Physical Constraint Finite Element Model for Medical Image Registration

Due to being derived from linear assumption, most elastic body based non-rigid image registration algorithms are facing challenges for soft tissues with complex nonlinear behavior and with large deformations. To take into account the geometric nonlinearity of soft tissues, we propose a registration algorithm on the basis of Newtonian differential equation. The material behavior of soft tissues is modeled as St. Venant-Kirchhoff elasticity, and the nonlinearity of the continuum represents the quadratic term of the deformation gradient under the Green- St.Venant strain. In our algorithm, the elastic force is formulated as the derivative of the deformation energy with respect to the nodal displacement vectors of the finite element; the external force is determined by the registration similarity gradient flow which drives the floating image deforming to the equilibrium condition. We compared our approach to three other models: 1) the conventional linear elastic finite element model (FEM); 2) the dynamic elastic FEM; 3) the robust block matching (RBM) method. The registration accuracy was measured using three similarities: MSD (Mean Square Difference), NC (Normalized Correlation) and NMI (Normalized Mutual Information), and was also measured using the mean and max distance between the ground seeds and corresponding ones after registration. We validated our method on 60 image pairs including 30 medical image pairs with artificial deformation and 30 clinical image pairs for both the chest chemotherapy treatment in different periods and brain MRI normalization. Our method achieved a distance error of 0.320±0.138 mm in x direction and 0.326±0.111 mm in y direction, MSD of 41.96±13.74, NC of 0.9958±0.0019, NMI of 1.2962±0.0114 for images with large artificial deformations; and average NC of 0.9622±0.008 and NMI of 1.2764±0.0089 for the real clinical cases. Student's t-test demonstrated that our model statistically outperformed the other methods in comparison (p-values <0.05)

Real-time Knowledge-based Fuzzy Logic Model for Soft Tissue Deformation

In this research, the improved mass spring model is presented to simulate the human liver deformation. The underlying MSM is redesigned where fuzzy knowledge-based approaches are implemented to determine the stiffness values. Results show that fuzzy approaches are in very good agreement to the benchmark model. The novelty of this research is that for liver deformation in particular, no specific contributions in the literature exist reporting on real-time knowledge-based fuzzy MSM for liver deformation

Real-time measurement corrected prediction of soft tissue response for medical simulations

