Research

23 pages, 6588 KiB

Open AccessArticle

Finite Element Analysis of Microwave Tumor Ablation Based on Open-Source Software Components

by Nikola Bošković, Marija Radmilović-Radjenović and Branislav Radjenović

Mathematics 2023, 11(12), 2654; https://doi.org/10.3390/math11122654 - 10 Jun 2023

Viewed by 1516

Microwave ablation is a procedure for treating various types of cancers during which a small needle-like probe is inserted inside the tumor, which delivers microwave energy, causes tissue heating, and effectively produces necrosis of the tumor tissue. Mathematical models of microwave ablation involve [...] Read more.

Microwave ablation is a procedure for treating various types of cancers during which a small needle-like probe is inserted inside the tumor, which delivers microwave energy, causes tissue heating, and effectively produces necrosis of the tumor tissue. Mathematical models of microwave ablation involve the modeling of multiple physical phenomena that occur during the procedure, including electromagnetic wave propagation, heat transfer, and tissue damage. In this study, a complete model of a microwave ablation procedure based on open-source software components is presented. First, the comprehensive procedure of mesh creation for the complete geometric arrangement of the microwave ablation, including a multi-slot coaxial antenna, a real liver tumor taken from the database, and the surrounding liver tissue, is described. It is demonstrated that utilizing smart meshing procedures significantly reduces the usage of computational resources and simulation time. An accurate custom explicit Euler time loop was designed to obtain temperature values and estimate tissue necrosis across the computational domain during the time of microwave ablation. The simulation results obtained by solving the electromagnetic field using the finite element method in the frequency domain are presented and analyzed. The simulation was performed for a microwave frequency of 2.45 GHz, and the volumetric distribution of temperature and estimation of cell damage over 600 s are presented. Full article

(This article belongs to the Special Issue Mathematical Modelling in Biomedicine III)

► Show Figures

Figure 1

23 pages, 39293 KiB

Open AccessArticle

Agent-Based Model for Studying the Effects of Solid Stress and Nutrient Supply on Tumor Growth

by Maxim Kuznetsov and Andrey Kolobov

Mathematics 2023, 11(8), 1900; https://doi.org/10.3390/math11081900 - 17 Apr 2023

Cited by 1 | Viewed by 899

Abstract

An off-lattice agent-based model of tumor growth is presented, which describes a tumor as a network of proliferating cells, whose dynamics depend on the stress generated by intercellular bonds. A numerical method is introduced that ensures the smooth dynamics of the cell network [...] Read more.

An off-lattice agent-based model of tumor growth is presented, which describes a tumor as a network of proliferating cells, whose dynamics depend on the stress generated by intercellular bonds. A numerical method is introduced that ensures the smooth dynamics of the cell network and allows for relative numerical cheapness while reproducing the effects typical of more complex approaches such as the elongation of cells toward low-pressure regions and their tendency to maximize the contact area. Simulations of free tumor growth, restricted only by the stress generated within the tumor, demonstrate the influence of the tissue hydraulic conductivity and strength of cell–cell interactions on tumor shape and growth rate. Simulations of compact tumor growth within normal tissue show that strong interaction between tumor cells is a major factor limiting tumor growth. Moreover, the effects of normal tissue size and strength of normal cell interactions on tumor growth are ambiguous and depend on the value of tissue hydraulic conductivity. Simulations of tumor growth in normal tissue with the account of nutrients yield different growth regimes, including growth without saturation for at least several years with the formation of large necrotic cores in cases of low tissue hydraulic conductivity and sufficiently high nutrient supply, which qualitatively correlates with known clinical data. Full article

(This article belongs to the Special Issue Mathematical Modelling in Biomedicine III)

► Show Figures

Figure 1

18 pages, 558 KiB

Open AccessArticle

Computational Analysis of Hemodynamic Indices Based on Personalized Identification of Aortic Pulse Wave Velocity by a Neural Network

by Timur Gamilov, Fuyou Liang, Philipp Kopylov, Natalia Kuznetsova, Artem Rogov and Sergey Simakov

Mathematics 2023, 11(6), 1358; https://doi.org/10.3390/math11061358 - 10 Mar 2023

Cited by 4 | Viewed by 1713

Abstract

Adequate personalized numerical simulation of hemodynamic indices in coronary arteries requires accurate identification of the key parameters. Elastic properties of coronary vessels produce a significant effect on the accuracy of simulations. Direct measurements of the elasticity of coronary vessels are not available in [...] Read more.

