A Numerical Investigation of Breast Compression: A Computer-Aided Design Approach for Prescribing Boundary Conditions

2876 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 58, NO. 10, OCTOBER 2011

A Numerical Investigation of Breast Compression:A Computer-Aided Design Approach for

Prescribing Boundary ConditionsMacArthur L. Stewart*, Lorenzo M. Smith, and Neal Hall

Abstract—Prior to performing an MRI-guided breast biopsy,the radiologist has to locate the suspect lesion with the breastcompressed between rigid plates. However, the suspect lesion istypically identified from a diagnostic MRI exam with the breasthanging freely under the force of gravity. There are several chal-lenges associated with localizing suspect lesions including, patientpositioning, the visibility of the lesion may fade after contrast injec-tion, menstrual cycles, and lesion deformation. Researchers havedeveloped finite element analysis (FEA) methodologies that simu-late breast compression with the intent of reducing these challenges.In this paper, we constructed a patient-specific finite element (FE)breast model from diagnostic MR images. In addition, we con-structed surfaces corresponding to the biopsy MR volume and usedthem to deform the FE breast mesh. The predicted results suggestthat the FE breast model, in its uncompressed configuration, canbe compressed to replicate the perimeter of the biopsy MR volume.The simulated lesion displacement was within 3 mm of its actualposition.

Index Terms—Breast boundary conditions, breast compression,breast finite element model, finite element lesion model, MRI-guided breast biopsy.

I. INTRODUCTION

BREAST cancer is one of the leading causes of death amongwomen in the Western world. According to the National

Cancer Institute, the 5-year survival rate is 98% when the canceris in situ and found in its early stages. When the cancer is foundin its later stages, the 5-year survival rate drops to 26% [1]. TheNational Cancer Institute estimated that 207 090 women werediagnosed with breast cancer with 39 840 associated deaths in2010 [1]. Mortality rates have decreased over the past severalyears due to improved cancer treatments and early detection [1].

A diagnostic breast MRI exam is an additional imaging testwhen cancer is suspected. Typically, the goal of this exam is toclarify an inconclusive mammogram or ultrasound exam [2]. If

Manuscript received February 2, 2011; revised March 28, 2011 and May16, 2011; accepted June 8, 2011. Date of publication July 14, 2011; date ofcurrent version September 21, 2011. This work was supported in part by anOakland University-Beaumont Multidisciplinary Research Award. Asterisk in-dicates corresponding author.

*M. L. Stewart is with Oakland University, Rochester, MI 48309 USA(e-mail: [email protected]).

L. M. Smith is with the Department of Mechanical Engineering, OaklandUniversity, Rochester, MI 48309 USA (e-mail: [email protected]).

N. Hall is with St. Joseph Mercy Hospital, Pontiac, MI 48341 USA (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TBME.2011.2162063

a suspect lesion is identified that cannot be felt from a palpationexam, an MRI-guided breast biopsy is typically performed [2].During the diagnostic breast MRI exam, the patient is positionedin the prone position with the breast hanging under the force ofgravity. However, the breast is compressed between rigid platesto stabilize the breast and prevent movement of suspect lesions,during the biopsy.

There are several technical challenges with performing anMRI-guided breast biopsy. There may be variation in the ap-pearance of the lesion between the diagnostic and biopsy MRimage volumes. This may be due to variation in positioning,the visibility of the lesion may fade after contrast injection, orphysical changes due to menstrual cycles. If the lesion cannot belocalized, a follow-up exam is scheduled. Breast compressioncan also cause lesion shape changes (due to lesion deformation).The nonrigid nature of the female breast together with these lim-itations can make it difficult to accurately locate the boundaryof a suspect lesion.

The objective of this paper was to investigate the efficacy ofconstructing surfaces corresponding to the biopsy MR volumeand using them to deform the FE breast mesh. We developedour FE model from patient-specific breast diagnostic and biopsyMR volumes. The following assumptions were considered inthis study.

1) Fat and fibroglandular tissues are the primary contributorsto the kinematic behavior of the female breast.

2) Breast tissue is homogeneous, isotropic, nonlinear, andnearly incompressible.

3) Except for the suspect lesion, the breast tissues were mod-eled as one tissue type consisting of the volume fractionsof fat and fibroglandular tissues.

4) The Neo-Hookean material model adequately models theconstitutive relationships of breast tissue.

5) The breast was allowed to freely hang during the diagnos-tic MRI.

6) Prior to compressing the breast in preparation for thebiopsy, the breast was allowed to freely hang.

7) The sternum is stable and reproducible.8) The breast coupled with the rigid plates forms a conserva-

tive system.Our FEA methodology was verified by visual inspection of

the deformed surface profile, calculating the difference betweenthe simulated and actual lesion travel, and overlaying the actuallesion onto the numerical results.

The major contributions to the published literature from thisstudy include the following.

0018-9294/$26.00 © 2011 IEEE

STEWART et al.: NUMERICAL INVESTIGATION OF BREAST COMPRESSION 2877

1) Ability to replicate surface boundary conditions includingthe compression and immobilization plates, and the intro-ducer sheath (biopsy equipment) without having to modelthem.

