Transversely isotropic properties of porcine liver tissue: experiments and constitutive modelling

Review of non-penetrating ballistic testing techniques for protection assessment: From biological data to numerical and physical surrogates

Human surrogates have long been employed to simulate human behaviour, beginning in the automotive industry and now widely used throughout the safety framework to estimate human injury during and after accidents and impacts. In the specific context of blunt ballistics, various methods have been developed to investigate wound injuries, including tissue simulants such as clays or gelatine ballistic, physical dummies and numerical models. However, all of these surrogate entities must be biofidelic, meaning they must accurately represent the biological properties of the human body. This paper provides an overview of physical and numerical surrogates developed specifically for blunt ballistic impacts, including their properties, use and applications. The focus is on their ability to accurately represent the human body in the context of blunt ballistic impact.

The mechanical behavior of bovine spinal cord white matter under various strain rate conditions: tensile testing and visco-hyperelastic constitutive modeling

The mechanical behavior of the white matter is important for estimating the damage of the spinal cord during accidents. In this study, we conducted uniaxial tension testing in vitro of bovine spinal cord white matter under extremely high strain rate conditions (up to 100 s^-1). A visco-hyperelastic constitutive law for modeling the strain rate-dependent behavior of the bovine spinal cord white matter was developed. A set of material constants was obtained using a Levenberg-Marquardt fitting algorithm to match the uniaxial tension experimental data with various strain rates. Our experimental data confirmed that the modulus and tensile strength increased when the strain rate is higher. For the extremely high strain rate condition (100 s^-1), we found that both the modulus and failure stress significantly increased compared with the low strain rate case. These new data in terms of mechanical response at high strain rate provide insight into the spine injury mechanism caused by high-speed impact. Moreover, the developed constitutive model will allow researchers to perform more realistic finite element modeling and simulation of spinal cord injury damage under various complicated conditions.

A parameter reduced adaptive quasi-linear viscoelastic model for soft biological tissue in uniaxial tension

Mechanical characterisation of soft viscous materials is essential for many applications including aerospace industries, material models for surgical simulation, and tissue mimicking materials for anatomical models. Constitutive material models are, therefore, necessary to describe soft biological tissues in physiologically relevant strain ranges. Hereby, the adaptive quasi-linear viscoelastic (AQLV) model enables accurate modelling of the strain-dependent non-linear viscoelastic behaviour of soft tissues with a high flexibility. However, the higher flexibility produces a large number of model parameters. In this study, porcine muscle and liver tissue samples were modelled in the framework of the originally published AQLV (3-layers of Maxwell elements) model using four incremental ramp-hold experiments in uniaxial tension. AQLV model parameters were reduced by decreasing model layers (M) as well as the number of experimental ramp-hold steps (N). Leave One out cross validation tests show that the original AQLV model (3M4N) with 19 parameters, accurately describes porcine muscle tissue with an average R² of 0.90 and porcine liver tissue, R² of 0.86. Reducing the number of layers (N) in the model produced acceptable model fits for 1-layer (R² of 0.83) and 2-layer models (R² of 0.89) for porcine muscle tissue and 1-layer (R² of 0.84) and 2-layer model (R² of 0.85) for porcine liver tissue. Additionally, a 2 step (2N) ramp-hold experiment was performed on additional samples of porcine muscle tissue only to further reduce model parameters. Calibrated spring constant values for 2N ramp-hold tests parameters k₁ and k₂ had a 16.8% and 38.0% deviation from those calibrated for a 4 step (4N) ramp hold experiment. This enables further reduction of material parameters by means of step reduction, effectively reducing the number of parameters required to calibrate the AQLV model from 19 for a 3M4N model to 8 for a 2M2N model, with the added advantage of reducing the time per experiment by 50%. This study proposes a 'reduced-parameter' AQLV model (2M2N) for the modelling of soft biological tissues at finite strain ranges. Sequentially, the comparison of model parameters of soft tissues is easier and the experimental burden is reduced.

A generalized strain approach to anisotropic elasticity

This work proposes a generalized Lagrangian strain function [Formula: see text] (that depends on modified stretches) and a volumetric strain function [Formula: see text] (that depends on the determinant of the deformation tensor) to characterize isotropic/anisotropic strain energy functions. With the aid of a spectral approach, the single-variable strain functions enable the development of strain energy functions that are consistent with their infinitesimal counterparts, including the development of a strain energy function for the general anisotropic material that contains the general 4th order classical stiffness tensor. The generality of the single-variable strain functions sets a platform for future development of adequate specific forms of the isotropic/anisotropic strain energy function; future modellers only require to construct specific forms of the functions [Formula: see text] and [Formula: see text] to model their strain energy functions. The spectral invariants used in the constitutive equation have a clear physical interpretation, which is attractive, in aiding experiment design and the construction of specific forms of the strain energy. Some previous strain energy functions that appeared in the literature can be considered as special cases of the proposed generalized strain energy function. The resulting constitutive equations can be easily converted, to allow the mechanical influence of compressed fibres to be excluded or partial excluded and to model fibre dispersion in collagenous soft tissues. Implementation of the constitutive equations in Finite Element software is discussed. The suggested crude specific strain function forms are able to fit the theory well with experimental data and managed to predict several sets of experimental data.

A hyperelastic-damage model to study the anisotropic mechanical behavior of coral-hydrogel bio-composite

In this research, a hyperelastic strain energy function was developed to investigate the anisotropic mechanical behavior of a soft bio-composite containing the coral collagen fibers and alginate hydrogel matrix. This hyperelastic function considers the matrix isotropic response, anisotropic behavior of soft crimpled fibers, and matrix-fiber interaction. The material parameters of the model were assumed as a function of the volume fraction of fibers to consider the fiber content. The published experimental data of matrix and bio-composites with different volume fractions of fibers in different directions were used to find the material parameters. A damage model was developed to take into account the damage of matrix, fibers, and fiber-matrix interaction. Results showed that the interaction contribution increases by increasing the volume fraction of fibers due to the crosslinks between the matrix and fibers. Moreover, by exceeding the fibers volume fraction from 20%, the anisotropic stiffening dominates the interaction stiffening in the longitudinal test owing to the load-bearing of soft fibers. Simulation results exhibited that cross-plied bio-composites show more uniform deformations than angle-plied bio-composites. Moreover, the damage results showed that the matrix plays a significant role in the failure of bio-composites.

