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Mathematics
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Computational Modeling and Finite Element Method in Computational Biomedicine
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Computational Modeling and Finite Element Method in Computational Biomedicine

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Biology".

Deadline for manuscript submissions: closed (30 April 2024) | Viewed by 2689

Special Issue Editor

Dr. Ana González-Suárez

E-Mail Website
Guest Editor
Lambe Institute, University of Galway, Galway, Ireland
Interests: cardiac arrhythmias; finite element method; thermal ablation; radiofrequency; pulsed field ablation
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Computational modeling is a fast and low-cost tool used to solve problems in real contexts. Computer modeling and numerical simulations using the Finite Element Method have great relevance in our understanding and solving of biomedicine problems as it helps reduce the complexity of real clinical scenarios. Computational modeling makes it possible to give an answer about a real clinical problem that is difficult to prove with experimental techniques. Computational modeling in the context of biomedicine is also important as it helps to reduce animal testing as much as possible.

This Special Issue will focus on the contributions of computational models and simulations solved by the Finite Element Method as applied to biomedical problems. Studies combining computational modeling and experimental validation are also welcome, along with those proposing new mathematical frameworks to solve cutting-edge problems.

Authors are invited to submit high-quality papers and original research with an emphasis on new developments in computational models to study, understand and solve problems applied to all biomedical applications.

Dr. Ana González-Suárez
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • biomedicine
  • in silico modeling
  • computational modeling
  • finite element method
  • mathematics
  • multiphysics modeling

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Published Papers (2 papers)

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Research

13 pages, 1938 KiB  
Article
Differences in the Electric Field Distribution Predicted with a Mathematical Model of Cylindrical Electrodes of Finite Length vs. Infinite Length: A Comparison Based on Analytical Solution
by Ricardo Romero-Mendez and Enrique Berjano
Mathematics 2023, 11(21), 4447; https://doi.org/10.3390/math11214447 - 27 Oct 2023
Cited by 1 | Viewed by 1197
Abstract
Cylindrical-shaped metal electrodes are used in numerous medical specialties to force an electric field into the surrounding tissue (e.g., in electrical stimulation and electroporation). Although these electrodes have a limited length in reality, previous mathematical modeling studies have simplified the physical situation and [...] Read more.
Cylindrical-shaped metal electrodes are used in numerous medical specialties to force an electric field into the surrounding tissue (e.g., in electrical stimulation and electroporation). Although these electrodes have a limited length in reality, previous mathematical modeling studies have simplified the physical situation and have built a model geometry based on a cylindrical electrode of infinite length, which allows for reducing the model from 2D to 1D. Our objective was to quantify the differences in the electric field values between the finite and infinite electrode cases and assess the adequacy of the mentioned simplification for different values of electrode diameter and length. We used analytical solutions for the electric field distribution. We found that the electric field distribution is substantially different for both cases, not only near the edges of the electrode (when finite length is assumed) and in close locations (<1 mm), but even in the central area and at distances greater than 2 mm. Our work presents analytical solutions for both cases (finite and infinite length), which, despite the oscillations derived from computational limitations, could be used by researchers involved in electric field modeling in biological tissues, in order to quantify the possible error generated with simple models in geometric terms that assume infinite length. Full article
(This article belongs to the Special Issue Computational Modeling and Finite Element Method in Computational Biomedicine)
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13 pages, 6728 KiB  
Article
Low-Frequency Electrical Conductivity of Trabecular Bone: Insights from In Silico Modeling
by María José Cervantes, Lucas O. Basiuk, Ana González-Suárez, C. Manuel Carlevaro and Ramiro M. Irastorza
Mathematics 2023, 11(19), 4038; https://doi.org/10.3390/math11194038 - 23 Sep 2023
Viewed by 1050
Abstract
Background: The electrical conductivity of trabecular bone at 100 kHz has recently been reported as a good predictor of bone volume fraction. However, quantifying its relationship with free water (or physiological solution) content and the conductivities of its constituents is still difficult. Methods: [...] Read more.
Background: The electrical conductivity of trabecular bone at 100 kHz has recently been reported as a good predictor of bone volume fraction. However, quantifying its relationship with free water (or physiological solution) content and the conductivities of its constituents is still difficult. Methods: In this contribution, in silico models inspired by microCT images of trabecular bovine samples were used to build realistic geometries. The finite element method was applied to solve the electrical problem and to robustly fit the conductivity of the constituents to the literature data. The obtained effective electrical conductivity was compared with the Bruggeman three-medium mixture model using a physiological solution, bone marrow and a bone matrix. Results: The values for the physiological solution plus bone marrow (together as one material) and the bone matrix that best captured the bone volume fraction in the two-medium finite element model were σps+bm = 298.4 mS/m and σb = 21.0 mS/m, respectively. Additionally, relatively good results were obtained with the three-medium Bruggeman mixture model, with σbm= 103 mS/m, σb= 21.0 mS/m and σps= 1200 mS/m. Simple linear relationships between the proportions of constituents depending on bone volume fraction were tested. Degree of anisotropy and fractal dimension do not show detectable changes in effective conductivity. Conclusions: These results provided some useful findings for simulation purposes. First, a higher value for the electrical conductivity of bone marrow has to be used in order to obtain similar values to those of experimental published data. Second, anisotropy is not detectable with conductivity measurements for small trabecular samples (5 mm cube). Finally, the simulations presented here showed relatively good fitting of the Bruggeman mixture model, which would potentially account for the free water content and could rescale the model for whole-bone electrical simulations. Full article
(This article belongs to the Special Issue Computational Modeling and Finite Element Method in Computational Biomedicine)
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