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19 pages, 15575 KiB

Open AccessArticle

A Parametric Tool for Studying a New Tracheobronchial Silicone Stent Prototype: Toward a Customized 3D Printable Prosthesis

by Jesús Zurita-Gabasa, Carmen Sánchez-Matás, Cristina Díaz-Jiménez, José Luis López-Villalobos and Mauro Malvè

Mathematics 2021, 9(17), 2118; https://doi.org/10.3390/math9172118 - 1 Sep 2021

Cited by 3 | Viewed by 2003

Abstract

The management of complex airway disorders is challenging, as the airway stent placement usually results in several complications. Tissue reaction to the foreign body, poor mechanical properties and inadequate fit of the stent in the airway are some of the reported problems. For [...] Read more.

The management of complex airway disorders is challenging, as the airway stent placement usually results in several complications. Tissue reaction to the foreign body, poor mechanical properties and inadequate fit of the stent in the airway are some of the reported problems. For this reason, the design of customized biomedical devices to improve the accuracy of the clinical results has recently gained interest. The aim of the present study is to introduce a parametric tool for the design of a new tracheo-bronchial stent that could be capable of improving some of the performances of the commercial devices. The proposed methodology is based on the computer aided design software and on the finite element modeling. The computational results are validated by a parallel experimental work that includes the production of selected stent configurations using the 3D printing technology and their compressive test. Full article

(This article belongs to the Special Issue Numerical Simulation in Biomechanics and Biomedical Engineering)

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19 pages, 2699 KiB

Open AccessArticle

Continuum Scale Non Newtonian Particle Transport Model for Hæmorheology

by Torsten Schenkel and Ian Halliday

Mathematics 2021, 9(17), 2100; https://doi.org/10.3390/math9172100 - 30 Aug 2021

Cited by 3 | Viewed by 2600

Abstract

We present a continuum scale particle transport model for red blood cells following collision arguments, in a diffusive flux formulation. The model is implemented in FOAM, in a framework suitable for haemodynamics simulations and adapted to multi-scaling. Specifically, the framework we present is [...] Read more.

We present a continuum scale particle transport model for red blood cells following collision arguments, in a diffusive flux formulation. The model is implemented in FOAM, in a framework suitable for haemodynamics simulations and adapted to multi-scaling. Specifically, the framework we present is able to ingest transport coefficient models to be derived, prospectively, from complimentary but independent meso-scale simulations. For present purposes, we consider modern semi-mechanistic rheology models, which we implement and test as proxies for such data. The model is verified against a known analytical solution and shows excellent agreement for high quality meshes and good agreement for typical meshes as used in vascular flow simulations. Simulation results for different size and time scales show that migration of red blood cells does occur on physiologically relevany timescales on small vessels below 1 mm and that the haematocrit concentration modulates the non-Newtonian viscosity. This model forms part of a multi-scale approach to haemorheology and model parameters will be derived from meso-scale simulations using multi-component Lattice Boltzmann methods. The code, haemoFoam, is made available for interested researchers. Full article

(This article belongs to the Special Issue Numerical Simulation in Biomechanics and Biomedical Engineering)

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8 pages, 815 KiB

Open AccessArticle

Obtaining Expressions for Time-Dependent Functions That Describe the Unsteady Properties of Swirling Jets of Viscous Fluid

by Eugene Talygin and Alexander Gorodkov

Mathematics 2021, 9(16), 1860; https://doi.org/10.3390/math9161860 - 5 Aug 2021

Viewed by 1478

Abstract

Previously, it has been shown that the dynamic geometric configuration of the flow channel of the left heart and aorta corresponds to the direction of the streamlines of swirling flow, which can be described using the exact solution of the Navier–Stokes and continuity [...] Read more.