Mechanical properties of whole-body soft human tissues: a review

The mechanical properties of soft tissues play a key role in studying human injuries and their mitigation strategies. While such properties are indispensable for computational modelling of biological systems, they serve as important references in loading and failure experiments, and also for the development of tissue simulants. To date, experimental studies have measured the mechanical properties of peripheral tissues (e.g. skin)in-vivoand limited internal tissuesex-vivoin cadavers (e.g. brain and the heart). The lack of knowledge on a majority of human tissues inhibit their study for applications ranging from surgical planning, ballistic testing, implantable medical device development, and the assessment of traumatic injuries. The purpose of this work is to overcome such challenges through an extensive review of the literature reporting the mechanical properties of whole-body soft tissues from head to toe. Specifically, the available linear mechanical properties of all human tissues were compiled. Non-linear biomechanical models were also introduced, and the soft human tissues characterized using such models were summarized. The literature gaps identified from this work will help future biomechanical studies on soft human tissue characterization and the development of accurate medical models for the study and mitigation of injuries.

A Review of Biomechanics Analysis of the Umbilical-Placenta System With Regards to Diseases

Placenta is an important organ that is crucial for both fetal and maternal health. Abnormalities of the placenta, such as during intrauterine growth restriction (IUGR) and pre-eclampsia (PE) are common, and an improved understanding of these diseases is needed to improve medical care. Biomechanics analysis of the placenta is an under-explored area of investigation, which has demonstrated usefulness in contributing to our understanding of the placenta physiology. In this review, we introduce fundamental biomechanics concepts and discuss the findings of biomechanical analysis of the placenta and umbilical cord, including both tissue biomechanics and biofluid mechanics. The biomechanics of placenta ultrasound elastography and its potential in improving clinical detection of placenta diseases are also discussed. Finally, potential future work is listed.

Proposal and validation of polyconvex strain-energy function for biological soft tissues

BACKGROUND

Mechanical simulations for biological tissues are effective technology for development of medical equipment, because it can be used to evaluate mechanical influences on the tissues. For such simulations, mechanical properties of biological tissues are required. For most biological soft tissues, stress tends to increase monotonically as strain increases.

OBJECTIVE

Proposal of a strain-energy function that can guarantee monotonically increasing trend of biological soft tissue stress-strain relationships and applicability confirmation of the proposed function for biological soft tissues.

METHOD

Based on convexity of invariants, a polyconvex strain-energy function that can reproduce monotonically increasing trend was derived. In addition, to confirm its applicability, curve-fitting of the function to stress-strain relationships of several biological soft tissues was performed.

RESULTS

A function depending on the first invariant alone was derived. The derived function does not provide such inappropriate negative stress in the tensile region provided by several conventional strain-energy functions.

CONCLUSIONS

The derived function can reproduce the monotonically increasing trend and is proposed as an appropriate function for biological soft tissues. In addition, as is well-known for functions depending the first invariant alone, uniaxial-compression and equibiaxial-tension of several biological soft tissues can be approximated by curve-fitting to uniaxial-tension alone using the proposed function.

Smoothed particle hydrodynamics simulation of biphasic soft tissue and its medical applications

Modeling the coupled fluid and elastic mechanics of blood perfused soft tissues is important for medical applications. In particular, the current study aims to capture the effect of tissue swelling and the transport of blood through damaged tissue under bleeding or hemorrhaging conditions. The soft tissue is considered a dynamic poro-hyperelastic material with blood-filled voids. A biphasic formulation-effectively, a generalization of Darcy's law-is utilized, treating the phases as occupying fractions of the same volume. A Stokes-like friction force and a pressure that penalizes deviations from volume fractions summing to unity serve as the interaction force between solid and liquid phases. The resulting equations for both phases are discretized with the method of smoothed particle hydrodynamics (SPH). The solver is validated separately on each phase and demonstrates good agreement with exact solutions in test problems. Simulations of oozing, hysteresis, swelling, drying and shrinkage, and tissue fracturing and hemorrhage are shown in the paper. Graphical Abstract In the paper, a new methodology for the numerical simulation of the full dynamic response of blood-perfused soft tissues was developed.

Modeling the initial-volume dependent approximate compressibility of porcine liver tissues using a novel volumetric strain energy model

Experimental observations in the open literature indicate that soft tissues are slightly compressible, and this characteristic affects not only their overall elastic response but also their damage evolution and failure mechanism. In this study, we find that the compressibility of liver tissues is also closely related to the initial specimen volume according to the confined compression tests: the samples with smaller initial volume exhibit more compressible behavior compared to the larger ones. To include this initial-volume dependent effect, we developed a novel volumetric strain energy model with two variables, i.e., the bulk modulus and the compressibility factor. A detailed scheme was proposed as well to identify these two parameters, and the relationship between the bulk modulus and the initial volume was clarified. Findings from this study will help to deepen the understanding of the biomechanical properties of soft tissues. STATEMENT OF SIGNIFICANCE: Liver is a highly vascular organ and traditionally assumed to be an incompressible medium. However, through the confined compression tests, we found that the samples with smaller initial volumes exhibit more compressible behavior. Hence, we developed a novel strain energy density model to characterize the initial-volume dependent hyperelastic response, and found that the bulk modulus of liver tissues is positively related to the initial volume. Our results suggest that the compressibility of liver tissues should be considered in the future study of liver biomechanics.

Estimation of boundary conditions for patient-specific liver simulation during augmented surgery

PURPOSE

Augmented reality can improve the outcome of hepatic surgeries, assuming an accurate liver model is available to estimate the position of internal structures. While researchers have proposed patient-specific liver simulations, very few have addressed the question of boundary conditions. Resulting mainly from ligaments attached to the liver, they are not visible in preoperative images, yet play a key role in the computation of the deformation.