2) A verification method that does not require a controlledpatient study.

II. REVIEW OF SELECTED RESEARCH

A number of biomechanical FE models have been proposedwith the intent of predicting the mechanical behavior of femalebreast tissue. These numerical models are differentiated, pri-marily, by how the breast geometry is discretized, applicationof boundary conditions, and/or the breast tissue elastic materialproperties.

There are five critical questions that require answering whenattempting to develop an FE model that simulates breast com-pression. 1) How will the geometry be isolated? 2) How willthe computational domain be discretized? 3) What experimentalstress–strain test captures the physics of the simulation problem?4) What material properties and material model best define theconstitutive relationships? Finally, how will the proposed finiteelement model be validated?

This review is arranged into five sections and it surveys thepublished literature in the area of FE breast modeling. Thesesections bring to light the debate regarding how to build a nu-merically accurate and computationally efficient biomechanicalFE model that simulates breast compression.

A. Breast Geometry Development

Different imaging technologies are available for extracting the3-D breast geometry [2], [3]. Perez del Palomar et al. [4] cre-ated their breast geometry from CT images. Samani et al. [5],Unlu et al. [6], Zhang et al. [7], Azar et al. [8], and Ruiteret al. [9] extracted breast geometry from patient-specific MRimages. Schnabel et al. [10] used contrast-enhanced (CE)MR mammographic images to extract patient-specific breastgeometry.

Each of these modalities gives an accurate representation ofthe breast surface, fat tissue, fibroglandular tissue region, andsuspect lesions. For this reason, the selected imaging methodwould simply depend on the convenience of the researchersand/or the physician’s order.

If segmented images are not required, a 3-D camera can beused to capture the geometry of the skin surface. Roose et al. [11]used this geometry extraction method to develop a breast finiteelement method that predicts the outcome of surgical breastaugmentation. Roose et al. compared their mass-spring modelwith a corresponding FE model and found their mass-springmodel to be less accurate. The verification model consisted ofa sphere segment that represented a breast implant. The spheresegment was positioned under a flat plate that represented breasttissue. The sphere segment was pressed into the flat plate andthe resulting plate height was measured.

TABLE IELEMENT QUALITY CRITERIA

B. Breast Tissue Discretization

The elements used to discretize the breast geometry variedamong previous researchers. Perez del Palormar et al. [4] usedlinear tetrahedral elements and linear triangular membrane el-ements to mesh breast and skin tissues, respectively. Samaniet al. [5], Azar et al. [8], and Ruiter et al. [9] developed 3-Dfinite element models for simulating breast compression usinglinear hexahedral finite elements. Samani et al. also used quadri-lateral membrane elements to mesh the skin. Tanner et al. [12],Schnabel et al. [10], and Zhang et al. [7] discretized the com-putational domain using quadratic tetrahedral elements. Zhanget al. also used an adaptive meshing strategy allowing meshrefinement in regions with small feature sizes.

In general, lower order elements provide reasonable accuracywith less computational expense. They are also robust for largedeformations and contact problems [13]. For this research, lineartetrahedral elements were used to discretize the complex breastand lesion geometries. The element sizes (the maximum elementedge length) for the breast and suspect lesion geometries were10 and 0.85 mm, respectively. These element sizes resulted inan accurate representation of the computational domains andthe element quality remained within reasonable bounds.

The element quality metrics and their corresponding boundsare shown in Table I. Warpage is used to describe how the face ofan element deviates from a plane. Aspect ratio is defined as theratio of the largest to the shortest edge of an element. Skew angleis the largest angle between vectors formed from the midpointsof opposite sides of an element. The minimum and maximumangles refer to the elements’ interior angles. Jacobian is used toquantify by how much an element deviates from its ideal shapewith a range of 0–1. For triangular elements, a Jacobian valueof 1.0 corresponds to an equilateral triangle [14].

C. Materials and Experimental Stress–Strain Data

Krouskop et al. [15] experimentally determined the stress–strain response of the following breast tissue types: fibrous, fat,glandular, carcinomas, intraductal carcinomas, and infiltratingductal carcinomas. These tissues were tested by subjecting themto a sinusoidal load at three frequencies: 0.1, 1.0, and 4.0 Hz.The intent was to characterize the viscoelastic behavior andto confirm whether or not the tissue could be modeled as anelastic material within the frequency range of interest. Above1 Hz, the static stiffness accounted for 93% of the total stiffness.Tissue samples were extracted during surgery and test sampleswere fabricated to ensure that the test specimen remained stableand that homogenous material behavior prevailed during com-pression testing. The homogenous assumption was justified by


analyzing the microstructure of the tissue samples. In addition,the individual tissues were assumed to be isotropic. These mate-rial assumptions were also made by Fung [16] and Wellman [17].The strain rate used during compression testing was selected sothat viscoelastic effects were negligible.

