Modeling Of Soft Tissue Deformation Research Articles

Efficient dynamic modeling of soft tissue deformation using a WSC-integrated order reduction method

Background and Objectives:Computational modeling of soft tissue deformation is a fundamental issue for engineering assistive medical procedures. However, existing methods are not suitable for online clinical scenes as these methods are not efficient due to high computational cost and complexity. Methods:A new Weighted Skinning and Cubature Integrated (WSC-integrated) order reduction method is proposed for dynamic modeling of soft tissue deformation. The presented method includes two integrated-based schemes for construction of sub-space and estimation of internal elastic forces: a weighted skinning integrated scheme and a cubature integrated scheme. The weighted skinning integrated scheme derived from handle-based reduced order method is adopted to construct a reduced-order sub-space, in which dynamics of soft tissue are governed by low-order system equations. The cubature integrated scheme is adopted to estimate internal elastic forces of soft tissue. The proposed method relies on integration schemes both in sub-space construction and internal forces estimation instead of precomputation of soft tissue deformation snapshots, making it possible to achieve efficient computation of soft tissue deformation. Results:Compared to a finite element method in full-space for computing soft tissue deformation, the proposed method has a relative root mean square error for strain–stress and volumetric responses is 4.27 % and 3.11 %, respectively, and for rotation-moment and volumetric responses is 2.15 % and 2.63 %, respectively. The computation time of the proposed method achieve significant improvement (ranges from 37× to 54× ) with proper choice of sample handles and elements. Simulation of left ventricle dynamics based on the proposed method takes (21.81 ms) approximately 1/43 amount of computation time of the finite element method during online stage, and difference between their results is negligible (with relative root mean square error of 2.4 %). Conclusions:The simulation results and comparison validated that the proposed method presents higher computational efficiency and comparable accuracy to the finite element method in full-space. The high degree of computational efficiency and accuracy of the proposed method makes it suitable for online clinical scenes.

Soft Tissue Deformation Modeling in the Procedure of Needle Insertion: A Kriging-Based Method

The simulation and planning system (SPS) requires accurate and real-time feedback regarding the deformation of soft tissues during the needle insertion procedure. Traditional mechanical-based models such as the finite element method (FEM) are widely used to compute the deformations of soft tissue. However, it is difficult for the FEM or other methods to find a balance between an acceptable image fidelity and real-time deformation feedback due to their complex material properties, geometries and interaction mechanisms. In this paper, a Kriging-based method is applied to model the soft tissue deformation to strike a balance between the accuracy and efficiency of deformation feedback. Four combinations of regression and correlation functions are compared regarding their ability to predict the maximum deformations of ten characteristic markers at a fixed insertion depth. The results suggest that a first order regression function with Gaussian correlation functions can best fit the results of the ground truth. The functional response of the Kriging-based method is utilized to model the dynamic deformations of markers at a series of needle insertion depths. The feasibility of the method is verified by investigating the adaptation to step variations. Compared with the ground truth of the finite element (FE) results, the maximum residual is less than 0.92 mm in the Y direction and 0.31 mm in the X direction. The results suggest that the Kriging metamodel provides real-time deformation feedback for a target and an obstacle to a SPS.

A new soft tissue deformation model based on Runge-Kutta: Application in lung

Flexible body deformation model is the most critical research in the field of telemedicine, which decides whether the deformation process of tissues and organs can be simulated in real time and realistically. Basically, the improvement of model accuracy often means the loss of real-time performance. In order to effectively balance between accuracy and real-time performance, this paper proposes a new model, which uses the step-variable fourth-order Runge-Kutta method for the first time to solve the relationship problem between the external force and displacement of the nodes in the finite element deformation of the lung. To improve the real-time performance of the model, a one-stage solution optimization algorithm is proposed to optimize the step size selection problem. Finally, an accelerated two-level node update algorithm is proposed to further improve the real-time performance. A lung surgery simulation platform with 3DMax2020 and OpenGL4.5 is built to verify the accuracy, efficiency, realism and applicability of the model. Experimental results show that the proposed lung model can achieve real-world visual reproduction during remote surgery, and exceeds other 13 reference models in real-time performance, with natural deformation effect, high simulation accuracy, which is suitable for modeling normal lung and four types of lungs suffering from diseases.