METHOD

We propose to estimate both the location and stiffness of ligaments by using a combination of a statistical atlas, numerical simulation, and Bayesian inference. Ligaments are modeled as polynomial springs connected to a liver finite element model. They are initialized using an anatomical atlas and stiffness properties taken from the literature. These characteristics are then corrected using a reduced-order unscented Kalman filter based on observations taken from the laparoscopic image stream.

RESULTS

Our approach is evaluated using synthetic data and phantom data. By relying on a simplified representation of the ligaments to speed up computation times, it is not estimating the true characteristics of ligaments. However, results show that our estimation of the boundary conditions still improves the accuracy of the simulation by 75% when compared to typical methods involving Dirichlet boundary conditions.

CONCLUSION

By estimating patient-specific boundary conditions, using tracked liver motion from RGB-D data, our approach significantly improves the accuracy of the liver model. The method inherently handles noisy observations, a substantial feature in the context of augmented reality.

Liver Bioreactor Design Issues of Fluid Flow and Zonation, Fibrosis, and Mechanics: A Computational Perspective

Tissue engineering, with the goal of repairing or replacing damaged tissue and organs, has continued to make dramatic science-based advances since its origins in the late 1980’s and early 1990’s. Such advances are always multi-disciplinary in nature, from basic biology and chemistry through physics and mathematics to various engineering and computer fields. This review will focus its attention on two topics critical for tissue engineering liver development: (a) fluid flow, zonation, and drug screening, and (b) biomechanics, tissue stiffness, and fibrosis, all within the context of 3D structures. First, a general overview of various bioreactor designs developed to investigate fluid transport and tissue biomechanics is given. This includes a mention of computational fluid dynamic methods used to optimize and validate these designs. Thereafter, the perspective provided by computer simulations of flow, reactive transport, and biomechanics responses at the scale of the liver lobule and liver tissue is outlined, in addition to how bioreactor-measured properties can be utilized in these models. Here, the fundamental issues of tortuosity and upscaling are highlighted, as well as the role of disease and fibrosis in these issues. Some idealized simulations of the effects of fibrosis on lobule drug transport and mechanics responses are provided to further illustrate these concepts. This review concludes with an outline of some practical applications of tissue engineering advances and how efficient computational upscaling techniques, such as dual continuum modeling, might be used to quantify the transition of bioreactor results to the full liver scale.

A novel machine learning based computational framework for homogenization of heterogeneous soft materials: application to liver tissue

Real-time simulation of organs increases comfort and safety for patients during the surgery. Proper generalized decomposition (PGD) is an efficient numerical method with coordinate errors below 1 mm and response time below 0.1 s that can be used for simulated surgery. For input of this approach, nonlinear mechanical properties of each segment of the liver need to be calculated based on the geometries of the patient's liver extracted using medical imaging techniques. In this research work, a map of the mechanical properties of the liver tissue has been estimated with a novel combined method of the finite element (FE) optimization. Due to the existence of major-size vessels in the liver that makes the surrounding tissue anisotropic, the simulation of hyperelastic material with two different sections is computationally expensive. Thus, a homogenized, anisotropic, and hyperelastic model with the nearest response to the real heterogeneous model was developed and presented. Because of various possibilities of the vessel orientation, position, and size, homogenization has been carried out for adequate samples of heterogeneous models to train artificial neural networks (ANNs) as machine learning tools. Then, an unknown sample of heterogeneous material was categorized and mapped to its homogenized material parameters with the trained networks for the fast and low-cost generalization of our combined FE optimization method. The results showed the efficiency of the proposed novel machine learning based technique for the prediction of effective material properties of unknown heterogeneous tissues.

Sex- and age-specific mechanical properties of liver tissue under dynamic loading conditions

The liver is the most commonly injured abdominal organ following either blunt or penetrating impact. Current mechanical properties available in the literature are typically only measured at low strain rates, low strains, or use linear viscoelastic models. There is also a dearth of high-rate, large strain, viscoelastic data available for liver tissue which are required to model the deformation of the liver during high-rate impacts. Furthermore, the issue of whether mouse liver's mechanical properties are sex-dependent has not been addressed previously. Here, we present the first in vitro sex- and age-controlled mechanical characterisation of mixed-strain (C57BL and wild-type) mouse liver tissue at a localised length scale using large-deformation and high strain rate micro-indentation. We also investigated the effects of age on the mechanical properties of liver tissue. Force-relaxation experiments were performed on both male and female mouse livers up to 35% strain at 10/s and allowed to relax for 1s. The neo-Hookean based quasi-linear viscoelastic model was fitted to the experimental data to determine the large-strain behaviour of the tissue. A comprehensive statistical analysis was performed to determine whether any significant differences existed for (i) the short-term shear moduli and (ii) long-term shear moduli between 10 weeks-old male and female mouse livers, and (iii) the short-term and (iv) long-term shear moduli for 6, 10, and 56 weeks-old mouse livers. No significant differences were found between the mechanical properties in the sex groups. The 56 weeks-old liver tissue was found to be significantly stiffer than the 6 weeks-old liver tissue, but not the 10 weeks-old.

In vivo Layer-specific Mechanical Characterization of Porcine Stomach Tissue using Ultrasound Elastography

This paper presents in vivo mechanical characterization of the muscularis, submucosa and mucosa of the porcine stomach wall under large deformation loading. This is important for the development of gastrointestinal pathology-specific surgical intervention techniques. The study is based on testing the cardiac and fundic glandular stomach regions using a custom-developed compression elastography setup. Particular attention has been paid to elucidate the heterogeneity and anisotropy of tissue response. A Fung hyperelastic material model has been used to model the mechanical response of each tissue layer. A univariate analysis comparing the initial shear moduli of the three layers indicates that the muscularis (5.69±4.06 kPa) is the stiffest followed by the submucosa (3.04±3.32 kPa) and the mucosa (0.56±0.28 kPa). The muscularis is found to be strongly distinguishable from the mucosa tissue in the cardiac and fundic region based on a multivariate discriminant analysis. The cardiac muscularis is observed to be stiffer than the fundic muscularis tissue (shear moduli of 7.96±3.82 kPa vs. 3.42±2.96 kPa), more anisotropic (anisotropic parameter of 2.21±0.77 vs. 1.41±0.38), and strongly distinguishable from its fundic counterpart. Finally, a univariate comparison of the in vivo and ex vivo initial shear moduli for each layer shows that the muscularis and submucosa tissues are softer while in vivo, but the mucosa tissue is stiffer while in vivo. The mechanical properties highlight the inhomogeneity and anisotropy of multilayer stomach tissue.

