# Towards a Clinically Applicable Computational Larynx Model

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## Abstract

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## Featured Application

**Potential application in medical diagnostic and therapeutic processes in the field of voice disorders.**

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Model and Measuring Techniques

#### 2.2. Numerical Model and Methods

#### 2.2.1. Geometry of Computational Model and Vocal Fold Motion

#### 2.2.2. Numerical Methods

`STAR-CCM+`(Siemens PLM Software, Plano, TX, USA) with a finite-volume cell-centered non-staggered grid. LES with a WALE (wall-adapting local eddy-viscosity) [61] subgrid scale model was performed to model the turbulent flow in the larynx. A central difference scheme with second-order accuracy was used to discretize the convective and diffusive terms of the Navier-Stokes equations. These pressure-velocity linked equations were solved non-iteratively within a PISO (Pressure-Implicit with Splitting of Operators) algorithm [62]. An algebraic multigrid (AMG) method with a Gauss-Seidel relaxation scheme and biconjugate gradient accelerator was used to solve the final linear system of equations. The density and kinematic viscosity of air were considered to be $\mathsf{\rho}=1.18\phantom{\rule{0.166667em}{0ex}}\mathrm{kg}/{\mathrm{m}}^{3}$ and $\mathsf{\nu}=1.57\times {10}^{-5}\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{2}/\mathrm{s}$, respectively.

#### 2.2.3. Boundary Conditions

#### 2.2.4. Mesh Generation and Mesh Motion

`STAR-CCM+`was employed to manage the mesh motion for moving boundaries. In this method, a fixed Eulerian background mesh is assigned to the whole numerical domain and an overset mesh wrapped around each vocal fold. The cells in the overset regions are always active and deform according to the movement of the boundaries in an Arbitrary Lagrangian-Eulerian (ALE) manner. The cells in the background region are fixed and become inactive wherever they overlap with the overset cells. As a result, the total number of cells changes during an oscillation cycle depending on the distance between the vocal folds. Furthermore, some cells are required between the overset and background regions as interpolation layers. Therefore, complete closure of the glottis was not possible in this model and a minimum glottal gap of 0.2 mm was forced in the glottis during the glottal closure, which caused negligible leakage.

#### 2.2.5. Reduction of Mesh Resolution

## 3. Validation of the Computational Model

## 4. Results and Discussion

#### 4.1. Reduction of Computational Costs

#### 4.2. Using HPC Resources to Reduce the Time-to-Solution

## 5. Summary and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic of the experimental larynx model with the locations of the pressure sensors and the ROI in the supraglottal channel for the PIV measurement. The high-speed camera downstream of the supraglottal exit recorded the motion of synthetic vocal folds from a superior view. All dimensions are in mm.

**Figure 2.**(

**a**) Schematic of the numerical larynx model. (

**b**) Glottal area waveform based on the experimental model flow-induced motion of vocal folds. (

**c**) Geometry of the vocal fold at the middle of the cycle. The medial surface is defined with blue. R1 = 1 mm and R2 = 2 mm.

**Figure 3.**Experimental (

**a**) subglottal pressure waveform (${\mathrm{P}}_{\mathrm{s}}^{\prime}\left(\mathrm{t}\right)$) and (

**b**) pressure waveform at 60 mm downstream of the glottis exit (${\mathrm{P}}_{60}^{\prime}\left(\mathrm{t}\right)$). The red lines are the corresponding mean pressure values.

**Figure 4.**Principle structure of the finest mesh. Gray: cells with base size. Yellow: Cells with basic refinement. Red: Cells with glottis refinement.

**Figure 6.**Planar velocity contours with vectors in the mid-coronal plane of the PIV measurement and case C4 at the middle of the oscillation cycle.

**Figure 7.**Time evolution of the magnitude of the velocity along the mid-axis of the supraglottal channel for an oscillation cycle. The velocity evolution of the computational model is related to one instantaneous cycle but the experimental velocity evolution is phase-averaged. The averaged velocity evolution of the computational model, smoothed by a low-pass filter (cutoff frequency = 5000 Hz), is added to the plots for the sake of better comparison.

**Figure 8.**Velocity magnitude contour plots with streamlines in the mid-coronal plane for all mesh resolutions MB-M3 (parts (

**a**–

**d**)) at the same time instance 0.8T in the oscillation cycle. The arrow shows the flow direction.

**Figure 9.**Velocity magnitude contours with slashed streamlines in the mid-coronal plane of the glottal duct of different meshes MB–M3 (parts (

**a**–

**d**)) at the time instance of maximum glottal divergent angle (0.58 T).

**Figure 10.**Velocity magnitude iso-surface of 50 $\mathrm{m}/\mathrm{s}$ at the time instance 0.58 T in the oscillation cycle in coronal (left column) and sagittal (right column) perspectives for meshes MB–M3 (parts (

**a**–

**d**)).

**Figure 12.**Instantaneous (

**a**) pressure and (

**b**) velocity evolutions for one cycle of oscillation at the point P1 introduced in Figure 1 for all the meshes. The pressure evolutions were smoothed by a low-pass filter (Savitzky-Golay filter [73] with a linear polynomial and a window size of 0.3 ms) to reduce numerical noise.