Previously, it has been shown that the dynamic geometric configuration of the flow channel of the left heart and aorta corresponds to the direction of the streamlines of swirling flow, which can be described using the exact solution of the Navier–Stokes and continuity equations for the class of centripetal swirling viscous fluid flows. In this paper, analytical expressions were obtained. They describe the functions

C_{0} (t)

and

Γ_{0} (t)

, included in the solutions, for the velocity components of such a flow. These expressions make it possible to relate the values of these functions to dynamic changes in the geometry of the flow channel in which the swirling flow evolves. The obtained expressions allow the reconstruction of the dynamic velocity field of an unsteady potential swirling flow in a flow channel of arbitrary geometry. The proposed approach can be used as a theoretical method for correct numerical modeling of the blood flow in the heart chambers and large arteries, as well as for developing a mathematical model of blood circulation, considering the swirling structure of the blood flow. Full article

(This article belongs to the Special Issue Numerical Simulation in Biomechanics and Biomedical Engineering)

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37 pages, 13125 KiB

Open AccessArticle

Size Effects in Finite Element Modelling of 3D Printed Bone Scaffolds Using Hydroxyapatite PEOT/PBT Composites

by Iñigo Calderon-Uriszar-Aldaca, Sergio Perez, Ravi Sinha, Maria Camara-Torres, Sara Villanueva, Carlos Mota, Alessandro Patelli, Amaia Matanza, Lorenzo Moroni and Alberto Sanchez

Mathematics 2021, 9(15), 1746; https://doi.org/10.3390/math9151746 - 24 Jul 2021

Viewed by 2451

Abstract

Additive manufacturing (AM) of scaffolds enables the fabrication of customized patient-specific implants for tissue regeneration. Scaffold customization does not involve only the macroscale shape of the final implant, but also their microscopic pore geometry and material properties, which are dependent on optimizable topology. [...] Read more.

Additive manufacturing (AM) of scaffolds enables the fabrication of customized patient-specific implants for tissue regeneration. Scaffold customization does not involve only the macroscale shape of the final implant, but also their microscopic pore geometry and material properties, which are dependent on optimizable topology. A good match between the experimental data of AM scaffolds and the models is obtained when there is just a few millimetres at least in one direction. Here, we describe a methodology to perform finite element modelling on AM scaffolds for bone tissue regeneration with clinically relevant dimensions (i.e., volume > 1 cm³). The simulation used an equivalent cubic eight node finite elements mesh, and the materials properties were derived both empirically and numerically, from bulk material direct testing and simulated tests on scaffolds. The experimental validation was performed using poly(ethylene oxide terephthalate)-poly(butylene terephthalate) (PEOT/PBT) copolymers and 45 wt% nano hydroxyapatite fillers composites. By applying this methodology on three separate scaffold architectures with volumes larger than 1 cm³, the simulations overestimated the scaffold performance, resulting in 150–290% stiffer than average values obtained in the validation tests. The results mismatch highlighted the relevance of the lack of printing accuracy that is characteristic of the additive manufacturing process. Accordingly, a sensitivity analysis was performed on nine detected uncertainty sources, studying their influence. After the definition of acceptable execution tolerances and reliability levels, a design factor was defined to calibrate the methodology under expectable and conservative scenarios. Full article

(This article belongs to the Special Issue Numerical Simulation in Biomechanics and Biomedical Engineering)

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13 pages, 26839 KiB

Open AccessArticle

Numerical Assessment of the Structural Effects of Relative Sliding between Tissues in a Finite Element Model of the Foot

by Marco A. Martínez Bocanegra, Javier Bayod López, Agustín Vidal-Lesso, Andrés Mena Tobar and Ricardo Becerro de Bengoa Vallejo

Mathematics 2021, 9(15), 1719; https://doi.org/10.3390/math9151719 - 22 Jul 2021

Cited by 4 | Viewed by 2082

Abstract

Penetration and shared nodes between muscles, tendons and the plantar aponeurosis mesh elements in finite element models of the foot may cause inappropriate structural behavior of the tissues. Penetration between tissues caused using separate mesh without motion constraints or contacts can change the [...] Read more.

