure dissipates a large amount of impact energy to protect the brain in its most natural way. The propagation path and distribution of stress wave in the skull and brain determine the mechanism of brain impact injury, which provides a theoretic basis for the diagnosis, treatment and protection of craniocerebral injury caused by facial impact.     

Development and validation of an atlas-based finite element brain model

Traumatic brain injury is a leading cause of disability and injury-related death. To enhance our ability to prevent such injuries, brain response can be studied using validated finite element (FE) models. In the current study, a high-resolution, anatomically accurate FE model was developed from the International Consortium for Brain Mapping brain atlas. Due to wide variation in published brain material parameters, optimal brain properties were identified using a technique called Latin hypercube sampling, which optimized material properties against three experimental cadaver tests to achieve ideal biomechanics. Additionally, falx pretension and thickness were varied in a lateral impact variation. The atlas-based brain model (ABM) was subjected to the boundary conditions from three high-rate experimental cadaver tests with different material parameter combinations. Local displacements, determined experimentally using neutral density targets, were compared to displacements predicted by the ABM at the same locations. Error between the observed and predicted displacements was quantified using CORrelation and Analysis (CORA), an objective signal rating method that evaluates the correlation of two curves. An average CORA score was computed for each variation and maximized to identify the optimal combination of parameters. The strongest relationships between CORA and material parameters were observed for the shear parameters. Using properties obtained through the described multiobjective optimization, the ABM was validated in three impact configurations and shows good agreement with experimental data. The final model developed in this study consists of optimized brain material properties and was validated in three cadaver impacts against local brain displacement data.     

Load transfer mechanics between trans-tibial prosthetic socket and residual limb--dynamic effects

The effects of inertial loads on the interface stresses between trans-tibial residual limb and prosthetic socket were investigated. The motion of the limb and prosthesis was monitored using a Vicon motion analysis system and the ground reaction force was measured by a force platform. Equivalent loads at the knee joint during walking were calculated in two cases with and without consideration of the material inertia. A 3D nonlinear finite element (FE) model based on the actual geometry of residual limb, internal bones and socket liner was developed to study the mechanical interaction between socket and residual limb during walking. To simulate the friction/slip boundary conditions between the skin and liner, automated surface-to-surface contact was used. The prediction results indicated that interface pressure and shear stress had the similar double-peaked waveform shape in stance phase. The average difference in interface stresses between the two cases with and without consideration of inertial forces was 8.4% in stance phase and 20.1% in swing phase. The maximum difference during stance phase is up to 19%. This suggests that it is preferable to consider the material inertia effect in a fully dynamic FE model.     

A combined numerical and experimental technique for estimation of the forces and moments in the lumbar intervertebral disc

Evaluation of the loads on lumbar intervertebral discs (IVD) is critically important since it is closely related to spine biomechanics, pathology and prosthesis design. Non-invasive estimation of the loads in the discs remains a challenge. In this study, we proposed a new technique to estimate in vivo loads in the IVD using a subject-specific finite element (FE) model of the disc and the kinematics of the disc endplates as input boundary conditions. The technique was validated by comparing the forces and moments in the discs calculated from the FE analyses to the in vitro experiment measurements of three corresponding lumbar discs. The results showed that the forces and moments could be estimated within an average error of 20%. Therefore, this technique can be a promising tool for non-invasive estimation of the loads in the discs and may be extended to be used on living subjects.     

Wave attenuation as a measure of muscle quality as measured by magnetic resonance elastography: Initial results

Advances in imaging technologies such as magnetic resonance elastography (MRE) have allowed researchers to gain insights into muscle function in vivo. MRE has been used to examine healthy and diseased muscle by calculating shear modulus. However, additional information can be measured from visualizing a mechanical wave as it passes through a tissue. One such measurable quantity is wave attenuation. The purpose of this study was to determine if a simple measure of wave attenuation could be used to distinguish between healthy and diseased muscle. Twenty seven subjects (14 healthy controls, 7 hyperthyroid myopathy patients, 6 myositis patients) participated in this study. Wave amplitude was determined along a linear profile through the center of the muscle, and an exponential decay curve was fit to the data. This measure was able to find significant differences in attenuation between healthy and diseased muscle. Furthermore, four hyperthyroid myopathy subjects who were tested following treatment all showed improvement by this measure. A likely reason for patients with hyperthyroid myopathy and myositis behaving similarly is that this measurement may reflect similar changes in the muscle extracellular matrix. In addition to modulus, attenuation seems to be an important parameter to measure in skeletal muscle. Further research is needed to investigate other potential measures of attenuation as well as examining other potential measures that can be found from visualizing wave propagation. Future studies should also include muscle biopsies to confirm that the changes seen are as a result of changes in extracellular matrix structure.     

The apparent critical isotherm for cryoinsult-induced osteonecrotic lesions in emu femoral heads

Cryoinsult-induced osteonecrosis (ON) in the emu femoral head provides a unique opportunity to systematically explore the pathogenesis of ON in an animal model that progresses to human-like femoral head collapse. Among the various characteristics of cryoinsult, the maximally cold temperature attained is one plausible determinant of tissue necrosis. To identify the critical isotherm required to induce development of ON in the cancellous bone of the emu femoral head, a thermal finite element (FE) model of intraoperative cryoinsults was developed. Thermal material property values of emu cancellous bone were estimated from FE simulations of cryoinsult to emu cadaver femora, by varying model properties until the FE-generated temperatures matched corresponding thermocouple measurements. The resulting FE model, with emu bone-specific thermal properties augmented to include blood flow effects, was then used to study intraoperatively performed in vivo cryoinsults. Comparisons of minimum temperatures attained at FE nodes corresponding to the three-dimensional histologically apparent boundary of the region of ON were made for six experimental cryoinsults. Series-wide, a critical isotherm of 3.5 degrees C best corresponded to the boundary of the osteonecrotic lesions.     

Viscoelastic properties of the tongue and soft palate using MR elastography

Biomechanical properties of the human tongue are needed for finite element models of the upper airway and may be important to elucidate the pathophysiology of obstructive sleep apneoa. Tongue viscoelastic properties have not been characterized previously. Magnetic resonance elastography (MRE) is an emerging imaging technique that can measure the viscoelastic properties of soft tissues in-vivo. In this study, MRE was used to measure the viscoelastic properties of the tongue and soft palate in 7 healthy volunteers during quiet breathing. Results show that the storage shear modulus of the tongue and soft palate is 2.67±0.29 and 2.53±0.31 kPa (mean ± SD), respectively. This is the first study to investigate the mechanical properties of the tongue using MRE, and it provides necessary data for future studies of patient groups with altered upper airway function.