Establishment of a Numerical Model to Design an Electro-Stimulating System for a Porcine Mandibular Critical Size Defect
<p>(<b>a</b>) Computer tomographic pictures of the head of a minipig. To reduce unnecessary computational costs in the later simulations the upper part of the head has been removed in the modelling process. (<b>b</b>) CAD model of a defective minipig mandible and its surrounding tissues, equipped with an electro-stimulating implant. The critical size defect (region of interest) is highlighted in red. (<b>c</b>) Bipolar electro-stimulating implant consisting of stimulating electrode (“Electrode 1”), insulator and counter-electrode (“Electrode 2”). The parameters <math display="inline"><semantics> <msub> <mi>h</mi> <mi>el</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>φ</mi> <mi>stim</mi> </msub> </semantics></math> are to be optimized.</p> "> Figure 2
<p>Equivalent circuit model for the electrode–tissue interface.</p> "> Figure 3
<p>Boundary conditions applied in the simulation model: We assigned Dirichlet boundary conditions to the surfaces of both electrodes (black), homogeneous Neumann boundary conditions to the surface of the skin (blue), and a floating potential boundary condition to the surface enclosing the defect (red).</p> "> Figure 4
<p>(<b>a</b>) Simulated electric field norm <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <munder> <mi mathvariant="bold">E</mi> <mo>̲</mo> </munder> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> in a slice through the electrically stimulated minipig mandible (<math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mi>el</mi> </msub> <mo>=</mo> <mn>25</mn> <mspace width="0.166667em"/> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>φ</mi> <mi>stim</mi> </msub> <mo>=</mo> <mn>0.523</mn> <mspace width="0.166667em"/> <mi mathvariant="normal">V</mi> </mrow> </semantics></math>). Scale is bounded for field strengths between 5 and 70 <math display="inline"><semantics> <mi mathvariant="normal">V</mi> </semantics></math>/<math display="inline"><semantics> <mi mathvariant="normal">m</mi> </semantics></math> and the arrow length is normalized. (<b>b</b>) Region with beneficially (top, green) and overstimulated (bottom, red) tissue around the electro-stimulating implant. The depicted mesh on the mandible bone corresponds to the finite-element discretization used in the simulations.</p> "> Figure 5
<p>Volume of under-, beneficially, and overstimulated tissue in the ROI at a stimulation amplitude of <math display="inline"><semantics> <mrow> <msub> <mi>φ</mi> <mi>stim</mi> </msub> <mo>=</mo> <mn>1</mn> <mspace width="0.166667em"/> <mi mathvariant="normal">V</mi> </mrow> </semantics></math> as a function of the electrode length <math display="inline"><semantics> <msub> <mi>h</mi> <mi>el</mi> </msub> </semantics></math>.</p> "> Figure 6
<p>Impact of changing the electrical conductivity <math display="inline"><semantics> <msub> <mi>σ</mi> <mi>defect</mi> </msub> </semantics></math> in the defect domain on the volume of stimulated tissue and the current flowing through the electrodes.</p> ">
Abstract
:1. Introduction
2. Materials and Methods
- setting up the anatomical and technical model, i.e., segmenting computer tomographic (CT) data and computer-aided design (CAD) modelling based on the segmentation.
- setting up the physical model, i.e., the anatomical and technical models are assigned their dielectric properties.
- setting up the corresponding boundary value problem, i.e., the needed equations for simulating the electric field distribution.
- solving the boundary value problem.
2.1. Anatomical and Technical Model Generation
2.2. Generation of the Physical Model
2.3. Modelling of the Electrode–Tissue Interface
2.4. Electro-Quasistatic Boundary Value Problem
2.5. Optimization of the Stimulation Parameters
2.6. Finite-Element Simulation
3. Results
3.1. Electric Field Distribution
3.2. Optimized Electrode Parameters
3.3. Impact of Varying Tissue Conductivity
4. Discussion
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Raben, H.; Kämmerer, P.W.; Bader, R.; van Rienen, U. Establishment of a Numerical Model to Design an Electro-Stimulating System for a Porcine Mandibular Critical Size Defect. Appl. Sci. 2019, 9, 2160. https://doi.org/10.3390/app9102160
Raben H, Kämmerer PW, Bader R, van Rienen U. Establishment of a Numerical Model to Design an Electro-Stimulating System for a Porcine Mandibular Critical Size Defect. Applied Sciences. 2019; 9(10):2160. https://doi.org/10.3390/app9102160
Chicago/Turabian StyleRaben, Hendrikje, Peer W. Kämmerer, Rainer Bader, and Ursula van Rienen. 2019. "Establishment of a Numerical Model to Design an Electro-Stimulating System for a Porcine Mandibular Critical Size Defect" Applied Sciences 9, no. 10: 2160. https://doi.org/10.3390/app9102160