Characterization of perfused and sectioned liver tissue in a full indentation cycle using a visco-hyperelastic model

Realistic modeling of biologic material is required for optimizing fidelity in computer-aided surgical training and assistance systems. The modeling of liver tissue has remained challenging due to its nonlinear viscoelastic properties and high hysteresis of the stress-strain relation. While prior studies have described the behavior of liver tissue during the loading status (in elongation, compression, or indentation tests) or unloading status (in stress relaxation or creep tests), a hysteresis curve with both loading and unloading processes was incompletely defined. We seek to use a single material model to characterize the mechanical properties of liver tissue in a full indentation cycle ex vivo perfused and then sectioned. Based on measurements taken from ex-vivo perfused porcine livers, we converted force-displacement curves to stress-strain curves and developed a visco-hyperelastic constitutive model to characterize the liver's mechanical behavior at different locations under various rates of indentation (1, 2, 5, 10, and 20 mm/s). The proposed model is a mixed visco-hyperelastic model with up to 6 coefficients. The normalized root mean square standard deviations of fitted curves are less than 5% and 10% in low (<0.05) and high strain (>0.3) conditions respectively.

Anisotropic stiffness and tensional homeostasis induce a natural anisotropy of volumetric growth and remodeling in soft biological tissues

Growth in soft biological tissues in general results in anisotropic changes of the tissue geometry. It remains a key challenge in biomechanics to understand, quantify, and predict this anisotropy. In this paper, we demonstrate that anisotropic tissue stiffness and the well-known mechanism of tensional homeostasis induce a natural anisotropy of the geometric changes resulting from volumetric growth in soft biological tissues. As a rule of thumb, this natural anisotropy makes differential tissue volume elements dilate mainly in the direction(s) of lowest stiffness. This simple principle is shown to explain the experimentally observed growth behavior in a host of different soft biological tissues without relying on any additional heuristic assumptions or quantities (such as ad hoc defined growth tensors).

Effects of postmortem time and storage fluid on the material properties of bovine liver parenchyma in tension

In motor vehicle collisions (MVCs), liver injuries are one of the most frequently reported types of abdominal organ trauma. Although finite element models are utilized to evaluate the risk of sustaining an abdominal organ injury in MVCs, these models must be validated based on biomechanical data in order to accurately assess injury risk. Given that previous studies that have quantified the tensile failure properties of human liver parenchyma have been limited to testing at 48 h postmortem, it is currently unknown how the material properties change between time of death and 48 h postmortem. Therefore, the objective of this study was to quantify the effects of postmortem degradation on the tensile material properties of bovine liver parenchyma with increasing postmortem time when stored in DMEM or saline. A total of 148 uniaxial tension tests were successfully conducted on parenchyma samples of fourteen bovine livers acquired immediately after death. Liver tissue was submerged in DMEM or saline and kept cool during sample preparation and storage. Twelve livers were stored as large blocks of tissue, while two livers were stored as small blocks and slices. Tension tests were performed on multiple dog-bone samples from each liver at three time points: ~6 h, ~24 h, and ~48 h postmortem. The data were then analyzed using a Linear Mixed Effect Model to determine if there were significant changes in the failure stress, failure strain, and modulus with respect to postmortem time. The results of the current study showed that the failure strain of bovine liver parenchyma decreased significantly between 6 h and 48 h after death when stored as large blocks in saline and refrigerated. Conversely, neither the failure stress nor failure strain changed significantly with respect to postmortem time when stored as large blocks in DMEM. The modulus did not change significantly with respect to postmortem time for tissue stored as large blocks in either saline or DMEM. Cellular disruption increased with postmortem time for tissue stored as large blocks, with tissue stored in saline showing the greatest increase at each time point. In addition, preliminary results indicated that reducing the tissue storage size had a negative effect on the material properties and cellular architecture. Overall, this study illustrated that the effects of postmortem liver degradation varied with respect to the preservation fluid, storage time, and storage block size.

Computational predictions of damage propagation preceding dissection of ascending thoracic aortic aneurysms

Dissections of ascending thoracic aortic aneurysms (ATAAs) cause significant morbidity and mortality worldwide. They occur when a tear in the intima-media of the aorta permits the penetration of the blood and the subsequent delamination and separation of the wall in 2 layers, forming a false channel. To predict computationally the risk of tear formation, stress analyses should be performed layer-specifically and they should consider internal or residual stresses that exist in the tissue. In the present paper, we propose a novel layer-specific damage model based on the constrained mixture theory, which intrinsically takes into account these internal stresses and can predict appropriately the tear formation. The model is implemented in finite-element commercial software Abaqus coupled with user material subroutine. Its capability is tested by applying it to the simulation of different exemplary situations, going from in vitro bulge inflation experiments on aortic samples to in vivo overpressurizing of patient-specific ATAAs. The simulations reveal that damage correctly starts from the intimal layer (luminal side) and propagates across the media as a tear but never hits the adventitia. This scenario is typically the first stage of development of an acute dissection, which is predicted for pressures of about 2.5 times the diastolic pressure by the model after calibrating the parameters against experimental data performed on collected ATAA samples. Further validations on a larger cohort of patients should hopefully confirm the potential of the model in predicting patient-specific damage evolution and possible risk of dissection during aneurysm growth for clinical applications.

