Sensitivity of damage predictions to tissue level yield properties and apparent loading conditions

High-resolution finite element models of trabecular bone failure could be used to augment current techniques for measuring damage in trabecular bone. However, the sensitivity of such models to the assumed tissue yield properties and apparent loading conditions is unknown. The goal of this study was to assess the sensitivity of the amount and mode (tension vs. compression) of tissue level yielding in trabecular bone to these factors. Linear elastic, high-resolution finite element models of nine bovine tibial trabecular bone specimens were used to calculate the fraction of the total tissue volume that exceeded each criterion for apparent level loading to the reported elastic limit in both on-axis and transverse compression and tension, and in shear. Four candidate yield criteria were studied, based on values suggested in the literature. Both the amount and the failure mode of yielded tissue were sensitive to the magnitudes of the tissue yield strains, the degree of tension-compression asymmetry of the yield criterion, and the applied apparent loads. The amount of yielded tissue was most sensitive to the orientation of the applied apparent loading, with the most tissue yielding for loading along the principal trabecular orientation and the least for loading perpendicular to it, regardless of the assumed tissue level yield criterion. Small changes in the magnitudes and the degree of asymmetry of the tissue yield criterion resulted in much larger changes in the amount of yielded tissue in the model. The results indicate that damage predictions based on high-resolution finite element models are highly sensitive to the assumed tissue yield properties. As such, good estimates of these values are needed before high-resolution finite element models can be applied to the study of trabecular bone damage. Regardless of the assumed tissue yield properties, the amount and type of damage that occurs in trabecular bone depends on the relative orientations of the applied apparent loads to the trabecular architecture, and this parameter should be controlled for both experimental and computational damage studies.     

Fitted hyperelastic parameters for Human brain tissue from reported tension,compression, and shear tests

The mechanical properties of human brain tissue are the subject of interest because of their use in understanding brain trauma and in developing therapeutic treatments and procedures. To represent the behavior of the tissue, we have developed hyperelastic mechanical models whose parameters are fitted in accordance with experimental test results. However, most studies available in the literature have fitted parameters with data of a single type of loading, such as tension, compression, or shear. Recently, Jin et al. (Journal of Biomechanics 46:2795−2801, 2013) reported data from ex vivo tests of human brain tissue under tension, compression, and shear loading using four strain rates and four different brain regions. However, they do not report parameters of energy functions that can be readily used in finite element simulations. To represent the tissue behavior for the quasi-static loading conditions, we aimed to determine the best fit of the hyperelastic parameters of the hyperfoam, Ogden, and polynomial strain energy functions available in ABAQUS for the low strain rate data, while simultaneously considering all three loading modes. We used an optimization process conducted in MATLAB, calling iteratively three finite element models developed in ABAQUS that represent the three loadings. Results showed a relatively good fit to experimental data in all loading modes using two terms in the energy functions. Values for the shear modulus obtained in this analysis (897−1653 Pa) are in the range of those presented in other studies. These energy-function parameters can be used in brain tissue simulations using finite element models.     

High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone

The ability to predict trabecular failure using microstructure-based computational models would greatly facilitate study of trabecular structure–function relations, multiaxial strength, and tissue remodeling. We hypothesized that high-resolution finite element models of trabecular bone that include cortical-like strength asymmetry at the tissue level, could predict apparent level failure of trabecular bone for multiple loading modes. A bilinear constitutive model with asymmetric tissue yield strains in tension and compression was applied to simulate failure in high-resolution finite element models of seven bovine tibial specimens. Tissue modulus was reduced by 95% when tissue principal strains exceeded the tissue yield strains. Linear models were first calibrated for effective tissue modulus against specimen-specific experimental measures of apparent modulus, producing effective tissue moduli of (mean±S.D.) 18.7±3.4 GPa. Next, a parameter study was performed on a single specimen to estimate the tissue level tensile and compressive yield strains. These values, 0.60% strain in tension and 1.01% strain in compression, were then used in non-linear analyses of all seven specimens to predict failure for apparent tensile, compressive, and shear loading. When compared to apparent yield properties previously measured for the same type of bone, the model predictions of both the stresses and strains at failure were not statistically different for any loading case (p>0.15). Use of symmetric tissue strengths could not match the experimental data. These findings establish that, once effective tissue modulus is calibrated and uniform but asymmetric tissue failure strains are used, the resulting models can capture the apparent strength behavior to an outstanding level of accuracy. As such, these computational models have reached a level of fidelity that qualifies them as surrogates for destructive mechanical testing of real specimens.     