Wang et al. [18] and Azar et al. [8] fitted experimental stress–strain curves, developed by Wellman [17], to an exponential ma-terial model. Wellman adopted a similar experimental method-ology as Krouskop et al., but tested more breast tissue types.In addition, Wellman experimentally developed breast tissuestress–strain curves over a wider strain range than that of priorresearchers, [15], [19], and [20].

Breast tissue material property testing is beyond the scope ofthis paper. For this reason, we adopted the experimental work ofWellman [17]. Wellman’s modulus of elasticity E versus stainε data for fat, fibroglandular, and lobular cancer tissues werefitted to third-order polynomials, E = E(ε). Integrating thesefunctions with respect to ε yields the corresponding stress σversus ε relationship. Samani et al. [5] considered a similarapproach.

D. Breast Tissue Material Properties and Material ModelSelection

In the published literature surveyed in this paper, it was as-sumed that the material properties were homogeneous, isotropic,and nonlinear. However, breast tissue material properties areanisotropic [21]. Furthermore, the overall breast structure is het-erogeneous and consists primarily of epithelium and connectivetissue types [22]. Several different material models have beensuggested for modeling the constitutive relationships of breasttissue. The predominate material models considered were linear,Neo-Hookean, Mooney–Rivlin, and exponential.

Hooke’s law, a relatively simple linear material model forwhich stress is assumed to be proportional to strain, was con-sidered by Hipwell et al. [23], Zhang et al. [7], and Schnabelet al. [10]. The modulus of elasticity E and Poisson’s ratio νare the only material parameters required to define a materialof this type [24]. Zhang assumed the same physical tissue pa-rameters for all the breast tissue types, commonly called thehomogenous tissue model. For small strains, the linear materialmodel tends to accurately characterize hyperelastic materials.In this paper, finite deformations are present. For this reason, anonlinear material model was considered to obtain accurate FEresults.

Ruiter et al. [9] and Perez del Palomar et al. [4] demonstratedthat the Neo-Hookean material model and the homogeneousbreast tissue model assumption provided sufficient numericalaccuracy. Perez del Palomar et al. initially estimated the ma-terial parameter C10 as the volume fraction average of fat andglandular tissues and iteratively modified it until the numeri-cal model correlated with the actual breast deformation. Chunget al. [25] used the Neo-Hookean material model to character-ize the mechanical behavior of a silicon gel breast phantom.The experimentally derived material model parameter C10 was0.7 kPa. For accurate material modeling, the selected material

model must characterize the constitutive relationship over thestrain range of interest.

Perez del Palomar et al. used a five-paramter Mooney–Rivlin hyperelastic material model to model the breast skin.Pathmanathan et al. [26] also used a five-parameter Mooney–Rivlin material model. Pathmanathan et al. modeled the fat andglandular tissues separately using the stress–strain relationshipsdeveloped by Samani et al. [5]. Similar to the concluding re-marks regarding the Neo-Hookean hyperelastic material model,the material model that best fits the material’s stress–strain re-lationship over the strain range of interest and with the leastcomputational expense should be considered.

Azar et al. [8] selected exponential and linear constitutiverelationships for glandular and fat tissue, respectively. Azaret al. assigned a material property to each element correspond-ing to fat, glandular, or tumor tissue. The percentage of eachtissue type was calculated in each element, and the tissue typewith the largest percentage was assigned to the element. Theskin was not modeled in their work. Azar et al. predicted thedisplacement of a cyst within 4.9 mm of its actual displacement.

Since the objective of this study was to investigate the efficacyof using rigid surfaces constructed from the biopsy MR volumeto compress the FE breast mesh, we made four simplifying as-sumptions. 1) Breast tissue was assumed to be homogeneous,isotropic, and nonlinear. 2) We assumed that the effects of differ-ent breast tissue types other than fat and fibroglandular tissueswere negligible. 3) Except for the suspect lesion, the breast tis-sues were modeled as one tissue type consisting of the volumefractions of fat and fibroglandular tissues. 4) The constitutiverelationships were fitted to the Neo-Hookean material model.These simplifying assumptions are consistent with previous re-searchers [4], [9].

E. Breast Finite Element Model Validation

Validation of a biomechanical FE breast model requires atest method that quantifies that accuracy at which it predicts themechanical behavior of breast tissue [12]. Since the accuracyrequired to localize the smallest visible tumor is 5 mm [25],the difference between the experimental and numerical resultsmust be less than 5 mm. Two types of validation procedureswere considered. First, MR or mammographic images of thebreast were obtained, in both the compressed and uncompressedstates, and registered into 3-D images. These two volumes, andcorresponding landmarks, were then registered together provid-ing a means to measure displacement. Tanner et al. [12] pub-lished this method of validation in 2001 using MR images. Azaret al. [8] and Schnabel et al. [10] used this validation methodto access the accuracy of their published work. Zhang et al. [7]and Ruiter et al. [9] used a similar validation procedure butcompared feature points from patient-specific mammographicimages.

