Algorithm for Simple Automated Breast MRI Deformation Modelling

Marta Danch-Wierzchowska, Damian Borys and Andrzej Swierniak

Institute of Automatic Control, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland

Keywords:

Breast Deformation, Finite Element Modeling, MRI Images.

Abstract:

Increasing incidence of breast cancer caused development of patient-speciﬁc treatment planning procedures.

The most effective tool for breast cancer visualisation is Magnetic Resonance Imaging (MRI). However, the

MRI scans represent patient data in prone position with breast placed in signal enhancement coils, while other

procedures, i.e. surgery, PET-CT (Positron Emission Tomography fused with Computer Tomography) are

performed in patient supine position. The bigger patient breast is, the bigger its shape differ in every patient

position, what inﬂuences its interior structure and tumour location. In this paper, we present our method for

automated breast model deformation, which is based on prone MRI dataset. Proposed algorithm allows to

obtain reliable breast model in supine position in a few simple steps, without manual intervention.

1 INTRODUCTION

Recent studies show that breast cancer is the most

frequent women’s cancer around the world and it is

the second most frequent among all human cancers.

Due to that, diagnosis needs to be precise and fast,

whereas treatment needs to be as personalised as pos-

sible. Therefore, breast tissue deformation has re-

cently gained interest in various medical applications.

Considering speciﬁc anatomy of the female breast any

examination or intervention results in breast defor-

mation. For that reason, on every examinated image

set the tumour in question is placed in different area.

Moreover, female breast is very complex and irreg-

ular structure, consists of glandular lobules, adipose,

milk ducts, connective tissues and skin. It is impossi-

ble to model glandular lobules and milk ducts as sep-

arate layers, since it is almost impossible to differenti-

ate them on the MRI (Magnetic Resonance Imaging).

Due to that, breast is usually modeled as four lay-

ers: ﬁbroglandular, fat, skin and muscle (Han et al.,

2012). In case of breast deformation modelling ge-

ometric transformation are mainly used for rigid and

minor non-rigid deformation (i.e. respiratory move-

ments) (Rueckert et al., 1999). To model major non-

rigid deformation (i.e. mammography compression or

prone to supine movement) knowledge-based trans-

formation inspired by biomechanical models is used.

FEM (Finite Element Modeling) is a numerical tech-

nique and, the same, allows approximate solving of

partial differential equations (PDE), which simpliﬁes

computations. The main motivation of biomechanical

FEM models usage is that more information enables

reliable estimation of complex deformation (Lee

et al., 2010).

There are several applications of biomechanical

breast modelling. Almost all of them are related

to breast cancer diagnostics and treatment. The

oldest praxis is a mammography simulation which

presents the breast deformation caused by the plates

compression (Han et al., 2012), (Pathmanathan et al.,

2008). Another, more recent, application is breast

deformation caused by the gravitational force. Such

simulation is commonly used when different breasts

shapes comparison is needed, e.g. MRI compared

with PET-CT (Han et al., 2014). Fusion of different

examinations helps with more accurate diagnosis

(Abreu et al., 2013). Breast shape simulation in

different patient positions is used in treatment plan-

ning and tumour location during medical procedures,

e.g. surgery, biopsy procedure (Azar et al., 2000).

Already published studies concentrate on creating

one breast model based on patient or phantom data

and its deformation with one or few methods. The

results presented are very precise, but methodology

impossible to be applied in a broader spectrum.

Different modalities of breast imaging are carried out

in different patient positions. Especially, MRI imag-

ing, the most powerful method nowadays, is acquired

in patients lying in prone body position, with the

breast hanging down into the coil. However, majority

of therapeutic procedures, like surgery or radiation

114

Danch-Wierzchowska, M., Borys, D. and Swierniak, A.

Algorithm for Simple Automated Breast MRI Deformation Modelling.

DOI: 10.5220/0006586201140119

In Proceedings of the 11th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2018) - Volume 2: BIOIMAGING, pages 114-119

ISBN: 978-989-758-278-3

therapy are carried out in supine body position, with

signiﬁcant displacement of breast tissue. Thus, the

simple method of breast deformation modelling will

be of clinical use, even if it is expected that the error

of this modelling will not allow for ideal transposition

of image. However, even rough transformation gives

better estimation of tissue relationships than the

routinely carried out visual assessment, regularly

used in the clinic.

There appear some limitations that cause inaccu-

racies of the created models. The main issue is

accurate tissue parameter estimation. Biomechanical

properties of breast tissues have been measured ex

vivo (A.Samani et al., 2007), (Wellman et al., 1999).

However living tissues have different properties than

those, extracted from body without blood circulation.