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

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

Developmental biomechanics of the cervical spine: Tension and compression

Epidemiological data and clinical indicia reveal devastating consequences associated with pediatric neck injuries. Unfortunately, neither injury prevention nor clinical management strategies will be able to effectively reduce these injuries or their effects on children, without an understanding of the cervical spine developmental biomechanics. Thus, we investigated the relationship between spinal development and the functional (stiffness) and failure biomechanical characteristics of the cervical spine in a baboon model. A correlation study design was used to define the relationships between spinal tissue maturation and spinal biomechanics in both tension and compression. Eighteen baboon cervical spine specimens distributed across the developmental spectrum (1–26 human equivalent years) were dissected into osteoligamentous functional spinal units. Using a servo-hydraulic MTS, these specimens (Oc–C2, C3–C4, C5–C6, C7–T1) were non-destructively tested in tension and compression and then displaced to failure in tension while measuring the six-axes of loads and displacements. The functions describing the developmental biomechanical response of the cervical spine for stiffness and normalized stiffness exhibited a significant direct relationship in both tension and compression loading. Similarly, the tensile failure load and normalized failure load demonstrated significant maturational increases. Further, differences in biomechanical response were observed between the spinal levels examined and all levels exhibited clinically relevant failure patterns. These data support our understanding of the child cervical spine from a developmental biomechanics perspective and facilitate the development of injury prevention or management schema for the mitigation of child spine injuries and their deleterious effects.     

Experimental and finite element analysis for prediction of kidney injury under blunt impact

Kidneys are third most injured organs in abdominal trauma after liver and spleen; this study therefore is an attempt to understand the behaviour of kidneys under blunt trauma. Dynamic impact tests were performed on 20 fresh porcine kidneys to study the injury propagation in the organ, and the acceleration of the impactor was measured. A kidney model was developed with structural details like capsule and cortex. The kidney cortex was modelled with solid hexahedral elements and the capsule was modelled with quadratic shell elements. The material models for the capsule and cortex were used from the experimental data reported in our previous study. The developed model was calibrated using previous and current experimental results to reproduce the injuries of the organ in terms of acceleration of the impactor, and the injuries sustained by the organ during the experiments. The developed kidney model is observed to be robust and can be integrated with the available human body finite element models to simulate accidents and to predict or simulate injuries.     

Detailed finite element modelling of deep needle insertions into a soft tissue phantom using a cohesive approach

Detailed finite element modelling of needle insertions into soft tissue phantoms encounters difficulties of large deformations, high friction, contact loading and material failure. This paper demonstrates the use of cohesive elements in high-resolution finite element models to overcome some of the issues associated with these factors. Experiments are presented enabling extraction of the strain energy release rate during crack formation. Using data from these experiments, cohesive elements are calibrated and then implemented in models for validation of the needle insertion process. Successful modelling enables direct comparison of finite element and experimental force–displacement plots and energy distributions. Regions of crack creation, relaxation, cutting and full penetration are identified. By closing the loop between experiments and detailed finite element modelling, a methodology is established which will enable design modifications of a soft tissue probe that steers through complex mechanical interactions with the surrounding material.     

Incorporating tissue anisotropy and heterogeneity in finite element models of trabecular bone altered predicted local stress distributions

