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¿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-ß 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

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

Coverage Estimation in Floorplan Visual Sensor Networks

The issue of Coverage in visual sensor networks (VSNs) has attracted considerable attention due to sensors unique directional sensing characteristic. It answers the question that how well the target field is monitored by a network of sensors with video/image capturing capability. In floorplan scenario the network is to monitor a plane parallel to the sensors' deployment plane. Coverage probability estimation based on both the sensors and the network related parameters is a fundamental issue in this field. For a large scale application in which the sensors' deployment is done by dropping sensors from an airplane, random sensors' placement and orientation according to their respective distribution is a practical assumption. Although some studies exist on the coverage problem of floorplan VSNs, none of them has derived a closed form solution for the coverage estimation, which is the main contribution of this paper. The Simulation results validated the proposed mathematical solution

The dichotomous Markov process with nonparametric test application; a decision support method in long-term river behavioural analysis: The Zayandeh Rud River; a case study from central Iran

We use the Dichotomous Markov Noise (DMN) model with constant transition rates to describe the dynamics of fluctuations in the water level as a stochastic process, which is imposed on river discharge changes. By applying this model, two different regimes are determined for the long-term behaviour of the river. Based on these regimes, we define two nonparametric classes of the overall increasing/decreasing nature of the water level in the long-term behaviour, which are separated by an exponential steady state regime. In this paper, we develop a nonparametric testing procedure to test exponentially (steady state regime) against an alternative overall decreasing level distribution. The proposed test predicts the long-term regime behaviour of the river. The mathematical tools introduced to handle the problem should be of general use and the testing procedure can be considered as a new mathematical tool in the study of water level dynamics. Under conditions of data austerity and as a case of study, we examine the stochastic characteristics of the Zayandeh Rud1 River (Isfahan, Iran) water level.Hydraulic EngineeringCivil Engineering and Geoscience