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A Finite Element Model of Remote Palpation of Breast LesionsUsing Radiation Force: Factors Affecting Tissue Displacement
KATHRYN R. NIGHTINGALE,1 ROGER W. NIGHTINGALE,1 MARK L. PALMERI1
AND GREGG E. TRAHEY1, 2
1Duke University, Department of Biomedical Engineering2Duke University Medical Center, Department of Radiology
Durham, NC [email protected]
The early detection of breast cancer reduces patient mortality. The most common method of breastcancer detection is palpation. However, lesions that lie deep within the breast are difficult to palpatewhen they are small. Thus, a method of remote palpation, which may allow the detection of small le-sions lying deep within the breast, is currently under investigation. In this method, acoustic radiationforce is used to apply localized forces within tissue (to tissue volumes on the order of 2 mm3) and the re-sulting tissue displacements are mapped using ultrasonic correlation based methods. A volume of tissuethat is stiffer than the surrounding medium (i.e., a lesion) distributes the force throughout the tissue be-neath it, resulting in larger regions of displacement, and smaller maximum displacements. The resultingdisplacement maps may be used to image tissue stiffness.
A finite-element-model (FEM) of acoustic remote palpation is presented in this paper. Using thismodel, a parametric analysis of the affect of varying tissue and acoustic beam characteristics on radia-tion force induced tissue displacements is performed. The results are used to evaluate the potential ofacoustic remote palpation to provide useful diagnostic information in a clinical setting. The potential forusing a single diagnostic transducer to both generate radiation force and track the resulting displace-ments is investigated.
KEY WORDS: Breast imaging; elastography; nonlinear ultrasound effects; radiation force; remote pal-pation; ultrasound.
1. INTRODUCTION
The early detection of breast cancer has been shown to significantly improve patient sur-vival. Present methods of breast cancer detection include screening mammography and pal-pation, either by patient self-examination or clinical breast exam. Palpation relies on themanual detection of differences in tissue stiffness between breast lesions and normal breasttissue. The success of palpation is due to the fact that the elastic modulus (or Young’s modu-lus) of malignant tumors is often an order of magnitude greater than that of normal breast tis-sue,1, 2 i.e., cancerous lesions feel ‘harder’ or ‘lumpy’ as compared to normal breast tissue.
This difference in Young’s modulii is the basis for the investigation of imaging modalitiesthat provide information about the stiffness of tissue. Traditionally, these have fallen intotwo categories: (1) sonoelasticity, in which low-frequency shear wave propagation is im-aged using Doppler methods, from which the elastic modulus (Young’s modulus) of tissuecan be estimated;3-7 and (2) elastography, in which local variations in tissue strain are deter-mined by measuring local displacements that occur during global tissue compression.1, 8-10 Areview of these methods is provided by Gao et al.11
Recently, several authors have proposed the use of ultrasonic radiation force to remotelycharacterize tissue stiffness.12-16 Each of these methods propose the use of radiation force todisplace tissue in a remote location; however, they differ in the processing of the resulting in-
ULTRASONIC IMAGING 22, 35-54 (2000)
35 0161-7346/00 $18.00
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formation. The method under investigation herein is called remote palpation. In thismethod, acoustic radiation force is used to apply localized forces within tissue (to volumeson the order of 2 mm3), and the resulting tissue displacements are mapped using ultrasoniccorrelation-based methods. A volume of tissue that is stiffer than the surrounding medium(i.e., a lesion) distributes the force throughout the tissue beneath it, resulting in larger regionsof displacement and smaller maximum displacements. If successful, this method would al-low the detection of small lesions lying deep within the breast, which are difficult to detectwith existing methods.
The purpose of the work presented here is to investigate the potential for using acoustic ra-diation force to characterize localized variations in tissue stiffness. Finite element methods(FEM) are used for this investigation, which allow the performance of a parametric analysisof varying tissue and acoustic beam parameters. The parameters that are studied include:acoustic beam intensity, transducer design and f-number, tissue stiffness, lesion size, and le-sion stiffness. These results will be used to guide the design of future remote palpation ex-periments.
2. BACKGROUND
Acoustic radiation force is a phenomenon associated with the propagation of acousticwaves through a dissipative medium. It is caused by the energy density gradient that occursin the medium, arising either from absorption or reflection of the wave. This gradient resultsin the application of a force in the direction of wave propagation.17 In an absorbing medium,and under plane wave assumptions, this force can be represented by the following equa-tion:17-20
where F is acoustic radiation force [kg/(s2cm2)], or [dynes/(1000 cm3)], Wabsorbed [Watts/(100cm3)] is the power absorbed by the medium at a given point in space, c [m/s] is the speed ofsound in the medium, � [m-1] is the absorption coefficient of the medium and I [Watts/cm2] isthe temporal average intensity at a given point in space. Equation (1) provides a simple rela-tionship between the temporal average intensity of an acoustic beam, and the resulting radia-tion force (which is in the form of a body force, or force per unit volume). A directrelationship between F and frequency is implied by the dependence on � , which increaseswith frequency.