Penetration and shared nodes between muscles, tendons and the plantar aponeurosis mesh elements in finite element models of the foot may cause inappropriate structural behavior of the tissues. Penetration between tissues caused using separate mesh without motion constraints or contacts can change the loading direction because of an inadequate mesh displacement. Shared nodes between mesh elements create bonded areas in the model, causing progressive or complete loss of load transmitted by tissue. This paper compares by the finite element method the structural behavior of the foot model in cases where a shared mesh has been used versus a separated mesh with sliding contacts between some important tissues. A very detailed finite element model of the foot and ankle that simulates the muscles, tendons and plantar aponeurosis with real geometry has been used for the research. The analysis showed that the use of a separate mesh with sliding contacts and a better characterization of the mechanical behavior of the soft tissues increased the mean of the absolute values of stress by 83.3% and displacement by 17.4% compared with a shared mesh. These increases mean an improvement of muscle and tendon behavior in the foot model. Additionally, a better quantitative and qualitative distribution of plantar pressure was also observed. Full article

(This article belongs to the Special Issue Numerical Simulation in Biomechanics and Biomedical Engineering)

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11 pages, 713 KiB

Open AccessArticle

Methodology to Calibrate the Dissection Properties of Aorta Layers from Two Sets of Experimental Measurements

by Itziar Ríos-Ruiz, Myriam Cilla, Miguel A. Martínez and Estefanía Peña

Mathematics 2021, 9(14), 1593; https://doi.org/10.3390/math9141593 - 7 Jul 2021

Cited by 2 | Viewed by 1952

Abstract

Aortic dissection is a prevalent cardiovascular pathology that can have a fatal outcome. However, the mechanisms that trigger this disease and the mechanics of its progression are not fully understood. Computational models can help understand these issues, but they need a proper characterisation [...] Read more.

Aortic dissection is a prevalent cardiovascular pathology that can have a fatal outcome. However, the mechanisms that trigger this disease and the mechanics of its progression are not fully understood. Computational models can help understand these issues, but they need a proper characterisation of the tissues. Therefore, we propose a methodology to obtain the dissection parameters of all layers in aortic tissue via the computational modelling of two different delamination tests: the peel and mixed tests. Both experimental tests have been performed in specimens of porcine aorta, where the intima-media and media-adventitia interfaces, as well as the medial layer, were dissected. These two tests have been modelled using a cohesive zone formulation for the separating interface and a hyperelastic anisotropic material model via an implicit static analysis. The dissection properties of each interface have been calibrated by reproducing the force-displacement curves obtained in the experimental tests. The values of peak and mean force of the experiments were fitted with an error below

10 %

. With this methodology, we intend to contribute to the development of reliable numerical tools for simulating aortic dissection and aortic aneurysm rupture. Full article

(This article belongs to the Special Issue Numerical Simulation in Biomechanics and Biomedical Engineering)

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18 pages, 3187 KiB

Open AccessArticle

A General Mechano-Pharmaco-Biological Model for Bone Remodeling Including Cortisol Variation

by Rabeb Ben Kahla, Abdelwahed Barkaoui, Moez Chafra and João Manuel R. S. Tavares

Mathematics 2021, 9(12), 1401; https://doi.org/10.3390/math9121401 - 17 Jun 2021

Cited by 3 | Viewed by 2214

Abstract

The process of bone remodeling requires a strict coordination of bone resorption and formation in time and space in order to maintain consistent bone quality and quantity. Bone-resorbing osteoclasts and bone-forming osteoblasts are the two major players in the remodeling process. Their coordination [...] Read more.

The process of bone remodeling requires a strict coordination of bone resorption and formation in time and space in order to maintain consistent bone quality and quantity. Bone-resorbing osteoclasts and bone-forming osteoblasts are the two major players in the remodeling process. Their coordination is achieved by generating the appropriate number of osteoblasts since osteoblastic-lineage cells govern the bone mass variation and regulate a corresponding number of osteoclasts. Furthermore, diverse hormones, cytokines and growth factors that strongly link osteoblasts to osteoclasts coordinated these two cell populations. The understanding of this complex remodeling process and predicting its evolution is crucial to manage bone strength under physiologic and pathologic conditions. Several mathematical models have been suggested to clarify this remodeling process, from the earliest purely phenomenological to the latest biomechanical and mechanobiological models. In this current article, a general mathematical model is proposed to fill the gaps identified in former bone remodeling models. The proposed model is the result of combining existing bone remodeling models to present an updated model, which also incorporates several important parameters affecting bone remodeling under various physiologic and pathologic conditions. Furthermore, the proposed model can be extended to include additional parameters in the future. These parameters are divided into four groups according to their origin, whether endogenous or exogenous, and the cell population they affect, whether osteoclasts or osteoblasts. The model also enables easy coupling of biological models to pharmacological and/or mechanical models in the future. Full article