Trabecular bone is composed of organized mineralized collagen fibrils, which results in heterogeneous and anisotropic mechanical properties at the tissue level. Recently, biomechanical models computing stresses and strains in trabecular bone have indicated a significant effect of tissue heterogeneity on predicted stresses and strains. However, the effect of the tissue-level mechanical anisotropy on the trabecular bone biomechanical response is unknown. Here, a computational method was established to automatically impose physiologically relevant orientation inherent in trabecular bone tissue on a trabecular bone microscale finite element model. Spatially varying tissue-level anisotropic elastic properties were then applied according to the bone mineral density and the local tissue orientation. The model was used to test the hypothesis that anisotropy in both homogeneous and heterogeneous models alters the predicted distribution of stress invariants. Linear elastic finite element computations were performed on a 3 mm cube model isolated from a microcomputed tomography scan of human trabecular bone from the distal femur. Hydrostatic stress and von Mises equivalent stress were recorded at every element, and the distributions of these values were analyzed. Anisotropy reduced the range of hydrostatic stress in both tension and compression more strongly than the associated increase in von Mises equivalent stress. The effect of anisotropy was independent of the spatial redistribution high compressive stresses due to tissue elastic heterogeneity. Tissue anisotropy and heterogeneity are likely important mechanisms to protect bone from failure and should be included for stress analyses in trabecular bone.     

Mechanical characterization of liver capsule through uniaxial quasi-static tensile tests until failure

Accidentology data showed that liver is often injured in car crashes; three types of injuries occur: hematoma, laceration and vessel failure. This paper focuses on surface laceration, which involves liver capsule and hepatic parenchyma. Liver capsule behavior has been studied but its failure properties are still unclear, particularly on a local point of view. In the present study, tensile quasi-static tests are run on parenchyma and capsule samples until failure to characterize capsule failure. Normalized load as well as failure properties—ultimate load per width unit and ultimate strain—are determined. Digital image correlation is used to measure the full local strain field on the capsule. Mean values of failure characteristics for hepatic capsule are 47±29% for the ultimate local strain and 0.3±0.3 N/mm for the ultimate load per width unit. A comparison between human and porcine tissues is conducted based on Mann–Whitney statistical test; it reveals that capsule characteristics are close between these two species; however, freezing preservation significantly affects porcine capsule failure properties. Therefore using porcine instead of human tissue to determine failure characteristics of liver capsule seems satisfactory only on fresh tissues.     

中华花龟五种器官组织学观察

利用石蜡切片法对中华花龟的心脏、肝脏、脾脏、肺和肾脏等组织器官进行了组织学观察.结果显示心肌的特点是暗带较窄,心肌纤维束状排列.肝脏分3叶,肝实质内结缔组织少,肝小叶分界不清楚.脾脏分被膜和实质两部分,实质由白髓和红髓构成,白髓包括椭球周围淋巴鞘(PELS)和动脉周围淋巴鞘(PALS),红髓由脾索和脾窦组成,未发现淋巴小结和生发中心.肺一对,为长形扁平囊,肺泡囊状,肺泡内可见管壁的结节状膨大.肾脏由肾小体、颈段、近曲小管、中间段、远曲小管和收集管6部分构成,肾小体由肾小球和肾小囊组成,在肾小体附近可见致密斑样结构.     

Mechanical properties of brain tissue in tension

This paper contains experimental results of in vitro, uniaxial tension of swine brain tissue in finite deformation as well as proposes a new hyper-viscoelastic constitutive model for the brain tissue. The experimental results obtained for two loading velocities, corresponding to strain rates of 0.64 and 0.64 x 10(-2)s(-1), are presented. We believe that these are the first ever experiments of this kind. The applied strain rates were similar to those applied in our previous study, focused on explaining brain tissue properties in compression. The stress-strain curves are convex downward for all extension rates. The tissue response stiffened as the loading speed increased, indicating a strong stress-strain rate dependence. Swine brain tissue was found to be considerably softer in extension than in compression. Previously proposed in the literature brain tissue constitutive models, developed based on experimental data collected in compression are shown to be inadequate to explain tissue behaviour in tension. A new, non-linear, viscoelastic model based on the generalisation of the Ogden strain energy hyper-elastic constitutive equation is proposed. The new model accounts well for brain tissue deformation behaviour in both tension and compression (natural strain in <-0.3,0.2>) for strain rates ranging over five orders of magnitude.     