Equation (1) can be used to model radiation force fields associated with complex intensityfield geometries by computing or measuring the temporal average intensity at each point in athree-dimensional region of interest. The shape of an intensity field is dependent upon theassociated transducer focal configuration, which is often characterized by the transducerf-number:
where z is the acoustic focal length and D is the aperture width. Therefore, the transducerconfigurations under investigation herein are differentiated by f-number throughout this pa-per. In referring to varying f-number transducers, the notation F/n is used, where n is the
36 NIGHTINGALE ET AL
,2
c
I
c
WF absorbed ���
(1)
,D
znumberf �� (2)
number. For example, a transducer with an f-number of 2 is referred to as an F/2 configura-tion.
In order to determine the effect that a specific radiation force field will have on a given tis-sue type, one can solve the equations of motion under the appropriate initial conditions andboundary conditions. The motion resulting from similar force fields when applied to a fluidcontained within spherical boundaries has been successfully predicted by numerically solv-ing the Navier-Stokes equations.21 The work presented herein involves the investigation ofthe effect of these force fields on elastic media.
3. METHODS
The finite element model of remote palpation presented herein determines tissue displace-ments resulting from the application of radiation force generated by various diagnostic trans-ducer configurations. Model implementation is performed using a two step approach: firstthe spatially-distributed intensity field from a given transducer and set of transmit parame-ters is determined and the associated radiation force field is computed using Eq. (1). Second,finite element methods are used to solve for the resulting tissue displacement patterns.
In order to determine the acoustic intensity field distribution associated with various diag-nostic transducer configurations that might be used in remote palpation (i.e., linear andmultirow arrays with varying aperture widths), the temporal average intensity fields corre-sponding to these transducers were modeled using FIELD_II (http://www.it.dtu.dk/~jaj/field/),22 an acoustic field simulation software program. This program allows the accuratemodeling of intensity fields from arbitrarily shaped transducer arrays. Two transducers weremodeled: the Siemens 75L40 linear transducer (one row of elements, center frequency 7.2MHz, element height 5 mm, aperture width dependent upon the number of active elements;Siemens Medical Systems, Ultrasound Group, Issaquah, WA), and a two-dimensional 8 x 128element custom diagnostic transducer developed for our research scanner (8 rows of ele-ments, center frequency 7.2 MHz, element height 1.45 mm, aperture width determined bythe number of active elements in both dimensions; Tetrad Corp., Englewood CO). Through-out this paper, these will be referred to as the linear transducer and the 2D transducer, respec-tively. The simulated voltage used to excite each element was fixed; thus, for a givenelement size, when more elements were excited, more energy was transmitted. Both trans-ducer arrays have an acoustic lens in the elevation dimension. All of the simulations wereperformed under the assumption that the transducers were electronically focused at the loca-tion of the focal point of their lens (i.e., z was held constant in Eq. (2)). Thus, the linear trans-ducer had a fixed elevation f-number, and the lateral f-numbers were varied between F/1 andF/3 by varying the number of active elements in the array. The 2D transducer was modeledusing all of its elements (8 x 128), and thus had an F/2 elevation and F/1 lateral configuration.
The intensity fields for each transducer configuration (or f-number) were computed in theaxial/lateral plane of the transducer, normalized, and discretized into three contours of con-stant intensity (Fig. 1). Once these contours and the desired boundaries were determined,they were imported into a finite element mesh generation program (Hypermesh, Altair Com-puting Inc., Troy, MI), and superimposed on the mesh.
The same mesh was used for all simulations. Forces were applied to different mesh ele-ments depending upon the imported contours for each transducer configuration. Tissueproperties were applied to different elements depending upon the lesion size being modeled.The breast and the lesion were modeled as elastic solids and meshed with hexahedral ele-ments. Although the lesion and breast are two different parts with different material proper-
ACOUSTIC REMOTE PALPATION 37
ties, they were modeled as a continuum (i.e., there was no interface modeled between thelesion and the surrounding breast). The mesh was generated within the axial/lateral plane,and then rotated 90� around its central axis, in order to achieve a three-dimensional model(Fig. 2). The model was constrained on the surface of the distal quarter of the hemisphere(opposite the transducer location); thus, modeling a breast resting on a concave platform.Because the boundary conditions did not allow motion normal to the planar surfaces in figure2, symmetry assumptions hold, and solution of this mesh simulates motion in one quarter ofthe axisymmetric three-dimensional spherical model. There were 7,440 elements in themesh.
In order to determine the radiation force value to be applied within each intensity contour,the normalized contours were scaled to a peak value of 90 W/cm2 for the linear, F/1 trans-ducer configuration. Equation (1) was then used, along with the tissue properties below, toconvert the regions of constant intensity to regions of constant body force. The resultingmaximum body force was 4882 dynes/cm3.
The tissue properties (� , c, � 0, and E) were selected to model realistic in vivo values.2, 23 Theabsorption coefficient of breast tissue was 0.415 cm-1, or 3.6 dB cm-1 (recall that the centerfrequency was 7.2 MHz). The speed of sound was 1,530 m s-1, the density of tissue was 1,000kg m-3, and the Young’s modulus was 10 kPa. When lesions of varying stiffness were intro-duced, the Young’s modulii ranged from 1 to 400 kPa, which is within the potential range ofnormal and diseased breast tissue.1, 2, 24
The equations of motion were solved using LS-DYNA3D, an explicit three-dimensionalfinite element code for analyzing the dynamic responses of solids (Livermore SoftwareTechnology Corporation, Livermore, CA). A dynamic solver was chosen because the timerequired to reach the peak displacement is a critical factor in the development of the beam se-quences and in the determination of patient risk due to heating of the tissue. The radiationforce was applied using a ramp and hold function, where the ramp up to the maximum forcevalue was linear, occurring over 2 ms, and the force was then applied continuously for 40 ms.