Adequate personalized numerical simulation of hemodynamic indices in coronary arteries requires accurate identification of the key parameters. Elastic properties of coronary vessels produce a significant effect on the accuracy of simulations. Direct measurements of the elasticity of coronary vessels are not available in the general clinic. Pulse wave velocity (AoPWV) in the aorta correlates with aortic and coronary elasticity. In this work, we present a neural network approach for estimating AoPWV. Because of the limited number of clinical cases, we used a synthetic AoPWV database of virtual subjects to train the network. We use an additional set of AoPWV data collected from real patients to test the developed algorithm. The developed neural network predicts brachial–ankle AoPWV with a root-mean-square error (RMSE) of

1.3

m/s and a percentage error of

16 %

. We demonstrate the relevance of a new technique by comparing invasively measured fractional flow reserve (FFR) with simulated values using the patient data with constant (

7.5

m/s) and predicted AoPWV. We conclude that patient-specific identification of AoPWV via the developed neural network improves the estimation of FFR from

4.4 %

to

3.8 %

on average, with a maximum difference of

2.8 %

in a particular case. Furthermore, we also numerically investigate the sensitivity of the most useful hemodynamic indices, including FFR, coronary flow reserve (CFR) and instantaneous wave-free ratio (iFR) to AoPWV using the patient-specific data. We observe a substantial variability of all considered indices for AoPWV below 10 m/s and weak variation of AoPWV above 15 m/s. We conclude that the hemodynamic significance of coronary stenosis is higher for the patients with AoPWV in the range from 10 to 15 m/s. The advantages of our approach are the use of a limited set of easily measured input parameters (age, stroke volume, heart rate, systolic, diastolic and mean arterial pressures) and the usage of a model-generated (synthetic) dataset to train and test machine learning methods for predicting hemodynamic indices. The application of our approach in clinical practice saves time, workforce and funds. Full article

(This article belongs to the Special Issue Mathematical Modelling in Biomedicine III)

► Show Figures

Figure 1

15 pages, 1746 KiB

Open AccessArticle

Mathematical Modelling of Leptin-Induced Effects on Electrophysiological Properties of Rat Cardiomyocytes and Cardiac Arrhythmias

by Tatiana Nesterova, Roman Rokeakh, Olga Solovyova and Alexander Panfilov

Mathematics 2023, 11(4), 874; https://doi.org/10.3390/math11040874 - 08 Feb 2023

Viewed by 1419

Abstract

Elevated plasma leptin levels, or hyperleptinemia, have been demonstrated to correlate with metabolic syndrome markers, including obesity, and may be an independent risk factor for the development of cardiovascular disease. In this paper, we use cardiac models to study possible effects of hyperleptinemia [...] Read more.

Elevated plasma leptin levels, or hyperleptinemia, have been demonstrated to correlate with metabolic syndrome markers, including obesity, and may be an independent risk factor for the development of cardiovascular disease. In this paper, we use cardiac models to study possible effects of hyperleptinemia on the electrophysiological properties of cardiomyocytes and cardiac arrhythmias. We modified the parameters of an improved Gattoni 2016 model of rat ventricular cardiomyocytes to simulate experimental data for the leptin effects on ionic currents. We used four model variants to investigate the effects of leptin-induced parameter modification at the cellular level and in 2D tissue. In all models, leptin was found to increase the duration of the action potential. In some cases, we observed a dramatic change in the shape of the action potential from triangular, characteristic of rat cardiomyocytes, to a spike-and-dome, indicating predisposition to arrhythmias. In all 2D tissue models, leptin increased the period of cardiac arrhythmia caused by a spiral wave and enhanced dynamic instability, manifesting as increased meandering, onset of hypermeandering, and even spiral wave breakup. The leptin-modified cellular models developed can be used in subsequent research in rat heart anatomy models. Full article

