Maximum likelihood-based extended Kalman filter for COVID-19 prediction.

Prediction of COVID-19 spread plays a significant role in the epidemiology study and government battles against the epidemic. However, the existing studies on COVID-19 prediction are dominated by constant model parameters, unable to reflect the actual situation of COVID-19 spread. This paper presents a new method for dynamic prediction of COVID-19 spread by considering time-dependent model parameters. This method discretises the susceptible-exposed-infected-recovered-dead (SEIRD) epidemiological model in time domain to construct the nonlinear state-space equation for dynamic estimation of COVID-19 spread. A maximum likelihood estimation theory is established to online estimate time-dependent model parameters. Subsequently, an extended Kalman filter is developed to estimate dynamic COVID-19 spread based on the online estimated model parameters. The proposed method is applied to simulate and analyse the COVID-19 pandemics in China and the United States based on daily reported cases, demonstrating its efficacy in modelling and prediction of COVID-19 spread.

Constrained Unscented Particle Filter for SINS/GNSS/ADS Integrated Airship Navigation in the Presence of Wind Field Disturbance.

Due to the disturbance of wind field, it is difficult to achieve precise airship positioning and navigation in the stratosphere. This paper presents a new constrained unscented particle filter (UPF) for SINS/GNSS/ADS (inertial navigation system/global navigation satellite system/atmosphere data system) integrated airship navigation. This approach constructs a wind speed model to describe the relationship between airship velocity and wind speed using the information output from ADS, and further establishes a mathematical model for SINS/GNSS/ADS integrated navigation. Based on these models, it also develops a constrained UPF to obtain system state estimation for SINS/GNSS/ADS integration. The proposed constrained UPF uses the wind speed model to constrain the UPF filtering process to effectively resist the influence of wind field on the navigation solution. Simulations and comparison analysis demonstrate that the proposed approach can achieve optimal state estimation for SINS/GNSS/ADS integrated airship navigation in the presence of wind field disturbance.

A Strap-Down Inertial Navigation/Spectrum Red-Shift/Star Sensor (SINS/SRS/SS) Autonomous Integrated System for Spacecraft Navigation.

This paper presents a new Strap-down Inertial Navigation System/Spectrum Red-Shift/Star Sensor (SINS/SRS/SS) system integration methodology to improve the autonomy and reliability of spacecraft navigation using the spectrum red-shift information from natural celestial bodies such as the Sun, Jupiter and the Earth. The system models for SINS/SRS/SS integration are established. The information fusion of SINS/SRS/SS integration is designed as the structure of the federated Kalman filter to fuse the local estimations of SINS/SRS and SINS/SS integrated subsystems to generate the global state estimation for spacecraft navigation. A new robust adaptive unscented particle filter is also developed to obtain the local state estimations of SINS/SRS and SINS/SS integrated subsystems in a parallel manner. The simulation results demonstrate that the proposed methodology for SINS/SRS/SS integration can effectively calculate navigation solutions, leading to strong autonomy and high reliability for spacecraft navigation.

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.

Random Weighting, Strong Tracking, and Unscented Kalman Filter for Soft Tissue Characterization.

This paper presents a new nonlinear filtering method based on the Hunt-Crossley model for online nonlinear soft tissue characterization. This method overcomes the problem of performance degradation in the unscented Kalman filter due to contact model error. It adopts the concept of Mahalanobis distance to identify contact model error, and further incorporates a scaling factor in predicted state covariance to compensate identified model error. This scaling factor is determined according to the principle of innovation orthogonality to avoid the cumbersome computation of Jacobian matrix, where the random weighting concept is adopted to improve the estimation accuracy of innovation covariance. A master-slave robotic indentation system is developed to validate the performance of the proposed method. Simulation and experimental results as well as comparison analyses demonstrate that the efficacy of the proposed method for online characterization of soft tissue parameters in the presence of contact model error.

Adaptive Square-Root Unscented Particle Filtering Algorithm for Dynamic Navigation.

This paper presents a new adaptive square-root unscented particle filtering algorithm by combining the adaptive filtering and square-root filtering into the unscented particle filter to inhibit the disturbance of kinematic model noise and the instability of filtering data in the process of nonlinear filtering. To prevent particles from degeneracy, the proposed algorithm adaptively adjusts the adaptive factor, which is constructed from predicted residuals, to refrain from the disturbance of abnormal observation and the kinematic model noise. Cholesky factorization is also applied to suppress the negative definiteness of the covariance matrices of the predicted state vector and observation vector. Experiments and comparison analysis were conducted to comprehensively evaluate the performance of the proposed algorithm. The results demonstrate that the proposed algorithm exhibits a strong overall performance for integrated navigation systems.

Maximum likelihood-based extended Kalman filter for soft tissue modelling.

