Can sulci protect the brain from traumatic injury?

The influence of sulci in dynamic finite element simulations of the human head has been investigated. First, a detailed 3D FE model was constructed based on an MRI scan of a human head. A second model with a smoothed brain surface was created based on the same MRI scan as the first FE model. These models were validated against experimental data to confirm their human-like dynamic responses during impact. The validated FE models were subjected to several acceleration impulses and the maximum principle strain and strain rate in the brain were analyzed. The results suggested that the inclusion of sulci should be considered for future FE head models as it alters the strain and strain distribution in an FE model.     

Methodology for predicting oxygen transport on an intravenous membrane oxygenator combining computational and analytical models

A computational methodology for accurately predicting flow and oxygen-transport characteristics and performance of an intravenous membrane oxygenator (IMO) device is developed, tested, and validated. This methodology uses extensive numerical simulations of three-dimensional computational models to determine flow-mixing characteristics and oxygen-transfer performance, and analytical models to indirectly validate numerical predictions with experimental data, using both blood and water as working fluids. Direct numerical simulations for IMO stationary and pulsating balloons predict flow field and oxygen transport performance in response to changes in the device length, number of and balloon pulsation frequency. Multifiber models are used to investigate interfiber interference and length effects for a stationary balloon whereas a single fiber model is used to analyze the effect of balloon pulsations on velocity and oxygen concentration fields and to evaluate oxygen transfer rates. An analytical lumped model is developed and validated by comparing its numerical predictions with experimental data. Numerical results demonstrate that oxygen transfer rates for a stationary balloon regime decrease with increasing number of fibers, independent of the fluid type. The oxygen transfer rate ratio obtained with blood and water is approximately two. Balloon pulsations show an effective and enhanced flow mixing, with time-dependent recirculating flows around the fibers regions which induce higher oxygen transfer rates. The mass transfer rates increase approximately 100% and 80%, with water and blood, respectively, compared with stationary balloon operation. Calculations with combinations of frequency, number of fibers, fiber length and diameter, and inlet volumetric flow rates, agree well with the reported experimental results, and provide a solid comparative base for analysis, predictions, and comparisons with numerical and experimental data.     

An anatomically detailed and personalizable head injury model: Significance of brain and white matter tract morphological variability on strain

Finite element head (FE) models are important numerical tools to study head injuries and develop protection systems. The generation of anatomically accurate and subject-specific head models with conforming hexahedral meshes remains a significant challenge. The focus of this study is to present two developmental works: first, an anatomically detailed FE head model with conforming hexahedral meshes that has smooth interfaces between the brain and the cerebrospinal fluid, embedded with white matter (WM) fiber tracts; second, a morphing approach for subject-specific head model generation via a new hierarchical image registration pipeline integrating Demons and Dramms deformable registration algorithms. The performance of the head model is evaluated by comparing model predictions with experimental data of brain–skull relative motion, brain strain, and intracranial pressure. To demonstrate the applicability of the head model and the pipeline, six subject-specific head models of largely varying intracranial volume and shape are generated, incorporated with subject-specific WM fiber tracts. DICE similarity coefficients for cranial, brain mask, local brain regions, and lateral ventricles are calculated to evaluate personalization accuracy, demonstrating the efficiency of the pipeline in generating detailed subject-specific head models achieving satisfactory element quality without further mesh repairing. The six head models are then subjected to the same concussive loading to study the sensitivity of brain strain to inter-subject variability of the brain and WM fiber morphology. The simulation results show significant differences in maximum principal strain and axonal strain in local brain regions (one-way ANOVA test, p < 0.001), as well as their locations also vary among the subjects, demonstrating the need to further investigate the significance of subject-specific models. The techniques developed in this study may contribute to better evaluation of individual brain injury and the development of individualized head protection systems in the future. This study also contains general aspects the research community may find useful: on the use of experimental brain strain close to or at injury level for head model validation; the hierarchical image registration pipeline can be used to morph other head models, such as smoothed-voxel models.

