preprint-to be submitted Imrpoving Strain Estimation in Breast Ultrasound Images Using Novel 1.5D Approach Simulation

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Imrpoving Strain Estimation in Breast Ultrasound

Images Using Novel 1.5D Approach (Simulation

and In-vivo results)

Irteza Enan Kabir

Electrical and Computer Engineering

University of Rochester

NY, United States

irtezaenan@gmail.com

Abstract—Ultrasound elastography is the method to image the

elasticity of compliant tissues due to a mechanical compression

applied to it. In elastography, the local strain of explored tissue

is estimated by analyzing the echo signals. This is accomplished

by a sonographer who uses ultrasound transducer to apply

pressure on the tissue area causing displacement of the tissue.

A set of data is obtained before and after the compression. This

stress along the axial direction not only causes deformation in

that direction but it can also cause lateral deformation in the

tissue. This relative deformation is later calculated using tracking

algorithms. Finally, estimating the elasticity, images are formed.

In this paper, we introduce a novel strain estimator. The proposed

1.5D strain estimator uses 1D windows for swift computations

and searches the lateral direction for taking the non-axial

movement into account. We have investigated the performance

of our estimator using simulated and in-vivo data of breast

tissue. The performance of our method is veriﬁed by comparing

with different methods up to 16% applied strain. The proposed

estimator has exhibited a superior performance compared to the

conventional methods. The image quality signiﬁcantly improves,

especially in the presence of higher applied strain, when the non-

axial motion is signiﬁcant.

Keywords—Correlation, Elastography, Elasticity Adaptive

stretching, Maximum-correlation, Stress, Strain, Breast, Pros-

trate, Ultrasound

I. INTRODUCTION

Ultrasound imaging has emerged with tremendous potential

as an imaging modality for the distinction of pathological

changes in tissue. Numerous applications have been explored

since it was ﬁrst proposed for cancer imaging more than two

decades ago. It is emerging due to the fact that breast cancer

is the second most fatal cancer among women worldwide [1].

An estimation indicates that, in USA, around 246,660 cases

of breast cancer was found in 2016, which accounts for 29%

of all the new cancer diagnoses [2]. Another estimation states

that 40,610 death cases were found in 2017 alone [3].

The needs of efﬁciently diagnosing cancer yields the ne-

cessity of elastography algorithms. Imaging tissue elasticity

parameters has rapidly drawn attention for its capability to

produce new noninvasive and in vivo information. The idea

of examining the mechanical properties of tissue is not new.

Clinicians have been using palpation for detecting lumps since

400 BC. But due to rapid improvement of medical imag-

ing technologies, high resolution imaging is now available,

which has triggered clinical trials in many areas. Currently

ultrasound imaging is widely utilized for prostrate, breast,

liver, thyroid applications, etc. [4], [5]. Existence prediction

and visualization of the behavior of tissue when subjected to

mechanical force is performed in the form of elastography [6].

Elastograms usually contain information not present in sono-

grams, which mainly gives information on acoustic scattering

properties. In elasticity imaging, echo signals are acquired

before and after the external pressure applied to the surface

by an operator using ultrasound transducer. Strain is calculated

from this pre and post compression echoes by using different

algorithms. The algorithms may calculate strain directly [7] or

it may be gradient based strain estimation [8]. Gradient based

estimators calculate strain from the gradient of displacement.

It relies on computing the displacement from the time delays

between gated pre and post-compression echo segments [9].

The location of the maximum peak of the cross-correlation

gives the estimation of time shift. Gradient based techniques

are vulnerable to noise. As a result of tissue compression,

decorrelation noise is present as a major source of estimation

error. Post-compression signals are not exact delayed versions

of the pre-compression signals. Thus, decorrelation noise

occurs which increases with higher applied strains. Noises

of high frequencies are generally ampliﬁed by the gradient

based estimators due to the fact the original signals are also

of high frequencies [10]. Direct strain estimators on the

other hand calculate strain directly from the echo segments of

pre and post-compression in time domain [11] or frequency

domain [12]. The techniques are based on stretching the post-

compression signal to correlate with the pre-compression or

shifting the pre-compression signal before the computation of

cross-correlation. Strain images with higher SNR compared to

gradient based approach can be found by these methods. As

no gradient operation is involved in the process, these methods

don’t suffer from noise ampliﬁcation problems associated with

gradient based methods.

arXiv:2210.06677v1 [eess.IV] 13 Oct 2022

Fig. 1: Lateral shift due pressure applied in the axial direction.