An Experimental Study to Measure the Mechanical Properties of the Human Liver

BACKGROUND

Since the liver is one of the most important organs of the body that can be injured during trauma, that is, during accidents like car crashes, understanding its mechanical properties is of great interest. Experimental data is needed to address the mechanical properties of the liver to be used for a variety of applications, such as the numerical simulations for medical purposes, including the virtual reality simulators, trauma research, diagnosis objectives, as well as injury biomechanics. However, the data on the mechanical properties of the liver capsule is limited to the animal models or confined to the tensile/compressive loading under single direction. Therefore, this study was aimed at experimentally measuring the axial and transversal mechanical properties of the human liver capsule under both the tensile and compressive loadings.

METHODS

To do that, 20 human cadavers were autopsied and their liver capsules were excised and histologically analyzed to extract the mean angle of a large fibers population (bundle of the fine collagen fibers). Thereafter, the samples were cut and subjected to a series of axial and transversal tensile/compressive loadings.

RESULTS

The results revealed the tensile elastic modulus of 12.16 ± 1.20 (mean ± SD) and 7.17 ± 0.85 kPa under the axial and transversal loadings respectively. Correspondingly, the compressive elastic modulus of 196.54 ± 13.15 and 112.41 ± 8.98 kPa were observed under the axial and transversal loadings respectively. The compressive axial and transversal maximum/failure stress of the capsule were 32.54 and 37.30 times higher than that of the tensile ones respectively. The capsule showed a stiffer behavior under the compressive load compared to the tensile one. In addition, the axial elastic modulus of the capsule was found to be higher than that of the transversal one.

CONCLUSIONS

The findings of the current study have implications not only for understanding the mechanical properties of the human capsule tissue under tensile/compressive loading, but also for providing unprocessed data for both the doctors and engineers to be used for diagnosis and simulation purposes.

Characterization of the mechanical properties of resected porcine organ tissue using optical fiber photoelastic polarimetry

Characterizing the mechanical behavior of living tissue presents an interesting challenge because the elasticity varies by eight orders of magnitude, from 50Pa to 5GPa. In the present work, a non-destructive optical fiber photoelastic polarimetry system is used to analyze the mechanical properties of resected samples from porcine liver, kidney, and pancreas. Using a quasi-linear viscoelastic fit, the elastic modulus values of the different organ systems are determined. They are in agreement with previous work. In addition, a histological assessment of compressed and uncompressed tissues confirms that the tissue is not damaged during testing.

Numerical simulation of microwave ablation incorporating tissue contraction based on thermal dose

Tissue contraction plays an important role during high temperature tumor ablation, particularly during device characterization, treatment planning and imaging follow up. We measured such contraction in 18 ex vivo bovine liver samples during microwave ablation by tracking fiducial motion on CT imaging. Contraction was then described using a thermal dose dependent model and a negative thermal expansion coefficient based on the empirical data. FEM simulations with integrated electromagnetic wave propagation, heat transfer, and structural mechanics were evaluated using temperature-dependent dielectric properties and the negative thermal expansion models. Simulated temperature and displacement curves were then compared with the ex vivo experimental results on different continuous output powers. The optimized thermal dose model indicated over 50% volumetric contraction occurred at the temperature over 102.1 °C. The numerical simulation results on temperature and contraction-induced displacement showed a good agreement with experimental results. At microwave powers of 55 W, the mean errors on temperature between simulation and experimental results were 8.25%, 2.19% and 5.67% at 5 mm, 10 mm and 20 mm radially from the antenna, respectively. The simulated displacements had mean errors of 16.60%, 14.08% and 23.45% at the same radial locations. Compared to the experimental results, the simulations at the other microwave powers had larger errors with 10-40% mean errors at 40 W, and 10-30% mean errors at 25 W. The proposed model is able to predict temperature elevation and simulate tissue deformation during microwave ablation, and therefore may be incorporated into treatment planning and clinical translation from numerical simulations.

STUDY ON MECHANICAL CHARACTERIZATION OF LIVER TISSUE BASED ON HAPTIC DEVICES FOR VIRTUAL SURGICAL SIMULATION

In recent years, virtual surgical simulation has been one of the hot direction of digital medical research, it is mainly used in teaching, training, diagnosis, preoperative planning, rehabilitation and modeling and analysis of surgical instruments. The modeling of soft tissue of human organs is the basis to realize the virtual surgical simulation. The quasi-linear viscoelastic (QLV) theory has been proposed by Fung, and it was widely used for modeling the constitutive equation of soft tissues. The purpose of this study is to determine the mechanical characterization of the liver soft tissue based on the PHANTOM Omni Haptic devices. Five parameters are included in the constitutive equation with QLV theory, which must be determined experimentally. The specimens were obtained from fresh porcine liver tissues in vitro. The liver tissues were cut into 14[Formula: see text]mm[Formula: see text][Formula: see text][Formula: see text]14[Formula: see text]mm[Formula: see text][Formula: see text][Formula: see text]14[Formula: see text]mm cubes. Two types of unconfined compression tests were performed on cube liver specimens. Puncture tests were performed on the complete liver. The material parameters of the QLV constitutive equation were obtained by fitting the experimental data. These parameters will provide the references for the computational modeling of the liver in the virtual surgical simulation.

Sample, testing and analysis variables affecting liver mechanical properties: A review

Given the critical role of liver mechanics in regulating cell response and directing the development of tissue fibrosis, accurately characterising its mechanical behaviour is of relevance for both diagnostic purposes as well as for tissue engineering and for the development of in-vitro models. Determining and quantifying the mechanical behaviour of soft biological tissues is, however, highly challenging due to their intrinsic labile nature. Indeed, a unique set of values of liver mechanical properties is still lacking to date; testing conditions can significantly affect sample status and hence the measured behaviour and reported results are strongly dependent on the adopted testing method and configuration as well as sample type and status. This review aims at summarising the bulk mechanical properties of liver described in the literature, discussing the possible sources of variation and their implications on the reported results. We distinguish between the intrinsic mechanical behaviour of hepatic tissue, which depends on sample variables, and the measured mechanical properties which also depend on the testing and analysis methods. Finally, the review provides guidelines on tissue preparation and testing conditions for generating reproducible data which can be meaningfully compared across laboratories.

