Modelling and simulation of porcine liver tissue indentation using finite element method and uniaxial stress–strain data

Characterisation of human penile tissue properties using experimental testing combined with multi-target inverse finite element modelling

This paper presents an inverse finite element (FE) approach aimed at estimating multi-layered human penile tissues. The inverse FE approach integrates experimental force-displacement and boundary deformation data of penile tissues with a developed FE model and uses new experimental data on human penile tissue. The experimental study encompasses whole organ plate-compression tests and individual layer tensile and compression tests, providing comprehensive insights into the tissue's mechanical behaviour. The biomechanical characterisation of penile tissue is of crucial significance for understanding its mechanical behaviour under various physiological and pathological conditions. The FE model is constructed using the realistic geometry of the penile segment and appropriate constitutive models for each tissue layer to leverage the accuracy and consistency of the model. Through systematic variation of tissue parameters in the inverse FE algorithm, simulations achieve the best match with both force-displacement and deformed boundary results obtained from the whole organ plate-compression tests. Test results from individual tissue layers are also utilised to assess the estimated parameters. The proposed inverse FE approach allows for the estimation of penile tissue parameters with high precision and reliability, shedding light on the mechanical properties of this complex biological organ. This work has applications not only in urology but also for researchers in various disciplines of biomechanics. As a result, our study contributes to advancing the understanding of human penile tissue mechanics whilst the methodology could also be applied to a range of other soft biological tissues. STATEMENT OF SIGNIFICANCE: This research uses a multi-target inverse finite element (FE) approach for estimating the material parameters of human penile tissues. By integrating experimental data and a realistic FE model, this study achieves high-precision constitutive model parameter estimation, offering key insights into penile tissue mechanics under various loading conditions. The significance of this work lies in the use of this inverse FE approach for fresh-frozen human penile tissues, to identify the mechanical properties and constitutive models for both segregated tunica albuginea and corpus cavernosum as well as intact penile tissue segments. The study's scientific impact lies in its advancement of the understanding of human urological tissue mechanics, impacting researchers and clinicians alike.

An Inverse Method to Determine Mechanical Parameters of Porcine Vitreous Bodies Based on the Indentation Test

The vitreous body keeps the lens and retina in place and protects these tissues from physical insults. Existing studies have reported that the mechanical properties of vitreous body varied after liquefaction, suggesting mechanical properties could be effective parameters to identify vitreous liquefaction process. Thus, in this work, we aimed to propose a method to determine the mechanical properties of vitreous bodies. Fresh porcine eyes were divided into three groups, including the untreated group, the 24 h liquefaction group and the 48 h liquefaction group, which was injected collagenase and then kept for 24 h or 48 h. The indentation tests were carried out on the vitreous body in its natural location while the posterior segment of the eye was fixed in the container. A finite element model of a specimen undertaking indentation was constructed to simulate the indentation test with surface tension of vitreous body considered. Using the inverse method, the mechanical parameters of the vitreous body and the surface tension coefficient were determined. For the same parameter, values were highest in the untreated group, followed by the 24 h liquefaction group and the lowest in the 48 h liquefaction group. For C₁₀ in the neo-Hookean model, the significant differences were found between the untreated group and liquefaction groups. This work quantified vitreous body mechanical properties successfully using inverse method, which provides a new method for identifying vitreous liquefactions related studies.

Fast and accurate nonlinear hyper-elastic deformation with a posteriori numerical verification of the convergence of solution: Application to the simulation of liver deformation

In this paper, we propose a new method to reduce the computational complexity of calculating the tangential stiffness matrix in a nonlinear finite element formulation. Our approach consists in partially updating the tangential stiffness matrix during a classic Newton-Raphson iterative process. The complexity of such an update process has the order of the number of mesh vertices to the power of two. With our approach, this complexity is reduced to the power of two of only the number of updated vertices. We numerically study the convergence of the solution with our modified algorithm. We describe the deformation through a strain energy density function which is defined with respect to the Lagrangian strain. We derive the conditions of convergence for a given tangential stiffness matrix and a given set of updated vertices. We use nonlinear geometric deformation and the nonlinear Mooney-Rivilin model with both tetrahedron and hexahedron element meshing. We provide extensive results using a cube with small and large number of elements. We provide results on nonlinearly deformed liver with multiple deformation ranges of updated vertices. We compare the proposed method to state-of-the-art work and we prove its efficiency at three levels: accuracy, speed of convergence and small radius of convergence.

