Real-time deformation of human soft tissues: A radial basis meshless 3D model based on Marquardt's algorithm. (January 2018) - Zhou, Jianyong; Luo, Zu; Li, Chunquan; Deng, Mi
Highlights: The displacements of nodes, used to present the deformation of soft tissue, are calculated by meshless method spending too much time. A geometric model with the modulus of human liver is set up. Marquardt's algorithm is used to fit the mathematical relation between the displacements (that are calculated by meshless method in advance) and exterior force for obtaining the fast calculation formulas. In the simulation of deformation, this improved method takes 0.1509 s and the maximum deformation error is less than 0.5 mm, moreover, it can preserve the authenticity of the deformation model's physical properties. Abstract: Background: When the meshless method is used to establish the mathematical-mechanical model of human soft tissues, it is necessary to define the space occupied by human tissues as the problem domain and the boundary of the domain as the surface of those tissues. Nodes should be distributed in both the problem domain and on the boundaries. Under external force, the displacement of the node is computed by the meshless method to represent the deformation of biological soft tissues. However, computation by the meshless method consumes too much time, which will affect the simulation of real-time deformation of human tissues in virtual surgery. Methods: In this article, the Marquardt's Algorithm is proposed to fit the nodal displacement at the problem domain's boundary and obtain the relationship between surface deformation and force. When different external forces are applied, the deformation of soft tissues can be quickly obtained based on this relationship. Results and conclusions: The analysis and discussion show that the improved model equations with Marquardt's Algorithm not only can simulate the deformation in real-time but also preserve the authenticity of the deformation model's physical properties.