Hunt-Crossley Model Based Soft Tissue Characterization

Considerable research efforts have been made on the development of robotic-aided medical applications that facilitate surgeons to rehearse surgical procedures, increase surgical precision and reduce surgical trauma. However, the performance of robotic systems is primarily affected by unknown dynamic environments. Therefore, it is crucial to recognize these dynamic characteristics to optimize the performance of a robotic system. Nevertheless, tissue mechanical properties vary with tissue layers, types of organs and physiological conditions; while describing the tool-tissue interaction dynamically is still challenging.

Many linear viscoelastic models have been proposed to characterize mechanical contacts with soft tissues. These models have shown their simplicity and excellent computational performance. However, due to the nonlinearities of living tissues, the uses of linear models involve significant physical inconsistency. To address this issue, a nonlinear Hunt-Crossley (HC) model has been proposed as an alternative, which extends the Hertz contact law by introducing a hysteretic damping factor and overcomes the inconsistency with viscous contact involved in a linear model. However, the nonlinearity of an HC model brings a new challenge when it is applied in soft tissue characterization.

This thesis established a methodology to characterize the mechanical properties of soft tissues dynamically based on the nonlinear HC model. Since linear estimation algorithms are mature, most of the current research applies various linearization approaches in the HC model. These estimation methods include recursive least square (RLS), linear mean square (LMS) and Kalman filter (KF). An HC model is most commonly linearized by the natural logarithmic factorization (NLF), but it results in an inappropriate factorization and non-Gaussian distribution that conflict with the objective of linear estimation. Artificial neural network (ANN) is an effective tool to approximate unknown functions and is widely used to model the nonlinearities and uncertainties of a system. However, conventional ANN requires complex computation due to multiple hidden layers and a large amount of sampling data for its learning process. It is not able to accomplish real-time performance in characterizing soft tissue. Different from conventional ANN with multiple hidden layers, a radial basis function neural network (RBFNN) uses one hidden layer to classify nonlinear behaviours; this reduces computational complexity and enables real-time applications. Furthermore, since the neurons in RBFNN are nonlinear Gaussian functions, a shallow network can yield similar results as conventional ANNs. Therefore, an RBFNN aided HC model is proposed to compensate for the errors caused by linearization. However, the kinematic motion is assumed to be given; it is uncertain and involves noise in real world. To consider the unknown kinematic motion of the mechanical tool in soft tissue characterization, the maximum likelihood (ML) theory is combined with Extended Kalman Filter (EKF) to identify HC model parameters dynamically based on online estimation of the mechanical tool’s motion. Furthermore, an Iterated Kalman filter (IKF) is proposed to enhance the accuracy and stability of the EKF in highly nonlinear systems. An IKF is an improvement of EKF; it is able to estimate the kinematic motion and the parameters of the HC model simultaneously. The results of simulations and experiments demonstrate that the proposed methods have estimated model parameters of the HC model accurately. In addition, all of the methodologies proposed in this thesis can achieve real-time performance in practice.