38 NIGHTINGALE ET AL
−0.5 0 0.5
−0.1
0
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0.6
axial distance from focus (cm)
late
ral d
ista
nce
from
axi
s (c
m)
0.90.5
0.1
FIG. 1 Simulated contours of constant temporal average intensity generated by FIELD_II for the linear, F/1transducer configuration. The black box indicates the transducer position. This plot also portrays two lesion bound-aries (0.5 and 1.0 cm diameter, the dashed lines). The intensity field values of the contours were normalized to thepeak value; contours represent levels of 0.9, 0.5, and 0.1 the peak value. After meshing, these contours were ‘spun’about the x (axial) axis to generate a three dimensional mesh.
ACOUSTIC REMOTE PALPATION 39
FIG. 2 Top: Finite element mesh used for these simulations. The black box indicates the transducer position.The diameter of the outer hemisphere is 5 cm, and is intended to represent an effectively infinite boundary condi-tion. This mesh was constrained on the distal quarter of the surface of the hemisphere (the right (front) side of thepage), in order to simulate a breast resting on a concave table, opposite the transducer. Bottom: This is a magnifiedversion of the central plane of the mesh, showing the increased element density in the focal region, the radiationforce field contours for the linear-F/1 transducer configuration, and the outline of a spherical 1.0 cm diameter lesion.The black box indicates the transducer position.
The impulsive nature of the loading and the elastic nature of the model result in a solutionwhich oscillates about the steady-state solution. This is a common problem in dynamic finiteelement analysis and is resolved by adding numerical damping to more efficiently determinethe steady-state solution. The best damping constant for a system is usually the criticaldamping constant,25 which was used for these simulations. Inclusion of numerical dampinginvolved first solving the model without damping, computing the natural frequency of thesystem, and then solving the model again with numerical damping. The run times variedwith Young’s modulus, and were anywhere from 5 minutes to 6 hours on a 450 MHzPentium PC.
4. RESULTS
In order to simplify the presentation of quantitative results, in many cases only the dis-placement profiles along the central axis the model are given, as computed at 20 ms afterforce initiation (Fig. 3, bottom row).
The displacements in normal breast tissue are largest along the central axis of the trans-ducer just in front of the focal point (first column of figure 3). The peak displacement in thissimulation was 2.8 � m, and the lateral extent of the motion (i.e., the lateral distance off axiswhere the displacement dropped to 50% of the peak) was 1.7 mm. The second column of fig-ure 3 provides the corresponding example when a 0.5 cm diameter lesion that is forty timesstiffer than the surrounding tissue is present (i.e., a Young’s modulus of 400 kPa). Note thatin this case, the lesion moves as a rigid body, and thus the lateral extent of the motion is muchlarger (3.9 mm), and the peak displacement is much smaller (0.9 � m). These figures suggestthat clear, quantifiable differences exist between the displacement patterns generated in thepresence or absence of a lesion.
Effect of increasing force
The simulations show a linear relationship between force and magnitude of displacementthroughout the entire three-dimensional volume. Figure 4 illustrates peak displacement as afunction of radiation force, clearly indicating that displacement increases linearly with force.
Effect of breast tissue stiffness
Figure 5 indicates that the stiffer the baseline tissue is, the lower the maximum displace-ment will be for a given force. As is expected in an elastic medium, figure 5 also shows thatstiffness and displacement are inversely proportional to each other.
Effect of transducer configuration
For each transducer configuration, the shape of the displacement pattern in normal breasttissue was similar to the shape of the associated intensity field (Fig. 6). Figure 7 illustratesthe shape of the intensity fields produced by the various transducer configurations (i.e., the0.1 level contour of figure 1 for each configuration), and table 1 provides the normalized in-tensity values for each configuration. Due to the increase in active aperture surface area as-sociated with the lower f-number configurations, they have the largest normalized intensityvalues.
The axial displacement profiles generated by the different transducer configurations arepresented in figure 8. Both the largest peak displacement, and the smallest axial extent of the
40 NIGHTINGALE ET AL
displacement profile were produced with the 2D transducer. For the linear transducer, theaxial extent of the displacement profiles increased with increasing f-number, whereas thepeak displacements decreased with increasing f-number. This trend was apparent in all butthe comparison between the F/1 and F/1.5 cases, in which the profiles are similar along theaxial extent of the F/1 profile, but the F/1.5 configuration exhibits a longer axial extent, witha larger maximum displacement.
