Special Issue "Numerical Simulation in Biomechanics and Biomedical Engineering"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: 31 May 2021.

Special Issue Editor

Prof. Dr. Mauro Malvè
E-Mail Website
Guest Editor
Department of Engineering, Universidad Pública de Navarra, Campus Arrosadía s/n, Edificio de los Pinos, E-31005, Pamplona, Navarra, Spain
Interests: fluid–structure interaction; biofluid mechanics; computational modelling in biomechanics; cardiovascular biomechanics in healthy and diseased conditions; animal biomechanics; respiratory mechanics; medical devices

Special Issue Information

Dear Colleagues,

In the last decades, the improvement of the computational technology has allowed for the introduction of advanced numerical models and high-performance simulations in several fields of the engineering. In particular, biomedical engineering, which can be considered as a bridge discipline between engineering and medicine, and combines the knowledge of several aspects of both fields, has received great attention from the scientific community for its direct relation to human health. In a more general meaning, biomedical engineering also includes the study of the processes related to nature and animals.

Specific applications can be found in the understanding of human pathologies and diseases; in the advancement of the medical health care; and in the improvement of the diagnosis, of the therapies, and of the clinical outcomes, among other aspects. However, biomedical engineering should theoretically also help to reduce the number of tests in animals, and should also contribute to the improvement of their health care. More recent applications can be found in the analysis of biological problems, such as the cells’ culture and motility, and the microfluidic and diffusion processes.

This Special Issue is focused on the numerical modelling of the complex problems in the field of biomechanical and biomedical engineering, which include, but are not limited to, cardiovascular mechanics, computational biofluid dynamics, the application of novel numerical algorithms to the biomedical engineering, advances on constitutive modelling in biomechanics, diffusion models in tissue engineering, and the use of the stenting technique in humans and animals. As such, high-quality original research papers are welcome.

Prof. Dr. Mauro Malvè
Guest Editor

Manuscript Submission Information

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Keywords

  • Computational biomechanics
  • Numerical modeling of medical devices
  • Computational biofluid mechanics
  • Patient-specific-based numerical models
  • Finite element method
  • Diffusion models in the tissue engineering
  • Constitutive models
  • Numerical methods in the biomedical engineering
  • Numerical algorithms and imaging technique

Published Papers (8 papers)