Application of micro-computer tomography and inverse finite element analysis for characterizing the visco-hyperelastic response of bulk liver tissue using indentation

Abstract

In-vitro mechanical indentation experimentation is performed on bulk liver tissue of lamb to characterize its nonlinear material behaviour. The material response is characterized by a visco-hyperelastic material model by the use of 2-dimensional inverse finite element (FE) analysis. The time-dependent behaviour is characterized by the viscoelastic model represented by a 4-parameter Prony series, whereas the large deformations are modelled using the hyperelastic Neo-Hookean model. The shear response described by the initial and final shear moduli and the corresponding Prony series parameters are optimized using ANSYS with the Root Mean Square (RMS) error being the objective function. Optimized material properties are validated using experimental results obtained under different loading histories. To study the efficacy of a 2D model, a three dimensional (3D) model of the specimen is developed using Micro-CT of the specimen. The initial elastic modulus of the lamb liver obtained was found to 13.5 kPa for 5% indentation depth at a loading rate of 1 mm/sec for 1-cycle. These properties are able to predict the response at 8.33% depth and a loading rate of 5 mm/sec at multiple cycles with reasonable accuracy.

Article highlights

NUMERICAL COUPLING ANALYSIS OF THE INFLUENCE OF BLOOD FLOW ON THE MECHANICAL RESPONSE FOR LIVER

As an important basis for determining the state of the liver, the mechanical responses are associated with many factors, and belong to a complex coupling system. Liver tissue has significantly complicated vascular channels. The vascular diameter, vascular deflection angle and vascular depth are defined as the key characteristic parameters. The influences of these parameters on the mechanical responses were analyzed. On the basis of the real mechanical parameters, the coupled numerical model of blood vessel, blood flow and liver tissue was established. The corresponding mechanical responses are obtained by utilizing the different vascular parameters. The effects of vascular parameters on the differences among the mechanical response difference and high strain modulus were analyzed. It was found that the blood vessels in the central area could reduce the liver mechanical response. The inner diameter parameter had main influences on the regions where the stain was more than 0.1. The mechanical difference is greater with larger inner diameter. The influences of vascular depth are greatest when the vascular depth was in the intermediate value, which would increase the liver mechanical responses. With the increment of vascular deflection angle, the liver mechanical response would also increase, and exceed the mechanical response without blood vessels. The findings after analyzing the influence of vascular parameters will provide a basis for the quantitative studies on the influence of blood vessels.

Mechanical characterization of porcine liver properties for computational simulation of indentation on cancerous tissue

An accurate characterization of soft biological tissue properties is essential for a realistic simulation of surgical procedures. Unconfined uniaxial compression tests with specimens affixed to the fixtures are often performed to characterize the stress-stretch curves of soft biological tissues, with which the material parameters can be obtained. However, the constrained boundary condition causes non-uniform deformation during the uniaxial test, posing challenges for accurate measurement of tissue deformation. In this study, we measured the deformation locally at the middle of liver specimens and obtained the corresponding stress-stretch curves. Since the effect of the constrained boundary condition on the local deformation of specimen is minimized, the stress-stretch curves are thus more realistic. Subsequently, we fitted the experimental stress-stretch curves with several constitutive models and found that the first-order Ogden hyperelastic material model was most suitable for characterizing the mechanical properties of porcine liver tissues. To further verify the characterized material properties, we carried out indentation tests on porcine liver specimens and compared the experimental data with computational results by using finite element simulations. A good agreement was achieved. Finally, we constructed computational models of liver tissue with a tumor and investigated the effect of the tumor on the mechanical response of the tissue under indentation. The computational results revealed that the liver specimen with tumor shows a stiffer response if the distance between the tumor and the indenter is small.