ACOUSTIC REMOTE PALPATION 41
−1 −0.5 0 0.5 1
−0.4
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0
0.2
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0.6
0.8
axial distance from focus (cm)
late
ral d
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−2 −1.5 −1 −0.5 0 0.5 1 1.5 20
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axial distance from focus (cm)
axia
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t (m
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FIG. 3 Displacements resulting from radiation force application using the 2D transducer. The top row illus-trates displacements across the entire mesh, whereas the middle row shows only the center 2 cm. The contour levelsin the middle row range from 0.3 to 2.8 � m, in increments of 0.06 � m. The bottom row provides quantitative dis-placement values along the central axis of the transducer. The black box in each image indicates the transducer posi-tion. Left column: Displacement pattern in normal breast tissue (Young’s modulus of 10 kPa) after 20 ms of forceapplication. Right column: Corresponding displacement images in the presence of a 0.5 cm diameter lesion with aYoung’s modulus of 400 kPa. The location of the lesion has been highlighted in gray.
42 NIGHTINGALE ET AL
0 20 40 60 80 1000
0.5
1
1.5
% force
peak
dis
plac
emen
t (m
icro
ns)
FIG. 4 Peak axial displacement for different radiation force levels assuming a Linear-F/1 transducer configura-tion and normal breast tissue with a Young’s modulus of 10kPa.
−2 −1 0 1 20
2
4
6
8
10
12
axial distance from focus (cm)
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1kPa 5kPa 10kPa18kPa30kPa
0 5 10 15 20 25 300
0.5
1
1.5
2
Young’s Modulus of breast (kPa)
inve
rse
peak
dis
plac
emen
t, (m
icro
ns−
1 )
FIG. 5 Top: Axial displacement along the central axis vs. stiffness of normal breast tissue, assuming a Lin-ear-F/1 transducer configuration. The black box indicates the transducer position. Bottom: Breast stiffness vs. theinverse of the peak displacement, at 20 ms after the initiation of radiation force application.
ACOUSTIC REMOTE PALPATION 43
−0.6 −0.4 −0.2 0 0.2 0.4 0.60
0.1
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axial distance from focus (cm)
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eral
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e fr
om a
xis
(cm
)
−0.6 −0.4 −0.2 0 0.2 0.4 0.60
0.1
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FIG. 6 Magnified view of contours of displacement (dashed lines) in normal breast tissue (E = 10kPa), for the2D transducer (top), and the Linear-F/1 transducer configuration (bottom). The black boxes indicate the transducerposition. The outer boundary of the associated intensity field (i.e., the 0.1 level contour of the intensity field) is su-perimposed on each figure as a solid black line. The contours are normalized; each level represents a 10% decreasein displacement from the maximum. Note that the shape of the displacement contours are similar to the shape of theintensity fields: the 2D contours are more symmetric about the focus, whereas the Linear-F/1 contours exhibit anasymmetry along the axial dimension, with larger displacements occurring in front of the focus (i.e., closer to thetransducer on the left side of the page).
−1.25 −1 −0.75 −0.5 −0.25 0 0.25 0.5 0.75 1 1.250
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axial distance from focus (cm)
late
ral d
ista
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axi
s (c
m)
2DF/1
F/1.5
F/2
F/2.5
F/3
FIG. 7 Outer boundary of the radiation force fields for different transducer configurations (i.e., the 0.1 level con-tours of the intensity fields). The black box indicates the transducer position. Note the different scales on the twoaxes.
Note that the shape of the axial displacement profile differs between the F/1 and 2D cases.Both profiles are approximately the length of their associated intensity fields. However, the2D profile is more symmetric, whereas the F/1 profile shows a linear decrease in displace-ment with increasing distance from the transducer (Fig. 8).
Effect of lesion stiffness and size
Figures 9 and 10 demonstrate the different displacement patterns associated with differentlesion sizes and stiffnesses for the 2D transducer. Figures 11 and 12 provide the same infor-mation for the linear-F/1 transducer. Note that for both transducers, in the absence of a le-sion, the dimensions of the displaced tissue follow the contours of the radiation force field,
44 NIGHTINGALE ET AL
TABLE 1Normalized peak intensity values for each transducer configuration. The lower the f-number, the more active ele-ments; thus, for the linear transducer, lower f-numbers have larger scale factors. The 2D array has more total surfacearea than any of the linear configurations, and thus it has the largest scale factor.
Configuration Scale Factor
2D 3.23
Linear-F/1 1.00
Linear-F/1.5 0.54
Linear-F/2 0.33
Linear-F/2.5 0.23
Linear-F/3 0.17
−2 −1 0 1 20
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1
1.5
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2.5
axial distance from focus (cm)
axia
l dis
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t (m
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ns)
2D F/1 F/1.5F/2 F/2.5F/3
FIG. 8 Displacement along the central axis of the tissue vs. transducer f-number, assuming normal breast tissuewith a Young’s modulus of 10 kPa. The black box indicates transducer position.
ACOUSTIC REMOTE PALPATION 45
−1 −0.5 0 0.5 1
0
0.5
1
no lesion
−1 −0.5 0 0.5 1
0
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1
1cm, 50kPa
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0
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1
0.5cm, 50kPa
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0
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1cm, 100kPa
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0
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1
0.5cm, 100kPa
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0
0.5
1
1cm, 400kPa
−1 −0.5 0 0.5 1
0
0.5
1
0.5cm, 400kPa
FIG. 9 Contours of displacement for different lesion sizes and stiffnesses using the 2D transducer. The contourlevels range from 0.3 to 2.8 � m, in increments of 0.06 � m. The Young’s modulus of normal breast tissue is 10 kPa.In the cases where a lesion is present, its shape has been highlighted in gray. The black boxes indicate transducer po-sition. Displacement values are quantified in figure 10.
