OGI

SCHOOL OF SCIENCE &

SPECKLE TRACKING IN 3D ECHOCARDIOGRAPHY WITH MOTION COHERENCE. Xubo Song, Andriy Myronenko and David J. Sahn

ENGINEERING

Department of Computer Science & Electrical Engineering, OGI, OHSU Cardiac Fluid Dynamics and Imaging Laboratory, OHSU Portland, OR, USA

INTRODUCTION

Illustration of the tracked speckles and their velocities for a complete scan.

p(B|A, V) = Tracking of speckles in echocardiography enables the study of myocardium deformation, and thus can provide insights about heart

scatterers in tissue and blood. The speckles follow the motion of the myocardium and undergo mild deformation when the temporal sam-

a challenging problem due to relatively low spatial and temporal resolution of 3D echocardiography. To ensure accurate and robust tracking, high level spatial and temporal constraints need to be incorporated. In this paper, we introduce a novel method for speckle tracking in 3D echocardiography. Instead of tracking each speckle independently and rely purely on speckle intensities, we enforce a motion coherence constraint, in conjunction with a dynamic model for the speckles. This method is validated on in vivo porcine hearts, and is proved to be accurate and robust.

2

METHOD

n=1 k=1

bkn = skn · nk(1) n ;

k k p(bn|an, vn)

(2)

akn = skn · nk(2) n

(3)

where elements skn denotes noiseless value of k th voxel intensity in nth k(1) k(2) speckle patch, and nn and nn are two independent noise elements πn −πn2 with the Rayleigh density function p(n) = 2 exp 4 , n > 0, k k p(bn|an, vn)

of the current methods are based on 2D speckle tracking, which sufin 3D overcomes such limitation. However, 3D speckle tracking is

N Y K Y

We use multiplicative Rayleigh noise model [1]:

pling rate is adequately high, which makes tracking possible. Most fers from errors due to through-plane decorrelation. Speckle tracking

p(bn|an, vn) =

n=1

structure and function. Speckles are intensity patterns formed by the interference of the backscattered echoes produced by ultrasonic

N Y

=

k k 2 2(bn/an) ((bkn/akn)2 + 1)2

(4)

Prior to regularize the motion coherence: We formulate coherence regularization of the velocity field v of speckles motion [2]: p(V|A) = exp

−λ

|˜ v (s)|2 ds ˜ R3 G(s)

R

min E(W)

p(B|A, V)p(V|A) p(V|B, A) = ∝ p(B|A, V)p(V|A) p(B|A)

(1)

T

• image It, speckle intensities AN ×K = [a1, . . . , aN ] , speckle centers XN ×3 = [x1, . . . , xN ]T , where N - total number of speckle patches, K - total number of voxels in a patch. T

• image It+1, speckle intensities BN ×K = [b1, . . . , bN ] , speckle centers YN ×3 = [y1, . . . , yN ]T • The collective velocity vector of all speckle patches V N ×3 = [v1, . . . , vn]T , (Y = X + V).

volume 5

volume 6

volume 7

volume 8

volume 9

volume 10

110

105 80

100

(5)



100

T

W GW

straint, characterized by the dynamics of the heart motion. We use a random walk on velocity model and a linear Kalman filter to update the state.

EXPERIMENTAL RESULTS

We show the performance of 3D speckle tracking on a set of 3D echocardiography sequences from open chest porcine hearts. One of the hearts has severe ischemia. The scans are acquired using Philips Sono 7500 with EKG gating. Ten different scans (3D sequences) are taken. Tracking mode Error (voxels) with motion coherence 0.3224 ± 0.1597 without motion coherence 2.4508 ± 2.2100

95 110

90 X(1)

120 130 X(1)

71 70 69

68

66

64

62

4

60

116 58

114

140 56

112

Y(2)

Y(2)

Tissue region normal ischemic



∂E(W) = · k 2 G (n, ·) + λGW k k 2 ∂W (an) + (bn) n=1 k=1 bn

3

volume 4

90

Dynamic model: Speckle motion is also subject to temporal con-

Adopting a Bayesian formulation, we pose the problem of speckle motion estimation between two images It and It+1 as finding the velocity vector V that maximizes the posterior probability:

volume 3

regions. The motion from the ischemic heart tissue is very limited.

The Gaussian bandwidth parameter σ controls the locality of the motion coherence constraint. Optimization procedure using steepest descent method: k k 2 k 2 = (−2 ln bn + 2 ln[(an) + (bn) ]) + λ tr n=1 k=1 K ∇bk (bk )2 − (ak )2 N X X n n n T

volume 2

3D speckle trajectories from normal (left) and ischemic (right) heart

PN the optimal velocity field v is of the form v(z) = n=1 wnG(z − xn ), 2 1 xi−xj −2 σ . thus V = GW. The matrix GN ×N has elements gij = e

K N X X

volume 1

Z(3)

1

Likelihood function:

110 70.5 70

108

Avarage motion range (voxels) 14.3106 ± 2.4085 3.2370 ± 0.9323

CONCLUSION

We present a method for 3D ultrasound speckle tracking, which enforces motion coherence by regularizing the high frequency content of the velocity field. The motion coherence constrains the nearby speckles to move coherently [2]. We also use a dynamic model to assure the temporal smoothness of the speckle trajectory, and a similarity function based on a multiplicative Rayleigh noise model assumption [1]. We demonstrate the performance of the method on 10 different 3D echocardiography scans from open chest porcine hearts. The method shows accurate and robust performance.

REFERENCES [1] B. Cohen, I. Dinstein: New maximum likelihood motion estimation schemes for noisy ultrasound images. Pattern Recognition, 35:455-463, 2002. ´ Carreira-Perpi˜na´n: Non-rigid point set registra[2] A. Myronenko, X. Song, M.A. tion: Coherent Point Drift, NIPS’19, pages 1009-1016, 2007.