# Three-Dimensional Modeling of Heart Soft Tissue Motion
## 2 Materials and Methods
### Viscoelastic Control Based on a Virtual Body Spring  
Considering that the spring mesh in the mass-spring model is only distributed on the surface of the model, the control ability of the mass-spring model to the model object is mostly concentrated on the surface of the model, which leads to the inflexibility of the mass-spring model in fitting the changes in the direction perpendicular to the surface. The reason for this is that the mass-spring model itself does not have variables that describe the characteristics in the vertical direction, this problem was significantly improved with the appearance of virtual body springs [26]. The method using virtual body springs is relatively simple, that is, the real-time position of the particle in the particle spring model and the corresponding initial position are connected by a virtual spring, and the relaxation length of the virtual spring is 0. The reason why it is called a virtual body spring is that the spring does not exist before the model changes, and it will only work after the model changes. During the process of model deformation, the force generated by the virtual body spring is dynamic. After the model loses the external force, all the particles can reach the stable state when they are at the initial position, that is, the model can finally recover to the initial state through the force generated by the virtual body spring. The main purpose of the virtual body spring method proposed by the original author is to give the model a sense of volume [26], and the model can automatically return to the original state after removing the external force, which can make the simulation of elastic deformation of the particle spring model more realistic. However, the virtual body spring enables the particle spring model to obtain the control ability in the vertical surface direction. Based on this, this study undertook further research and, inspired by the dynamic parameters mentioned above, some improvements were made to the virtual body spring to enhance the ability of the model to fit the biological characteristics in the vertical surface direction. The two previous optimizations are mainly used to improve the particle spring in response to the characteristics of soft tissue anisotropy and stress-strain nonlinearity. However, the spring mesh is coincident with the curved surface, and thus, it is difficult to show the viscoelasticity of biological tissue in the vertical direction, including creep, relaxation, and hysteresis [16]. To solve this problem, a method was proposed in this study. Based on the virtual body spring structure, the elastic coefficient in the virtual body spring is remapped to make the elastic force produced by the virtual body spring more consistent with the viscoelastic characteristics. The virtual body spring is still special in essence and the elastic force generated by it can be expressed as  
\[f_{v}=Kl+cv \tag{15}\]In this study, the remapping of the elastic coefficient \(K\) was used to make Formula (15) better fit the viscoelasticity of biological tissue. Since the function of the damper itself is to reflect the hysteresis characteristics of elastic objects in the deformation process, to reduce the complexity of remapping, this study aimed to use the damper to fit the hysteresis characteristics and fit the creep and relaxation characteristics of biological tissue through remapping. To fit the above characteristics, first, it was necessary to determine the relationship between the force and the creep relaxation reaction. Generally, the creep characteristic is mainly manifested in the process of biological tissue deformation, while the relaxation characteristic is mainly manifested in the process of biological tissue restitution [19]. In terms of creep characteristics, when biological tissue is deformed from the initial state, even if the initial force is relatively small, the tissue will appear obviously offset, but the effect of the force on the offset distance will rapidly decrease with the increase in the offset distance of the object.