Realistic modelling of human soft tissue is very important in medical applications. This paper proposes a novel method by dynamically incorporating soft tissue characterisation in the process of soft tissue modelling to increase the modelling fidelity. This method defines nonlinear tissue deformation with unknown mechanical properties as a problem of nonlinear filtering identification to dynamically identify mechanical properties and further estimate nonlinear deformation behaviour of soft tissue. It combines maximum likelihood theory, nonlinear filtering and nonlinear finite element method (NFEM) for modelling of nonlinear tissue deformation behaviour based on dynamic identification of homogeneous tissue properties. On the basis of hyperelasticity, a nonlinear state-space equation is established by discretizing tissue deformation through NFEM for dynamic filtering. A maximum likelihood algorithm is also established to dynamically identify tissue mechanical properties during the deformation process. Upon above, a maximum likelihood-based extended Kalman filter is further developed for dynamically estimating tissue nonlinear deformation based on dynamic identification of tissue mechanical properties. Simulation and experimental analyses reveal that the proposed method not only overcomes the NFEM limitation of expensive computations, but also absorbs the NFEM merit of high accuracy for modelling of homogeneous tissue deformation. Further, the proposed method also effectively identifies tissue mechanical properties during the deformation modelling process.

Extended Kalman filter based on stochastic epidemiological model for COVID-19 modelling.

This paper presents a new stochastic-based method for modelling and analysis of COVID-19 spread. A new deterministic Susceptible, Exposed, Infectious, Recovered (Re-infected) and Deceased-based Social Distancing model, named SEIR(R)D-SD, is proposed by introducing the re-infection rate and social distancing factor into the traditional SEIRD (Susceptible, Exposed, Infectious, Recovered and Deceased) model to account for the effects of re-infection and social distancing on COVID-19 spread. The deterministic SEIRD(R)D-SD model is further converted into the stochastic form to account for uncertainties involved in COVID-19 spread. Based on this, an extended Kalman filter (EKF) is developed based on the stochastic SEIR(R)D-SD model to simultaneously estimate both model parameters and transmission state of COVID-19 spread. Simulation results and comparison analyses demonstrate that the proposed method can effectively account for the re-infection and social distancing as well as uncertain effects on COVID-19 spread, leading to improved accuracy for prediction of COVID-19 spread.

Extended Kalman filter for online soft tissue characterization based on Hunt-Crossley contact model.

Real-time soft tissue characterization is significant to robotic assisted minimally invasive surgery for achieving precise haptic control of robotic surgical tasks and providing realistic force feedback to the operator. This paper presents a nonlinear methodology for online soft tissue characterization. An extended Kalman filter (EKF) is developed based on dynamic linearization of the nonlinear H-C contact model in terms of system state for online characterization of soft tissue parameters. To handle the resultant linearization modelling error, an innovation orthogonal EKF is further developed by incorporating an adaptive factor in the EKF filtering to adaptively adjust the innovation covariance according to the principle of innovation orthogonality. Simulation and experimental results as well as comparison analysis demonstrate that the proposed methodology can effectively characterize soft tissue parameters, leading to dramatically improved accuracy comparing to recursive least square estimation. Further, the proposed methodology also requires a smaller computational load and can achieve the real-time performance for soft tissue characterization.

Finite-element kalman filter with state constraint for dynamic soft tissue modelling.

This research work proposes a novel method for realistic and real-time modelling of deformable biological tissues by the combination of the traditional finite element method (FEM) with constrained Kalman filtering. This methodology transforms the problem of deformation modelling into a problem of constrained filtering to estimate physical tissue deformation online. It discretises the deformation of biological tissues in 3D space according to linear elasticity using FEM. On the basis of this, a constrained Kalman filter is derived to dynamically compute mechanical deformation of biological tissues by minimizing the error between estimated reaction forces and applied mechanical load. The proposed method solves the disadvantage of costly computation in FEM while inheriting the superiority of physical fidelity.

Extended Kalman Filter Nonlinear Finite Element Method for Nonlinear Soft Tissue Deformation.

BACKGROUND AND OBJECTIVE: Soft tissue modelling is crucial to surgery simulation. This paper introduces an innovative approach to realistic simulation of nonlinear deformation behaviours of biological soft tissues in real time. METHODS: This approach combines the traditional nonlinear finite-element method (NFEM) and nonlinear Kalman filtering to address both physical fidelity and real-time performance for soft tissue modelling. It defines tissue mechanical deformation as a nonlinear filtering process for dynamic estimation of nonlinear deformation behaviours of biological tissues. Tissue mechanical deformation is discretized in space using NFEM in accordance with nonlinear elastic theory and in time using the central difference scheme to establish the nonlinear state-space models for dynamic filtering. RESULTS: An extended Kalman filter is established to dynamically estimate nonlinear mechanical deformation of biological tissues. Interactive deformation of biological soft tissues with haptic feedback is accomplished as well for surgery simulation. CONCLUSIONS: The proposed approach conquers the NFEM limitation of step computation but without trading off the modelling accuracy. It not only has a similar level of accuracy as NFEM, but also meets the real-time requirement for soft tissue modelling.

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.

Modeling of soft tissue thermal damage based on GPU acceleration.

