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

Elastic parameter identification of three-dimensional soft tissue based on deep neural network

In the field of virtual surgery and deformation simulation, the identification of elastic parameters of human soft tissues is a critical technology that directly affects the accuracy of deformation simulation. Current research on soft tissue deformation simulation predominantly assumes that the elasticity of tissues is fixed and already known, leading to the difficulty in populating with the elasticity measured or identified from specific tissues of real patients. Existing elasticity modeling efforts struggle to be implemented on irregularly structured soft tissues, failing to adapt to clinical surgical practices. Therefore, this paper proposes a new method for identifying human soft tissue elastic parameters based on the finite element method and the deep neural network, UNet. This method requires only the full-field displacement data of soft tissues under external loads to predict their elastic distribution. The performance and validity of the algorithm are assessed using test data and clinical data from rhinoplasty surgeries. Experiments demonstrate that the method proposed in this paper can achieve an accuracy of over 99% in predicting elastic parameters. Clinical data validation shows that the predicted elastic distribution can reduce the error in finite element deformation simulations by more than 80% at the maximum compared to the error with traditional uniform elastic parameters, effectively enhancing the computational accuracy in virtual surgery simulations and soft tissue deformation modeling.

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.

Real-time non-uniform surface refinement model for lung adenocarcinoma surgery

Soft tissue models play a crucial role in virtual surgery. However, most existing methods use uniform meshes and overall refinement to construct inhomogeneous soft tissues for virtual lungs. This leads to a complex computation and poor model realism. Therefore, a real-time non-uniform surface refinement model (RNSM) for lung adenocarcinoma surgery is proposed in this paper. First, to better describe the inhomogeneous soft tissues, the tetrahedra are subdivided to different degrees depending on their densities, which reduce the model's complexity while ensuring accuracy. Second, to improve the model accuracy, the model surface is subdivided using the Loop subdivision method. Finally, an optimal algorithm based on deformation radius is designed to enhance the deformation in real-time, in which a linear attenuation method of physical quantities is used to simulate the deformation of the weak deformation regions directly, and the finite element method (FEM) is used for the strong deformation regions. The experimental results show that the model is more accurate and faster than the existing soft tissue models for lung adenocarcinoma surgery simulation.

A high-fidelity virtual liver model incorporating biological characteristics

Flexible tissue modeling plays an important role in the field of telemedicine. It is related to whether the soft tissue deformation process can be accurately, real-time and vividly simulated during surgery. However, most existing models lack the unique biological characteristics. To solve this problem, we proposed a high-fidelity virtual liver model incorporating biological characteristics, such as the viscoelastic, anisotropic and nonlinear biological characteristics. Besides, to the best of our knowledge, our study is the first to introduce the viscoplasticity of biological tissues to improve the fidelity of the liver model. This mothod was proposed to describe the viscoplastic characteristics of the diseased liver resection process, when the liver is in a state of excessive deformation and loss of elasticity, however, there are few works focusing on this problem. The 3DMax2020 and OpenGL4.6 were used to build a liver surgery simulation platform, and the PHANTOM OMNI manual controller was used to sense the feedback force during the operation. The proposed model was verified from three aspects of accuracy, fidelity and real-time performance. The experimental results show that the proposed virtual liver model can enhance visual perception ability, improve deformation accuracy and fidelity.

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.

A deformation model of pulsating brain tissue for neurosurgery simulation

BACKGROUND AND OBJECTIVES

For neurological simulation, an accurate deformation model of brain tissue is of key importance for faithful visual feedback. Existing models, however, do not take into account intracranial pulsation, which degrades significantly the realism of visual feedback.

METHODS

In this paper, a finite element model incorporating intracranial pressure is proposed for simulating brain tissue deformation with pulsation. An implicit Euler method is developed to calculate the deformation of brain tissue. A circuit model of intracranial pressure dynamics is established based on cerebral blood and cerebrospinal fluid circulations. The intracranial pulsation of pressure is introduced into the deformation model, so that the simulated brain tissues pulsate with a rhythm in accord with the changes of intracranial pressure, which resembles real-life neurosurgery.

RESULTS AND CONCLUSIONS

The experimental implementation of the proposed deformation model and the calculation method shows that it provides realistic simulation of brain tissue pulsation and real-time performance is achieved on an ordinary computer for certain procedures of neurosurgery.

HyperMSM: A new MSM variant for efficient simulation of dynamic soft-tissue deformations

BACKGROUND AND OBJECTIVE

Fast, accurate, and stable simulation of soft tissue deformation is a challenging task. Mass-Spring Model (MSM) is one of the popular methods used for this purpose for its simple implementation and potential to provide fast dynamic simulations. However, accurately simulating a non-linear material within the mass-spring framework is still challenging. The objective of the present study is to develop and evaluate a new efficient hyperelastic Mass-Spring Model formulation to simulate the Neo-Hookean deformable material, called HyperMSM.

METHODS

Our novel HyperMSM formulation is applicable for both tetrahedral and hexahedral mesh configurations and is compatible with the original projective dynamics solver. In particular, the proposed MSM variant includes springs with variable rest-lengths and a volume conservation constraint. Two applications (transtibial residual limb and the skeletal muscle) were conducted.

RESULTS

Compared to finite element simulations, obtained results show RMSE ranges of [2.8%-5.2%] and [0.46%-5.4%] for stress-strain and volumetric responses respectively for strains ranging from -50% to +100%. The displacement error range in our transtibial residual limb simulation is around [0.01mm-0.7 mm]. The RMSE range of relative nodal displacements for the skeletal psoas muscle model is [0.4%-1.7%].

CONCLUSIONS

Our novel HyperMSM formulation allows hyperelastic behavior of soft tissues to be described accurately and efficiently within the mass-spring framework. As perspectives, our formulation will be enhanced with electric behavior toward a multi-physical soft tissue mass-spring modeling framework. Then, the coupling with an augmented reality environment will be performed.

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.