Dynamics Of Cellular Neural Networks Research Articles

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.

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.

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.

Complex behavior of polynomial FitzHugh–Nagumo cellular neural network model

In this paper, a cellular neural network (CNN) model of FitzHugh–Nagumo system with two diffusion coefficients is introduced. The dynamical behavior of the polynomial CNN model is investigated using harmonic balance method. Local activity domain and edge of chaos domain of the parameter space were found for the model. Numerical simulations of the CNN dynamics confirm the so-called edge of chaos phenomena and help in the better understanding of genesis and emergence of complexity in FitzHugh–Nagumo system.

Complex dynamics in one‐dimensional CNNs

AbstractThe effect of boundary conditions on the global dynamics of cellular neural networks (CNNs) is investigated. As a case study one‐dimensional template CNNs are considered. It is shown that if the off‐diagonal template elements have opposite sign, then the boundary conditions behave as bifurcation parameters and can give rise to a very rich and complex dynamic behaviour. In particular, they determine the equilibrium point patterns, the transition from stability to instability and the occurrence of several bifurcation phenomena leading to strange and/or chaotic attractors and to the coexistence of several attractors. Then the influence of the number of cells on the global dynamics is studied, with particular reference to the occurrence of hyperchaotic behaviour. Copyright © 2006 John Wiley & Sons, Ltd.

A DOUBLE TIME—SCALE CNN FOR SOLVING TWO-DIMENSIONAL NAVIER—STOKES EQUATIONS

A practical cellular neural network (CNN) approximation to the Navier-Stokes equation describing the viscous flow of incompressible fluids is presented. The implementation of the CNN templates based on a finite-difference discretization scheme, including the double-timescale CNN dynamics and the treatment of various types of boundary conditions are explained. The operation of the continuous-time model is demonstrated through several examples.