A high-resolution model for soft tissue deformation based on point primitives

Highlights

• A high-resolution model for soft tissue deformation based on point primitives is proposed.

• Octree data structure is used to record the topology relationship in this model.

• The high-resolution model has been implemented into the development of a neurosurgery simulator.

• The visual effects and computation cost of the proposed model are evaluated and compared with conventional primitives-based methods.

Abstract

Background and objectives: In order to achieve a high degree of visual realism in surgery simulation, we propose a new model, which is based on point primitives and continuous elastic mechanics theory, for soft tissue deformation, tearing and/or cutting.

Methods: The model can be described as a two-step local high-resolution strategy. First, appropriate volumetric data are sampled and assigned with proper physical properties. Second, sparsely sampled points in non-deformed regions and densely-sampled points in the deformed zone are selected and evaluated. By using a meshless deformation model based on point primitives for all volumetric data, the affine transform matrix of collision points can be computed. The new positions of neighboring points in the collided surface can be then calculated, and more details in the local deformed zone can be obtained for rendering. Technical details about the derivations of the proposed model as well as its implementation are given.

Results: The visual effects and computation cost of the proposed model are evaluated and compared with conventional primitives-based methods. Experimental results show that the proposed model provides users (trainees) with improved visual feedback while the computational cost is at the same magnitude of other similar methods.

Conclusions: The proposed method is especially suitable for the simulation of soft tissue deformation and tearing because no grid information needs to be maintained. It can simulate soft tissue deformation in a high degree of authenticity with real-time performance. It could be considered implemented in the development of a mixed reality application of neurosurgery simulators in the future.

Introduction

The simulation of the deformation and movement process of soft objects has long been an active research topic in virtual reality simulation. A number of deformation models have been reported [1], [2], [3], [4], [5] and they can be broadly divided into two categories: geometrically based models and physically based models. The key idea of geometrically based models is that the deformation process is implemented through the direct control of data points or curves on the surface of the object. Because of their high computation efficiency and robustness, geometrically based models are widely adopted, and many results have been published in recent years [6], [7], [8]. However, these models are not directly suitable for applications where the requirements on the visual realism and accuracy are critical, such as surgical simulators. Physically based models are usually preferred for these types of applications since the material parameters of soft objects are considered, potentially providing improved visual and haptic simulation effects. Physical based models mainly include the mass-spring model, finite element method (FEM) and meshless method.

The spring-mass model is often used in surgery simulation because of its simple architecture and fast computation, but it is difficult to set proper parameter values and the accuracy is limited due to its high level of simplicity [9], [10]. In addition, the addition or removal of springs of the model (e.g., in the simulation of cutting) can lead to system instability. The main advantage of the FEM-based model is its capability to describe accurately the behaviors of a wide range of materials, from rigid body to soft body, by changing the material constitutive equation. In the meanwhile, the realism of simulation can be improved by incorporating more material physical properties into the FEM model, but on the other hand, the introduction of a large number of material parameters will unavoidably make the mathematical formulation complicated and increase the computational complexity [11], [12]. In addition, one significant drawback of traditional FEM models is the high computational cost due to grid reconstruction when the topology is changed during maneuvers, such as tearing and cutting.

Compared with spring-mass and FEM models, the continuum of the object is discretized using unstructured point samples in meshless models. Since meshless models do not need to maintain the topological information among data points, the problems associated with the complicated topology (such as pathological grid, grid distortion and topological structure reconstruction), which are inherent in traditional grid-based models, are avoided. In addition, meshless models are able to ensure a high level of accuracy if the system is properly designed. Because of these advantages and potentials, meshless point-based approaches are gaining significant attention in recent years. For instance, De et al. [13] developed a mesh-free technique, the point collocation-based method of finite spheres (PCMFS), for the simulation of soft tissues in minimally invasive surgery. Compared with the traditional finite element method, the developed method improves both the calculation speed and accuracy. Lim et al. [14] extended the PCMFS technique to tissue deformations that are geometrically nonlinear and combined a multiresolution approach with a fast reanalysis scheme to improve system performance. Müller et al. proposed point-based animation for a wide spectrum of volumetric objects [15]. Meshless methods have also been used in offline fracturing [16] and interactive cutting [17], [18]. Horton et al. [19] presented a meshless total Lagrangian explicit dynamics algorithm to achieve geometrically nonlinear deformation of soft tissue. The experimental results are compared with finite element simulation to verify the usefulness of the method. Zhang et al. [20] proposed an explicit nonlinear dynamic meshless method, which is based on the element-free Galerkin method using total Lagrangian formulation and moving least square (MLS) approximation, and imposes essential boundary conditions exactly by coupling MLS shape functions with a finite element interpolation in the close region of essential boundary. The results indicates the ability of the method to facilitate robust and accurate prediction of the organ responses subjected to large localized deformation. Liu et al. [21] presented a coupling deformable model based on viscoelastic mechanics equations which integrated the element-free Galerkin (EFG) with the mass-spring. The EFG was used to model material behavior to topology change and the mass-spring model was used in regions away from deformation. Seamless coupling of two regions was achieved according to the balance conditions of forces and displacements that should be satisfied by transitional joint points. The hybrid model improves the calculation accuracy and computational efficiency, however, its limitation is to realize seamless coupling of transition units.

While meshless models show a considerable number of advantages over spring-mass and FEM models, they also pose limitations, among which the high computational cost is the most significant. In order to achieve rich details and good visual effect, the computational complexity of meshless models is bound to increase exponentially, making it difficult to achieve real-time performance in ordinary PCs.

In order to combat the problem of high computational cost associated with meshless models, we propose a new deformation model, which is based on point primitives and continuous elastic mechanics theory, for the simulation of cutting and deformation of soft tissue in surgery simulation. In order to achieve a high-resolution deformation model, the object to be simulated is first subdivided to obtain its volumetric data using Netgen software [22]. Then, appropriate volumetric data are sampled and assigned with proper physical properties. Next, sparsely sampled points in non-deformed zones and densely-sampled points in the deformed zone are selected and evaluated. By using a meshless deformation model based on point primitives for the volumetric data, the affine transform matrix of collision points can be computed. Accordingly, the new positions of neighboring points in the collided surface can be calculated, and thus more details in the local deformed area can be achieved for rendering. In the paper, details about the derivations of the proposed model as well as the implementation are given. The proposed model were implemented in the development of a neurosurgery simulator. The visual effects and computational cost of the model were evaluated and compared with conventional primitives-based methods. Experimental results show that the proposed model provides users with excellent visual feedback compared with other similar methods.

This paper is organized as follows. In Section 2, we describe a meshless deformation model based on point primitives and propose a local high-resolution soft tissue deformation model, which is able to provide high-quality deformation simulation effect and maintain low calculation cost. Section 3 shows that the proposed model provides superior simulation quality in terms of visual effect compared with classical meshless deformation models based on point primitives and the interpolating displacement vector of a known surface element method. The paper is concluded with some suggestions to future work in Section 4.