Hyperthermia treatments require precise control of thermal energy to form the coagulation zones which sufficiently cover the tumor without affecting surrounding healthy tissues. This has led modeling of soft tissue thermal damage to become important in hyperthermia treatments to completely eradicate tumors without inducing tissue damage to surrounding healthy tissues. This paper presents a methodology based on GPU acceleration for modeling and analysis of bio-heat conduction and associated thermal-induced tissue damage for prediction of soft tissue damage in thermal ablation, which is a typical hyperthermia therapy. The proposed methodology combines the Arrhenius Burn integration with Pennes' bio-heat transfer for prediction of temperature field and thermal damage in soft tissues. The problem domain is spatially discretized on 3-D linear tetrahedral meshes by the Galerkin finite element method and temporally discretized by the explicit forward finite difference method. To address the expensive computation load involved in the finite element method, GPU acceleration is implemented using the High-Level Shader Language and achieved via a sequential execution of compute shaders in the GPU rendering pipeline. Simulations on a cube-shape specimen and comparison analysis with standalone CPU execution were conducted, demonstrating the proposed GPU-accelerated finite element method can effectively predict the temperature distribution and associated thermal damage in real time. Results show that the peak temperature is achieved at the heat source point and the variation of temperature is mainly dominated in its direct neighbourhood. It is also found that by the continuous application of point-source heat energy, the tissue at the heat source point is quickly necrotized in a matter of seconds, while the entire neighbouring tissues are fully necrotized in several minutes. Further, the proposed GPU acceleration significantly improves the computational performance for soft tissue thermal damage prediction, leading to a maximum reduction of 55.3 times in computation time comparing to standalone CPU execution.

Deformable Models for Surgical Simulation: A Survey.

This paper presents a survey of the state-of-the-art deformable models studied in the literature, with regard to soft tissue deformable modeling for interactive surgical simulation. It first introduces the challenges of surgical simulation, followed by discussions and analyses on the deformable models, which are classified into three categories: the heuristic modeling methodology, continuum-mechanical methodology, and other methodologies. It also examines linear and nonlinear deformable modeling, model internal forces, and numerical time integrations, together with modeling of soft tissue anisotropy, viscoelasticity, and compressibility. Finally, various issues in the existing deformable models are discussed to outline the remaining challenges of deformable models in surgical simulation.

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.

Soft tissue deformation estimation by spatio-temporal Kalman filter finite element method.

BACKGROUND: Soft tissue modeling plays an important role in the development of surgical training simulators as well as in robot-assisted minimally invasive surgeries. It has been known that while the traditional Finite Element Method (FEM) promises the accurate modeling of soft tissue deformation, it still suffers from a slow computational process. OBJECTIVE: This paper presents a Kalman filter finite element method to model soft tissue deformation in real time without sacrificing the traditional FEM accuracy. METHODS: The proposed method employs the FEM equilibrium equation and formulates it as a filtering process to estimate soft tissue behavior using real-time measurement data. The model is temporally discretized using the Newmark method and further formulated as the system state equation. RESULTS: Simulation results demonstrate that the computational time of KF-FEM is approximately 10 times shorter than the traditional FEM and it is still as accurate as the traditional FEM. The normalized root-mean-square error of the proposed KF-FEM in reference to the traditional FEM is computed as 0.0116. CONCLUSIONS: It is concluded that the proposed method significantly improves the computational performance of the traditional FEM without sacrificing FEM accuracy. The proposed method also filters noises involved in system state and measurement data.

Master-slave robotic system for needle indentation and insertion.

Bilateral control of a master-slave robotic system is a challenging issue in robotic-assisted minimally invasive surgery. It requires the knowledge on contact interaction between a surgical (slave) robot and soft tissues. This paper presents a master-slave robotic system for needle indentation and insertion. This master-slave robotic system is able to characterize the contact interaction between the robotic needle and soft tissues. A bilateral controller is implemented using a linear motor for robotic needle indentation and insertion. A new nonlinear state observer is developed to online monitor the contact interaction with soft tissues. Experimental results demonstrate the efficacy of the proposed master-slave robotic system for robotic needle indentation and needle insertion.

Non-Fourier based thermal-mechanical tissue damage prediction for thermal ablation.

Prediction of tissue damage under thermal loads plays important role for thermal ablation planning. A new methodology is presented in this paper by combing non-Fourier bio-heat transfer, constitutive elastic mechanics as well as non-rigid motion of dynamics to predict and analyze thermal distribution, thermal-induced mechanical deformation and thermal-mechanical damage of soft tissues under thermal loads. Simulations and comparison analysis demonstrate that the proposed methodology based on the non-Fourier bio-heat transfer can account for the thermal-induced mechanical behaviors of soft tissues and predict tissue thermal damage more accurately than classical Fourier bio-heat transfer based model.

ChainMail based neural dynamics modeling of soft tissue deformation for surgical simulation.

BACKGROUND: Realistic and real-time modeling and simulation of soft tissue deformation is a fundamental research issue in the field of surgical simulation. OBJECTIVE: 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. METHOD: 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. RESULTS: Experiments demonstrate that the proposed neural network approach is capable of modeling the soft tissues' nonlinear deformation and typical mechanical behaviors. CONCLUSIONS: 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.

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.