This paper presents a survey of the state-of-the-art deformable models studied in the literature, with regard to soft tissue deformable modeling for interactive surgical simulation. It first introduces the challenges of surgical simulation, followed by discussions and analyses on the deformable models, which are classified into three categories: the heuristic modeling methodology, continuum-mechanical methodology, and other methodologies. It also examines linear and nonlinear deformable modeling, model internal forces, and numerical time integrations, together with modeling of soft tissue anisotropy, viscoelasticity, and compressibility. Finally, various issues in the existing deformable models are discussed to outline the remaining challenges of deformable models in surgical simulation.

Deformable Models for Surgical Simulation: A Survey

Mass spring models (MSMs) are a popular choice for representation of soft bodies in computer graphics and virtual reality applications. In this paper, we investigate physical properties of the simplest MSMs composed of mass points and linear springs. The nodes are either placed on a cubic lattice or positioned randomly within the system. We calculate the elastic moduli for such models and relate the results to other studies. We show that there is a well-defined relationship between the geometric characteristics of the MSM systems and physical properties of the modeled materials. It is also demonstrated that these models exhibit a proper convergence to a unique solution upon mesh refinement and thus can represent elastic materials with a high precision.

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Elastic moduli of simple mass spring models

A novel meshless deformation model of biological soft tissue, which is mainly based on the radial basis function point interpolation, is presented for interactive simulation applications such as virtual surgery simulators. Compared with conventional mesh models, the proposed model is particularly suitable for simulating large deformation, sucking and cutting tasks since there is no need to maintain grid information. Kelvin viscoelasticity, which represents relaxation, creep, and hysteresis of soft tissue, is integrated into the proposed model, making the simulation much more realistic than many existing meshless models. To verify the validity of the proposed model, a biomechanical test was performed on real-life biological tissue and the results show that the maximum relative error between the forces from the biomechanical test and those obtained from the model is less than 5.8%. The proposed model was also implemented on a neurosurgery simulator, which showed that the deformation of the brain tumor can be simulated in a high degree of accuracy with real-time performance. In particular, the error and distortion from the remeshing process inherited in conventional mesh models when deformation is large are avoided.

A New Deformation Model of Biological Tissue for Surgery Simulation

This paper introduces a new technique to synthesize dexterous manipulation of cloth. Given a simple description of the desired cloth motion, our algorithm computes appropriate joint torques for physically simulated hands, such that, via contact forces, the result of cloth simulation follows the desired motion. Instead of optimizing the hand control forces directly, we formulate an optimization problem that solves for the commanding forces from the hands to the cloth, which have more direct impact on the dynamic state of the hands and that of the cloth. The solution of the optimization provides commanding forces that achieve the desired cloth motion described by the user, while respecting the kinematic constraints of the hands. These commanding forces are then used to guide the joint torques of the hands. To balance between the effectiveness of control and computational costs, we formulate a model-predictive-control problem as a quadratic program at each time step. We demonstrate our technique on a set of cloth manipulation tasks in daily activities, including folding laundry, wringing a towel, and putting on a scarf.

Dexterous manipulation of cloth

This paper presents a survey of the state-of-the-art deformable models studied in the literature concerning soft tissue deformable modeling for interactive surgical simulation. It first introduces the challenges of surgical simulation, followed by discussions and analyses on the deformable models, which are classified into three categories: the heuristic modeling methodology, continuum-mechanical methodology, and other methodologies. It also examines linear and nonlinear deformable modeling, model internal forces, and numerical time integrations, together with modeling of soft tissue anisotropy, viscoelasticity, and compressibility. Finally, various issues in the existing deformable models are discussed to outline the remaining challenges of deformable models in surgical simulation.

Mass-Spring Models (MSMs) are used to simulate the mechanical behavior of deformable bodies such as soft tissues in medical applications. Although they are fast to compute, they lack accuracy and their design remains still a great challenge. The major difficulties in building realistic MSMs lie on the spring stiffness estimation and the topology identification. In this work, the mechanical behavior of MSMs under tensile loads is analyzed before studying the spring stiffness estimation. In particular, the performed qualitative and quantitative analysis of the behavior of cubical MSMs shows that they have a nonlinear response similar to hyperelastic material models. According to this behavior, a new method for spring stiffness estimation valid for linear and nonlinear material models is proposed. This method adjusts the stress-strain and compressibility curves to a given reference behavior. The accuracy of the MSMs designed with this method is tested taking as reference some soft-tissue simulations based on nonlinear Finite Element Method (FEM). The obtained results show that MSMs can be designed to realistically model the behavior of hyperelastic materials such as soft tissues and can become an interesting alternative to other approaches such as nonlinear FEM.

G. San-Vicente

Papers

Cubical Mass-Spring Model Design Based on a Tensile Deformation Test and Nonlinear Material Model