     

Computational neurotrauma—design, simulation, and analysis of controlled cortical impact model

The controlled cortical impact (CCI) model is widely used in many laboratories to study traumatic brain injury (TBI). Although external impact parameters during CCI tests could be clearly defined, little is known about the internal tissue-level mechanical responses of the rat brain. Furthermore, the external impact parameters tend to vary considerably among different labs making the comparison of research findings difficult if not impossible. In this study, a design of computer experiments was performed with typical external impact parameters commonly found in the literature. An anatomically detailed finite element (FE) rat brain model was used to simulate the CCI experiments to correlate external mechanical parameters (impact depth, impact velocity, impactor shape, impactor size, and craniotomy pattern) with rat brain internal responses, as predicted by the FE model. Systematic analysis of the results revealed that impact depth was the leading factor affecting the predicted brain internal responses. Interestingly, impactor shape ranked as the second most important factor, surpassing impactor diameter and velocity which were commonly reported in the literature as indicators of injury severity along with impact depth. The differences in whole brain response due to a unilateral or a bilateral craniotomy were small, but those of regional intracranial tissue stretches were large. The interaction effects of any two external parameters were not significant. This study demonstrates the potential of using numerical FE modeling to engineer better experimental TBI models in the future.     

Design and numerical implementation of a 3-D non-linear viscoelastic constitutive model for brain tissue during impact

Finite Element (FE) head models are often used to understand mechanical response of the head and its contents during impact loading in the head. Current FE models do not account for non-linear viscoelastic material behavior of brain tissue. We developed a new non-linear viscoelastic material model for brain tissue and implemented it in an explicit FE code. To obtain sufficient numerical accuracy for modeling the nearly incompressible brain tissue, deviatoric and volumetric stress contributions are separated. Deviatoric stress is modeled in a non-linear viscoelastic differential form. Volumetric behavior is assumed linearly elastic. Linear viscoelastic material parameters were derived from published data on oscillatory experiments, and from ultrasonic experiments. Additionally, non-linear parameters were derived from stress relaxation (SR) experiments at shear strains up to 20%. The model was tested by simulating the transient phase in the SR experiments not used in parameter determination (strains up to 20%, strain rates up to 8s(-1)). Both time- and strain-dependent behavior were predicted accurately (R2>0.96) for strain and strain rates applied. However, the stress was overestimated systematically by approximately 31% independent of strain(rate) applied. This is probably caused by limitations of the experimental data at hand.     

A simple method to estimate the exponential material parameters of heart valve tissue based on analogy between uniaxial tension and micropipette aspiration

Micropipette aspiration (MA) has been widely used to measure the biomechanical properties of cells and biomaterials. To estimate material parameters from MA experimental data, analytical half-space models and inverse finite element (FE) analyses are typically used. The half-space model is easy to implement but cannot account for nonlinear material properties and complex geometrical boundary conditions that are inherent to MA. Inverse FE approaches can account for geometrical and material nonlinearities, but their implementation is resource-intensive and not widely available. Here, by making analogy between an analytical uniaxial tension model and a FE model of MA, we proposed an easily implementable and accurate method to estimate the material parameters of tissues tested by MA. We first adopted a strain invariant-based isotropic exponential constitutive model and implemented it in both the analytical uniaxial tension model and the FE model. The two models were fit to experimental data generated by MA of porcine aortic valve tissue (45 spots on four leaflets) to estimate material parameters. We found no significant differences between the effective moduli estimated by the two models ( $p > 0.39$ ), with the effective moduli estimated by the uniaxial tension model correlating significantly with those estimated by the FE model ( $p < 0.001; R^{2}= 0.96$ ) with a linear regression slope that was not different than unity ( $p = 0.38$ ). Thus, the analytical uniaxial tension model, which avoids solving resource-intensive numerical problems, is as accurate as the FE model in estimating the effective modulus of valve tissue tested by MA.     

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.     