Compressive mechanical properties of atherosclerotic plaques—Indentation test to characterise the local anisotropic behaviour

Accurate material models and associated parameters of atherosclerotic plaques are crucial for reliable biomechanical plaque prediction models. These biomechanical models have the potential to increase our understanding of plaque progression and failure, possibly improving risk assessment of plaque rupture, which is the main cause of ischaemic strokes and myocardial infarction. However, experimental biomechanical data on atherosclerotic plaque tissue is scarce and shows a high variability. In addition, most of the biomechanical models assume isotropic behaviour of plaque tissue, which is a general over-simplification. This review discusses the past and the current literature that focus on mechanical properties of plaque derived from compression experiments, using unconfined compression, micro-indentation or nano-indentation. Results will be discussed and the techniques will be mutually compared. Thereafter, an in-house developed indentation method combined with an inverse finite element method is introduced, allowing analysis of the local anisotropic mechanical properties of atherosclerotic plaques. The advantages and limitations of this method will be evaluated and compared to other methods reported in literature.     

Changes to the mechanical properties of the glenohumeral capsule during anterior dislocation

The glenohumeral joint is the most frequently dislocated major joint in the body, and instability due to permanent deformation of the glenohumeral capsule is a common pathology. The corresponding change in mechanical properties may have implications for the ideal location and extent of plication, which is a common clinical procedure used to repair the capsule. Therefore, the objective of this study was to quantify the mechanical properties of four regions of the glenohumeral capsule after anterior dislocation and compare the properties to the normal glenohumeral capsule. Six fresh-frozen cadaveric shoulders were dislocated in the anterior direction with the joint in the apprehension position using a robotic testing system. After dislocation, mechanical testing was performed on the injured glenohumeral capsule by loading the tissue samples in tension and shear. An inverse finite element optimization routine was used to simulate the experiments and obtain material coefficients for each tissue sample. Cauchy stress–stretch curves were then generated to represent the mechanical response of each tissue sample to theoretical loading conditions. Based on several comparisons (average of the material coefficients, average stress–stretch curve for each region, and coefficients representing the average curves) between the normal and injured tissue samples, the mechanical properties of the injured tissue samples from multiple regions were found to be lower than those of the normal tissue in tension but not in shear. This finding indicates that anterior dislocation primarily affects the tensile behavior of the glenohumeral capsule rather than the shear behavior, and this phenomenon could be caused by plastic deformation of the matrix, permanent collagen fiber rotation, and/or collagen fiber failure. These results suggest that plication and suturing may not be sufficient to return stability to the shoulder after dislocation in all individuals. Thus, surgeons may need to perform a procedure that reinforces or stiffens the tissue itself, such as reconstruction or augmentation, to improve repair procedures.     

Numerical investigations of rib fracture failure models in different dynamic loading conditions

Rib fracture is one of the most common thoracic injuries in vehicle traffic accidents that can result in fatalities associated with seriously injured internal organs. A failure model is critical when modelling rib fracture to predict such injuries. Different rib failure models have been proposed in prediction of thorax injuries. However, the biofidelity of the fracture failure models when varying the loading conditions and the effects of a rib fracture failure model on prediction of thoracic injuries have been studied only to a limited extent. Therefore, this study aimed to investigate the effects of three rib failure models on prediction of thoracic injuries using a previously validated finite element model of the human thorax. The performance and biofidelity of each rib failure model were first evaluated by modelling rib responses to different loading conditions in two experimental configurations: (1) the three-point bending on the specimen taken from rib and (2) the anterior–posterior dynamic loading to an entire bony part of the rib. Furthermore, the simulation of the rib failure behaviour in the frontal impact to an entire thorax was conducted at varying velocities and the effects of the failure models were analysed with respect to the severity of rib cage damages. Simulation results demonstrated that the responses of the thorax model are similar to the general trends of the rib fracture responses reported in the experimental literature. However, they also indicated that the accuracy of the rib fracture prediction using a given failure model varies for different loading conditions.     

Numerical investigation of bone remodelling around immediately loaded dental implants using sika deer (Cervus nippon) antlers as implant bed

This study combines finite element method and animal studies, aiming to investigate tissue remodelling processes around dental implants inserted into sika deer antler and to develop an alternative animal consuming model for studying bone remodelling around implants. Implants were inserted in the antlers and loaded immediately via a self-developed loading device. After 3, 4, 5 and 6 weeks, implants and surrounding tissue were taken out. Specimens were scanned by μCT scanner and finite element models were generated. Immediate loading and osseointegration conditions were simulated at the implant-tissue interface. A vertical force of 10 N was applied on the implant. During the healing time, density and Young’s modulus of antler tissue around the implant increased significantly. For each time point, the values of displacement, stresses and strains in the osseointegration model were lower than those of the immediate loading model. As the healing time increased, the displacement of implants was reduced. The 3-week immediate loading model (9878 ± 1965 μstrain) illustrated the highest strains in the antler tissue. Antler tissue showed similar biomechanical properties as human bone in investigating the bone remodelling around implants, therefore the use of sika deer antler model is a promising alternative in implant biomechanical studies.     

