Research Papers

Characterizing the Biomechanical Properties of the Pubovisceralis Muscle Using a Genetic Algorithm and the Finite Element Method

[+] Author and Article Information
Elisabete Silva

Faculty of Engineering,
University of Porto,
Rua Roberto Frias s/n,
Porto 4200–465, Portugal
e-mail: silva.elisabete3@gmail.com

Marco Parente

Faculty of Engineering,
University of Porto,
Rua Roberto Frias s/n,
Porto 4200–465, Portugal
e-mail: mparente@fe.up.pt

Sofia Brandão

Department of Radiology,
CHSJ-EPE/Faculty of Medicine,
University of Porto,
Hernâni Monteiro,
Porto 4200–319, Portugal
e-mail: sofia.brand@gmail.com

Teresa Mascarenhas

Department of Obstetrics and Gynecology,
CHSJ-EPE/Faculty of Medicine,
University of Porto,
Hernâni Monteiro,
Porto 4200–319, Portugal
e-mail: tqc@sapo.pt

Renato Natal Jorge

Faculty of Engineering,
University of Porto,
Rua Roberto Frias s/n,
Porto 4200–465, Portugal
e-mail: rnatal@fe.up.pt

1Corresponding author.

This work was developed in the Institute of Science and Innovation in Mechanical and Industrial Engineering (INEGI) of the Faculty of Engineering of the University of Porto.

Manuscript received December 15, 2017; final manuscript received August 28, 2018; published online October 22, 2018. Assoc. Editor: Steven D. Abramowitch.

J Biomech Eng 141(1), 011009 (Oct 22, 2018) (11 pages) Paper No: BIO-17-1592; doi: 10.1115/1.4041524 History: Received December 15, 2017; Revised August 28, 2018

To better understand the disorders in the pelvic cavity associated with the pelvic floor muscles (PFM) using computational models, it is fundamental to identify the biomechanical properties of these muscles. For this purpose, we implemented an optimization scheme, involving a genetic algorithm (GA) and an inverse finite element analysis (FEA), in order to estimate the material properties of the pubovisceralis muscle (PVM). The datasets of five women were included in this noninvasive analysis. The numerical models of the PVM were built from static axial magnetic resonance (MR) images, and the hyperplastic Mooney–Rivlin constitutive model was used. The material parameters obtained were compared with the ones established through a similar optimization scheme, using Powell's algorithm. To validate the values of the material parameters that characterize the passive behavior of the PVM, the displacements obtained via the numerical models with both methods were compared with dynamic MR images acquired during Valsalva maneuver. The material parameters (c1 and c2) were higher for the GA than for Powell's algorithm, but when comparing the magnitude of the displacements in millimeter of the PVM, there was only a 5% difference, and 4% for the principal logarithmic strain. The GA allowed estimating the in vivo biomechanical properties of the PVM of different subjects, requiring a lower number of simulations when compared to Powell's algorithm.

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Fig. 2

T2w axial images segmented through semi-automatic segmentation (a) and finite element mesh created in the abaqus Software (b). (Coc—coccyx; OIM—obturator internus muscle; PVM—pubovisceralis muscle; SP—symphysis pubis).

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Fig. 1

MR images in the mid-sagittal plane acquired at rest (a) and at maximal Valsalva maneuver (b). The levator hiatus length (Llh) measured in the MR image acquired in the axial plane (c) and in the numerical model (d). The main pelvic structures are identified (Bla—bladder; Coc—coccyx; Llh: length of the levator hiatus; PR—puborectalis muscle; PVM: pubovisceralis muscle; SP—symphysis pubis; Vag: vagina: Ur: urethra.)

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Fig. 3

Flowchart of the inverse FEA. Several steps were executed in order to obtain the optimized material parameters (c1 and c2) for the Mooney–Rivlin constitutive model.

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Fig. 5

Function behavior along the number of simulations for the all subjects (a) and average function behavior curves (b), using the Genetic and Powell's algorithms

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Fig. 6

PVM displacement (1) and maximum principal logarithmic strain (2) for Valsalva maneuver, using the material parameters obtained through the GA (a) and Powell's algorithm (b)

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Fig. 4

Flowchart of the genetic algorithm

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Fig. 7

Antero—posterior displacement obtained for subjects 1 and 4, using the GA and Powell' algorithm

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Fig. 8

Magnitude of the displacement for three different meshes used to perform the mesh convergence analysis: (a) less refined, (b) normal (used to obtain results), and (c) more refined



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