(This article belongs to the Special Issue Mathematical Modelling in Biomedicine III)

► Show Figures

Figure 1

13 pages, 940 KiB

Open AccessArticle

Combining Computational Modelling and Machine Learning to Identify COVID-19 Patients with a High Thromboembolism Risk

by Anass Bouchnita, Anastasia Mozokhina, Patrice Nony, Jean-Pierre Llored and Vitaly Volpert

Mathematics 2023, 11(2), 289; https://doi.org/10.3390/math11020289 - 05 Jan 2023

Cited by 2 | Viewed by 1425

Abstract

Severe acute respiratory syndrome of coronavirus 2 (SARS-CoV-2) is a respiratory virus that disrupts the functioning of several organ systems. The cardiovascular system represents one of the systems targeted by the novel coronavirus disease (COVID-19). Indeed, a hypercoagulable state was observed in some [...] Read more.

Severe acute respiratory syndrome of coronavirus 2 (SARS-CoV-2) is a respiratory virus that disrupts the functioning of several organ systems. The cardiovascular system represents one of the systems targeted by the novel coronavirus disease (COVID-19). Indeed, a hypercoagulable state was observed in some critically ill COVID-19 patients. The timely prediction of thrombosis risk in COVID-19 patients would help prevent the incidence of thromboembolic events and reduce the disease burden. This work proposes a methodology that identifies COVID-19 patients with a high thromboembolism risk using computational modelling and machine learning. We begin by studying the dynamics of thrombus formation in COVID-19 patients by using a mathematical model fitted to the experimental findings of in vivo clot growth. We use numerical simulations to quantify the upregulation in the size of the formed thrombi in COVID-19 patients. Next, we show that COVID-19 upregulates the peak concentration of thrombin generation (TG) and its endogenous thrombin potential. Finally, we use a simplified 1D version of the clot growth model to generate a dataset containing the hemostatic responses of virtual COVID-19 patients and healthy subjects. We use this dataset to train machine learning algorithms that can be readily deployed to predict the risk of thrombosis in COVID-19 patients. Full article

(This article belongs to the Special Issue Mathematical Modelling in Biomedicine III)

► Show Figures

Figure 1

19 pages, 973 KiB

Open AccessArticle

Estimating the Risk of Contracting COVID-19 in Different Settings Using a Multiscale Transmission Dynamics Model

by Dramane Sam Idris Kanté, Aissam Jebrane, Anass Bouchnita and Abdelilah Hakim

Mathematics 2023, 11(1), 254; https://doi.org/10.3390/math11010254 - 03 Jan 2023

Cited by 6 | Viewed by 2266

Abstract

Airborne transmission is the dominant route of coronavirus disease 2019 (COVID-19) transmission. The chances of contracting COVID-19 in a particular situation depend on the local demographic features, the type of inter-individual interactions, and the compliance with mitigation measures. In this work, we develop [...] Read more.

Airborne transmission is the dominant route of coronavirus disease 2019 (COVID-19) transmission. The chances of contracting COVID-19 in a particular situation depend on the local demographic features, the type of inter-individual interactions, and the compliance with mitigation measures. In this work, we develop a multiscale framework to estimate the individual risk of infection with COVID-19 in different activity areas. The framework is parameterized to describe the motion characteristics of pedestrians in workplaces, schools, shopping centers and other public areas, which makes it suitable to study the risk of infection under specific scenarios. First, we show that exposure to individuals with peak viral loads increases the chances of infection by 99%. Our simulations suggest that the risk of contracting COVID-19 is especially high in workplaces and residential areas. Next, we determine the age groups that are most susceptible to infection in each location. Then, we show that if 50% of the population wears face masks, this will reduce the chances of infection by 8%, 32%, or 45%, depending on the type of the used mask. Finally, our simulations suggest that compliance with social distancing reduces the risk of infection by 19%. Our framework provides a tool that assesses the location-specific risk of infection and helps determine the most effective behavioral measures that protect vulnerable individuals. Full article

(This article belongs to the Special Issue Mathematical Modelling in Biomedicine III)

