| In clinical practice,the elasticity of human tissues can significantly indicate the degree of disease development.Therefore,palpation,as a basic and effective test that can sense elasticity,can enable doctors to have a preliminary knowledge of the pathological conditions of certain tissues,such as cancer,inflammation and fibrosis.However,palpation application is limited because of the restriction of human perception.Furthermore,common medical imaging technology,such as CT,MRI and US,can’t quantize elasticity,makes the development of a quantitative evaluation of elastic special imaging technology an important subject.Magnetic Resonance Elastograpy(MRE),as a new non-traumatic imaging technology,is a traditional mechanical and quantitative means of palpation.It is not limited by the location of diagnosis,so it is called image palpation.The basic idea of MRE is to provide information about tissue elasticity by measuring the propagation of mechanical waves in the organization.MRE technology is still in its initial stage,because the propagation of shear waves in heterogeneous media is quite complex,it is necessary to study and adopt effective image processing methods to achieve accurate imaging of tissue elasticity.At present,the model used to study MRE is basically based on the general linear elastography model,and certain conditional assumptions are made and improved,Isotropic incompressible stationary scalar model and Modified Stokes model,for example.In these models,a valuable inverse problem is how to reconstruct viscoelasiticity coefficient γ with the known data of the tissue density ρ,frequency ω and a component of the displacement vector of a shear wave u.Starting from the MRE scalar model,this paper firstly explain the background and causes of viscoelasticity coefficient,then uses the analytical solution solved by the piecewise constant coeffcient scalar model of circular domain to simulate the data of component of the displacement vector of a shear wave u,finally introduces some basic knowledge of two types of numerical inversion algorithms,and recovers parameters by numerical tests based on the simulation data.We use a commonly applied regularized iterative algorithm: Levenberg-Marquardt algorithm as the deterministic inversion algorithm.As for the statistical inversion algorithm,we begin with the common algorithm of the Markov chain Monte Carlo method based on the Metropolis–Hastings criterion,but the random walk in this algorithm makes the Markov chain converge to a fixed distribution with low efficiency because of little information of proposal distribution.Next,we discuss the slice sampling algorithm that do not require the proposed distribution.After testing,we find that these inversion algorithms can be used to achieve the inversion of the viscosity coefficient,except that Levenberg-Marquardt algorithm highly depends on inital guess and is easy to get struck in local minimal.While undeterministic inversion algorithm performs well to avoid it. |