Medical simulators, such as in palpation and disease diagnosis, require an efficient model of the biological soft tissue deformation. Hence, a computationally fast and accurate algorithm is required to support and enhance user interactions in near real-time simulations. The visual accuracy of such simulators is dependent on the user&amp;iquest;s reaction time. Static visual images that update at a rate of 25 Hz are perceived as real-time moving images. Hence, visualizing software requires fast algorithms to compute the deformation of soft tissue to facilitate a meaningful simulation. Furthermore, soft tissue behaviour should be modelled accurately while compatible with real-time computation. This work proposes a fast solver for the linearized finite element method (FEM) and validates the proposed algorithm with experimental results. The novelty of the method lies in the utilization of real-time force/displacement measurements that are embedded in the solution via the Kalman filter. A novel computational algorithm that utilizes the strength of the FEM in terms of accuracy and employs direct measurements from the manipulated tissue to overcome the slow computational process of the FEM is proposed in the first part of the thesis. As the behaviour of the mechanically loaded tissue can be regarded as linearly responding at each time step, a constant acceleration temporal discretization method, i.e., the Newmark-&amp;szlig; is employed. In real-time applications, the accuracy of the target variable highly depends on the accuracy of the inputs while differentiating noise from the signal is hardly ever possible. To address this problem, a Kalman filter-based method is developed. The proposed algorithm not only filters the noise from the measurements but also adapts the filter gain to the estimates of the target variable, i.e., the resulting tissue deformation. For a simulated tension test of a cubic model, the proposed algorithm achieves the update frequency of 63.3 Hz. This rate is a significant improvement in computational speed compared to the 5.8 Hz update rate by the classic FEM. Besides, this novel combination of the KF and the FEM makes it possible to expand the displacement estimates in the spatial domain when the measurements are only partially available at certain points. The performance of the above method is validated experimentally through a comparison with indentation tests on artificial human tissue-like material and with the FEM result under identical simulation conditions. The test is repeated on several samples, and the displacement variation from the FEM outcome is considered as the model error. Simulation results show that the proposed method achieves the deformation update frequency of 145.7 Hz compared to the 2.7 Hz from the reference FEM. The proposed method shows the same predictive ability, only 0.47% difference from FEM on average. Experimental validation of the proposed KF-FEM confirms that by consideration of both the measurement noise and the model error, the proposed method is capable of achieving high-frequency response without sacrificing the accuracy. Further to this, the experiments confirmed the linearized model response is reliable within the applied displacement range and therefore proving that KF can be employed. The developed KF-FEM was modified in the next study to address the problem resulting from inaccurate external loads measurements by the force sensors. In the modified version, both the external force, i.e., driving variable, and the displacement, i.e., driven variable, are taken as system states. It is considered that the uncertainty of the model input influences the accuracy of the system estimates. The modified model is calibrated to differentiate the system noise from the input noise. Numerical simulations were conducted on a liver shape geometrical model, and the simulation results demonstrate that more than 90% of the measurement noise is removed. The computational speed is also increased, delivering up to 89 Hz update rate. While the uncertainty of the external load is replicated in the displacements in an FEM solution, the developed algorithm can differentiate the measurement noise, including the displacement and external forces, from the system error, i.e., the FE model error. In the last study, the proposed model was developed to reflect the nonlinear behaviour of the manipulated tissue. The Central Difference time discretization method was used to model large deformations. A novel feature is that the Equation of motion is formulated within the element level rather than in the global spatial domain. This approach helped to improve the computational speed. Indentation with strains of slightly over 10% was simulated to assess the performance of the proposed model. The developed algorithm achieved the 33.85 Hz update frequency on a standard-issue PC and confirmed its suitability for real-time applications. Also, the proposed model achieved estimates with a maximum 5.75% mean absolute error (MAE) concerning the measurements while the classic FEM showed 6.20% MAE under identical simulation condition. Results confirm that deformation estimates for noisy boundary loads of the FEM can be improved with the help of direct measurements and yet be realistic in terms of real-time visual update. This study proposed a novel computational algorithm that achieved update frequencies of higher than 25 Hz to be perceived as real-time in human eyes. The developed KF-FEM model has also shown the potential of improving the FEM accuracy with the help of direct measurements. The proposed algorithm used partially available measurements and expanded its estimates in the spatial domain. The method was experimentally validated, and the model input uncertainty, as well as the nonlinear behaviour of the soft tissue, were assessed and verified

Conical spring and localised region methodologies for modelling of soft tissue deformation.