Landmarks located on the actual patient and compared tocorresponding locations on the finite element model was anothervalidation approach used in the published literature. In additionto this validation method, Perez del Palomar et al. [4] scannedthe actual breast, 3-D, and overlaid the image onto the numerical


results. Azar et al. [8] tracked a visible cyst, located inside thebreast, and two vitamin E pills, attached to the surface of thebreast.

An additional goal of this research was to assess the clin-ical usefulness of the proposed FE modeling method with-out the need of modifying the current standard of care. Forthis reason, the MR image volumes were taken from a patientthat underwent a typical MRI-guided breast biopsy, not a con-trolled patient study. The diagnostic MR image volumes werealigned at the sternum (a stable and reproducible anatomical fea-ture), which allowed for an independent measurement of lesiondisplacement.

III. FINITE ELEMENT METHOD AND ELASTICITY FOR

MODELING BREAST TISSUE

A. Nonlinear Geometry

An MRI-guided breast biopsy results in finite breast de-formation which means that geometric changes between theundeformed and compressed breast are not negligible. Whenfinite deformations are present, geometric nonlinearity shouldbe considered for accurate FE modeling. Geometric nonlinear-ity is usually resolved by writing the equilibrium equations inincremental form [K]{ΔD} = {ΔR}. In this mathematical re-lationship, [K], {D}, and {R} are the stiffness matrix, elementdisplacement vector, and nodal load vector, respectively. [K] isa function of {D} which is computed iteratively. Iterating con-tinues until the magnitude of the residual force vector is smallerthan the specified tolerance. The residual force vector is de-fined by the difference between the external and internal forcevectors. Once the convergence tolerance is satisfied, the current{D} becomes the sum of the preceding {ΔD}s and the current[K] is used to calculate the next displacement increment. Thedisplacement vector and stiffness matrix are updated and theprocess is repeated until the specified external loading condi-tion is applied. Simply stated, the load–displacement curve isapproximated as a series of line segments [27].

In this research, large displacement–large strain theoryis assumed. Breast tissue displacements were analyzed inLagrangian coordinates. The displacement, differentiation, andintegration are referenced back to the original domain in theLagrangian approach. As the displacement increases, higher or-der terms are added to the strain–displacement relationship inorder to account for geometric nonlinearity. Lagrangian coordi-nates are typically used where large strains are present [13].

B. Material Nonlinearity

The breast tissue constitutive relationships were modeled us-ing the Neo-Hookean hyperelastic material model. The stress–strain relationship for a hyperelastic material is defined by astrain energy density function

Si =∂W

∂λi(1)

where Si , W, and λi are the second Piola–Kirchoff stress, strainenergy density, and principal stretches, respectively [13]. De-pending on the type of hyperelastic model, the strain energy

function is written as a function of strain invariants or stretchratios, defined by

I1 = λ21 + λ2

2 + λ23

I2 = λ21λ

22 + λ2

2λ23 + λ2

3λ21

I3 = λ21λ

22λ

23 . (2)

The terms in (2) are derived from the deformation gradient Fij .The deformation gradient maps position vectors in the reference(undeformed) configuration Xi to the corresponding location inthe deformed geometry xi [28]

Fij =∂xi

∂Xj; i, j = 1, 2, 3. (3)

The finite deformation formulation defines the current posi-tion of a point xi by adding the displacement ui to the corre-sponding reference (undeformed) position of the point Xi [28]

xi = Xi + ui. (4)

The Neo-Hookean WNH material model assumes that thestrain energy density, elastically stored energy per unit volume,is a polynomial function of the principal strain invariants. Thisstrain energy density function contains only first-order straininvariant terms [29]

WNH = C10 (I1 − 3) + 3.5K(I

1/63 − 1

)2. (5)

The variable C10 is the material parameter which is derivedfrom curve fitting the stress–strain data, and K is the bulk mod-ulus. The first term in (5) is derived by expanding I1 , in (2),into a power series and neglecting higher order terms [13], de-viatoric component. The second term represents the volumetriccomponent which is zero for incompressible materials.

C. Finite Element Analysis Contact Algorithms

Typically, the surface area between contacting bodiesincreases with load. In the finite element method, the displace-ments of the contacting nodes, in the normal direction, are con-strained to be equal. If slip is allowed, relative displacementin the tangent direction can occur. There are several numericalalgorithms for detecting contact. MARC uses the direct con-straints procedure [29]. If the contact node is within the contactzone, constraint equations are employed to move the node to thecontact surface. Additional constraints can be imposed to allowfor separation due to changes in load.

IV. MRI-DERIVED FEA BREAST MODEL

Three commercially available computer software programswere used as our primary research tools. 1) ANALYZE [30]was used to view and manipulate the MR images. ANALYZEis a biomedical image viewing software developed by the MayoClinic. 2) The computational domain was discretized usingHyperMesh [31]. HyperMesh is an FEA preprocessor, AltairEngineering, Inc. 3) Except for meshing, our FEA model wasconstructed and processed using MARC/Mentat which is amultipurpose nonlinear FEA software package, MSC SoftwareCorporation.


Fig. 1. Overview of the proposed FE breast model construction.