II. METHOD

The proposed 1.5D strain estimation method was applied

on the conventional strain estimator, which calculates gradient

of estimated displacements (no stretching) and on the adaptive

stretching estimator that uses the stretch factor as an estimator

of the strain. The method consists of two main steps:

a. Finding the lateral shift of the post-compression signal

segments and the strain map.

b. Finding the strain values to compute the strain map.

A. Finding the lateral shift of the post-compression signal

segments

Pre-compression echo signals are segmented into overlap-

ping 1D windows, in a single column. This segment from pre-

compression signal is correlated with several neighboring post-

compression data segments. For example, a segment from pre-

compression ith data stream is correlated with the correspond-

ing segments of (i-n) th to (i+n) th post-compression columns

or data streams (Value of n can be varied. We have chosen n=6

for our computation). For each post-compression segment, the

maximum correlation is calculated yielding (2n+1) correlation

values. We then calculate which among the (2n+1) values is

the highest. If the ith pre-compression data line segment has

the highest correlation with the (i+j) th post-compression data

segment, it means that the tissue deformation took place in

such a way that the corresponding post-compression segment

has shifted +j columns. This lateral movement found for one

segment is also used for the following segments to predict

lateral movement adaptively which makes the algorithm com-

putation efﬁcient

Fig. 2: Lateral motion estimation using correlation analysis of

a gated pre-compression data segment with several neighbor-

ing post-compression data segments.

While doing correlation analysis for ﬁnding lateral move-

ment, a slightly different approach is exercised. For the

correlation between a pre and a post window, the windows

are further divided into sub windows. Sub-windows from pre

are correlated with corresponding sub windows of post, each

time providing a maximum correlation value. When all the sub

window analysis is complete for a pair of windows, the median

value among the maximums provided by the small segments

is taken. This helps to avoid getting a false correlation peak.

Even if one sub window provides a false peak, the chance of

getting the true peak is high due to the approach.

B. Finding the strain values to compute the strain map

Fig. 3: Finding out appropriate stretch factor from Correlation

Coefﬁcient peaks.

In gradient based estimator, strain is calculated from the

difference of displacements between two consecutive signal

segments. In time domain, the lags between segment of pre

and corresponding segment from post give the displacement.

By sliding the pre and post-compression windows, the dis-

placement map is computed for each of the pre-compression

window we considered earlier. The strain is then calculated

from the gradient of these displacements. Signiﬁcant amount

of noise is associated with the gradient method. The selection

of window size and overlap between windows can affect the

amount of noise introduced [13]. Small window size and large

overlap introduces more noise in the strain estimation. But

overlap around 90% can give strain images with high axial

resolution [14]. Keeping this trade-off in mind, we have used

a 3mm data window size and a window shift of 0.5mm.

In adaptive stretching method, stretch factor itself gives

an estimation of strain. Post-compression signal segment is

stretched for matching best with the pre-compression coun-

terpart signal segment. For different stretching factor αi ,

similarity measure is calculated by means of cross-correlation

(CC). Suppose, in ﬁgure 3, for three different stretch factors,

we get three different peaks and “Peak 2” is maximum among

all three peaks. Then strain will be calculated from α2 as

follows,

Strain = 1- α2

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preprint-tobesubmittedImrpovingStrainEstimationinBreastUltrasoundImagesUsingNovel1.5DApproach(SimulationandIn-vivoresults)IrtezaEnanKabirElectricalandComputerEngineeringUniversityofRochesterNY,UnitedStatesirtezaenan@gmail.comAbstractUltrasoundelastographyisthemethodtoimagetheelasticityofcompliantti...

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