Constrained finite element method for runtime modeling of soft tissue deformation

This paper presents a new constrained FEM (finite element method) for accurate and runtime modeling of soft tissue's mechanical deformation from measurement of local surface displacement. This method turns the modeling problem of tissue deformation with unknown loading input into a constrained estimation problem to online estimate physical tissue deformation. Based on linear FEM discretization, a constrained estimation algorithm is developed to optimally estimate unknown loading input and online calculate deformation from measurement of local surface displacement. Results of simulation and experimentation exhibit that the proposed method significantly promotes the FEM computational performance but still inherits the FEM advantage of physical accuracy.

A Review of Virtual Surgical Object Modeling Technology Based on Force Feedback

Abstract The early virtual surgical system was only developed on the computer software, and users could only interact with the surgical model through the mouse. The disadvantage of this way was that users could not get tactile feelings. Therefore, with the development and progress of virtual reality technology, force feedback equipment has been introduced into virtual surgery, and has become a research hotspot in this field, in order to make efforts to feedback equipment in the research institute and higher and higher utilization rate. Researchers, teachers and students used force feedback devices to improve the immersion of virtual surgical system. This article mainly introduced the virtual modeling method in the operation, including geometric modeling and physical modeling, the geometric modeling of the two models are introduced, and summarizes their advantages and disadvantages, the physical modeling of soft tissue deformation modeling of three models are analyzed and compared, and the feedback force calculation model are introduced, finally, expounds some problems faced by modeling technology, virtual surgery The future development is also prospected.

Reduced-Order Extended Kalman Filter for Deformable Tissue Simulation

Modelling of soft tissue deformation is a key issue in surgical simulation. Despite extensive research studies on this issue, accurate modelling of soft tissue deformation in run time still remains challenging. This paper proposes a new reduced-order nonlinear Kalman filter to emulate nonlinear behaviors of biological deformable tissues. This approach defines the deformable modelling problem as a reduced-order filtering problem to accurately calculate soft tissue deformation in real time. Soft tissue deformation is discretized in space using nonlinear finite element method based on hyperelasticity and further formulated as a nonlinear state-space equation for filtering estimation. Subsequently, the order of this nonlinear state-space equation is reduced using proper orthogonal decomposition to reduce the computational cost. Upon this reduced-order state-space equation, an extended Kalman filter is constructed to online calculate nonlinear behaviors of tissue physical deformation. Simulation results and comparison analysis prove the effectiveness of the suggested method for accurate simulation of tissue physical deformation in real time.

Flexible Mass Spring Method for Modelling Soft Tissue Deformation

It is well accepted that soft tissue deformation is a combination of linear and nonlinear response. During small displacements, soft tissues deform linearly while during large displacements, soft tissues show nonlinear deformation. This paper presents a new approach for modelling of soft tissue deformation, from the standpoint of Mass Spring Method (MSM). The proposed MSM model is developed using conical spring methodology which allow the MSM model to have different stiffnesses at different displacements during deformation. The stiffness variation creates flexibility in the model to simulate any linear and nonlinear deformations. Experimental results demonstrate that the deformations by the proposed method are in good agreement with those real and phantom soft tissue deformations. Isotropic and anisotropic deformations can be accommodated by the proposed methodology via conical spring geometry and configuration of the springs. The proposed model also able to simulate typical viscoelastic behaviour of soft tissue.

