The spring model treats human soft tissue as a series of discrete discrete mass points that are interconnected by a spring damper. The particle spring model is generally divided into a face model and a body model. The mesh density of the surface model can be divided according to the requirements of the simulation. The calculation efficiency is high and can meet the real-time performance of the simulation. However, the surface model can only reflect the deformation characteristics of the surface of the tissue, and can not describe the internal structure of the three-dimensional entity. To ensure real-time performance at the expense.
The volume model is a model of a solid tissue with a certain volume, which can represent both the surface and the internal structure. Common topologies are tetrahedral, hexahedral, and superhexahedral. The hexahedral model has a simple structure and uniform distribution of particles. It is more suitable for models with uniform shape and uniform quality, but the calculation accuracy is low and the stability is poor. The nature of the hyperhexahedral model is still under investigation. The tetrahedral model is basically consistent with the geometric model of human tissue. Under the same volume, the number of springs is increased by about 50% compared with the hexahedral model. It has good stability and can better describe the physical properties of the tissue. Therefore, this paper uses a particle-spring body model based on a tetrahedral topology to construct a virtual liver.
Numerical method for error comparison of different numerical methods, local error explicit Euler method O(h2) implicit Euler method O(h3) Runge-Kutta method O(h4) explicit Euler method is small, but generally Only the first-order convergence, the precision is not high, in order to achieve realistic simulation effects, the time step needs to be set small, which leads to the extension of the whole deformation process, and it is not suitable for the particle-spring model due to the presence of the retreating shock wave. The implicit Euler method has high precision and good stability, but the calculation amount is large. The Runge-Kutta method also has high precision and stability. However, in the one-step calculation, the value of the quadratic function needs to be calculated, so the calculation amount is large and the real-time performance is poor. Considering the real-time and precision of deformation, an improved Euler method is proposed to solve the velocity and displacement vector, as shown in the formula. The explicit Euler method is used to iteratively solve vi, and the calculation result of vi is directly used, and xi is solved by the implicit Euler method. Compared with the simple implicit Euler method, the calculation amount is reduced, and the accuracy and stability of the implicit Euler method are guaranteed.
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