Comparison of Ventricular Geometry for Two Real-Time 3D Ultrasound Machines with Three-dimensional Level Set

Elsa D. Angelini, Rio Otsuka, Shunishi Homma, Andrew F. Laine

The Heffner Biomedical Imaging LabDepartment of Biomedical Engineering, Columbia University, New York, NY, USA

Average error (1) = 0.86%, (2) = 1%.Gaussian kernel for (3) lead to the smallest error (0.03%).Anisotropic diffusion (3-4) reduces measurement errors for first-order interpolation kernels.

RESULTSRESULTS

Computation Times

Measurements of cylinder diameter were performed manually by a user on B-scan slices for different data processing: (1) Original data (scale=1); (2) Original data (scale=2); (3) Original data (scale=2 with smoothing);(4) Diffused data (thresholds=5, 10 iterations) (scale=1); (5) Diffused data (variable threshold, 10 iterations) (scale=1).

INTRODUCTIONINTRODUCTIONThree-dimensional ultrasound machines based on mat

rix phased-array transducers are gaining predominanc

e for real-time dynamic screening in cardiac and obstet

ric practice.

Comparison of the quantification of cardiac function fro

m two matrix-phased array 3D ultrasound machines:

RT3D machine from Volumetrics Medical Imaging.

Entire cardiac volume is acquired with an array of 64

64 elements and a downsampling factor of 4 between

receive/transmit modes.

Sonos 7500 machine from Philips Medical Systems.

Four cardiac sub-volumes and no downsampling.

DATADATART3D data were acquired by a RT3D Volumetri

cs© machine using acquisition parameters iden

tical to clinical settings.

Phantom object: Two cylinders (diameter = 10

mm) with different signal-to-noise ratios (SNR).

Our experiments focused on a SNR of 2dB.

In-vitro phantom: myocardium muscle sample

in a water tank.

Clinical data: Echocardiographic volume of a h

ealthy volunteer.

DISCUSSIODISCUSSIONNDownscaling with smoothing and anisotropic diffusion

can efficiently reduce speckle noise and sampling artifacts.

Anisotropic diffusion with variable gradient threshold significantly improves image quality.

Manual tracing on denoised RT3D data showed high spatial measurement accuracy for scales 1 and 2 on phantom data.

Anisotropic diffusion is less computational expensive than spatial Brushlet denoising and provided similar visual improvement of image quality.

Anisotropic diffusion lowers the order of the interpolation kernels for scan conversion enabling optimization of data processing for real-time denoising and visualization.

SEGMENTATIONSEGMENTATIONHomogeneity-based Implicit Deformable Model

Segmentation algorithm: Initially proposed by Chan and Vese [1], and derived from the Mumford-Shah functional [2]. The segmentation of a volume data I is performed via deformation of an initial curve C to minimize the following energy functional:

REFERENCREFERENCESES1. O. V. Ramm and S. W. Smith, "Real time volumetric ultrasound imaging

system." Journal of Digital Imaging, Vol. 3, No. 4, pp. 261-266, 1990.

2. Q. Duan, E. D. Angelini, T. Song and A. Laine, "Fast interpolation algorithms for real-time three-dimensional cardiac ultrasound", IEEE EMBS Annual International Conference, pp. 1192-1195, Cancun, Mexico, 2003.

3. Y. Yu and S. T. Acton, "Speckle reducing anisotropic diffusion." IEEE Transactions on Image Processing, Vol. 11, No. 11, pp. 1260-1270, 2002.

4. P. Perona and J. Malik, "Scale-space and edge detection using anisotropic diffusion." IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 12, No. 7, pp. 629-639, 1990.

5. J. Weickert, B. M. t. H. Romeny and M. A. Viergever, "Efficient and reliable schemes for nonlinear diffusion filtering." IEEE Transactions on Image Processing, Vol. 7, No. 3, pp. 398-410, 1998.

6. E. Angelini, A. Laine, S. Takuma, J. Holmes and S. Homma, "LV volume quantification via spatio-temporal analysis of real-time 3D echocardiography." IEEE Transactions on Medical Imaging, Vol. 20, No. 6, pp. 457-469, 2001.

CONCLUSICONCLUSIONONA fast 3D scan conversion algorithm combined with

smoothing and anti-aliasing was introduced for RT3D ultrasound.

A fast denoising method based on anisotropic diffusion with varying gradient threshold was described for RT3D ultrasound.

Quantitative assessment was performed, showing high spatial accuracy of RT3D ultrasound.

(a)

(b)

Cylindrical phantom object. (a) Anisotropic diffusion with a fixed gradient threshold. (b) Anisotropic diffusion with a variable gradient threshold.

(a)

(b)

(c) Scan conversion result of

Phantom (a) Scale =1 (b) Scale =2 (c) Scale=2 with smoothing.

(a)

(b)

(c) Endocardiographic data (a) Original data. (b) Anisotropic diffusion with a variable gradient threshold. (c) Brushlet threshold in tra

nsform space.

(a)

(b)

in-vitro myocardium tissue sample. (a) Original data. (b)

Data after anisotropic diffusion with a variable gradient

threshold.

RESULTSRESULTSMETHODOLOGYMETHODOLOGY2.2 Anisotropic Filtering

Original framework of Perona and Malik with the diffu

sion function proposed by Weickert.

The parameter λ serves as a gradient threshold. A lin

ear model is proposed for iterative adaptivity:

ACKNOWLEDGEMENTSACKNOWLEDGEMENTSThe authors would like to thank to Dr. Homma, Dr. Hirata and Dr. Otsuka from the Echocardiograph

y Laboratories at Columbia Presbyterian Hospital for providing the ultrasound data sets.

Data

Matrix size in

spherical coordinate

s

Scale of scan

conversion

Smoothing option for scan

conversion

Matrix size in Cartesian coordinates

Diffusion computati

on time for one

iteration(seconds)

Scan conversio

n computati

on time(seconds)

Phantom object

64x64x373 1 No 389x389x376 0.38 106

Cardiac tissue

64x64x258 1 No 274x274x261 0.25 37

Clinical exam

64x64x438 1 No 454x454x441 - 169

Clinical exam

64x64x438 2 No 228x228x221 - 21

Clinical exam

64x64x438 2 Yes 228x228x221 - 23

Clinical exam

64x64x438 1 No 454x454x441 0.51 169

Measurements of Object Dimensions of a

Cylinder

( ) ( ) ( )( )( )

220 1 0 0 0 1 0 1, ,

insideC outsideCE C c c L C A C I c d I c dm n l l= + + - W+ - Wò ò

Numerical implementation:

Implementation with a 3D level set framework.

implicit numerical scheme for unconditional

stability. Parameters controlled and optimized:

Smoothness: Yes/No

Scale: [original voxel size: (0.308 mm)3]

Filter width (1/2/3) (optimized in previous studies)

- c0 and c1 = average of the volume data I inside and outside of the curve C.

- L(C) = length of the curve.- A(C) = area of the curve.