A Fast and Accurate Vascular Tissue Simulation Model Based on Point Primitive Method

Virtual surgery simulation is indispensable for virtual vascular interventional training system, which provides the doctor with visual scene between catheter and vascular. Soft tissue deformation, as the most significant part, determines the success or failure of the virtual surgery simulation. However, most soft tissue deformation model cannot simultaneously meet the requirement of high deformation accuracy and real-time interaction. To solve the challenge mentioned above, this paper proposes a fast and accurate vascular tissue simulation model based on point primitive method. Firstly, the proposed model simulates a deformation of the internal structure of the vascular tissue by adopting a point primitive method. Besides, the stretching constraint and elastic potential energy constraint are introduced to control and correct node motion. Furthermore, a mapping function from the interior to the surface of the vascular tissue is constructed based on moving least squares algorithm to render the visual effect of deformation. Finally, a training system based on the proposed model is set up on the PHANTOM OMNI force-tactile feedback device to realize the deformation simulation of the virtual vascular tissue. Experimental results shows that the proposed model can enhance real-time performance of the training system under the premise of ensuring deformation accuracy, as well as simulate the elasticity of soft tissue.

Kalman Filter Finite Element Method for Real-Time Soft Tissue Modeling

Soft tissue modelling plays a significant role in surgery simulation as well as surgical procedure planning and training. However, it is a challenging research task to satisfy both physical realism and real-time simulation for soft tissue deformation. The finite element method (FEM) is a representative strategy for modelling of soft tissue deformation with highly physical realism. However, it suffers from expensive computations, unable to meet the requirement of real-time simulation. This paper proposes a novel method by combining FEM with the Kalman filter for real-time and accurate modelling of soft tissue deformation. The novelty of this method is that soft tissue deformation is formulated as a filtering identification process to online estimate soft tissue deformation from local measurement of displacement. To construct the discrete system state equation for filtering estimation, soft tissue deformation is discretised based on elastic theory in the space domain by FEM and is further discretised in the time domain by using the Wilson- $\theta $ implicit integration to solve the dynamic equilibrium equation of FEM deformation modelling. Subsequently, a Kalman filter is developed for online estimation and analysis of soft tissue deformation according to local measurement of displacement. Interactive tool-tissue interaction with haptic feedback is also achieved for surgery simulation. The presented method significantly improves the computational performance of the traditional FEM, but still maintains a similar level of accuracy. It not only achieves the real-time performance, but also exhibits the similar deformation behaviours as the traditional FEM and enables the use of large time steps to improve the simulation efficiency.

Soft Tissue Deformation Model Based on Marquardt Algorithm and Enrichment Function

In order to solve the problem of high computing cost and low simulation accuracy caused by discontinuity of incision in traditional meshless model, this paper proposes a soft tissue deformation model based on the Marquardt algorithm and enrichment function. The model is based on the element-free Galerkin method, in which Kelvin viscoelastic model and adjustment function are integrated. Marquardt algorithm is applied to fit the relation between force and displacement caused by surface deformation, and the enrichment function is applied to deal with the discontinuity in the meshless method. To verify the validity of the model, the Sensable Phantom Omni force tactile interactive device is used to simulate the deformations of stomach and heart. Experimental results show that the proposed model improves the real-time performance and accuracy of soft tissue deformation simulation, which provides a new perspective for the application of the meshless method in virtual surgery.

Neural network modelling of soft tissue deformation for surgical simulation.

This paper presents a new neural network methodology for modelling of soft tissue deformation for surgical simulation. The proposed methodology formulates soft tissue deformation and its dynamics as the neural propagation and dynamics of cellular neural networks for real-time, realistic, and stable simulation of soft tissue deformation. It develops two cellular neural network models; based on the bioelectric propagation of biological tissues and principles of continuum mechanics, one cellular neural network model is developed for propagation and distribution of mechanical load in soft tissues; based on non-rigid mechanics of motion in continuum mechanics, the other cellular neural network model is developed for governing model dynamics of soft tissue deformation. The proposed methodology not only has computational advantage due to the collective and simultaneous activities of neural cells to satisfy the real-time computational requirement of surgical simulation, but also it achieves physical realism of soft tissue deformation according to the bioelectric propagation manner of mechanical load via dynamic neural activities. Furthermore, the proposed methodology also provides stable model dynamics for soft tissue deformation via the nonlinear property of the cellular neural network. Interactive soft tissue deformation with haptic feedback is achieved via a haptic device. Simulations and experimental results show the proposed methodology exhibits the nonlinear force-displacement relationship and associated nonlinear deformation of soft tissues. Furthermore, not only isotropic and homogeneous but also anisotropic and heterogeneous materials can be modelled via a simple modification of electrical conductivity values of mass points.