Fig. 1 gives a general overview on how we constructed ourFEA model. This section is arranged into six parts that dis-cuss the components of our FEA method which include 1) MRIdata and geometry construction; 2) rigid registration; 3) geom-etry discretization; 4) material properties and material modelselection; 5) boundary conditions; and 6) numerical solutionmethods.

A. MRI Data and Geometry Construction

For this study, the left breast was considered. It containeda single lesion, situated laterally, and was diagnosed as nonin-vasive cancer. T1-weighted diagnostic and biopsy MR imageswere acquired. The voxel sizes in the diagnostic and biopsy MRvolumes were 0.94 × 0.94 × 2.5 mm3 and 0.66 × 0.66 ×2 mm3 , respectively. The biopsy was performed 18 days afterthe diagnostic MRI exam. Fig. 2 shows the 3-D rendering of theleft breast and a maximum intensity projection (MIP) highlight-ing the suspect lesion. Fig. 3 shows the corresponding biopsyvolume.

B. MR Volume Rigid Registration

Since the diagnostic and biopsy MR volumes were notaligned, we took an anatomical landmark-based registration ap-proach to align these 3-D medical images [32]. The sternum wasused as the anatomical landmark due to its constant nature [33].Anatomically, the breast architecture was assumed constant dueto scaffolding support by Cooper’s ligaments [34]. With ster-

Fig. 2. Breast diagnostic MR volume and a maximum intensity projectionhighlighting the suspect lesion.

Fig. 3. Breast biopsy MR volume: immobilization plate side (left) and com-pression plate side.

Fig. 4. (White) 2-D MR slice of the biopsy MRI volume overlaid on (gray)diagnostic MR volume, registered at the sternum.

num alignment, the difference between the two MR volumeswas breast compression.

The rigid registration tool in ANALYZE was used to aligntwo MR volumes (see Fig. 4). This allowed for an indepen-dent measurement of lesion displacement (lesion travel fromthe diagnostic MRI to the biopsy MRI).

C. Breast and Lesion Geometry Discretization

Fig. 5 is a flowchart that describes how the breast FE meshwas constructed; the mesh development process was dividedinto five steps. 1) The diagnostic breast MR images were ren-dered into a 3-D image. 2) Using ANALYZE, we segmented thebreast and lesion surfaces from the MR volume. 3) Since thesurface mesh quality was insufficient for FEA, these two sur-faces were imported into HyperMesh and refined. 4) The breastand lesion surfaces were then independently discretized. Thebreast triangular mesh was discretized resulting in 4612 tetrahe-dral elements. The average edge length of the surface elementswas 10 mm. The lesion geometry was meshed with a surfaceedge length of 0.85 mm resulting in 3211 tetrahedral elements.5) We used a kinematic constraint that tied the lesion nodes tothe breast nodes based on their isoparametric locations withinthe breast mesh [35].


Fig. 5. Breast and lesion geometry discretization process.

Fig. 6. Homogenous breast tissue model and lesion stress–strain curves.

D. Elastic Material Properties and Material Model Selection

In this paper, we assumed that the effects of different normalbreast tissue types other than the fat and fibroglandular tissueswere negligible. In addition, the normal breast tissues were mod-eled as one tissue type consisting of the volume fractions of thefat and fibroglandular tissues. These volume fractions were cal-culated by segmenting the fat tissue from the diagnostic MRIand calculating its volume. The total breast volume was alsocalculated. The fat tissue/total breast volume ratio was 0.67.

Our elastic material properties for the homogeneous breasttissue model were derived by first considering the volume frac-tion rule

E (ε)breast = E (ε)fat Vfat + E (ε)fibroglandular (1 − Vfat) .(6)

The variable Vfat is the volume fraction of fat tissue. Thefunctions E(ε)fat and E(ε)fibroglandular were derived by fittingWellman’s [14] experimentally derived elastic modulus versusstrain data for fat and fibroglandular tissues to third-order poly-nomials. Equation (6) was then integrated with respect to strain(ε) resulting in the constitutive relationship for the homogeneousbreast tissue model (see Fig. 6).

Using Wellman’s [17] material property data for lobular can-cer, the constitutive relationship for the suspect lesion was sim-ilarly derived. The elastic modulus versus strain data was fittedto a third-order polynomial and integrated with respect to strain.

Fig. 7. Construction of surface boundary conditions from the biopsy MRvolume.

The corresponding stress versus strain relationship is also shownin Fig. 6.

The constitutive relationships for the breast and lesion tissueswere imported into Mentat and fitted to the Neo-Hookean mate-rial model. C10 , the Neo-Hookean material parameter, was 1.1and 4.2 kPa for the breast and lesion tissues, respectively.