(This article belongs to the Special Issue Numerical Simulation in Biomechanics and Biomedical Engineering)

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17 pages, 1525 KiB

Open AccessArticle

Simulating Extraocular Muscle Dynamics. A Comparison between Dynamic Implicit and Explicit Finite Element Methods

by Jorge Grasa and Begoña Calvo

Mathematics 2021, 9(9), 1024; https://doi.org/10.3390/math9091024 - 1 May 2021

Cited by 3 | Viewed by 1653

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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21 pages, 8627 KiB

Open AccessArticle

CFD Simulations of Radioembolization: A Proof-of-Concept Study on the Impact of the Hepatic Artery Tree Truncation

by Unai Lertxundi, Jorge Aramburu, Julio Ortega, Macarena Rodríguez-Fraile, Bruno Sangro, José Ignacio Bilbao and Raúl Antón

Mathematics 2021, 9(8), 839; https://doi.org/10.3390/math9080839 - 12 Apr 2021

Cited by 6 | Viewed by 2549

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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19 pages, 6702 KiB

Open AccessArticle

Impact of Malapposed and Overlapping Stents on Hemodynamics: A 2D Parametric Computational Fluid Dynamics Study

by Manuel Lagache, Ricardo Coppel, Gérard Finet, François Derimay, Roderic I. Pettigrew, Jacques Ohayon and Mauro Malvè

Mathematics 2021, 9(8), 795; https://doi.org/10.3390/math9080795 - 7 Apr 2021

Cited by 8 | Viewed by 2362

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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16 pages, 2942 KiB

Open AccessArticle

Empowering Advanced Driver-Assistance Systems from Topological Data Analysis

by Tarek Frahi, Francisco Chinesta, Antonio Falcó, Alberto Badias, Elias Cueto, Hyung Yun Choi, Manyong Han and Jean-Louis Duval

Mathematics 2021, 9(6), 634; https://doi.org/10.3390/math9060634 - 16 Mar 2021

Cited by 8 | Viewed by 2295

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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22 pages, 3345 KiB

Open AccessArticle

Analysis of the Parametric Correlation in Mathematical Modeling of In Vitro Glioblastoma Evolution Using Copulas

by Jacobo Ayensa-Jiménez, Marina Pérez-Aliacar, Teodora Randelovic, José Antonio Sanz-Herrera, Mohamed H. Doweidar and Manuel Doblaré

Mathematics 2021, 9(1), 27; https://doi.org/10.3390/math9010027 - 24 Dec 2020

Cited by 2 | Viewed by 2849

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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23 pages, 8633 KiB

Open AccessArticle

A Computational Model for Cardiomyocytes Mechano-Electric Stimulation to Enhance Cardiac Tissue Regeneration

by Pau Urdeitx and Mohamed H. Doweidar

Mathematics 2020, 8(11), 1875; https://doi.org/10.3390/math8111875 - 29 Oct 2020

Cited by 7 | Viewed by 2710

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

{Vm}^{- 1}

, 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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13 pages, 11830 KiB

Open AccessArticle

Finite Element Analysis of Custom Shoulder Implants Provides Accurate Prediction of Initial Stability

by Jonathan Pitocchi, Mariska Wesseling, Gerrit Harry van Lenthe and María Angeles Pérez

Mathematics 2020, 8(7), 1113; https://doi.org/10.3390/math8071113 - 6 Jul 2020

Cited by 4 | Viewed by 3926

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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21 pages, 3941 KiB

Open AccessReview

Wall Shear Stress Topological Skeleton Analysis in Cardiovascular Flows: Methods and Applications

by Valentina Mazzi, Umberto Morbiducci, Karol Calò, Giuseppe De Nisco, Maurizio Lodi Rizzini, Elena Torta, Giuseppe Carlo Alp Caridi, Claudio Chiastra and Diego Gallo

Mathematics 2021, 9(7), 720; https://doi.org/10.3390/math9070720 - 26 Mar 2021

Cited by 22 | Viewed by 5403

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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