−2 −1.5 −1 −0.5 0 0.5 1 1.5 20
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axial distance from focus (cm)
axia
l dis
plac
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t (m
icro
ns)
no lesion0.5/50 0.5/100 0.5/400 1/50 1/100 1/400
FIG. 10 Axial displacement along the central axis of the 2D transducer for different lesion sizes and stiffnessescorresponding to the results in figure 9. The Young’s modulus of normal breast tissue is 10 kPa, and the lesion diam-eters are 0.5 and 1.0 cm with varying Young’s moduli (50, 100 and 400 kPa). The black box indicates transducer po-sition. The legend notation indicates lesion diameter (cm)/lesion Young’s modulus (kPa).
46 NIGHTINGALE ET AL
−1 −0.5 0 0.5 1
0
0.5
1
no lesion
−1 −0.5 0 0.5 1
0
0.5
1
1cm, 50kPa
−1 −0.5 0 0.5 1
0
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1
0.5cm, 50kPa
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1cm, 100kPa
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0.5cm, 100kPa
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1cm, 400kPa
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0.5cm, 400kPa
FIG. 11 Contours of displacement for different lesion diameters and stiffnesses using the linear transducer in anF/1 configuration. The contour levels range from 0.3 to 1.2 microns, in increments of 0.03 microns. The Young’smodulus of normal breast tissue is 10 kPa. In the cases where a lesion is present, its shape has been highlighted ingray. The black boxes indicate transducer position. Displacement values are quantified in Figure 12.
−2 −1.5 −1 −0.5 0 0.5 1 1.5 20
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1
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axial distance from focus (cm)
axia
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t (m
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no lesion0.5/50 0.5/100 0.5/400 1/50 1/100 1/400
FIG. 12 Axial displacement along the central axis of the linear-F/1 transducer for different lesion sizes andstiffnesses corresponding to the results in figure 11. The Young’s modulus of normal breast tissue is 10 kPa, and thelesion diameters are 0.5 and 1.0 cm with varying Young’s moduli (50, 100 and 400 kPa). The black box indicatestransducer position. The legend notation indicates lesion diameter (cm)/lesion Young’s modulus (kPa).
with the largest axial displacement near the focal point. In the presence of a lesion, the dis-placement patterns vary depending upon lesion size and Lesion-to-Tissue-Stiffness Ratio(LTSR). The larger the LTSR, the more uniform the displacement across the lesion be-comes; for the maximum LTSR investigated (40), the entire lesion appears to move as a rigidbody. In all cases, the maximum displacement that occurs within a lesion is considerablysmaller than that in the corresponding homogeneous case.
A series of simulations was also run in which both the breast tissue stiffness and the lesionstiffness were modified, but the LTSR was held constant (i.e., an LTSR of 10 was run for thefollowing lesion and tissue stiffnesses, respectively: 100 and 10 kPa, 50 and 5 kPa, and 200and 20 kPa). LTSRs of 10 and 20 were investigated. Although the percent change in maxi-mum displacement between normal breast tissue and the same tissue with an embedded le-sion varied with the stiffness of the breast tissue, the trends with respect to increasing LTSRwere consistent. The greater the LTSR, the greater the difference in maximum displacementbetween the lesion and normal breast tissue cases.
Timing issues
The response of tissue when exposed to radiation force is an initial large displacement fol-lowed by a slowly increasing or creeping displacement (Fig. 13). The temporal extent of theinitial large displacement varies with the presence or absence of a lesion, the size of the le-sion and the relative stiffness of the lesion and the surrounding tissue (LTSR). In order toquantify this initial ramp up time, an effective time constant is defined to be the time the tis-sue takes to reach 70% of its displacement at 20 ms. This ranges from 2 to 5 ms for the casesshown in figure 13.
Another series of simulations was performed in which the force was removed after 20 msof application, in order to evaluate relaxation time. Figure 14 portrays the relaxation re-sponse associated with normal breast tissue of varying stiffness. For the purpose of this dis-cussion, the relaxation time is defined to be the time it takes for the displacement to decreaseto 70% of its maximum value. Relaxation time decreases with increasing stiffness, with theshortest relaxation time being 0.2 ms (E = 18kPa) and the longest being 1 ms (E = 1kPa).
