Motion Estimation and Visualization of Cardiac Ultrasound Imaging

Tian Cao, Chaowei Tan, Dong C. Liu

Introduction

The cardiac ultrasound imaging is an important application in medical ultrasound. In this application, cardiac structure and tissue motion estimated from the ultrasonic image sequence constitutes an important aid for quantification of the tissue properties such as elasticity and structure contractility, and the visualization technology could extract the information of motion dynamics and offer more direct information for the clinician to analyze the tissue motion of heart.

A Curve Minimum Mean of Absolute Difference (CMMAD) method is presented for motion estimation using adaptive curve regions as criteria, and it has better effect for speckle tracking in series of ultrasound images. And the Thin-Plate Spline (TPS) interpolation algorithm is introduced as an non-rigid method to recover the motion of heart structure and reconstruct the local motion field. Finally, applying the Unsteady Flow Line Integral Convolution (UFLIC) to the vector field for motion visualization.

Overview of the Methods

Adaptive Curve Region Based Motion Estimation

• Adaptive Comparison Region Size Decision

To decide the comparison region size using the following equation,

f_c is the constant coefficient from experiment. For a scanning depth of Z mm and N pixels in axial direction, the e_d is ,

where ΔT is proportional to the standard deviation of a Gaussian-enveloped pulse in the time domain and C₀ is the sound speed.

• Curve Region as Matching Criteria

To compute four points to define the curve region R₀ with the center point t^',

Then to transform the curve region R₀ into a regular S₀×S₀ block B₀ that is convenient for comparison.

• CMMAD Searching Strategy in Polar Coordinate

To position two regions and construct their corresponding blocks using the above way, and implement the searching algorithm in polar coordinate to obtain the motion vector.

Thin-Plate Spline for Non-rigid Interpolation

To interpolate the motion vectors of pixels among these sampling points, we introduce the TPS method. In TPS method, n one-to-one corresponding points sets q and p fulfill the equation q_i = u(p_i), i = 1, ..., n, where u is the transformation function that minimizes the

bending energy J^d_m(u). When d = 2 and m = 2, we could get the minimizing solution of J²₂ in the following,

where the parameters a_c0, a_c1, a_x0, a_x1, a_y0 and a_y1 are the linear affine transformation, and the parameters w_xi and w_yi are the weights of the non-linear elastic interpolation function U,

Using the above equations, we can get the interpolated point p’ = (u_x, u_y) from the original point p = (x, y), and the corresponding motion vector v = p’ － p.

Unsteady Flow Line Integral Convolution for Ultrasound Imaging

UFLIC is a new LIC method for visualizing time-varying vector fields. Starting from a white noise texture, the UFLIC algorithm successively advects the texture to create a sequence of flow images. This algorithm has two main components, the time-accurate value scattering scheme and the successive texture feed-forward strategy. The algorithm is implemented as the Fig. 1.

Experiment and Results

We have tested a series of successive cardiac ultrasound images using in vivo data. The standard test set contains 30 images. The vector fields generated from our algorithms is displayed in Fig.2 to 4 successively. The detected motion vectors are superimposed on the original images. The visualization of the corresponding vector fields using UFLIC is shown in Fig. 5 to 7 correspondingly.

Conclusion

• 1. Presenting an adaptive curve region matching algorithm for motion estimation. Each curve region is regularized to a rectangular block for matching.

  2. The CMMAD motion estimation method is suitable for cardiac ultrasound images acquired by a phase array probe.

  3. And the use of TPS nonlinear interpolation has obtained a precise vector field based on the sampling points.

  4. The visualization of UFLIC towards the time-varying vector fields could create highly coherent flow animation