Considerable research efforts have been dedicated to the development of virtual reality simulators that facilitate medical students in learning anatomy and surgery in the virtual environment and to allow surgeons to rehearse the surgical procedures. The level of realism depends upon the simulation accuracy and the computational efficiency of underlying deformable models. Ideally, the deformable models should be able to simulate accurately mechanical behaviours of soft tissues with real-time visual and force feedback. Modelling soft tissue deformation is not an easy task. Due to the complexity of soft tissue properties, many methods have been proposed to model soft tissue properties. One of the most well-known methods is the Finite Element Method (FEM). In this method, the soft tissue is represented by multiple elements that are derived based on complex mathematical formulations. It has been proven that the method is able to simulate soft tissue properties accurately, but it requires high computational cost to produce real-time interaction. In this regard, the Mass Spring Method (MSM) has been proposed as an alternative. The traditional MSM model simulates soft tissue deformation by discretising the soft tissue into several mass points that are connected to each other by linear springs. The major advantage of MSM is it has an excellent computational performance. However, the MSM application is limited to linear deformation, which does not represent the actual behaviour of the soft tissue deformation. In this thesis, an improved MSM model has been proposed to simulate the complex behaviour of soft tissue deformations. The improved MSM model is called conical spring model which considers the general behaviour of soft tissue deformation that is a combination of linear and nonlinear responses. Piecewise approach is used to discretise each response individually, and the conical spring methodology is used to model the deformation behaviours during all the responses. The piecewise approach gives precision in modelling while the conical spring methodology that was founded on stiffness variation, has improved the accuracy of the simulation due to its ability to model any type of linear and nonlinear responses. Moreover, the generated conical spring model is based on the force propagation approach. The computational performance of the model relies on the number of nodes involved in the propagation of the force. Inherently, computational time can be improved by considering the nodes only in a deformation area, and ignoring the other nodes. Soft tissue deformation commonly occurs only within a local region. As the effect of the deformation outside the local region is very little, it can be ignored in real practice. In this thesis, methods to define the local region were proposed. The methods are based on the linear elastic theory. As reported in Chapter 4 of this thesis, the localised region was generated based on displacement value induced when the simulation model was subjected to an external load. The Boussinesq method, which is widely used in the soil mechanics, was used to estimate the induced displacement value. However, the Boussinesq method is limited to the isotropic material. Therefore, as described in Chapter 5, the study has extended the isotropic localised region to anisotropic localised region by introducing an anisotropic factor which was derived based on cross-anisotropic properties. By using the anisotropic factor, the anisotropic localised region is determined from the corresponding isotropic case. Alternatively, in Chapter 6, we have presented a localised region that was generated based on stress value induced during a loading process. It is shown for point load type of contact, in comparison to ABAQUS analysis, stress based localisation has a better accuracy than the displacement based localisation. However, the stress value that is also determined using the Boussinesq method, has no relation to the material properties. Hence, a combination of the Hertzian and the Boussinesq method was used to generate localised regions with respect to the material properties and loading conditions. In the final chapter, contributions of the study were discussed, and some of the future works to expand the research were listed out

Real-time simulation of soft tissue deformation for surgical simulation

Surgical simulation plays an important role in the training, planning and evaluation of many surgical procedures. It requires realistic and real-time simulation of soft tissue deformation under interaction with surgical tools. However, it is challenging to satisfy both of these conflicting requirements. On one hand, biological soft tissues are complex in terms of material compositions, structural formations, and mechanical behaviours, resulting in nonlinear deformation characteristics under an external load. Due to the involvement of both material and geometric nonlinearities, the use of nonlinear elasticity causes a highly expensive computational load, leading to the difficulty to achieve the real-time computational performance required by surgical simulation. On the other hand, in order to satisfy the real-time computational requirement, most of the existing methods are mainly based on linear elasticity under the assumptions of small deformation and homogeneity to describe deformation of soft tissues. Such simplifications allow reduced runtime computation; however, they are inadequate for modelling nonlinear material properties such as anisotropy, heterogeneity and large deformation of soft tissues. In general, the two conflicting requirements of surgical simulation raise immense complexity in modelling of soft tissue deformation. This thesis focuses on establishment of new methodologies for modelling of soft tissue deformation for surgical simulation. Due to geometric and material nonlinearities in soft tissue deformation, the existing methods have only limited capabilities in achieving nonlinear soft tissue deformation in real-time. In this thesis, the main focus is devoted to the real-time and realistic modelling of nonlinear soft tissue deformation for surgical simulation. New methodologies, namely new ChainMail algorithms, energy propagation method, and energy balance method, are proposed to address soft tissue deformation. Results demonstrate that the proposed methods can simulate the typical soft tissue mechanical properties, accommodate isotropic and homogeneous, anisotropic and heterogeneous materials, handle incompressibility and viscoelastic behaviours, conserve system energy, and achieve realistic, real-time and stable deformation. In the future, it is projected to extend the proposed methodologies to handle surgical operations, such as cutting, joining and suturing, for topology changes occurred in surgical simulation