**Figure 13.**Time-averaged (

**a**) static pressure distribution at the center axis of the mid-coronal plane and (

**b**) velocity profile in a cross-section of the mid-coronal plane 8 mm downstream of the glottal exit (P1 in Figure 1) for all the grids.

**Figure 14.**(

**a**) Wall time for the first 0.1 ms of the simulation and the speed-up factor versus number of cores within one node. (

**b**) Wall time for one oscillation cycle and the speed-up factor versus number of nodes, each with 10 requested physical cores (20 threads).

**Table 1.**Simulation cases with boundary conditions for comparison with the experimental results. ${\mathrm{P}}^{\prime}\left(\mathrm{t}\right)$, ${\mathrm{P}}_{\mathrm{s}}$, ${\mathrm{P}}_{\mathrm{out}}$ and ${\mathrm{P}}_{60}$ are the time-varying experimental pressure, subglottal pressure, outlet pressure and pressure at 60 mm downstream of the glottis exit, respectively.

${\mathbf{P}}_{\mathbf{s}}$ | ${\mathbf{P}}_{\mathbf{out}}$ | Supraglottal Channel Length | |
---|---|---|---|

C1 | ${\mathrm{P}}_{\mathrm{s}}^{\prime}\left(\mathrm{t}\right)$ | ${\mathrm{P}}_{0}$ | 60 mm |

C2 | $\overline{{\mathrm{P}}_{\mathrm{s}}^{\prime}}$ | ${\mathrm{P}}_{0}$ | 60 mm |

C3 | ${\mathrm{P}}_{\mathrm{s}}^{\prime}\left(\mathrm{t}\right)$ | ${\mathrm{P}}_{60}^{\prime}\left(\mathrm{t}\right)$ | 60 mm |

C4 | $\overline{{\mathrm{P}}_{\mathrm{s}}^{\prime}}$ | ${\mathrm{P}}_{60}^{\prime}\left(\mathrm{t}\right)$ | 60 mm |

C5 | $\overline{{\mathrm{P}}_{\mathrm{s}}^{\prime}}$ | ${\mathrm{P}}_{0}$ | 190 mm |

**Table 2.**Summary of the meshes used for the grid resolution reduction study and their properties. The basic and glottis refinement areas are represented in Figure 4.

Mesh | Base Size (mm) | Basic Refinement (mm) | Glottis Refinement (mm) | Average No. of Cells | $\mathbf{\Delta}\mathbf{t}$ (s) |
---|---|---|---|---|---|

MB | 0.5 | 0.25 | 0.0625 | 2.4 M | 1.00 $\times {10}^{-6}$ |

M1 | 0.56 | 0.28 | 0.070 | 1.8 M | 1.12 $\times {10}^{-6}$ |

M2 | 0.64 | 0.32 | 0.080 | 1.3 M | 1.28 $\times {10}^{-6}$ |

M3 | 0.68 | 0.34 | 0.085 | 1.1 M | 1.36 $\times {10}^{-6}$ |

${\mathbf{Err}}_{\mathbf{rel}}^{{\mathbf{L}}^{2}}$ | P1 | P2 | P3 | P4 | P5 |
---|---|---|---|---|---|

C1 | 0.76 | 0.71 | 0.78 | 0.93 | 0.99 |

C2 | 0.69 | 0.72 | 0.77 | 0.91 | 0.95 |

C3 | 0.50 | 0.46 | 0.53 | 0.28 | 0.22 |

C4 | 0.22 | 0.20 | 0.33 | 0.28 | 0.22 |

C5 | 0.47 | 0.44 | 0.49 | 0.60 | 0.60 |

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**MDPI and ACS Style**

Sadeghi, H.; Kniesburges, S.; Falk, S.; Kaltenbacher, M.; Schützenberger, A.; Döllinger, M. Towards a Clinically Applicable Computational Larynx Model. *Appl. Sci.* **2019**, *9*, 2288.
https://doi.org/10.3390/app9112288

**AMA Style**

Sadeghi H, Kniesburges S, Falk S, Kaltenbacher M, Schützenberger A, Döllinger M. Towards a Clinically Applicable Computational Larynx Model. *Applied Sciences*. 2019; 9(11):2288.
https://doi.org/10.3390/app9112288

**Chicago/Turabian Style**

Sadeghi, Hossein, Stefan Kniesburges, Sebastian Falk, Manfred Kaltenbacher, Anne Schützenberger, and Michael Döllinger. 2019. "Towards a Clinically Applicable Computational Larynx Model" *Applied Sciences* 9, no. 11: 2288.
https://doi.org/10.3390/app9112288