Patient-specific finite-element analyses of the proximal femur with orthotropic material properties validated by experiments

Patient-specific high order finite-element (FE) models of human femurs based on quantitative computer tomography (QCT) with inhomogeneous orthotropic and isotropic material properties are addressed. The point-wise orthotropic properties are determined by a micromechanics (MM) based approach in conjunction with experimental observations at the osteon level, and two methods for determining the material trajectories are proposed (along organs outer surface, or along principal strains). QCT scans on four fresh-frozen human femurs were performed and high-order FE models were generated with either inhomogeneous MM-based orthotropic or empirically determined isotropic properties. In vitro experiments were conducted on the femurs by applying a simple stance position load on their head, recording strains on femurs' surface and head's displacements. After verifying the FE linear elastic analyses that mimic the experimental setting for numerical accuracy, we compared the FE results to the experimental observations to identify the influence of material properties on models' predictions. The strains and displacements computed by FE models having MM-based inhomogeneous orthotropic properties match the FE-results having empirically based isotropic properties well, and both are in close agreement with the experimental results. When only the strains in the femoral neck are being compared a more pronounced difference is noticed between the isotropic and orthotropic FE result. These results lay the foundation for applying more realistic inhomogeneous orthotropic material properties in FEA of femurs.     

A new method to investigate in vivo knee behavior using a finite element model of the lower limb

Several finite element models have been developed for estimating the mechanical response of joint internal structures, where direct or indirect in vivo measurement is difficult or impossible. The quality of the predictions made by those models is largely dependent on the quality of the experimental data (e.g. load/displacement) used to drive them. Also numerical problems have been described in the literature when using implicit finite element techniques to simulate problems that involve contacts and large displacements. In this study, a unique strategy was developed combining high accuracy in vivo three-dimensional kinematics and a lower limb finite element model based on explicit finite element techniques. The method presents an analytical technique applied to a dynamic loading condition (impact during hopping on one leg). The validation of the lower limb model focused on the response of the whole model and the knee joint in particular to the imposed 3D femoral in vivo kinematics and ground reaction forces. The approach outlined in this study introduces a generic tool for the study of in vivo knee joint behavior.     

MRI-based finite-element analysis of left ventricular aneurysm

Tagged MRI and finite-element (FE) analysis are valuable tools in analyzing cardiac mechanics. To determine systolic material parameters in three-dimensional stress-strain relationships, we used tagged MRI to validate FE models of left ventricular (LV) aneurysm. Five sheep underwent anteroapical myocardial infarction (25% of LV mass) and 22 wk later underwent tagged MRI. Asymmetric FE models of the LV were formed to in vivo geometry from MRI and included aneurysm material properties measured with biaxial stretching, LV pressure measurements, and myofiber helix angles measured with diffusion tensor MRI. Systolic material parameters were determined that enabled FE models to reproduce midwall, systolic myocardial strains from tagged MRI (630 +/- 187 strain comparisons/animal). When contractile stress equal to 40% of the myofiber stress was added transverse to the muscle fiber, myocardial strain agreement improved by 27% between FE model predictions and experimental measurements (RMS error decreased from 0.074 +/- 0.016 to 0.054 +/- 0.011, P < 0.05). In infarct border zone (BZ), end-systolic midwall stress was elevated in both fiber (24.2 +/- 2.7 to 29.9 +/- 2.4 kPa, P < 0.01) and cross-fiber (5.5 +/- 0.7 to 11.7 +/- 1.3 kPa, P = 0.02) directions relative to noninfarct regions. Contrary to previous hypotheses but consistent with biaxial stretching experiments, active cross-fiber stress development is an integral part of LV systole; FE analysis with only uniaxial contracting stress is insufficient. Stress calculations from these validated models show 24% increase in fiber stress and 115% increase in cross-fiber stress at the BZ relative to remote regions, which may contribute to LV remodeling.     

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.     

Specimen-specific predictions of contact stress under physiological loading in the human hip: validation and sensitivity studies