E. Boundary Conditions

Fig. 7 is a flowchart that shows how we constructed surfacesfrom the biopsy MR volume and prescribed them as boundaryconditions. The process was divided into six steps. 1) With thebiopsy MRI aligned with the diagnostic MRI, it was renderedinto a 3-D image. 2) Similar to the diagnostic MR volume, thebreast surface was segmented from the biopsy MR volume andconverted into a triangular shell mesh. 3) Since the surface meshquality was insufficient for FEA, this surface was imported intoHyperMesh and refined. 4) The breast surface triangular shellmesh was converted into IGES format using the mesh-to-surfacetool in HyperMesh. 5) The surface was then divided into twohalves to reflect the effects of the compression and immobiliza-tion plates. In addition, a medial section was developed fromthe IGES surface to replicate the medial section of the breast.These three surfaces were defined as rigid contact surfaces (theinterfacing breast elements were defined as deformable contactelements). They were initially positioned so that there was nosurface to mesh contact. The simulation was carried out by sim-ply reversing their initial positions (the surfaces translate fromtheir positions in step 5 back their positions in step 4) (seeFig. 7).

In this study, it was assumed that the nodes at the pectoralfascia and rib interface do not move.

F. FEA Solution Methods

Our FEA methodology for simulating breast compression issummarized here.

1) Element type: 7823 linear tetrahedral, full integration Her-rmann formulation.

2) Contact: rigid, touching contact (rigid surface–breast FEmesh interface).


Fig. 8. Convergence curve: relative residual force magnitude.

3) Links: insert kinematic constraint (lesion-breast nodes).4) Boundary conditions: displacement controlled.5) Dynamic effects: none (quasi-static).6) Solution control: large displacement, large strain,

Lagrangian, Newton-Raphson.7) Stepping procedure: Multicriteria adaptive.8) Convergence criteria: relative residual force magnitude,

tolerance ≤0.1.

V. RESULTS

In this section, we present the predicted breast tissue defor-mation results. Thirty-six increments were used to process theproposed FE breast model. During increments 1–17, the medialsection was applied. The surfaces representing the compressionand immobilization plates were simultaneously applied duringincrements 18–36. The convergence tolerance, 0.1, was satisfiedat each increment (see Fig. 8). On a Hewlett Packard notebook(dv7-3085dx), the total processing time was 20 min.

The results are arranged into the following: 1) notable in-cremental deformation configurations and deformation contourplots; 2) suspect lesion travel; and 3) suspect lesion overlaidonto the FEA results.

A. Notable Incremental Deformation Configurations andContour Plots

Table II highlights the FE breast model’s incremental de-formation configurations. The prescribed medial section travelwas complete at increment 17. This was followed by the si-multaneous application of the compression and immobilizationplate surfaces. Contact with the compression and immobiliza-tion plate surfaces began at increments 26 and 32, respectively.Finally, the rigid surface travel was complete at increment 36.

Fig. 9 shows the displacement contour plot overlaid on thedeformed FE breast model after the rigid surfaces have beenapplied, increment 36. As expected, the deformed surface profilereplicates the surface profile of the biopsy MR volume. Thepeak compression and immobilization plate travel is 46 mm and15 mm, respectively.

TABLE IINOTABLE INCREMENTAL DEFORMATION CONFIGURATIONS

B. Suspect Lesion Travel

ANALYZE was used to calculate the position coordinates ofthe suspect lesion’s centroid in the undeformed and compressedbreast volumes. The lesion’s displacement vector was calculatedby subtracting the lesion’s position vector in the biopsy MR vol-ume from the lesion’s position vector in the diagnostic MR vol-ume; the corresponding displacement magnitude was calculatedfrom this position vector difference. The centroidal coordinates,in mm, of the lesion from the diagnostic and biopsy MR vol-umes were (79.7, 219.3, 44.5) and (68.7, 218, 40.1), respectively.The corresponding magnitude difference was 11.81 mm whichrepresents lesion travel between the diagnostic and biopsy MRvolumes.

After applying the rigid surfaces, the predicted travel of thelesion’s centroid was (7.8, 4.7, 1.0), in mm. The correspondingmagnitude was 9.2 mm. The difference between the actual andsimulated lesion travel, at the centroid, was 2.6 mm.

C. Suspect Lesion Overlaid Onto the FEA Results

Fig. 10 shows the actual lesion (left), segmented from thebiopsy MR volume, overlaid onto the FEA results (right). The


Fig. 9. Displacement contour plots: view from (top) immobilization plate sideand (bottom) compression plate side.

Fig. 10. Actual lesion (left) overlaid onto the FEA results (right). The amountof overlap is highlighted (black).

amount of overlap is highlighted in black. The volumes of thelesion segmented from the diagnostic and biopsy MRIs were390 and 463 mm2 , respectively. The overlapping volume was151 mm2 . CAD tools were used to calculate the lesion volumes.The overlapping volume was created from the intersection ofthe lesion surfaces.

It is hypothesized that the deviation between these surfaceswas due, primarily, to the anisotropic nature of breast tissueand the difference in lesion visualization between the breastdiagnostic and biopsy MR volumes. Breast tissue anisotropyis beyond the scope this paper; modeling anisotropic materialbehavior may increase the amount of overlap between the actualand predicted lesion positions and should be considered in futureresearch.