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Research

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Open AccessArticle
Simulating Extraocular Muscle Dynamics. A Comparison between Dynamic Implicit and Explicit Finite Element Methods
Mathematics 2021, 9(9), 1024; https://doi.org/10.3390/math9091024 (registering DOI) - 01 May 2021
Viewed by 187
Abstract
The finite element method has been widely used to investigate the mechanical behavior of biological tissues. When analyzing these particular materials subjected to dynamic requests, time integration algorithms should be considered to incorporate the inertial effects. These algorithms can be classified as implicit [...] Read more.
The finite element method has been widely used to investigate the mechanical behavior of biological tissues. When analyzing these particular materials subjected to dynamic requests, time integration algorithms should be considered to incorporate the inertial effects. These algorithms can be classified as implicit or explicit. Although both algorithms have been used in different scenarios, a comparative study of the outcomes of both methods is important to determine the performance of a model used to simulate the active contraction of the skeletal muscle tissue. In this work, dynamic implicit and dynamic explicit solutions are presented for the movement of the eye ball induced by the extraocular muscles. Aspects such as stability, computational time and the influence of mass-scaling for the explicit formulation were assessed using ABAQUS software. Both strategies produced similar results regarding range of movement of the eye ball, total deformation and kinetic energy. Using the implicit dynamic formulation, an important amount of computational time reduction is achieved. Although mass-scaling can reduce the simulation time, the dynamic contraction of the muscle is drastically altered. Full article
(This article belongs to the Special Issue Numerical Simulation in Biomechanics and Biomedical Engineering)
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Open AccessArticle
CFD Simulations of Radioembolization: A Proof-of-Concept Study on the Impact of the Hepatic Artery Tree Truncation
Mathematics 2021, 9(8), 839; https://doi.org/10.3390/math9080839 - 12 Apr 2021
Viewed by 271
Abstract
Radioembolization (RE) is a treatment for patients with liver cancer, one of the leading cause of cancer-related deaths worldwide. RE consists of the transcatheter intraarterial infusion of radioactive microspheres, which are injected at the hepatic artery level and are transported in the bloodstream, [...] Read more.
Radioembolization (RE) is a treatment for patients with liver cancer, one of the leading cause of cancer-related deaths worldwide. RE consists of the transcatheter intraarterial infusion of radioactive microspheres, which are injected at the hepatic artery level and are transported in the bloodstream, aiming to target tumors and spare healthy liver parenchyma. In paving the way towards a computer platform that allows for a treatment planning based on computational fluid dynamics (CFD) simulations, the current simulation (model preprocess, model solving, model postprocess) times (of the order of days) make the CFD-based assessment non-viable. One of the approaches to reduce the simulation time includes the reduction in size of the simulated truncated hepatic artery. In this study, we analyze for three patient-specific hepatic arteries the impact of reducing the geometry of the hepatic artery on the simulation time. Results show that geometries can be efficiently shortened without impacting greatly on the microsphere distribution. Full article
(This article belongs to the Special Issue Numerical Simulation in Biomechanics and Biomedical Engineering)
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Open AccessArticle
Impact of Malapposed and Overlapping Stents on Hemodynamics: A 2D Parametric Computational Fluid Dynamics Study
Mathematics 2021, 9(8), 795; https://doi.org/10.3390/math9080795 - 07 Apr 2021
Viewed by 187
Abstract
Despite significant progress, malapposed or overlapped stents are a complication that affects daily percutaneous coronary intervention (PCI) procedures. These malapposed stents affect blood flow and create a micro re-circulatory environment. These disturbances are often associated with a change in Wall Shear Stress (WSS), [...] Read more.
Despite significant progress, malapposed or overlapped stents are a complication that affects daily percutaneous coronary intervention (PCI) procedures. These malapposed stents affect blood flow and create a micro re-circulatory environment. These disturbances are often associated with a change in Wall Shear Stress (WSS), Time-averaged WSS (TAWSS), relative residence time (RRT) and oscillatory character of WSS and disrupt the delicate balance of vascular biology, providing a possible source of thrombosis and restenosis. In this study, 2D axisymmetric parametric computational fluid dynamics (CFD) simulations were performed to systematically analyze the hemodynamic effects of malapposition and stent overlap for two types of stents (drug-eluting stent and a bioresorbable stent). The results of the modeling are mainly analyzed using streamlines, TAWSS, oscillatory shear index (OSI) and RRT. The risks of restenosis and thrombus are evaluated according to commonly accepted thresholds for TAWSS and OSI. The small malapposition distances (MD) cause both low TAWSS and high OSI, which are potential adverse outcomes. The region of low OSI decrease with MD. Overlap configurations produce areas with low WSS and high OSI. The affected lengths are relatively insensitive to the overlap distance. The effects of strut size are even more sensitive and adverse for overlap configurations compared to a well-applied stent. Full article
(This article belongs to the Special Issue Numerical Simulation in Biomechanics and Biomedical Engineering)
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Open AccessArticle
Empowering Advanced Driver-Assistance Systems from Topological Data Analysis
Mathematics 2021, 9(6), 634; https://doi.org/10.3390/math9060634 - 16 Mar 2021
Viewed by 281
Abstract
We are interested in evaluating the state of drivers to determine whether they are attentive to the road or not by using motion sensor data collected from car driving experiments. That is, our goal is to design a predictive model that can estimate [...] Read more.
We are interested in evaluating the state of drivers to determine whether they are attentive to the road or not by using motion sensor data collected from car driving experiments. That is, our goal is to design a predictive model that can estimate the state of drivers given the data collected from motion sensors. For that purpose, we leverage recent developments in topological data analysis (TDA) to analyze and transform the data coming from sensor time series and build a machine learning model based on the topological features extracted with the TDA. We provide some experiments showing that our model proves to be accurate in the identification of the state of the user, predicting whether they are relaxed or tense. Full article
(This article belongs to the Special Issue Numerical Simulation in Biomechanics and Biomedical Engineering)
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Open AccessArticle
Analysis of the Parametric Correlation in Mathematical Modeling of In Vitro Glioblastoma Evolution Using Copulas
Mathematics 2021, 9(1), 27; https://doi.org/10.3390/math9010027 - 24 Dec 2020
Viewed by 553
Abstract
Modeling and simulation are essential tools for better understanding complex biological processes, such as cancer evolution. However, the resulting mathematical models are often highly non-linear and include many parameters, which, in many cases, are difficult to estimate and present strong correlations. Therefore, a [...] Read more.
Modeling and simulation are essential tools for better understanding complex biological processes, such as cancer evolution. However, the resulting mathematical models are often highly non-linear and include many parameters, which, in many cases, are difficult to estimate and present strong correlations. Therefore, a proper parametric analysis is mandatory. Following a previous work in which we modeled the in vitro evolution of Glioblastoma Multiforme (GBM) under hypoxic conditions, we analyze and solve here the problem found of parametric correlation. With this aim, we develop a methodology based on copulas to approximate the multidimensional probability density function of the correlated parameters. Once the model is defined, we analyze the experimental setting to optimize the utility of each configuration in terms of gathered information. We prove that experimental configurations with oxygen gradient and high cell concentration have the highest utility when we want to separate correlated effects in our experimental design. We demonstrate that copulas are an adequate tool to analyze highly-correlated multiparametric mathematical models such as those appearing in Biology, with the added value of providing key information for the optimal design of experiments, reducing time and cost in in vivo and in vitro experimental campaigns, like those required in microfluidic models of GBM evolution. Full article
(This article belongs to the Special Issue Numerical Simulation in Biomechanics and Biomedical Engineering)
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Open AccessArticle
A Computational Model for Cardiomyocytes Mechano-Electric Stimulation to Enhance Cardiac Tissue Regeneration
Mathematics 2020, 8(11), 1875; https://doi.org/10.3390/math8111875 - 29 Oct 2020
Cited by 1 | Viewed by 463
Abstract
Electrical and mechanical stimulations play a key role in cell biological processes, being essential in processes such as cardiac cell maturation, proliferation, migration, alignment, attachment, and organization of the contractile machinery. However, the mechanisms that trigger these processes are still elusive. The coupling [...] Read more.
Electrical and mechanical stimulations play a key role in cell biological processes, being essential in processes such as cardiac cell maturation, proliferation, migration, alignment, attachment, and organization of the contractile machinery. However, the mechanisms that trigger these processes are still elusive. The coupling of mechanical and electrical stimuli makes it difficult to abstract conclusions. In this sense, computational models can establish parametric assays with a low economic and time cost to determine the optimal conditions of in-vitro experiments. Here, a computational model has been developed, using the finite element method, to study cardiac cell maturation, proliferation, migration, alignment, and organization in 3D matrices, under mechano-electric stimulation. Different types of electric fields (continuous, pulsating, and alternating) in an intensity range of 50–350 Vm1, and extracellular matrix with stiffnesses in the range of 10–40 kPa, are studied. In these experiments, the group’s morphology and cell orientation are compared to define the best conditions for cell culture. The obtained results are qualitatively consistent with the bibliography. The electric field orientates the cells and stimulates the formation of elongated groups. Group lengthening is observed when applying higher electric fields in lower stiffness extracellular matrix. Groups with higher aspect ratios can be obtained by electrical stimulation, with better results for alternating electric fields. Full article
(This article belongs to the Special Issue Numerical Simulation in Biomechanics and Biomedical Engineering)
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Open AccessArticle
Finite Element Analysis of Custom Shoulder Implants Provides Accurate Prediction of Initial Stability
Mathematics 2020, 8(7), 1113; https://doi.org/10.3390/math8071113 - 06 Jul 2020
Viewed by 770
Abstract
Custom reverse shoulder implants represent a valuable solution for patients with large bone defects. Since each implant has unique patient-specific features, finite element (FE) analysis has the potential to guide the design process by virtually comparing the stability of multiple configurations without the [...] Read more.
Custom reverse shoulder implants represent a valuable solution for patients with large bone defects. Since each implant has unique patient-specific features, finite element (FE) analysis has the potential to guide the design process by virtually comparing the stability of multiple configurations without the need of a mechanical test. The aim of this study was to develop an automated virtual bench test to evaluate the initial stability of custom shoulder implants during the design phase, by simulating a fixation experiment as defined by ASTM F2028-14. Three-dimensional (3D) FE models were generated to simulate the stability test and the predictions were compared to experimental measurements. Good agreement was found between the baseplate displacement measured experimentally and determined from the FE analysis (Spearman’s rank test, p < 0.05, correlation coefficient ρs = 0.81). Interface micromotion analysis predicted good initial fixation (micromotion <150 µm, commonly used as bone ingrowth threshold). In conclusion, the finite element model presented in this study was able to replicate the mechanical condition of a standard test for a custom shoulder implants. Full article
(This article belongs to the Special Issue Numerical Simulation in Biomechanics and Biomedical Engineering)
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Review