Hip osteoarthritis may be initiated and advanced by abnormal cartilage contact mechanics, and finite element (FE) modeling provides an approach with the potential to allow the study of this process. Previous FE models of the human hip have been limited by single specimen validation and the use of quasi-linear or linear elastic constitutive models of articular cartilage. The effects of the latter assumptions on model predictions are unknown, partially because data for the instantaneous behavior of healthy human hip cartilage are unavailable. The aims of this study were to develop and validate a series of specimen-specific FE models, to characterize the regional instantaneous response of healthy human hip cartilage in compression, and to assess the effects of material nonlinearity, inhomogeneity and specimen-specific material coefficients on FE predictions of cartilage contact stress and contact area. Five cadaveric specimens underwent experimental loading, cartilage material characterization and specimen-specific FE modeling. Cartilage in the FE models was represented by average neo-Hookean, average Veronda Westmann and specimen- and region-specific Veronda Westmann hyperelastic constitutive models. Experimental measurements and FE predictions compared well for all three cartilage representations, which was reflected in average RMS errors in contact stress of less than 25 %. The instantaneous material behavior of healthy human hip cartilage varied spatially, with stiffer acetabular cartilage than femoral cartilage and stiffer cartilage in lateral regions than in medial regions. The Veronda Westmann constitutive model with average material coefficients accurately predicted peak contact stress, average contact stress, contact area and contact patterns. The use of subject- and region-specific material coefficients did not increase the accuracy of FE model predictions. The neo-Hookean constitutive model underpredicted peak contact stress in areas of high stress. The results of this study support the use of average cartilage material coefficients in predictions of cartilage contact stress and contact area in the normal hip. The regional characterization of cartilage material behavior provides the necessary inputs for future computational studies, to investigate other mechanical parameters that may be correlated with OA and cartilage damage in the human hip. In the future, the results of this study can be applied to subject-specific models to better understand how abnormal hip contact stress and contact area contribute to OA.     

From single muscle fiber to whole muscle mechanics: a finite element model of a muscle bundle with fast and slow fibers

Muscles exhibit highly complex, multi-scale architecture with thousands of muscle fibers, each with different properties, interacting with each other and surrounding connective structures. Consequently, the results of single-fiber experiments are scarcely linked to the macroscopic or whole muscle behavior. This is especially true for human muscles where it would be important to understand of how skeletal muscles disorders affect patients’ life. In this work, we developed a mathematical model to study how fast and slow muscle fibers, well characterized in single-fiber experiments, work and generate together force and displacement in muscle bundles. We characterized the parameters of a Hill-type model, using experimental data on fast and slow single human muscle fibers, and comparing experimental data with numerical simulations obtained from finite element (FE) models of single fibers. Then, we developed a FE model of a bundle of 19 fibers, based on an immunohistochemically stained cross section of human diaphragm and including the corresponding properties of each slow or fast fiber. Simulations of isotonic contractions of the bundle model allowed the generation of its apparent force–velocity relationship. Although close to the average of the force–velocity curves of fast and slow fibers, the bundle curve deviates substantially toward the fast fibers at low loads. We believe that the present model and the characterization of the force–velocity curve of a fiber bundle represents the starting point to link the single-fiber properties to those of whole muscle with FE application in phenomenological models of human muscles.     

Development of a parametric finite element model of the proximal femur using statistical shape and density modelling

Skeletal fractures associated with bone mass loss are a major clinical problem and economic burden, and lead to significant morbidity and mortality in the ageing population. Clinical image-based measures of bone mass show only moderate correlative strength with bone strength. However, engineering models derived from clinical image data predict bone strength with significantly greater accuracy. Currently, image-based finite element (FE) models are time consuming to construct and are non-parametric. The goal of this study was to develop a parametric proximal femur FE model based on a statistical shape and density model (SSDM) derived from clinical image data. A small number of independent SSDM parameters described the shape and bone density distribution of a set of cadaver femurs and captured the variability affecting proximal femur FE strength predictions. Finally, a three-dimensional FE model of an 'unknown' femur was reconstructed from the SSDM with an average spatial error of 0.016 mm and an average bone density error of 0.037 g/cm(3).     

Subject-specific finite element model of the pelvis: development, validation and sensitivity studies

A better understanding of the three-dimensional mechanics of the pelvis, at the patient-specific level, may lead to improved treatment modalities. Although finite element (FE) models of the pelvis have been developed, validation by direct comparison with subject-specific strains has not been performed, and previous models used simplifying assumptions regarding geometry and material properties. The objectives of this study were to develop and validate a realistic FE model of the pelvis using subject-specific estimates of bone geometry, location-dependent cortical thickness and trabecular bone elastic modulus, and to assess the sensitivity of FE strain predictions to assumptions regarding cortical bone thickness as well as bone and cartilage material properties. A FE model of a cadaveric pelvis was created using subject-specific computed tomography image data. Acetabular loading was applied to the same pelvis using a prosthetic femoral stem in a fashion that could be easily duplicated in the computational model. Cortical bone strains were monitored with rosette strain gauges in ten locations on the left hemipelvis. FE strain predictions were compared directly with experimental results for validation. Overall, baseline FE predictions were strongly correlated with experimental results (r2=0.824), with a best-fit line that was not statistically different than the line y=x (experimental strains = FE predicted strains). Changes to cortical bone thickness and elastic modulus had the largest effect on cortical bone strains. The FE model was less sensitive to changes in all other parameters. The methods developed and validated in this study will be useful for creating and analyzing patient-specific FE models to better understand the biomechanics of the pelvis.     