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.

Robot-assisted flexible needle insertion using universal distributional deep reinforcement learning

PURPOSE

Flexible needle insertion is an important minimally invasive surgery approach for biopsy and radio-frequency ablation. This approach can minimize intraoperative trauma and improve postoperative recovery. We propose a new path planning framework using multi-goal deep reinforcement learning to overcome the difficulties in uncertain needle-tissue interactions and enhance the robustness of robot-assisted insertion process.

METHODS

This framework utilizes a new algorithm called universal distributional Q-learning (UDQL) to learn a stable steering policy and perform risk management by visualizing the learned Q-value distribution. To further improve the robustness, universal value function approximation is leveraged in the training process of UDQL to maximize generalization and connect to diagnosis by adapting fast re-planning and transfer learning.

RESULTS

Computer simulation and phantom experimental results show our proposed framework can securely steer flexible needles with high insertion accuracy and robustness. The framework also improves robustness by providing distribution information to clinicians for diagnosis and decision making during surgery.

CONCLUSIONS

Compared with previous methods, the proposed framework can perform multi-target needle insertion through single insertion point qunder continuous state space model with higher accuracy and robustness.

Phenomenological tissue fracture modeling for an Endoscopic Sinus and Skull Base Surgery training system based on experimental data

The ideal simulator for Endoscopic Sinus and Skull Base Surgery (ESSS) training must be supported by a physical model and provide repetitive behavior in a controlled environment. Development of realistic tissue models is a key part of ESSS virtual reality (VR)-based surgical simulation. Considerable research has been conducted to address haptic or force feedback and propose a phenomenological tissue fracture model for sino-nasal tissue during surgical tool indentation. Mechanical properties of specific sino-nasal regions of the sheep head have been studied in various indentation and relaxation experiments. Tool insertion at different indentation rates into coronal orbital floor (COF) tissue is modeled as a sequence of three events: deformation, fracture, and cutting. The behavior in the deformation phase can be characterized using a non-linear, rate-dependent modified Kelvin-Voigt model. A non-linear model for tissue behavior prior to the fracture point is presented. The overall model shows a non-positive dependency of maximum force on tool indentation rate, which indicates faster tool insertion velocity decreases the maximum final fracture force. The tissue cutting phase has been modeled to characterize the force necessary to slice through the COF. The proposed model in this study can help develop VR-based ESSS base simulators in otolaryngology and ophthalmology surgeries. Such simulators are useful in preoperative planning, accurate surgical simulation, intelligent robotic assistance, and treatment applications.

The estimation method of friction in unconfined compression tests of liver tissue

In traditional unconfined compression tests, the friction between platform and specimen is often considered negligible or minimized by lubrication or other means. However, friction can affect the estimation of material parameters. The percentage difference in radial deformation was investigated in this study. A novel friction estimation method was established and verified using a finite element method. The proposed method was based on the radial deformation during the compression process. Three different hyperelastic material parameters of liver tissue were applied in the simulations. The hyperelastic parameters H1 were obtained by no-slip compression tests, while the others were extracted from the literature. The results showed that the percentage difference in radial deformation was mainly influenced by the friction coefficient and diameter-to-height ( d/ h) ratio of the specimen in unconfined compression tests. The percentage difference increased as the friction coefficient and d/ h increased. Different d/ h and friction coefficient values were tested to validate the proposed method, and the accuracy was estimated to exceed 86%. An optimization strategy for material parameters in unconfined compression tests was proposed accordingly.