STATEMENT OF SIGNIFICANCE

Soft tissue mechanics is widely investigated, but poorly understood. This review identifies and discusses sample and testing variables which can influence the mechanical behaviour of hepatic tissue and consequently the measured mechanical properties. To encourage the biomaterial community towards more standardized testing of soft tissues and enable comparisons between data from different laboratories, we have established new testing methods and experimental recommendations for sample preparation and testing. The review could be of wide interest to scientists involved in biomaterials research because it addresses and proposes guidelines for several issues related to the mechanical testing of soft tissues whose implications have not been considered together before.

Assessment of Tissue Damage due to Mechanical Stresses

While there are many benefits to minimally invasive surgery (MIS), force feedback or touch sensation is limited in the currently available MIS tools, such as surgical robots, creating the potential for excessive force application during surgery and unintended tissue injury. The goal of this work was to develop a methodology with which to identify stress magnitudes and durations that can be safely applied with a MIS grasper to di ferent tissues, potentially improving MIS device design and reducing potentially adverse clinically relevant consequences. Using the porcine model, stresses typically applied in MIS were applied to liver, ureter and small bowel using a motorized endoscopic grasper. Acute indicators of tissue damage including cellular death and infiltration of inflammatory cells were measured using histological and image analysis techniques. Finite element analysis was used to identify approximate stress distributions experienced by the tissues. Parameters used in these finite element models specifically reflected the properties of liver, which served as an initial proxy for all tissues, as stress distributions rather than absolute values were desired. Local regions predicted to have uniform stress by the computational models were mapped to and analyzed in the tissue samples for acute damage. Analysis of variance (ANOVA) and post-hoc analyses were used to detect stress magnitudes and durations that caused significantly increased tissue damage with the goal to ultimately identify safe stress `thresholds' during grasping of the studied tissues. Preliminary data suggests a graded non-linear response between applied stress magnitude and apoptosis in liver and small bowel as well as neutrophil infiltration in the small bowel. The ureter appeared to be more resistant to injury at the tested stress levels. By identifying stress magnitudes and durations within the range of grasping loads applied in MIS, it may be possible for researchers to create a `smart' surgical robot that can guide a surgeon to manipulate tissues with minimal resulting damage. In addition, surgical simulator design can be improved to reflect more realistic tissue responses and evaluate trainees' tissue handling skills.

Damage Models for Soft Tissues: A Survey

Damage to soft tissues in the human body has been investigated for applications in healthcare, sports, and biomedical engineering. This paper reviews and classifies damage models for soft tissues to summarize achievements, identify new directions, and facilitate finite element analysis. The main ideas of damage modeling methods are illustrated and interpreted. A few key issues related to damage models, such as experimental data curve-fitting, computational effort, connection between damage and fractures/cracks, damage model applications, and fracture/crack extension simulation, are discussed. Several new challenges in the field are identified and outlined. This review can be useful for developing more advanced damage models and extending damage modeling methods to a variety of soft tissues.

Mapped Chebyshev pseudo-spectral method for simulating the shear wave propagation in the plane of symmetry of a transversely isotropic viscoelastic medium

Shear wave elastography is a versatile technique that is being applied to many organs. However, in tissues that exhibit anisotropic material properties, special care must be taken to estimate shear wave propagation accurately and efficiently. A two-dimensional simulation method is implemented to simulate the shear wave propagation in the plane of symmetry in transversely isotropic viscoelastic media. The method uses a mapped Chebyshev pseudo-spectral method to calculate the spatial derivatives and an Adams-Bashforth-Moulton integrator with variable step sizes for time marching. The boundaries of the two-dimensional domain are surrounded by perfectly matched layers to approximate an infinite domain and minimize reflection errors. In an earlier work, we proposed a solution for estimating the apparent shear wave elasticity and viscosity of the spatial group velocity as a function of rotation angle through a low-frequency approximation by a Taylor expansion. With the solver implemented in MATLAB, the simulated results in this paper match well with the theory. Compared to the finite element method simulations we used before, the pseudo-spectral solver consumes less memory and is faster and achieves better accuracy.

Modeling of human artery tissue with probabilistic approach

Accurate modeling of biological soft tissue properties is vital for realistic medical simulation. Mechanical response of biological soft tissue always exhibits a strong variability due to the complex microstructure and different loading conditions. The inhomogeneity in human artery tissue is modeled with a computational probabilistic approach by assuming that the instantaneous stress at a specific strain varies according to normal distribution. Material parameters of the artery tissue which are modeled with a combined logarithmic and polynomial energy equation are represented by a statistical function with normal distribution. Mean and standard deviation of the material parameters are determined using genetic algorithm (GA) and inverse mean-value first-order second-moment (IMVFOSM) method, respectively. This nondeterministic approach was verified using computer simulation based on the Monte-Carlo (MC) method. Cumulative distribution function (CDF) of the MC simulation corresponds well with that of the experimental stress-strain data and the probabilistic approach is further validated using data from other studies. By taking into account the inhomogeneous mechanical properties of human biological tissue, the proposed method is suitable for realistic virtual simulation as well as an accurate computational approach for medical device validation.

Probabilistic predictive modelling of carbon nanocomposites for medical implants design

Modelling of the mechanical properties of carbon nanocomposites based on input variables like percentage weight of Carbon Nanotubes (CNT) inclusions is important for the design of medical implants and other structural scaffolds. Current constitutive models for the mechanical properties of nanocomposites may not predict well due to differences in conditions, fabrication techniques and inconsistencies in reagents properties used across industries and laboratories. Furthermore, the mechanical properties of the designed products are not deterministic, but exist as a probabilistic range. A predictive model based on a modified probabilistic surface response algorithm is proposed in this paper to address this issue. Tensile testing of three groups of different CNT weight fractions of carbon nanocomposite samples displays scattered stress-strain curves, with the instantaneous stresses assumed to vary according to a normal distribution at a specific strain. From the probabilistic density function of the experimental data, a two factors Central Composite Design (CCD) experimental matrix based on strain and CNT weight fraction input with their corresponding stress distribution was established. Monte Carlo simulation was carried out on this design matrix to generate a predictive probabilistic polynomial equation. The equation and method was subsequently validated with more tensile experiments and Finite Element (FE) studies. The method was subsequently demonstrated in the design of an artificial tracheal implant. Our algorithm provides an effective way to accurately model the mechanical properties in implants of various compositions based on experimental data of samples.