5. DISCUSSION
The goal of the work presented herein is to investigate some of the fundamental issues as-sociated with remote palpation, including the generation of acoustic radiation force in tissueand the response of the tissue to these forces, in order to guide the design of an experimentalsystem. A clinical remote palpation imaging system would be implemented by multiple se-quential applications of radiation force at different locations throughout a two-dimensionalregion-of-interest (ROI), using a single diagnostic transducer to both generate the requiredradiation force and track the resulting displacements. The ROI would be a subset of a con-ventional B-mode image, thus the operator would hold the transducer in a single locationwhile the remote palpation beam sequence was fired and the image was generated. Given therapid response time of the tissue (Fig. 13), it should be possible to generate remote palpationimages using frame rates of up to 2 frames per second (fps), with up to 100 force locations ineach image. At each force location within the ROI, a group of low intensity ‘tracking lines’that interrogate the tissue surrounding the force location would be fired and stored for refer-ence. Then a series of tightly-focused, high-intensity ‘pushing lines’ would be fired along asingle line of flight in the center of the tracking lines for approximately 5 ms. Finally, an-
ACOUSTIC REMOTE PALPATION 47
other group of tracking lines would be fired, which could be interspersed with pushing linesin order to avoid relaxation of the tissue during the time it takes to interrogate the region.Each tracking line would then be divided into sequential axial search regions, and the crosscorrelation between the reference lines and tracking lines would be computed in order to de-termine the tissue motion in the region surrounding each force location.8-10, 26
The resolution of a remote palpation imaging system will be dependent upon the trans-ducer parameters (i.e., shape, size, and magnitude of the intensity field), the number of forc-ing locations, the spatial relationship of the forcing locations, the pulse length and kernel sizeused for the tracking algorithm, and the method that is selected to display the information.The sensitivity and dynamic range of the remote palpation imaging system will be dependent
48 NIGHTINGALE ET AL
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0.5ms1ms 1.5ms3ms 20ms 80ms
0 5 10 15 200
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time (msec)
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ns)
No lesion, 5 kPaNo lesion, 10kPa0.5cm,10&100kPa 0.5cm,10&200kPa No lesion, 30kPa1cm,10&100kPa 1cm,10&200kPa
FIG. 13 Top: Displacement along the central axis of the linear-F/1 transducer in normal breast tissue (Young’smodulus 10kPa) through time. The black box indicates transducer position. Bottom: Displacement at the focalpoint of the linear-F/1 transducer (i.e., x=0 on the top plot) through time for different types of tissue. Note that al-though the ramp up time varies, after 20 ms each case is near its steady-state displacement.
upon the signal-to-noise ratio (SNR), the stiffness of the tissue, and the size and relative stiff-ness of the lesions (LTSR). The work presented herein investigates the effects of transducerparameters, tissue characteristics and lesion characteristics on tissue displacements gener-ated at a single forcing location.
An example of the effect of transducer parameters on displacement profile is shown in fig-ure 6. The optimum lesion detectability will be achieved by the transducer configuration as-sociated with the smallest volume of displaced tissue, and the largest peak displacement inthe normal breast tissue case. This suggests that the 2D transducer, followed by the F/1 lin-ear transducer, will provide the best performance and the F/3 transducer will provide theworst performance (Fig. 8). This could be anticipated by evaluating the size of the intensityfields associated with each transducer configuration (Fig. 7). In addition, under the assumedcondition of a fixed excitation voltage being applied to each element, the transducers withmore active elements generate larger forces than those with fewer transmit elements (see ta-ble 1). It is interesting to note the differences in the shapes of the displacement profilesshown in figure 8. For all of the linear transducer configurations, the largest displacementoccurs at the front of the axial displacement profile in front of the focus, whereas the axialdisplacement profile for the 2D configuration is more symmetric about the focus. This is dueto the different shapes of the radiation force fields for the different transducer configurations(Fig. 7). The linear transducer force fields are asymmetric about the focus, with much largerlateral extents in front of the focal point than behind, whereas the radiation force field associ-ated with the 2D transducer is more symmetric about the focus. The complex stresses intro-duced by the nonuniform radiation force fields clearly result in complex displacementprofiles. The variations in displacement pattern with transducer configuration presentedherein are consistent with those observed in experiments presented elsewhere.27
The displacement magnitudes that will be achieved in vivo will clearly be dependent uponthe Young’s modulus of the tissue (Fig. 5). This is a challenging parameter to experimen-tally characterize that has been attempted by only a few researchers. The reported numbersfor normal breast tissue range from 1 to 30 kPa.1, 2, 24 Assuming a peak displacement of 5 � m
ACOUSTIC REMOTE PALPATION 49
0 0.5 1 1.5 20
0.2
0.4
0.6
0.8
1
time after force cessation (msec)
norm
aliz
ed a
xial
dis
plac
emen
t
1 kPa 5 kPa 10 kPa18 kPa
FIG. 14 Normalized displacement at the focal point of the linear-F/1 transducer through time after force cessa-tion for normal breast tissue of different Young’s modulii.
in normal breast tissue will be adequate for successful remote palpation implementation, thevariability in these Young’s modulii suggests that the required radiation force will be any-where from a factor of 0.5 to 12 times that assumed in these simulations.