Integrating viscoelastic mass spring dampers into position-based dynamics to simulate soft tissue deformation in real time

We propose a novel method to simulate soft tissue deformation for virtual surgery applications. The method considers the mechanical properties of soft tissue, such as its viscoelasticity, nonlinearity and incompressibility; its speed, stability and accuracy also meet the requirements for a surgery simulator. Modifying the traditional equation for mass spring dampers (MSD) introduces nonlinearity and viscoelasticity into the calculation of elastic force. Then, the elastic force is used in the constraint projection step for naturally reducing constraint potential. The node position is enforced by the combined spring force and constraint conservative force through Newton's second law. We conduct a comparison study of conventional MSD and position-based dynamics for our new integrating method. Our approach enables stable, fast and large step simulation by freely controlling visual effects based on nonlinearity, viscoelasticity and incompressibility. We implement a laparoscopic cholecystectomy simulator to demonstrate the practicality of our method, in which liver and gallbladder deformation can be simulated in real time. Our method is an appropriate choice for the development of real-time virtual surgery applications.

The use of porcine corrosion casts for teaching human anatomy

In teaching and learning human anatomy, anatomical autopsy and prosected specimens have always been indispensable. However, alternative methods must often be used to demonstrate particularly delicate structures. Corrosion casting of porcine organs with Biodur E20^® Plus is valuable for teaching and learning both gross anatomy and, uniquely, the micromorphology of cardiovascular, respiratory, digestive, and urogenital systems. Assessments of casts with a stereomicroscope and/or scanning electron microscope as well as highlighting cast structures using color coding help students to better understand how the structures that they have observed as two-dimensional images actually exist in three dimensions, and students found using the casts to be highly effective in their learning. Reconstructions of cast hollow structures from (micro-)computed tomography scans and videos facilitate detailed analyses of branching patterns and spatial arrangements in cast structures, aid in the understanding of clinically relevant structures and provide innovative visual aids. The casting protocol and teaching manual we offer can be adjusted to different technical capabilities and might also be found useful for veterinary or other biological science classes.

Can hyperelastic material parameters be uniquely determined from indentation experiments?

Uniqueness of hyperelastic parameters depends on a simple criterion: whether dimensionless material parameters are coupled with indentation displacement.

Deformation behavior of micro-indentation defects under uniaxial and biaxial loads

The microdefects of structure frequently act as the source to generate initial cracks and lead to the fracture failure. Study on the deformation behaviors of embedded defects would be conducive to better understand the failure mechanisms of structural materials. Micro-indentation technique was applied to prepare the initial indentations as embedded surface defects at the gauge length section and central section of a cross-shaped AZ31B magnesium alloy specimen. A novel in situ biaxial tensile device was developed to apply the synchronous biaxial loads. Via the observation by an optical microscope with three-dimensional imaging and measurement functions, the changing laws of the indentation topographies under uniaxial and biaxial tensile loads were discussed. Compared with the gauge length section, the increasing trend of the indentation length of the central section was relatively flat, and the decreasing trend of the indentation depth was more significant. The changes of indentation topographies were explained by the Poisson effect, and the significant plastic tensile stress has led to the releasing of the residual stress around the indentation location and also promoted the planarization of the pileup.

Finite element analysis for evaluating liver tissue damage due to mechanical compression

The development of robotic-assisted minimally invasive surgery (RMIS) has resulted in increased research to improve surgeon training, proficiency and patient safety. Minimizing tissue damage is an essential consideration in RMIS. Various studies have reported the quantified tissue damage resulting from mechanical compression; however, most of them require bench work analysis, which limits their application in clinical conditions of RMIS. We present a new methodology based on nonlinear finite element (FE) analysis that can predict damage degree inside tissue. The effects of the boundary conditions and material property of the FE model on the simulated von Mises stress value and tissue damage were investigated. Four FE models were analyzed: two-dimensional (2D) plane strain model, 2D plane stress model, full three-dimensional (3D) model, and 3D thin membrane model. Nonlinear material properties of liver tissue used in the FEA were derived from previously reported in vivo and in vitro experiments. Our study showed that for integrated von Mises stress and tissue damage computations, the 3D thin membrane model yielded results closest to the full 3D analysis and required only 0.2% of the compute time. The results from 3D thin membrane and the full 3D models fell below plane-strain model and above the plane-stress model. Both stress and necrosis distributions were impacted by the material property of FE models. This study can guide engineers to design surgical instruments to improve patient safety. Additionally it is useful for improving the surgical simulator performance by reflecting more realistic tissue material property and displaying tissue damage severity.