Isotropic incompressible hyperelastic models for modelling the mechanical behaviour of biological tissues: a review

Modelling the mechanical behaviour of biological tissues is of vital importance for clinical applications. It is necessary for surgery simulation, tissue engineering, finite element modelling of soft tissues, etc. The theory of linear elasticity is frequently used to characterise biological tissues; however, the theory of nonlinear elasticity using hyperelastic models, describes accurately the nonlinear tissue response under large strains. The aim of this study is to provide a review of constitutive equations based on the continuum mechanics approach for modelling the rate-independent mechanical behaviour of homogeneous, isotropic and incompressible biological materials. The hyperelastic approach postulates an existence of the strain energy function – a scalar function per unit reference volume, which relates the displacement of the tissue to their corresponding stress values. The most popular form of the strain energy functions as Neo-Hookean, Mooney-Rivlin, Ogden, Yeoh, Fung-Demiray, Veronda-Westmann, Arruda-Boyce, Gent and their modifications are described and discussed considering their ability to analytically characterise the mechanical behaviour of biological tissues. The review provides a complete and detailed analysis of the strain energy functions used for modelling the rate-independent mechanical behaviour of soft biological tissues such as liver, kidney, spleen, brain, breast, etc.

Biomechanical analysis of traumatic mesenteric avulsion

Mesenteric avulsion, corresponding to a tearing of intestine's root, generally results from high deceleration in road accidents. The biomechanical analysis of bowel and mesenteric injuries is a major challenge for injury prevention, particularly because seat belt restraint may paradoxically increase their risk of occurrence. The aim of this study was to identify the biomechanical behavior of mesentery and small bowel (MSB) tissue samples under dynamical loading conditions. A dedicated test bench was designed in order to perform tensile tests on fresh MSB porcine specimens, with quasi-static (1 mm/s) and dynamic (100 mm/s) loading conditions. The mechanical behavior of MSB specimens was investigated and compared to isolated mesenteric and isolated small bowel specimens. The results show a high sensitivity of MSB stiffness (1.0 ± 0.2 and 1.3 ± 0.3 N/mm at 1 and 100 mm/s, p = 0.001) and ultimate force (22 ± 5 and 35 ± 8 N at 1 and 100 mm/s, p = 0.001) to the loading rate but not for the displacement at failure. This leads to postulate on a failure criteria based on strain level regardless of the strain rate. These experimental results could be further used to develop refined finite element models and to further investigate on injury mechanisms associated to seat belt restraints, as well as to evaluate and improve protective devices.

Dynamics of tissue shrinkage during ablative temperature exposures

There is a lack of studies that examine the dynamics of heat-induced shrinkage of organ tissues. Clinical procedures such as radiofrequency ablation, microwave ablation or high-intensity focused ultrasound, use heat to treat diseases such as cancer and cardiac arrhythmia. When heat is applied to tissues, shrinkage occurs due to protein denaturation, dehydration and contraction of collagen at temperatures greater 50 °C. This is particularly relevant for image-guided procedures such as tumor ablation, where pre- and post-treatment images are compared and any changes in dimensions must be considered to avoid misinterpretations of the treatment outcome. We present data from ex vivo, isothermal shrinkage tests in porcine liver tissue, where axial changes in tissue length were recorded during 15 min of heating to temperatures between 60 and 95 °C. A mathematical model was developed to accurately describe the time and temperature-dependent shrinkage behavior. The shrinkage dynamics had the same characteristics independent of temperature; the estimated relative shrinkage, adjusted for time since death, after 15 min heating to temperatures of 60, 65, 75, 85 and 95 °C, was 12.3, 13.8, 16.6, 19.2 and 21.7%, respectively. Our results demonstrate the shrinkage dynamics of organ tissues, and suggest the importance of considering tissue shrinkage for thermal ablative treatments.

Statistical modeling of human liver incorporating the variations in shape, size, and material properties

The liver is one of the most frequently injured abdominal organs during motor vehicle crashes. Realistic numerical assessments of liver injury risk for the entire occupant population require incorporating inter-subject variations into numerical models. The main objective of this study was to quantify the shape variations of human liver in a seated posture and the statistical distributions of its material properties. Statistical shape analysis was applied to construct shape models of the livers of 15 adult human subjects, recorded in a typical seated (occupant) posture. The principal component analysis was then utilized to obtain the modes of variation, the mean model, and 95% statistical boundary shape models. In addition, a total of 52 tensile tests were performed on the parenchyma of three fresh human livers at four loading rates (0.01, 0.1, 1, and 10 s^-1) to characterize the rate-dependent and failure properties of the human liver. A FE-based optimization approach was employed to identify the material parameters of an Ogden material model for each specimen. The mean material parameters were then determined for each loading rate from the characteristic averages of the stress-strain curves, and a stochastic optimization approach was utilized to determine the standard deviations of the material parameters. Results showed that the first five modes of the human liver shape models account for more than 60% of the overall anatomical variations. The distributions of the material parameters combined with the mean and statistical boundary shape models could be used to develop probabilistic finite element (FE) models, which may help to better understand the variability in biomechanical responses and injuries to the abdominal organs under impact loading.

Effect of Strain Rate on the Material Properties of Human Liver Parenchyma in Unconfined Compression

The liver is one of the most frequently injured organs in abdominal trauma. Although motor vehicle collisions are the most common cause of liver injuries, current anthropomorphic test devices are not equipped to predict the risk of sustaining abdominal organ injuries. Consequently, researchers rely on finite element models to assess the potential risk of injury to abdominal organs such as the liver. These models must be validated based on appropriate biomechanical data in order to accurately assess injury risk. This study presents a total of 36 uniaxial unconfined compression tests performed on fresh human liver parenchyma within 48 h of death. Each specimen was tested once to failure at one of four loading rates (0.012, 0.106, 1.036, and 10.708 s−1) in order to investigate the effects of loading rate on the compressive failure properties of human liver parenchyma. The results of this study showed that the response of human liver parenchyma is both nonlinear and rate dependent. Specifically, failure stress significantly increased with increased loading rate, while failure strain significantly decreased with increased loading rate. The failure stress and failure strain for all liver parenchyma specimens ranged from −38.9 kPa to −145.9 kPa and from −0.48 strain to −1.15 strain, respectively. Overall, this study provides novel biomechanical data that can be used in the development of rate dependent material models and the identification of tissue-level tolerance values, which are critical to the validation of finite element models used to assess injury risk.