Utilizing multiple scale models to improve predictions of extra-axial hemorrhage in the immature piglet

Traumatic brain injury (TBI) is a leading cause of death and disability in the USA. To help understand and better predict TBI, researchers have developed complex finite element (FE) models of the head which incorporate many biological structures such as scalp, skull, meninges, brain (with gray/white matter differentiation), and vasculature. However, most models drastically simplify the membranes and substructures between the pia and arachnoid membranes. We hypothesize that substructures in the pia–arachnoid complex (PAC) contribute substantially to brain deformation following head rotation, and that when included in FE models accuracy of extra-axial hemorrhage prediction improves. To test these hypotheses, microscale FE models of the PAC were developed to span the variability of PAC substructure anatomy and regional density. The constitutive response of these models were then integrated into an existing macroscale FE model of the immature piglet brain to identify changes in cortical stress distribution and predictions of extra-axial hemorrhage (EAH). Incorporating regional variability of PAC substructures substantially altered the distribution of principal stress on the cortical surface of the brain compared to a uniform representation of the PAC. Simulations of 24 non-impact rapid head rotations in an immature piglet animal model resulted in improved accuracy of EAH prediction (to 94 % sensitivity, 100 % specificity), as well as a high accuracy in regional hemorrhage prediction (to 82–100 % sensitivity, 100 % specificity). We conclude that including a biofidelic PAC substructure variability in FE models of the head is essential for improved predictions of hemorrhage at the brain/skull interface.     

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.     

Dynamic finite element modeling of poroviscoelastic soft tissue

Clinical evidences relative to biomechanical factors have demonstrated their important contribution to the behaviour of soft tissues. Finite element (FE) analysis is used to study the mechanical behaviour of soft tissue because it can provide numerical solutions to problems that are intractable to analytic solutions. This study focuses on the development of a FE model of a poroelastic biological tissue, which incorporates the viscoelastic material behaviour, finite deformation and inertial effect. The FE formulation is based on the weak form derived from the governing equation, and Newmark-beta method as well as Newton's method is incorporated into the implicit non-linear solutions. One-dimensional analytical solutions were used to verify the theoretical formulation and the numerical implementation of the proposed model. This study was further extended to analyze two-dimensional biomechanical models and the results clearly demonstrate the importance of including finite deformation, viscoelasticity and inertial effects.     

Determination of orthotropic bone elastic constants using FEA and modal analysis

Finite element models have been widely employed in an effort to quantify the stress and strain distribution around implanted prostheses and to explore the influence of these distributions on their long-term stability. In order to provide meaningful predictions, such models must contain an appropriate reflection of mechanical properties. Detailed geometrical and density information is now readily available from CT scanning. However, despite the use of phantoms, a method of determining mechanical properties (or elastic constants) from bone density has yet to be made available in a usable form.In this study, a cadaveric bone was CT scanned and its natural frequencies were measured using modal analysis. Using the geometry obtained from the CT scan data, a finite element mesh was created with the distribution of density established by matching the mass of the FE bone model with the mass of the cadaveric bone. The maximum values of the orthotropic elastic constants were then established by matching the predictions from FE modal analyses to the experimental natural frequencies, giving a maximum error of 7.8% over 4 modes of vibration. Finally, the elastic constants of the bone derived from the analyses were compared with those measured using ultrasound techniques. This produced a difference of <1% for both the maximum density and axial Young's Modulus. This study has thereby produced an orthotropic finite element model of a human femur. More importantly, however, is the implication that it is possible to create a valid FE model by simply comparing the FE results with the measured resonant frequency of the CT scanned bone.