Moreover existing in vivo measuring methods (i.e.

elastography) do not provide information precise

enough to estimate big deformation (Insana et al.,

2005). Another issue is accurate mesh selection.

Different types of mesh elements and different mesh

node density give different results (Samani et al.,

2001) and in some cases the FE mesh requires man-

ual intervention (Han et al., 2012) as well as image

segmentation (Han et al., 2014), (Pathmanathan

et al., 2008). Further difﬁculty provides boundary

conditions setting, especially on chest wall side,

where the model ends but the real body consistency

needs to be preserved (Tanner et al., 2002). Still

unsolved modelling issue remains patient-speciﬁc,

fully-automated image deformation algorithm, which

is essential in clinical practice.

In this paper we present a basic idea of a simple

breast model and its deformation, paying a special

attention to further use in clinical practice. Pre-

sented paper is an extension to our previous work

described in (Danch-Wierzchowska et al., 2016b).

More precisely, previously presented algorithm was

extended to 3D, so that image dataset is processed

as one 3D object, instead of processing images one

by one separately. The algorithm itself was mod-

iﬁed to eliminate issues, that were not signiﬁcant,

nor present in 2D model. The biggest challenges

were to determine dependencies between nodes and

set model’s boundary conditions and to preserve

computational-time efﬁciency, while processing

signiﬁcantly bigger number of nodes, than in 2D

analysis. In our work, we concentrated on simple and

efﬁcient way to model breast deformation, that would

help with breast cancer diagnosis and could be used

in clinical practice.

Figure 1: Exemplary breast MR image (internal green con-

tour is a chestwall boundary, external green contour is a

body boundary).

2 MATERIAL AND METHODS

2.1 Breast MRI Data Acquisition

MRI is widely used in medical diagnosis, in partic-

ular breast imaging (Behrens et al., 2007). It is safe

technique because the MRI does not use the ioniz-

ing radiation. The possibility of multiple contrasts

acquisitions, both anatomical and functional, plays a

key role in MRI breast cancer detection. In this work

we use T1-weighted MRI scans, which were acquired

at the Center of Oncology ... with a Siemens scan-

ner. The data consist of 50 axial slices of patient in

prone position covering the area of interest. Obtained

data cover approximately 0.7x0.7x3 mm real volume

per voxel. Exemplary image, with Region of Inter-

est (ROI) outlined is shown in the Figure 1. The ob-

tained MRI data constitutes basis for FEM construc-

tion. This method requires domain (image set) dis-

cretisation, tissue parameter estimation, transforma-

tion equation deﬁnition, boundary condition setting

(see 2.2).

2.2 Deformation Algorithm

Deformation algorithm consist of a few main steps

based on FEM best practices and is fully implemented

in MATLAB.

Breast Segmentation. To obtain breast mask based

on MRI image, a fuzzy c-means algorithm is used

(Wu et al., 2013). However, after segmentation, man-

ual correction is needed. The breast mask used in our

algorithm is based on ROI presented in the Figure 1,

but to the point of a widest diameter of a patient chest.

Exemplary image mask is presented in the Figure 2.

Dividing into Left/Right Part. To shorten compu-

tational time, the model is divided into left and right

Algorithm for Simple Automated Breast MRI Deformation Modelling

115

Figure 2: Exemplary breast MR image mask.

Figure 3: Exemplary resulting mesh for image set (one

point represents one mesh node).

breast, which are joined in one model after deforma-

tion. Since there is no difference in methodology we

present only one half of the model.

Mesh Generation. Mesh generation is a process

where the coordinates of object domain nodes are set.

In case of breast MRI transformation the mesh gen-

eration is performed in two steps: (1) - generating

equidistant mesh for whole image set - domain vol-

ume, (2) - choosing nodes, which overlap a segmented

images mask. The resulting mesh is presented in the

Figure 3. For more details about mesh type see 4.

Finding Boundary Nodes. To set different param-

eters, the created model is divided into three parts

(See Figure 4): skin nodes, chestwall nodes and other

(fat and ﬁbroglandular as one type) nodes. Boundary

nodes are set using neighborhood dependencies and

spatial localization.

Setting Nodes Parameters. Tissue parameters

were set according to (Azar et al., 2002) as isotropic,

homogeneous and incompressible material. Since the

data was obtained from patients at age 50-70 with

relatively big breast, it is justiﬁable to use simpliﬁ-

cation of the breast model based on assumption, that

fat material parameters have much more inﬂuence on

Figure 4: Boundary conditions for mesh, chestwall nodes

(red), skin nodes (green).

deformation than ﬁbroglandular ones (Pathmanathan

et al., 2008). Skin nodes constrain collision detection

and reaction. Chestwall nodes are set as stationary.