A Constitutive Model of Soft Tissue Deformation for Virtual Surgical Simulation: A Literature Review

Realistic modeling of soft tissue deformation has been recognized as an essential requirement for virtual surgical simulators. As a consequence, the constitutive model is crucial for modeling soft tissue deformation. In this paper, the significance and characteristics of soft tissue deformation in virtual surgery simulation studies are introduced and analyzed its challenges. We have been focusing on investigating the constitutive relations in the soft tissue mechanical models: viscoelastic models and hyper-elastic models. Moreover, some techniques are given to determine and optimize model parameters through biomechanical experiments. Finally, based on the existing constitutive model, a novel notion for optimizing the soft tissue deformation constitutive model is proposed. The contribution of this paper is to provide theoretical guidance for the simulation of soft tissue deformation in the virtual surgery simulation system and to supply various practical suggestions for developing new constitutive models in the future.

Soft tissue deformation modelling through neural dynamics-based reaction-diffusion mechanics.

Soft tissue deformation modelling forms the basis of development of surgical simulation, surgical planning and robotic-assisted minimally invasive surgery. This paper presents a new methodology for modelling of soft tissue deformation based on reaction-diffusion mechanics via neural dynamics. The potential energy stored in soft tissues due to a mechanical load to deform tissues away from their rest state is treated as the equivalent transmembrane potential energy, and it is distributed in the tissue masses in the manner of reaction-diffusion propagation of nonlinear electrical waves. The reaction-diffusion propagation of mechanical potential energy and nonrigid mechanics of motion are combined to model soft tissue deformation and its dynamics, both of which are further formulated as the dynamics of cellular neural networks to achieve real-time computational performance. The proposed methodology is implemented with a haptic device for interactive soft tissue deformation with force feedback. Experimental results demonstrate that the proposed methodology exhibits nonlinear force-displacement relationship for nonlinear soft tissue deformation. Homogeneous, anisotropic and heterogeneous soft tissue material properties can be modelled through the inherent physical properties of mass points. Graphical abstract Soft tissue deformation modelling with haptic feedback via neural dynamics-based reaction-diffusion mechanics.

Soft tissue deformation estimation by spatio-temporal Kalman filter finite element method.

BACKGROUND: Soft tissue modeling plays an important role in the development of surgical training simulators as well as in robot-assisted minimally invasive surgeries. It has been known that while the traditional Finite Element Method (FEM) promises the accurate modeling of soft tissue deformation, it still suffers from a slow computational process.OBJECTIVE: This paper presents a Kalman filter finite element method to model soft tissue deformation in real time without sacrificing the traditional FEM accuracy.METHODS: The proposed method employs the FEM equilibrium equation and formulates it as a filtering process to estimate soft tissue behavior using real-time measurement data. The model is temporally discretized using the Newmark method and further formulated as the system state equation.RESULTS: Simulation results demonstrate that the computational time of KF-FEM is approximately 10 times shorter than the traditional FEM and it is still as accurate as the traditional FEM. The normalized root-mean-square error of the proposed KF-FEM in reference to the traditional FEM is computed as 0.0116.CONCLUSIONS: It is concluded that the proposed method significantly improves the computational performance of the traditional FEM without sacrificing FEM accuracy. The proposed method also filters noises involved in system state and measurement data.