VI. DISCUSSION

Potentially, radiologist would use our method for prescrib-ing boundary conditions, in combination with FEA methodsdeveloped by previous researchers, to assist in targeting sus-pect lesions that are difficult to localize with the breast com-pressed between rigid plates. Previous researchers have devel-oped stand-alone algorithms for segmenting the breast surface,lesions, and fibroglandular tissue. The physician would simu-late breast compression in three stages: 1) with the sternum usedas a rigid registration feature, they would align the diagnosticand biopsy MR volumes; 2) CAD surfaces would then be con-structed representing the perimeter of the biopsy MR volume;

and 3) using these surfaces as prescribed boundary conditions,a patient-specific FE breast model would be used to predict thelocation of suspect lesions.

VII. CONCLUSION

In conclusion, this research made two points. 1) Construct-ing surfaces from the biopsy MR volume and using them todeform the FE breast mesh appears to be a viable alternativefor simulating breast compression. With this method, the effectsof external contacting bodies are considered without having todirectly model them. 2) The results suggest that the effects ofbreast compression during an MRI-guided biopsy can be pre-dicted from only the diagnostic and biopsy MRI data. Additionalapplications include nonrigid image registration, elastography,and surgical planning for brachytherapy treatment.

Since our FEA method was demonstrated on a single case,our evidence is limited to this patient. For this reason, we willuse our proposed FEA method to study additional cases. Theseadditional cases will include different types of suspect lesiontissue, lesions situated in different quadrants of the breast, andmultiple suspect lesions (dual biopsy). In addition, we plan toautomate surface construction from the deformed MRI data.Automating the construction of boundary conditions is a keyenabler for transferring this technology from the bench to thebedside.

ACKNOWLEDGMENT

The authors would like to thank Dr. Kathy Schilling, MedicalDirector of Imaging and Intervention, for the Boca RadiologyGroup, Boca Raton, FL. He supplied the MR image volumesand the corresponding diagnostic details.

REFERENCES

[1] (2010). [Online]. Available:http://www.cancer.gov/cancertopics/types/breast.

[2] S. A. Kane, Introduction to Physics in Modern Medicine. Boca Raton,Fl: CRC Press, 2003, pp. 315–316.

[3] L Sider, Ed., Introduction to Diagnostic Imaging. New York, NY:Churchill Livingstone Inc., 1986, pp. 36–38.

[4] A. Perez del Palomar, B. Calvo, J. Herrero, J. Lopez, and M. Doblare, “Afinite element model to accurately predict real deformations of the breast,”Med. Eng. Phys., vol. 30, no. 9, pp. 1089–1097, Nov. 2008.

[5] A. Samani, A. J. Bishop, M. J. Yaffe, and D. B. Plewes, “Biomechanical3-D finite element modeling of the human breast using MRI data,” IEEETrans. Med. Imag., vol. 20, no. 4, pp. 271–279, Apr. 2001.

[6] M. Z. Unlu, A. Krol, A. Magri, J. A. Mandel, W. Lee, K. G. Baum,E. D. Lipson, I. L. Coman, and D. H. Feiglin, “Computerized methodfor nonrigid MR-to-PET breast-image registration,” Comput. Biol. Med.,vol. 40, no. 1, pp. 37–53, Jan. 2010.

[7] O. Zhang, A. Qiu, D. B. Goldgof, S. Sarkar, and L. Li, “3D finite elementmodeling of nonrigid breast deformation for feature registration in X-rayand MR images,” in Proc. IEEE Workshop Appl. Comput. Vision, Feb.2007, pp. 38–44.

[8] F. S. Azar, D. N. Metaxas, and M. D. Schnall, “Methods for modeling andpredicting mechanical deformations of the breast under external pertur-bations,” in Proc. IEEE Workshop Math. Methods Biomed. Image Anal.,vol. 6, no. 1, Mar. 2002, pp. 1–27.

[9] N. V. Ruiter, R. Stotzka, T. O. Muller, and H. Gemmeke, “Model-basedregistration of X-ray mammograms and MR images of the female breast,”in Proc. IEEE Symp. Conf. Nuclear Sci., Oct.16–22, 2004, vol. 5, pp. 3290–3294.

[10] J. A Schnabel, C. Tanner, A. D. Castellano-Smith, A. Degenhard,M. O. Leach, D. R. Hose, D. L. G. Hill, and D. J. Hawkes, “Validation of


nonrigid image registration using finite-element methods: application tobreast MR images,” IEEE Trans. Med. Imag., vol. 22, no. 2, pp. 238–247,Feb. 2003.

[11] L. Roose, W. De Maerteleire, W. Mollemans, and P. Suetens, “Validationof different soft tissue simulation methods for breast augmentation,” inProc. Int. Congr. Series Comput. Assisted Radiol. Surg., vol. 1281, May2005, pp. 485–490.

[12] C. Tanner, A. Degenhard, J. A. Schnabel, A. C. Smith, C. Hayes,L. I. Sonoda, M. O. Leach, D. R. Hose, D. L. G. Hill, and D. J. Hawkes,“A method for the comparison of biomechanical breast models,” in Proc.IEEE Workshop Mathematical Methods in Biomedical Image Analysis,2001, pp. 11–18.

