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.

In-vivo left atrial surface motion and strain measurement using novel mesh regularized image block matching method with 4D-CTA.

Atrial strain and motion play important roles in evaluation of stroke risks for patients with atrial fibrillation. While cardiac computed tomographic angiography (CTA) provides detailed left atrial morphology with unparallel image resolution, finding a suitable strain measurement method for CTA remains a considerable challenge. In this paper, for the first time, we introduced a mesh regularized image block matching method to estimate 3D left atrial (LA) surface strain with 4D CTA. A series of performance tests with ex-vivo phantom and in-vivo 4D-CTA data were deployed. In conclusion, our proposed method could provide reliable LA motion and strain data within limited time.

Quantifying irregular pulsation of intracranial aneurysms using 4D-CTA.

Recent studies have suggested that irregular pulsation of intracranial aneurysm during the cardiac cycle may be potentially associated with aneurysm rupture risk. However, there is a lack of quantification method for irregular pulsations. This study aims to quantify irregular pulsations by the displacement and strain distribution of the intracranial aneurysm surface during the cardiac cycle using four-dimensional CT angiographic image data. Four-dimensional CT angiography was performed in 8 patients. The image data of a cardiac cycle was divided into approximately 20 phases, and irregular pulsations were detected in four intracranial aneurysms by visual observation, and then the displacement and strain of the intracranial aneurysm was quantified using coherent point drift and finite element method. The displacement and strain were compared between aneurysms with irregular and normal pulsations in two different ways (total and stepwise). The stepwise first principal strain was significantly higher in aneurysms with irregular than normal pulsations (0.20±0.01 vs 0.16±0.02, p=0.033). It was found that the irregular pulsations in intracranial aneurysms usually occur during the consecutive ascending or descending phase of volume changes during the cardiac cycle. In addition, no statistically significant difference was found in the aneurysm volume changes over the cardiac cycle between the two groups. Our method can successfully quantify the displacement and strain changes in the intracranial aneurysm during the cardiac cycle, which may be proven to be a useful tool to quantify intracranial aneurysm deformability and aid in aneurysm rupture risk assessment.

Constrained estimation of intracranial aneurysm surface deformation using 4D-CTA.

BACKGROUND AND OBJECTIVE: Intracranial aneurysms are relatively common life-threatening diseases, and assessing aneurysm rupture risk and identifying the associated risk factors is essential. Parameters such as the Oscillatory Shear Index, Pressure Loss Coefficient, and Wall Shear Stress are reliable indicators of intracranial aneurysm development and rupture risk, but aneurysm surface irregular pulsation has also received attention in aneurysm rupture risk assessment. METHODS: The present paper proposed a new approach to estimate aneurysm surface deformation. This method transforms the estimation of aneurysm surface deformation into a constrained optimization problem, which minimizes the error between the displacement estimated by the model and the sparse data point displacements from the four-dimensional CT angiography (4D-CTA) imaging data. RESULTS: The effect of the number of sparse data points on the results has been discussed in both simulation and experimental results, and it shows that the proposed method can accurately estimate the surface deformation of intracranial aneurysms when using sufficient sparse data points. CONCLUSIONS: Due to a potential association between aneurysm rupture and surface irregular pulsation, the estimation of aneurysm surface deformation is needed. This paper proposed a method based on 4D-CTA imaging data, offering a novel solution for the estimation of intracranial aneurysm surface deformation.

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.

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.