Ellipsoid bounding region-based ChainMail algorithm for soft tissue deformation in surgical simulation

Real-time modelling of force interaction with soft tissues is of great importance for interactive surgical simulation. This paper presents a new ChainMail algorithm for real-time modelling of soft tissue deformation under force interaction. Unlike traditional ChainMails using a box-shaped bounding region, the proposed method defines an ellipsoid-shaped bounding region according to the concept of principal strains in continuum mechanics to control the movement of chain elements. Based on this ellipsoid-shaped bounding region, new position adjustment rules are developed and further integrated with temporal-domain model dynamics for dynamic simulation of soft tissue deformation. Haptic interaction with soft tissues is achieved via force input, soft tissue deformation, and force feedback. Experimental results demonstrate that the proposed ChainMail can simulate soft tissue mechanical behaviours, accommodate isotropic and homogeneous, anisotropic and heterogeneous materials, and handle large deformation. The proposed ChainMail also requires only small computational time, capable of achieving real-time computational performance.

Energy balance method for modelling of soft tissue deformation

This paper presents a novel methodology for modelling of soft tissue deformation, from the standpoint of work–energy balance based on the law of conservation of energy. The work done by an external force is always balanced against the strain energy due to the internal force of the object. A position-based incremental approach is established, in which the work–energy balance is achieved via an iterative position increment process for the new equilibrium state of the object. The position-based incremental approach is further combined with non-rigid mechanics of motion to govern the dynamics of soft tissue deformation. The proposed method employs nonlinear geometric and material formulations to account for the nonlinear soft tissue deformation. Soft tissue material properties can be accommodated by specifying strain energy density functions. Integration with a haptic device is also achieved for soft tissue deformation with haptic feedback for surgical simulation. Experimental results demonstrate that the deformations by the proposed method are in good agreement with those by a commercial package of finite element analysis. Isotropic and anisotropic deformations, as well as soft tissue viscoelastic behaviours, can be accommodated by the proposed methodology via strain energy density functions.

ChainMail based neural dynamics modeling of soft tissue deformation for surgical simulation.

Realistic and real-time modeling and simulation of soft tissue deformation is a fundamental research issue in the field of surgical simulation. In this paper, a novel cellular neural network approach is presented for modeling and simulation of soft tissue deformation by combining neural dynamics of cellular neural network with ChainMail mechanism. The proposed method formulates the problem of elastic deformation into cellular neural network activities to avoid the complex computation of elasticity. The local position adjustments of ChainMail are incorporated into the cellular neural network as the local connectivity of cells, through which the dynamic behaviors of soft tissue deformation are transformed into the neural dynamics of cellular neural network. Experiments demonstrate that the proposed neural network approach is capable of modeling the soft tissues' nonlinear deformation and typical mechanical behaviors. The proposed method not only improves ChainMail's linear deformation with the nonlinear characteristics of neural dynamics but also enables the cellular neural network to follow the principle of continuum mechanics to simulate soft tissue deformation.

Energy propagation modeling of nonlinear soft tissue deformation for surgical simulation

Realistic modeling of nonlinear soft tissue deformation in real-time is a challenging research topic in surgical simulation. This article presents an energy propagation method based on Poisson propagation for modeling of nonlinear soft tissue deformation for surgical simulation. It carries out soft tissue deformation from the viewpoint of potential energy propagation, in which the mechanical load of an external force applied to soft tissues is considered as the equivalent potential energy, according to the law of conservation of energy, and is further propagated in the volume of soft tissues based on the principle of Poisson energy propagation. The proposed method combines Poisson propagation of mechanical load and non-rigid mechanics of motion to govern the dynamics of soft tissue deformation. Computer simulation results demonstrate that the proposed method is not only able to handle homogeneous, anisotropic, and heterogeneous materials, but also able to accommodate nonlinear deformation of soft tissues.

Modeling of Three-Dimensional Soft Tissue Deformation with Dynamic Nonlinear Finite Element

Soft tissue deformation is a significant part of surgical simulation. This paper presents a dynamic nonlinear finite element method for modeling of soft tissue deformation. This method models large-range deformation via the secondorder Piola-Kirchhoff stress. It condenses the stiffness matrix to reduce the degrees of freedom of the entire soft body at each node for every time step to improve the computational performance. Simulations and comparison analysis show that the proposed method can predict the nonlinear behaviors of soft tissues and requires a small amount of time.

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

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. 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. 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. 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.