[13] A. N. Gent, Ed., Engineering with Rubber: How to Design Rubber Compo-nents. Cincinnati, OH: Hanser Gardner Publications, Inc., 2001, pp. 50–54.

[14] Getting Started With MSC. Nastran: User’s Guide, MSC Software Cor-poration, Santa Ana, CA, 2009.

[15] T. A. Krouskop, T. M. Wheeler, F. Kallel, B. S. Garra, and T. Hall, “Elasticmoduli of breast and prostate tissues under compression,” Ultrason. Imag.,vol. 20, pp. 260–274, 1998.

[16] Y. C. Fung, Biomechanics: Mechanical Properties of Living Tissues. 2nded., New York: Springer-Verlag, 1993.

[17] P. S. Wellman, “Tactile Sensing,” Ph.D. dissertation, Div. Eng. Comput.Sci., Harvard Univ., 1999.

[18] Z. G. Wang, Y. Liu, G. Wang, and L. Z. Sun, “Elastography method forreconstruction of nonlinear breast tissue properties,” Int. J. Biomed. Imag.,vol. 2009, article ID 406854, p. 9, 2009.

[19] A. R. Skovoroda, A. N. Klishko, D. A. Gusakyan, Y. I. Mayevskii,V. D. Yermilova, G. A. Oranskaya, and A. P. Sarvazyan, “Quantitativeanalysis of the mechanical characteristics of pathologically changed softbiological tissues,” Biophysics, vol. 40, no. 6, pp. 1359–1364, 1995.

[20] A. P. Sarvazyan, A. R. Skovoroda, and Y. P. Pyt’ev, “Mechanical in-troscopy: A new modality of medical imaging for detection of breastand prostate cancer,” in Proc. Int. Workshop Interaction Ultrasound withBiological Media, Valenciennes, France, 1994, pp. 69–81.

[21] C. Tanner, M. White, S. Guarino, M. A. Hall-Craggs, M. Douek, andD. J. Hawkes, “Anisotropic behaviour of breast tissue for large compres-sions,” in Proc. IEEE Int. Symp. Biomed. Imag.: From Nano to Macro,Jun. 28, 2009/Jul. 1, 2009, pp. 1223–1226.

[22] L. L. Hench, and J. R. Jones, Eds., Biomaterials, Artificial Organs andTissue Engineering. Boca Raton, FL: CRC Press, 2005.

[23] J. H. Hipwell, C. Tanner, W. R. Crum, J. A. Schnabel, and D. J. Hawkes,“A new validation method for X-ray mammogram registration algorithmsusing a projection model of breast X-ray compression,” IEEE Trans. Med.Imag., vol. 26, no. 9, pp. 1190–1200, Sep. 2007.

[24] W. D. Callister, Material Science and Engineering: An Introduction.New York, NY: Wiley, 1994, pp. 516–518.

[25] J. H. Chung, V. Rajagopal, T. A. Laursen, P. M. F. Nielsen, and M. P. Nash,“Frictional contact mechanics methods for soft materials: Application totracking breast cancers,” J. Biomech., vol. 41, no. 1, pp. 69–77, 2008.

[26] P. Pathmanathan, D. J. Gavaghan, J. P. Whiteley, S. J. Chapman, andJ. M. Brady, “Predicting tumor location by modeling the deformation ofthe breast,” IEEE Trans. Biomed. Eng., vol. 55, no. 10, pp. 2471–2480,Oct. 2008.

[27] R. D. Cook, Concepts and Applications of Finite Element Analysis, 2nded. New York, NY: Wiley, 1981, pp. 351–353.

[28] J. Bonet and R. Wood, Nonlinear Continuum Mechanics for Finite ElementAnalysis. New York, NY: Cambridge Univ. Press, 1997, pp. 57–64.

[29] MSC.Marc R©Volume A: Theory and User Information, MSC SoftwareCorporation, Santa Ana, CA, 2005.

[30] Analyze 10.0 Essential Training Guide, AnalyzeDirect, Overland Park,KS, 2010.

[31] HyperMesh 10.0, User Manual, Altair Engineering, Troy, MI, 2010.[32] I. N. Bankman, Handbook of Medical Imaging Processing and Analysis..

San Diego: Academic Press, 2000.[33] M. Betke, H. Hong, D. Thomas, C. Prince, and J. Ko, “Landmark detection

in the chest and registration of lung surfaces with an application to noduleregistration,” J. Med. Image Anal., vol. 7, pp. 265–281, 2003.

[34] F. H. Netter, Atlas of Human Anatomy, 2nd ed. East Hanover, NJ: No-vartis, 1997.

[35] M. L. Stewart, L. M. Smith, and N. Hall, “A numerical investigation ofbreast compression: Lesion modeling,” Int. J. Contemp. Adv. Math., 2011.

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A Numerical Investigation of Breast Compression: A Computer-Aided Design Approach for Prescribing Boundary Conditions