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Open AccessReview
Wall Shear Stress Topological Skeleton Analysis in Cardiovascular Flows: Methods and Applications
Mathematics 2021, 9(7), 720; https://doi.org/10.3390/math9070720 - 26 Mar 2021
Viewed by 551
Abstract
A marked interest has recently emerged regarding the analysis of the wall shear stress (WSS) vector field topological skeleton in cardiovascular flows. Based on dynamical system theory, the WSS topological skeleton is composed of fixed points, i.e., focal points where WSS locally vanishes, [...] Read more.
A marked interest has recently emerged regarding the analysis of the wall shear stress (WSS) vector field topological skeleton in cardiovascular flows. Based on dynamical system theory, the WSS topological skeleton is composed of fixed points, i.e., focal points where WSS locally vanishes, and unstable/stable manifolds, consisting of contraction/expansion regions linking fixed points. Such an interest arises from its ability to reflect the presence of near-wall hemodynamic features associated with the onset and progression of vascular diseases. Over the years, Lagrangian-based and Eulerian-based post-processing techniques have been proposed aiming at identifying the topological skeleton features of the WSS. Here, the theoretical and methodological bases supporting the Lagrangian- and Eulerian-based methods currently used in the literature are reported and discussed, highlighting their application to cardiovascular flows. The final aim is to promote the use of WSS topological skeleton analysis in hemodynamic applications and to encourage its application in future mechanobiology studies in order to increase the chance of elucidating the mechanistic links between blood flow disturbances, vascular disease, and clinical observations. Full article
(This article belongs to the Special Issue Numerical Simulation in Biomechanics and Biomedical Engineering)
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