However, their material parameters are set, to sim-

ulate breast tissues sliding along muscles. Material

parameters used in the algorithm are presented in the

Table 1.

Table 1: Model parameters.

Node type Young Modulus Poission’s ratio

Skin 101 kPa 0.4995

Chestwall 5 kPa 0.1

Other 50 kPa 0.48

Incorporation of Gravitational Force. To imple-

ment deformation model (Azar et al., 2002) simpliﬁed

Lagrange equation of motion was used. The gravita-

tional force is applied to every node (except chestwall

nodes) in the mesh. Displacement of each node is iter-

atively calculated according to implemented equation

of motion. For more details see 4.

The incorporation of the gravitational force in the

model is performed in two steps: (1) Removal of the

gravitational force resulting from prone patient posi-

tion, (2) Application of gravitational force resulting

from supine patient position.

3 RESULTS

The exemplary deformation result is presented as

breast mesh in the supine plan. Figure 5 shows se-

lected mesh stages for an image set. The left image

is the original mesh, the middle is stage (1) of de-

formation - unload model (See 2.2), while the right

image contains the resulting mesh in supine patient

position. The resulting mesh was compared with AN-

SYS model created for the same patient in our pre-

vious work (Danch-Wierzchowska et al., 2016a) (See

BIOIMAGING 2018 - 5th International Conference on Bioimaging

116

Figure 5: Selected mesh deformation stages: original mesh

(upper left), unload mesh (upper right), resulting mesh (bot-

tom), (green - skin nodes, red - stiffened nodes, blue - other

nodes).

Figure 6: Reference ANSYS model (Danch-Wierzchowska

et al., 2016a).

Figure 6). Differences are easily visible. However,

the main shape is preserved.

Presented results are obtained in less than 30 min

per dataset on average portable computer, with mostly

automated algorithm. The only part, that requires

manual correction and extend computation time is

the image segmentation. This allows us to believe,

that our algorithm, optimised and improved, would

be useful in clinical practice.

4 DISCUSSION AND

CONCLUSIONS

It is clear that results obtained could not be precise.

There are many more conditions inﬂuencing tissue

movement than the gravitational force. There is still

muscle tension, which inﬂuences breast shape. It

is impossible to mimic all body dependencies and

movements personalized for every patient in limited

time. However, there are image processing algo-

rithms, like free-form deformation (FFD), which were

successfully used for small non-linear deformation

(Rueckert et al., 1999). The FFD algorithm could help

with a precise ﬁtting of MRI image to supine refer-

ence image. Such images are obtained during PET-

CT for example, which is also common practice in

breast cancer diagnosis. Unfortunately, FFD is inefﬁ-

cient for large image deformations and cannot be used

as the only deformation tool.

In our previous work we have presented two differ-

ent approaches to breast deformation modelling. In

(Danch-Wierzchowska et al., 2016a) we created a

simpliﬁed woman’s chest model and simulate prone

to supine position changing in ANSYS. This work

was focused on tumour displacement while patient

position changing. The modelling error of tumour

displacement was less than 2 cm for approx. 1cm

tumour diameter and the results were deemed useful

by collaborating physicians. However, working with

ANSYS required too much effort to be used in ev-

eryday clinical practice. Moreover, costs of license

and training are to expensive for average medical unit.

Our second approach (Danch-Wierzchowska et al.,

2016b) was based on one image deformation, i.e. only

2D deformation model was required. Obtained results

were comparable with the result obtained with AN-

SYS model. The 2D results were compared with ref-

erenced, cross-section images from ANSYS model.

The 3D algorithm presented in this paper eliminate

the main cause of inaccuracy in 2D modelling by

adding movement in anteroposterior axis and main-

tains tissue continuity in every direction. Neverthe-

less it is not free from inaccuracy yet and needs fur-

ther improvement.

Modelling of breast deformation is mainly focused

on the impact of gravitational force on the breast

shape. One of the main challenges is a compromise

between model accuracy and efﬁciency. Complex tis-

sue models, represent every type of tissue, present in

the breast as separate layer (Han et al., 2012), could

never be used in clinical practice, since adapting them

to each patient would be too time-consuming. To

represent real breast movement several types of con-

stitutive models was created. Most popular way to

describe stress-strain relationship for fat and glandu-

lar tissue is the hyperelastic neo-Hookean constitutive

model (Hopp et al., 2012). Analysis using available

commercial software (i.e. ANSYS) gives acceptable

results and allows to use complex constitutive tissue

models, but implementing a body geometry inside it

is still highly time-consuming (Danch-Wierzchowska

et al., 2016a), (Han et al., 2012). The best solution

would be to create a fully automated algorithm, which

build geometry based directly on medical images and

deform it, without using any third-party software, es-

pecially when using it requires manual cooperation.