The LTSRs utilized in these simulations (5, 10, 20 and 40) are consistent with measure-ments reported for diseased and normal breast tissue.1, 2, 24 Young’s modulii for infiltratingductal carcinoma have been reported to be between 3 and 5 times larger than normal breasttissue.1, 2, 24 Young’s modulii for fibroadenomas are reported to be between 3 and 10 timeslarger than normal breast tissue.1, 2, 24 In addition, Krouskop et al report that a 20%precompression of the tissue results in relatively minor increases in the Young’s modulus ofnormal breast tissue, and considerably larger increases in the Young’s modulii of fibro-adenomas and ductal carcinoma, resulting in LTSRs of between 6 and 30.2
As expected, the higher the LTSR, the greater the difference in the displacement patternsin the presence and absence of a lesion (Figs. 9-12). Rigid body motion of both the 0.5 and1.0 cm diameter lesions was effectively achieved at an LTSR of 40. This behavior is consis-tent with that observed in experiments presented elsewhere.27 For the more clinically rele-vant LTSRs (5 and 10), the lesions did not demonstrate rigid body motion; however,significant differences are clearly apparent in the presence and absence of a lesion. The max-imum displacements at the focus are much smaller (a factor of ~2 or more) and the lateral dis-placement profiles are considerably broader in the presence of a lesion. This increase inlateral profile breadth will likely be the primary indicator of the presence of a lesion in re-mote palpation images.
For both transducer configurations (Figs. 10 and 12), in the 1.0 cm lesions with LTSRs of 5and 10, the axial displacement profiles have similar shapes to the normal tissue case, how-ever they have much lower maximum displacements. In the instance where the lesionboundary is contained within the radiation force field (the linear-F/1 transducer in the 0.5 cmdiameter cyst), the shape of the axial displacement profile is consistent with the normal tis-sue case in front of the lesion boundary (albeit with a lower peak magnitude); however, it de-creases more sharply within the lesion (Fig. 12). The greater the LTSR, the sharper thisdecrease appears. These differences in displacement profiles support the potential for re-mote palpation to be used to identify lesions in the breast.
The implications of the assumptions made in the finite element analysis should not alterthe trends observed herein. The damping that exists in a visco-elastic medium will differfrom the critical numerical damping that was applied herein; however, the observed trendswith respect to the temporal responses of different lesion sizes and tissue stiffnesses shouldbe valid (Figs. 13 and 14). The assumption of axial symmetry of the intensity field allowedaccurate mesh generation of spatially-complex intensity field contours while providing athree-dimensional solution. This could result errors in the estimation of the volume of the ra-diation force field for low f-number configurations. However, given that the lateral and ele-vation dimensions are an order of magnitude smaller than the axial dimension of the intensityfields, variations between the lateral and elevation dimensions will have only a slight impacton the displacement profiles.
Both elastography methods and remote palpation are intended to image variations in tissuestiffness. The fundamental difference between the proposed remote palpation imagingmethod and elastography lies in the forcing function. In elastography, images of strain (thederivative of displacement) due to external, global force application are generated.1, 8-11 In re-mote palpation, localized forces are generated deep within the tissue. This results in severalpotential advantages for the remote palpation method. Elastography imaging is susceptibleto artifacts arising from varying boundary conditions. Because the forces used in remote pal-pation are localized deep within the breast, the boundaries are effectively infinite. In addi-tion, remote palpation does not require external fixtures, and given the rapid tissue
50 NIGHTINGALE ET AL
response (5 ms), remote palpation can likely be implemented in pseudo-real-time (i.e. 2frames per second) utilizing conventional free-hand scanning methods. One potential dis-advantage to remote palpation is that the displacement profiles are much more complexthan those obtained using the global compression methods of elastography. Even in the ab-sence of a lesion, a complex relationship between displacement profiles and transducer pa-rameters is observed (Fig. 8). Further work is required to determine the optimum method fordisplaying remote palpation information.
In the implementation of remote palpation, a significant issue is whether or not it is feasi-ble to use a single transducer to both generate the radiation force and track the resulting dis-placements. This would be advantageous for several reasons. First, it would facilitate easeof clinical implementation, possibly as an option on conventional diagnostic systems. Sec-ond, it would allow a direct overlay of remote palpation images with conventional B-modeimages. Finally, it would avoid the considerable challenges associated with aligning multi-ple transducers, and possibly allow free-hand scanning methods. The primary challenge forsingle transducer implementation is generating enough force to produce detectable displace-ments. The definition of a ‘detectable displacement profile’ is dependent upon the sensitiv-ity of the displacement tracking algorithm. The theoretical lower limit on the distance thatcan be tracked using correlation based algorithms can be estimated using the Cramer-RaoLower Bound.28 Assuming a good signal-to-noise ratio (40 dB), and a high correlation be-tween the reference and tracking lines (0.998), the estimated lower limit on the distance thatcan be tracked during remote palpation is 0.5 � m. Therefore, in order to achieve reasonabledynamic range, peak displacements of at least five � m would be desirable.
Equation (1) indicates that increases in radiation force over that used in the simulationswill occur with increases in absorption of tissue, decreases in the speed of sound in tissue,and increases in the intensity field generated by the transducer. In addition, a significantsource of increased radiation force that is not modeled by Eq. (1) is that of nonlinear propaga-tion. Although Eq. (1) does not indicate a dependence between pressure amplitude and radi-ation force, several researchers have demonstrated that there is an increase in radiation forceassociated with increasing pressure amplitude, due to nonlinear propagation.12, 20-21 For thesame temporal average intensity, a wave with higher pressure amplitude and shorter pulseduration generates a larger radiation force than does a lower amplitude, longer durationwave. This is due to the higher order harmonics generated by nonlinear propagation, whichresult in an increase in absorption.12, 20, 29-30 We have observed increases in radiation force by afactor of 2.6 in breast applications in vivo.21 For a thorough theoretical treatment of nonlinearenhancement of radiation force, the reader is referred elsewhere.12
The simulations were performed assuming a peak in situ intensity of 90 W/cm2, which re-sulted in a peak displacement of 1.2 � m within 20 ms for the linear-F/1 transducer. Given thelinear relationship between displacement and force (Fig. 4), and the desired peak displace-ment of at least 5 � m, four times this intensity is desirable (assuming the values used for ab-sorption, sound speed and Young’s modulus of tissue are valid). When the enhancing effectsof nonlinear propagation are accounted for (an increase of 2.6), the required increase drops to1.5 (or 135 W/cm2).
