Research Papers

Advances in Finite Element Simulations of Elastosonography for Breast Lesion Detection

[+] Author and Article Information
Simona Celi

 Istituto di Fisiologia Clinica, Consiglio Nazionale delle Ricerche, IFC-CNR, Via Aurelia Sud, Massa 54100 Italy, e-mail: s.celi@ifc.cnr.it

Francesca Di Puccio

Dipartimento di Ingegneria Meccanica, Nucleare e della Produzione,  Università di Pisa, Largo Lucio Lazzarino 1, Pisa 56122 Italyfrancesca.dipuccio@dimnp.unipi.it

Paola Forte

Dipartimento di Ingegneria Meccanica, Nucleare e della Produzione,  Università di Pisa, Largo Lucio Lazzarino 1, Pisa 56122 Italypaola.forte@dimnp.unipi.it

J Biomech Eng 133(8), 081006 (Sep 06, 2011) (13 pages) doi:10.1115/1.4004491 History: Received July 29, 2010; Revised June 10, 2011; Posted June 30, 2011; Published September 06, 2011; Online September 06, 2011

Among the available tools for the early diagnosis of breast cancer, the elastographic technique based on ultrasounds has many advantages such as the noninvasive measure, the absence of ionizing effects, the high tolerability by patients, and the wide diffusion of the ecographic machines. However this diagnostic procedure is strongly affected by many subjective factors and is considered not reliable enough even to reduce the number of biopsies used to identify the nature of lesions. Therefore in the literature experimental and numerical simulations on physical and virtual phantoms are presented to test and validate procedures and algorithms and to interpret elastosonographic results. In this work, first a description of the elastographic technique and a review of the principal finite element (FE) models are provided and second diagnostic indexes employed to assess the nature of a lump mass are presented. As advances in FE simulations of elastosonography, axisymmetric phantom, and anthropomorphic models are described, which, with respect to the literature, include some features of breast mechanics. In particular deterministic analyses were used to compare the various details of virtual elastograms and also to investigate diagnostic indexes with respect to the regions where strains were considered. In order to improve the reliability of the elastosonographic procedure, univariate and multivariate sensitivity analyses, based on a probabilistic FE approach, were also performed to identify the parameters that mostly influence the deformation contrast between healthy and cancerous tissues. Moreover, synthetic indicators of the strain field, such as the strain contrast coefficient, were evaluated in different regions of interest in order to identify the most suitable for lesion type assessment. The deterministic analyses show that the malignant lesion is characterized by a uniform strain inside the inclusion due to the firmly bonding condition, while in the benign inclusion (loosely bonded) a strain gradient is observed independently from the elastic modulus contrast. The multivariate analyses reveal that the strain contrast depends linearly on the relative stiffness between the lesion and the healthy tissue and not linearly on the interface friction coefficient. The anthropomorphic model shows other interesting features, such as the layer or curvature effects, which introduce difficulties in selecting a reference region for strain assessment. The results show that a simple axisymmetric model with linear elastic material properties can be suitable to simulate the elastosonographic procedure although the breast curvature and layer distinction play a significant role in the strain assessment.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

(a) A mimicking phantom with hard and soft inclusions pre and post compression. (b) RF data from an uncompressed and a compressed echo. (c) Signal processing procedure from sonogram to ES strain map obtained by means of a block-matching algorithm.

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Figure 2

Anatomy of the breast (adapted from Wikimedia; original author: Patrick J. Lynch)

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Figure 3

Stress-strain curves for (a) fat and (b) glandular tissues, according to published studies (LE = linear elastic; Exp = exponential; NH = neo-Hookean; MR = Mooney Rivlin)

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Figure 4

Axisymmetric models of (a) a cylindrical phantom and (b) of an anthropomorphic breast geometry with skin layer and distinction between fatty and glandular tissue

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Figure 5

Regions of interest used for the evaluation of Cs

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Figure 6

Axial strain plots for loosely bonded model with (a) soft and (b) hard inclusion; firmly bonded model with (c) soft and (d) hard inclusion (soft or hard lesion corresponds to Cm  = 1.5 or 7, respectively)

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Figure 8

Principal strain directions for (a) a soft benign lesion without friction and for (b) a fully bonded malignant hard inclusion, and (c) and (d) corresponding zoomed windows. (Soft or hard lesion corresponds to Cm  = 1.5 or 7.)

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Figure 9

Strain maps for benign inclusion (Cm  = 1.5) with layer: (a) ɛyy and (b) ɛxy ; corresponding maps for malignant inclusion (Cm  = 7)

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Figure 11

Cs plots as function of the (a) friction coefficient and with (b) simultaneous variation of stiffness and friction

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Figure 12

(a) Correlation coefficients for Cs with respect to the input variables. (b) Cs5 trend in the whole input variables space. The dashed line represents the case for Cm  = 3 reported in Fig. 1 while the dashed-dotted line represents the results reported in Fig. 1.

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Figure 13

Strain maps (ɛyy ) of different inclusion types in a breast model with (a) and (c) 20% and (b) and (d) 40% of fatty tissue; soft and loosely bonded lesion in (a) and (b) and hard and firmly bonded lesion in (c) and (d). (Soft or hard lesion corresponds to Cm  = 1.5 and 7, respectively.)

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Figure 14

(a) Cs plots as function of the friction coefficient and (b) with simultaneous variation of stiffness and friction

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Figure 15

(a) Correlation coefficients of the Cs with respect to the input variables. (b) Cs5 trend in the whole input variables space.

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Figure 10

Cs plots as function of the material properties for a (a) loosely and (b) firmly bonded model

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Figure 7

(a) Plot of strain ɛyy along four vertical lines for the (b) benign soft and (c) malignant hard inclusion




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