Chengfan Gu

A new ChainMail approach for real-time soft tissue simulation.

ABSTRACT This paper presents a new ChainMail method for real-time soft tissue simulation. This method enables the use of different material properties for chain elements to accommodate various materials. Based on the ChainMail bounding region, a new time-saving scheme is developed to improve computational efficiency for isotropic materials. The proposed method also conserves volume and strain energy. Experimental results demonstrate that the proposed ChainMail method can not only accommodate isotropic, anisotropic and heterogeneous materials but also model incompressibility and relaxation behaviors of soft tissues. Further, the proposed method can achieve real-time computational performance.

A NEW PARAMETER ESTIMATION METHOD FOR ONLINE SOFT TISSUE CHARACTERIZATION

Dynamic soft tissue characterization is of importance to robotic-assisted minimally invasive surgery. The traditional linear regression method is unsuited to handle the non-linear Hunt–Crossley (HC) model and its linearization process involves a linearization error. This paper presents a new non-linear estimation method for dynamic characterization of mechanical properties of soft tissues. In order to deal with non-linear and dynamic conditions involved in soft tissue characterization, this method improves the non-linearity and dynamics of the HC model by treating parameter p as independent variable. Based on this, an unscented Kalman filter is developed for online estimation of soft tissue parameters. Simulations and comparison analysis demonstrate that the proposed method is able to estimate mechanical parameters for both homogeneous tissues and heterogeneous and multi-layer tissues, and the achieved performance is much better than that of the linear regression method.

Asymptotic Properties of Random Weighted Empirical Distribution Function

This article studies the asymptotic properties of the random weighted empirical distribution function of independent random variables. Suppose X1, X2, ⋅⋅⋅, Xn is a sequence of independent random variables, and this sequence is not required to be identically distributed. Denote the empirical distribution function of the sequence by Fn(x). Based on the random weighting method and Fn(x), the random weighted empirical distribution function Hn(x) is constructed and the asymptotic properties of Hn are discussed. Under weak conditions, the Glivenko–Cantelli theorem and the central limit theorem for the random weighted empirical distribution function are obtained. The obtained results have also been applied to study the distribution functions of random errors of multiple sensors.

Energy balance method for modelling of soft tissue deformation

Abstract 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.

Prediction of tissue thermal damage

This paper presents a method to characterize tissue thermal damage by taking into account the thermal-mechanical effect of soft tissues for thermal ablation. This method integrates the bio-heating conduction and non-rigid motion dynamics to describe thermal-mechanical behaviors of soft tissues and further extends the traditional tissue damage model to characterize thermal-mechanical damage of soft tissues. Simulations and comparison analysis demonstrate that the proposed method can effectively predict tissue thermal damage and it also provides reliable guidelines for control of the thermal ablation procedure.

Random weighting estimation of kinematic model error for dynamic navigation

This paper presents a new random weighting method to deal with the systematic error of the kinematic model for dynamic navigation. This method incorporates random weights in the kinematic model to control the systematic error of the kinematic model for improving the navigation accuracy. A theory of random weighting estimation is established, showing that 1) the random weighting estimation of the kinematic models systematic error is unbiased and 2) the covariance matrix of the predicted state vector can be controlled by adjusting the covariance matrices of the predicted residual vector and estimated state vector to improve the accuracy of state prediction. Random weighting estimations are also constructed for the systematic error of the kinematic model as well as the covariance matrices of predicted residual vector, predicted state vector, and state noise vector. Experimental results demonstrate the effectiveness of the proposed random weighting method in resisting the disturbances of the kinematic model noise for improving the accuracy of dynamic navigation.

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.

Multi-Sensor Optimal Data Fusion Based on the Adaptive Fading Unscented Kalman Filter

This paper presents a new optimal data fusion methodology based on the adaptive fading unscented Kalman filter for multi-sensor nonlinear stochastic systems. This methodology has a two-level fusion structure: at the bottom level, an adaptive fading unscented Kalman filter based on the Mahalanobis distance is developed and serves as local filters to improve the adaptability and robustness of local state estimations against process-modeling error; at the top level, an unscented transformation-based multi-sensor optimal data fusion for the case of N local filters is established according to the principle of linear minimum variance to calculate globally optimal state estimation by fusion of local estimations. The proposed methodology effectively refrains from the influence of process-modeling error on the fusion solution, leading to improved adaptability and robustness of data fusion for multi-sensor nonlinear stochastic systems. It also achieves globally optimal fusion results based on the principle of linear minimum variance. Simulation and experimental results demonstrate the efficacy of the proposed methodology for INS/GNSS/CNS (inertial navigation system/global navigation satellite system/celestial navigation system) integrated navigation.

Cellular neural network modelling of soft tissue dynamics for surgical simulation

BACKGROUND Currently, the mechanical dynamics of soft tissue deformation is achieved by numerical time integrations such as the explicit or implicit integration; however, the explicit integration is stable only under a small time step, whereas the implicit integration is computationally expensive in spite of the accommodation of a large time step. OBJECTIVE This paper presents a cellular neural network method for stable simulation of soft tissue deformation dynamics. METHOD The non-rigid motion equation is formulated as a cellular neural network with local connectivity of cells, and thus the dynamics of soft tissue deformation is transformed into the neural dynamics of the cellular neural network. RESULTS Results show that the proposed method can achieve good accuracy at a small time step. It still remains stable at a large time step, while maintaining the computational efficiency of the explicit integration. CONCLUSION The proposed method can achieve stable soft tissue deformation with efficiency of explicit integration for surgical simulation.

Neural dynamics-based Poisson propagation for deformable modelling

This paper presents a new methodology from the standpoint of energy propagation for real-time and nonlinear modelling of deformable objects. It formulates the deformation process of a soft object as a process of energy propagation, in which the mechanical load applied to the object to cause deformation is viewed as the equivalent potential energy based on the law of conservation of energy and is further propagated among masses of the object based on the nonlinear Poisson propagation. Poisson propagation of mechanical load in conjunction with non-rigid mechanics of motion is developed to govern the dynamics of soft object deformation. Further, these two governing processes are modelled with cellular neural networks to achieve real-time computational performance. A prototype simulation system with a haptic device is implemented for real-time simulation of deformable objects with haptic feedback. Simulations, experiments as well as comparisons demonstrate that the proposed methodology exhibits nonlinear force–displacement relationship, capable of modelling large-range deformation. It can also accommodate homogeneous, anisotropic and heterogeneous materials by simply changing the constitutive coefficient value of mass points.