A musculoskeletal finite element model of rat knee joint for evaluating cartilage biomechanics during gait

Abnormal loading of the knee due to injuries or obesity is thought to contribute to the development of osteoarthritis (OA). Small animal models have been used for studying OA progression mechanisms. However, numerical models to study cartilage responses under dynamic loading in preclinical animal models have not been developed. Here we present a musculoskeletal finite element model of a rat knee joint to evaluate cartilage biomechanical responses during a gait cycle. The rat knee joint geometries were obtained from a 3-D MRI dataset and the boundary conditions regarding loading in the joint were extracted from a musculoskeletal model of the rat hindlimb. The fibril-reinforced poroelastic (FRPE) properties of the rat cartilage were derived from data of mechanical indentation tests. Our numerical results showed the relevance of simulating anatomical and locomotion characteristics in the rat knee joint for estimating tissue responses such as contact pressures, stresses, strains, and fluid pressures. We found that the contact pressure and maximum principal strain were virtually constant in the medial compartment whereas they showed the highest values at the beginning of the gait cycle in the lateral compartment. Furthermore, we found that the maximum principal stress increased during the stance phase of gait, with the greatest values at midstance. We anticipate that our approach serves as a first step towards investigating the effects of gait abnormalities on the adaptation and degeneration of rat knee joint tissues and could be used to evaluate biomechanically-driven mechanisms of the progression of OA as a consequence of joint injury or obesity.     

Scale-dependent mechanical properties of native and decellularized liver tissue

Decellularization, a technique used in liver regenerative medicine, is the removal of all the cellular components from a tissue or organ, leaving behind an intact structure of extracellular matrix. The biomechanical properties of this novel scaffold material are currently unknown and are important due to the mechanosensitivity of liver cells. Characterizing this material is important for bioengineering liver tissue from this decellularized scaffold as well as creating new 3-dimensional mimetic structures of liver extracellular matrix. This study set out to characterize the biomechanical properties of perfused liver tissue in its native and decellularized states on both a macro- and nano-scale. Poroviscoelastic finite element models were then used to extract the fluid and solid mechanical properties from the experimental data. Tissue-level spherical indentation-relaxation tests were performed on 5 native livers and 8 decellularized livers at two indentation rates and at multiple perfusion rates. Cellular-level spherical nanoindentation was performed on 2 native livers and 1 decellularized liver. Tissue-level results found native liver tissue to possess a long-term Young’s modulus of 10.5 kPa and decellularized tissue a modulus of 1.18 kPa. Cellular-level testing found native tissue to have a long-term Young’s modulus of 4.40 kPa and decellularized tissue to have a modulus of 0.91 kPa. These results are important for regenerative medicine and tissue engineering where cellular response is dependent on the mechanical properties of the engineered scaffold.     

Influence of a freeze-thaw cycle on the stress-stretch curves of tissues of porcine abdominal organs

The paper investigates both fresh porcine spleen and liver and the possible decomposition of these organs under a freeze-thaw cycle. The effect of tissue preservation condition is an important factor which should be taken into account for protracted biomechanical tests. In this work, tension tests were conducted for a large number of tissue specimens from twenty pigs divided into two groups of 10. Concretely, the first group was tested in fresh state; the other one was tested after a freeze-thaw cycle which simulates the conservation conditions before biomechanical experiments. A modified Fung model for isotropic behavior was adopted for the curve fitting of each kind of tissues. Experimental results show strong effects of the realistic freeze-thaw cycle on the capsule of elastin-rich spleen but negligible effects on the liver which virtually contains no elastin. This different behavior could be explained by the autolysis of elastin by elastolytic enzymes during the warmer period after thawing. Realistic biomechanical properties of elastin-rich organs can only be expected if really fresh tissue is tested. The observations are supported by tests of intestines.