# Fluid-Structure Interaction Analysis of Subject-Specific Mitral Valve Regurgitation Treatment with an Intra-Valvular Spacer

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Model Development

#### 2.2. Fiber Orientation

#### 2.3. Constitutive Model

#### 2.4. Numerical Methods

^{®}(IMPETUS Afea AS, Norway), and IMPETUS Afea Solver

^{®}were used for all simulations. Both fluid and solid domains, and their interaction, were solved with an explicit time-integration scheme. All simulations were solved on a standard workstation. Parallel acceleration was achieved with a Tesla K40 GPU with 12 GB of Graphic DDR memory and 2880 CUDA Cores.

#### 2.5. Application to Assessment of Spacer Efficacy

^{2}, which was subtracted from the predictions of ROA in this study [30]. Subsequently, the same nodes were used to compute the enclosed area in the FSI results of the spacer simulations, minus the corresponding cross-sectional area of the spacer.

## 3. Results

## 4. Discussion

## 5. Limitations and Future Work

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

MR | Mitral Regurgitation |

DMR | Degenerative Mitral Regurgitation |

FMR | Functional Mitral Regurgitation |

FDA | Food and Drug Administration |

MV | Mitral Valve |

FSI | Fluid-Structure Interaction |

ROA | Regurgitant Orifice Area |

$\mu $CT | Micro-Computed Tomography |

SPH | Smoothed Particle Hydrodynamics |

GPU | Graphics Processing Unit |

3D | Three-Dimensional |

1D | One-Dimensional |

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**Figure 1.**The detailed MV model extracted from DICOM $\mu $CT images with all chords preserved; and schematic showing the fluid particles confined in a pipe-like rigid structure surrounding the MV model. Prescribed velocity boundary conditions are applied to the open ends via the use of moving pistons in z-direction.

**Figure 2.**Pipeline of the computational process from a medical imaging technique (micro-computed tomography, i.e., $\mu $CT) to post-processing the results in order to investigate the anatomy and physiology of the mitral valve.

**Figure 3.**Geometries reached with simulations of full (

**a**) and partial (

**b**) closures at the T = T

_{sys}. Partial closure was obtained by removing a set of chords from the healthy model.

**Figure 4.**Cutaway of the computational model showing the location ($\#9$) of the ruptured chordae tendinae (in red) used in this study to simulate functional mitral regurgitation.

**Figure 6.**Two different closures reached depending on the stiffness of the springs used. (

**a**) Springs with k = 0.1 KN/m, (

**b**) Springs with k = 1 KN/m.

**Figure 7.**(

**a**) The distance which the spacer has translated by the time of MV closure and the resulting elongation of the springs depending on their stiffness. (

**b**) The decomposed distance which the spacer has translated by the time of MV closure depending on the spring stiffness. (

**c**) The forces in the springs attached to the spacer depending on their stiffness. (

**d**) The anatomic regurgitant orifice area depending on the stiffness of the springs used.

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**MDPI and ACS Style**

Toma, M.; Einstein, D.R.; Bloodworth, C.H., IV; Kohli, K.; Cochran, R.P.; Kunzelman, K.S.; Yoganathan, A.P.
Fluid-Structure Interaction Analysis of Subject-Specific Mitral Valve Regurgitation Treatment with an Intra-Valvular Spacer. *Prosthesis* **2020**, *2*, 65-75.
https://doi.org/10.3390/prosthesis2020007

**AMA Style**

Toma M, Einstein DR, Bloodworth CH IV, Kohli K, Cochran RP, Kunzelman KS, Yoganathan AP.
Fluid-Structure Interaction Analysis of Subject-Specific Mitral Valve Regurgitation Treatment with an Intra-Valvular Spacer. *Prosthesis*. 2020; 2(2):65-75.
https://doi.org/10.3390/prosthesis2020007

**Chicago/Turabian Style**

Toma, Milan, Daniel R. Einstein, Charles H. Bloodworth, IV, Keshav Kohli, Richard P. Cochran, Karyn S. Kunzelman, and Ajit P. Yoganathan.
2020. "Fluid-Structure Interaction Analysis of Subject-Specific Mitral Valve Regurgitation Treatment with an Intra-Valvular Spacer" *Prosthesis* 2, no. 2: 65-75.
https://doi.org/10.3390/prosthesis2020007