The model should be based only on breast essential

Algorithm for Simple Automated Breast MRI Deformation Modelling

117

structures chosen as an compromise between accu-

racy and efﬁciency. Developing a fully-automated

tool for creating a simpliﬁed model and incorporating

gravitational force will speed up the image analysis

signiﬁcantly, along with time of diagnosis.

Our results show, that it is possible to create a sim-

ple model and in a few steps to deform it in a way

useful for treatment planning. Our main goal was

to mimic body displacement in the smallest possi-

ble number of steps with automated procedure, and

it is clear that the results obtained have a limited pre-

cision. We concluded, that there is no need to use

more sophisticated tissue constitutive model. Since

the simplest one gives acceptable results, preserving

computational efﬁciency, there is no purpose in com-

plicating the model. At the moment the methodology

does not require exact numerical Performance Index,

since the shape differences are easily visible. How-

ever, with such simple tissue model and simple defor-

mation equation, the results are promising.

Improving the deformation algorithm, creating MRI

images from obtained deformed mesh and proper seg-

mentation methods will be under further investigation

of our work.

ACKNOWLEDGEMENTS

This work was supported by the Polish Na-

tional Center of Research and Development grant

no. STRATEGMED2/267398/4/NCBR/2015 (MILE-

STONE - Molecular diagnostics and imaging in in-

dividualized therapy for breast, thyroid and prostate

cancer) (AS, DB) and the Institute of Automatic Con-

trol, Silesian University of Technology under Grant

No. BKM-508/RAU1/2017/t.1 (MDW).

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APPENDIX

Discretisation of the Domain

First step in the ﬁnite element analysis is object

domain discretisation - division into smaller domain

elements. It replaces the body with inﬁnite degrees

of freedom by a ﬁnite number of elements with ﬁnite

and strictly deﬁned degrees of freedom.

For three dimensional analysis one can discriminate

two main type of elements: four node tetrahedral el-

ement (T4) and eight node hexahedral element (Q8).

In this paper we focus on Q8 - linear brick element.

The Q8 element described in local coordinates (ξ, η,

µ) is presented below. (See Figure 7).

Figure 7: Linear brick element in local coordinates (Kattan,

2008).

Basic Equations in FEM Elastic

Deformation

The linear brick element is described by eight shape

functions listed as follows in terms of local ξ, η and µ

coordinates:

(1 − ξ)(1 − η)(1 +µ),

(1 − ξ)(1 − η)(1 − µ),

(1 − ξ)(1 + η)(1 − µ),

(1 − ξ)(1 + η)(1 + µ),

(1 + ξ)(1 − η)(1 + µ),

(1 + ξ)(1 − η)(1 − µ),

(1 + ξ)(1 + η)(1 − µ),

(1 + ξ)(1 + η)(1 + µ),

(1)

The strain displacement matrix is described as fol-

lows:

B =

|J|

(2)

Table 2: Point coordinates and weights for two points

Gauss-Legendre quadrature.

n ξ

= η

= µ

2 ξ

= ξ

= ±0.577350269189626 W

= W

= 1

where J is the Jacobian determinant and the nodal B

matrix is given by:







∂N

∂x

0 0

∂N

∂y

0 0

∂N

∂z

∂N

∂y

∂N

∂x

∂N

∂z

∂N

∂y

∂N

∂z

∂N

∂x







. (3)

Element plane strain matrix is given as follows:

D =

(1+ν)(1−2ν)







1 − ν ν ν 0 0 0

ν 1 −ν ν 0 0 0

ν ν 1 − ν 0 0 0

0 0 0

1−2ν

0 0

0 0 0 0

1−2ν

0 0 0 0 0

1−2ν







. (4)

with Young Modulus E and Poisson’s ratio ν.

The element stiffness matrix is given by:

k =

−1

DBJdξdηdµ.

(5)

Two points Gauss-Legendre quadrature (Golub and

Welsch, 1969) is used for practical evaluation of in-

tegrals (5) over the element volume. The point coor-

dinates and weights are presented in the Table 2.

To calculate nodal displacement the following struc-

tural equation is used:

U = FK

−1

(6)

where U is a node displacement matrix, F is nodal

forces matrix and K is a global stiffness matrix. Once

the boundary conditions are set, matrix U is solved

by partitioning and Gaussian elimination. For more

details see (Kattan, 2008).

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