Characterising soft tissues under large amplitude oscillatory shear and combined loading

Characterising soft biological tissues outside the linear viscoelastic regime is challenging due to their complex behaviour. In addition, the viscoelastic properties of tissues have been shown to be sensitive to sample preparation and loading regime resulting in inconsistent data varying by orders magnitude in the literature. This paper presents a novel technique to characterise the non-linear behaviour of tissues which uses Fourier Transformation to decompose the stress output waveform under large amplitude oscillatory shear (LAOS) into harmonic contributions. The effect of varying preload, the compressive strain exerted on a liver tissue specimen prior to shear testing to minimise slip, was also investigated. Results showed that in the linear regime, preload affects the viscoelastic response of liver. Histological analysis indicated that there were structural changes as a result of the preload that may be linked to the differences in observed behaviour. Fourier analysis was used to extract the first and third harmonic components of the shear moduli at large strain. At 50% shear strain, a change in the third harmonic component of the shear moduli was accompanied by a marked change in the micro-structural arrangement of the sinusoids. This paper demonstrates a method of efficiently characterising soft biological tissues under large amplitude oscillatory shear under combined loading.

Reality based modeling and simulation of gallbladder shape deformation using variational methods

PURPOSE

Accurate soft tissue deformation modeling is important for realistic surgical simulation. The aim of this study is to develop a reality-based gallbladder model and to determine material constants that represent gallbladder wall mechanical properties.

METHODS

Mechanical experiments on porcine gallbladder were performed to investigate tissue deformation, and an exponential strain energy function was used to describe the nonlinear stress-strain behavior of the gallbladder wall. A new volumetric function based upon the exponential strain energy function was proposed to model the gallbladder organ. A genetic algorithm was used to identify the material parameters of the proposed biomechanical model from the experimental data.

RESULTS

The material constants of the exponential strain energy model were determined based on the experimental data. Deformation simulation and haptic rendering using the proposed gallbladder model were presented. Comparison between deformation predicted by the proposed model and that of the experimental data on gallbladder wall and gallbladder organ tissues demonstrates the applicability of this reality-based variational method for deformation simulation.

CONCLUSION

An accurate soft tissue deformation model was developed using material constants identified for gallbladder. The model is suitable for interactive haptic rendering and deformation simulation. This model has potential applications for simulation of other hollow organs.

Effect of storage methods on indentation-based material properties of abdominal organs

To investigate the possible changes in material properties of cadaveric abdominal organs due to the preservation methods, the indentation data obtained from porcine abdominal organs (kidney, liver, and spleen) preserved by cooling and freezing are analyzed statistically in this study. Indentation tests were first conducted on fresh specimens. One half of the specimens of each organ were then frozen (preserved at −12 °C), and the other half of the specimens were cooled (preserved at 4 °C). All preserved specimens were retested after 20 days. Force and displacement data recorded during indentation were analyzed using a quasi-linear viscoelastic model. The results show that both cooling and freezing storage increased the kidney stiffness. In contrast, both storage methods decreased the stiffness of the spleen specimens. While cooling increased the liver stiffness, no significant changes of the instantaneous elastic response were observed in the liver specimens preserved by freezing. The liver and spleen’s reduced relaxation responses and the liver’s instantaneous elastic response were significantly different when comparing between cooling and freezing effects after 20 days of preservation. This study showed that both cooling and freezing storage methods significantly changed the material properties of abdominal organs, especially the instantaneous elastic response. More research is needed in investigating the effect of preservation on failure properties and mechanical properties under large deformation.

Experimental mechanical characterization of abdominal organs: liver, kidney & spleen

Abdominal organs are the most vulnerable body parts during vehicle trauma, leading to high mortality rate due to acute injuries of liver, kidney, spleen and other abdominal organs. Accurate mechanical properties and FE models of these organs are required for simulating the traumas, so that better designing of the accident environment can be done and the organs can be protected from severe damage. Also from biomedical aspect, accurate mechanical properties of organs are required for better designing of surgical tools and virtual surgery environments. In this study porcine liver, kidney and spleen tissues are studied in vitro and hyper-elastic material laws are provided for each. 12 porcine kidneys are used to perform 40 elongation tests on renal capsule and 60 compression tests on renal cortex, 5 porcine livers are used to perform 45 static compression tests on liver parenchyma and 5 porcine spleens are used to carry out 20 compression tests. All the tests are carried out at a static speed of 0.05 mm/s. A comparative analysis of all the results is done with the literature and though the results are of same order of magnitude, a slight dissonance is observed for the renal capsule. It is also observed that the spleen is the least stiff organ in the abdomen whereas the kidney is the stiffest. The results of this study would be essential to develop the FE models of liver, kidney and spleen which can be further used for impact biomechanical and biomedical applications.

Analysis of several biomechanical models for the simulation of lamb liver behaviour using similarity coefficients from medical image

In this study, six biomechanical models for simulating lamb liver behaviour are presented. They are validated using similarity coefficients from Medical Image on reconstructed volumes from computerised tomography images. In particular, the Jaccard and Hausdorff coefficients are used. Loads of 20 and 40 g are applied to the livers and their deformation is simulated by means of the finite element method. The models used are a linear elastic model, a neo-Hookean model, a Mooney-Rivlin model, an Ogden model, a linear viscoelastic model and a viscohyperelastic model. The model that provided a behaviour that is closest to reality was the viscohyperelastic model, where the hyperelastic part was modelled with an Ogden model.