title: A regularization-free elasticity reconstruction method for ultrasound elastography with freehand scan.
abstract: BACKGROUND
  In ultrasound elastography, reconstruction of tissue elasticity (e.g., Young's modulus) requires regularization and known information of forces and/or displacements on tissue boundaries. In practice, it is challenging to choose an appropriate regularization parameter; and the boundary conditions are difficult to obtain in vivo. The purpose of this study is to develop a more applicable algorithm that does not need any regularization or boundary force/displacement information.
  
  
  METHODS
  The proposed method adopts the bicubic B-spline as the tissue motion model to estimate the displacement fields. Then the estimated displacements are input to the finite element inversion scheme to reconstruct the Young's modulus of each element. In the inversion, a modulus boundary condition is used instead of force/displacement boundary conditions. Simulation and experiments on tissue-mimicking phantoms are carried out to test the proposed method.
  
  
  RESULTS
  The simulation results demonstrate that Young's modulus reconstruction of the proposed method has a relative error of -3.43 ± 0.43% and root-squared-mean error of 16.94 ± 0.25%. The phantom experimental results show that the target hardening artifacts in the strain images are significantly reduced in the Young's modulus images. In both simulation and phantom studies, the size and position of inclusions can be accurately depicted in the modulus images.
  
  
  CONCLUSIONS
  The proposed method can reconstruct tissue Young's modulus distribution with a high accuracy. It can reduce the artifacts shown in the strain image and correctly delineate the locations and sizes of inclusions. Unlike most modulus reconstruction methods, it does not need any regularization during the inversion procedure. Furthermore, it does not need to measure the boundary conditions of displacement or force. Thus this method can be used with a freehand scan, which facilitates its usage in the clinic.
authors.forename: Xiaochang
authors.initials: X
authors.lastname: Pan
authors.forename: Ke
authors.initials: K
authors.lastname: Liu
authors.forename: Jing
authors.initials: J
authors.lastname: Bai
authors.affiliation: Department of Biomedical Engineering, School of Medicine, Tsinghua University, Beijing 100084, China. luo_jianwen@tsinghua.edu.cn.
authors.forename: Jianwen
authors.initials: J
authors.lastname: Luo
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D055119:Elastic Modulus / Q000502:physiology*; D054459:Elasticity Imaging Techniques / Q000379:methods*; D020342:Finite Element Analysis; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008962:Models, Theoretical; D019047:Phantoms, Imaging; D013314:Stress, Mechanical; D014465:Ultrasonics / Q000379:methods*