There are two potential challenges associated with these intensity levels: (1) they exceedthe FDA limit for diagnostic intensity levels; and (2) they may approach the maximumpower output of currently available diagnostic scanners. The FDA currently limits the spa-tial peak temporal average intensity to 0.72 W/cm2 in situ, in order to avoid potential tissuedamage due to heating. However, this limit was determined assuming an indefinite applica-tion time. The simulations indicate that the force need only be applied for 5 ms. Short dura-tion, high intensity acoustic pulses were not foreseen in the development of the FDA limit. Amore appropriate thermal safety indicator for this type of pulse can be determined using Eq.
ACOUSTIC REMOTE PALPATION 51
(3), which predicts the temporal average intensity (I in W/cm2) that would be required to gen-erate a thermal injury, or burn, due to ultrasound exposure in a given time period (t, in sec-onds):31
Assuming a 5 ms application time, 1,400 W/cm2 would be required to cause thermal damage.Under linear propagation assumptions, this provides a safety factor of four over what wouldbe required for remote palpation. Although nonlinear propagation will result in an increasein radiation force, and thus a decrease in the required intensity, it will also result in an in-crease in tissue heating;32, 33 hence, the safety factor of four will remain.
Another potential challenge for remote palpation related to heating is the effect that tem-perature increases have on the temporal shifts detected using correlation based trackingmethods.34, 35 Changes in temperature result in changes in the sound speed of tissue, which re-sult in apparent temporal shifts in rf data. This would clearly compromise the estimates of ra-diation force induced tissue displacement. However, ultrasonically induced increases intemperature occur over a period of on the order of hundreds of milliseconds, whereas radia-tion force induced displacements occur during a period of on the order of ten milliseconds.Therefore, the deleterious effects of tissue heating on displacement tracking will likely benegligible during remote palpation implementation. Even so, we are currently investigatingthe potential thermal effects associated with remote palpation.
Another parameter that the FDA uses to monitor the safety of diagnostic ultrasound sys-tems is the mechanical index (MI). This parameter is intended to provide an indication of thepotential for nonthermal bioeffects (i.e., cavitation). It is defined to be the peak negative de-rated pressure amplitude divided by the square root of the center frequency of an acousticpulse.36 By definition, nonlinear propagation and hence nonlinear increases in radiationforce are associated with higher MIs. The FDA limits the MI of diagnostic ultrasound sys-tems to 1.9. Given that the factor of 2.6 increase in radiation force observed in vivo was asso-ciated with a pulse with an MI of 1.5,21 it is not anticipated that the pulses used for remotepalpation will exceed the limit of 1.9.
The question of the maximum power output from diagnostic scanners is complex. Be-cause the FDA limits are considerably lower than the maximum capacity of current diagnos-tic scanners, manufacturers do not quantify this parameter. After modifying the systemsoftware to remove the built-in safety features, we have measured spatial peak temporal av-erage intensities from the 75L40 array on our Siemens Elegra scanner that correspond to invivo values of 10.0 W/cm2. Simulations indicate that the 2D 8 x 128 transducer will be capa-ble of generating three times this amount (table 1); only 4.5 times more power is required forremote palpation implementation. Manufacturers are actively pursuing the development ofmore powerful diagnostic transducers for other applications, including harmonic and con-trast imaging. Thus, the development of diagnostic transducers capable of generating the re-quired intensities seems plausible in the near future.
6. CONCLUSION
For a clinically relevant range of elastic modulii and lesion sizes, considerably differentdisplacement patterns were generated in the presence/absence of a lesion. The simulationsindicate that a low f-number transducer configuration is preferable for the implementation of
52 NIGHTINGALE ET AL
.100
*10t
I �(3)
remote palpation, because this provides more force and a smaller intensity field volume thanhigher f-number configurations. The rapid temporal response of the tissue (5 ms) indicatesthat real time implementation of remote palpation is feasible. The acoustic power that is re-quired to achieve peak displacements of several microns in vivo is higher than that currentlyused in diagnostic ultrasound. These findings provide the design criteria for experimentalremote palpation beam sequences. While further research is required to investigate the ther-mal and power issues, remote palpation as proposed herein appears to have considerableclinical potential.
ACKNOWLEDGMENTS
This work was supported by DOD BCRP grant BC972755. We thank Altair Computing,Inc. for their considerable support with meshing and postprocessing. We thank SiemensMedical Systems, Ultrasound Group for their guidance on system specifications. We thankIntel Corporation for their technical and in-kind support.
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