► Show Figures

Figure 1

11 pages, 561 KiB

Open AccessArticle

Data-Driven Constitutive Modeling via Conjugate Pairs and Response Functions

by Victoria Salamatova

Mathematics 2022, 10(23), 4447; https://doi.org/10.3390/math10234447 - 25 Nov 2022

Cited by 1 | Viewed by 883

Abstract

Response functions completely define the constitutive equations for a hyperelastic material. A strain measure providing an orthogonal stress response, grants response functions directly from experimental curves. One of these strain measures is the Laplace stretch based on QR-decomposition of the deformation gradient. Such [...] Read more.

Response functions completely define the constitutive equations for a hyperelastic material. A strain measure providing an orthogonal stress response, grants response functions directly from experimental curves. One of these strain measures is the Laplace stretch based on QR-decomposition of the deformation gradient. Such a recovery of response functions from experimental data fits the paradigm of data-driven modeling. The set of independent conjugate stress–strain base pairs were proposed as a simple alternative for constitutive modeling and thus might be efficient for data-driven modeling. In the present paper we explore applicability of the conjugate pairs approach for data-driven modeling. The analysis is based on representation of the conjugate pairs in terms of the response functions due to the Laplace stretch. Our analysis shows that one can not guarantee independence of these pairs except in the case of infinitesimal strain. Full article

(This article belongs to the Special Issue Mathematical Modelling in Biomedicine III)

► Show Figures

Figure 1

25 pages, 3792 KiB

Open AccessArticle

Coupling Chemotaxis and Growth Poromechanics for the Modelling of Feather Primordia Patterning

by Nicolás A. Barnafi, Luis Miguel De Oliveira Vilaca, Michel C. Milinkovitch and Ricardo Ruiz-Baier

Mathematics 2022, 10(21), 4096; https://doi.org/10.3390/math10214096 - 03 Nov 2022

Cited by 1 | Viewed by 1194

Abstract

In this paper we propose a new mathematical model for describing the complex interplay between skin cell populations with fibroblast growth factor and bone morphogenetic protein, occurring within deformable porous media describing feather primordia patterning. Tissue growth, in turn, modifies the transport of [...] Read more.

In this paper we propose a new mathematical model for describing the complex interplay between skin cell populations with fibroblast growth factor and bone morphogenetic protein, occurring within deformable porous media describing feather primordia patterning. Tissue growth, in turn, modifies the transport of morphogens (described by reaction-diffusion equations) through diverse mechanisms such as advection from the solid velocity generated by mechanical stress, and mass supply. By performing an asymptotic linear stability analysis on the coupled poromechanical-chemotaxis system (assuming rheological properties of the skin cell aggregates that reside in the regime of infinitesimal strains and where the porous structure is fully saturated with interstitial fluid and encoding the coupling mechanisms through active stress) we obtain the conditions on the parameters—especially those encoding coupling mechanisms—under which the system will give rise to spatially heterogeneous solutions. We also extend the mechanical model to the case of incompressible poro-hyperelasticity and include the mechanisms of anisotropic solid growth and feedback by means of standard Lee decompositions of the tensor gradient of deformation. Because the model in question involves the coupling of several nonlinear PDEs, we cannot straightforwardly obtain closed-form solutions. We therefore design a suitable numerical method that employs backward Euler time discretisation, linearisation of the semidiscrete problem through Newton–Raphson’s method, a seven-field finite element formulation for the spatial discretisation, and we also advocate the construction and efficient implementation of tailored robust solvers. We present a few illustrative computational examples in 2D and 3D, briefly discussing different spatio-temporal patterns of growth factors as well as the associated solid response scenario depending on the specific poromechanical regime. Our findings confirm the theoretically predicted behaviour of spatio-temporal patterns, and the produced results reveal a qualitative agreement with respect to the expected experimental behaviour. We stress that the present study provides insight on several biomechanical properties of primordia patterning. Full article

(This article belongs to the Special Issue Mathematical Modelling in Biomedicine III)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Mathematical Modelling in Biomedicine III

Share This Special Issue

Special Issue Editors

Special Issue Information

Keywords

Published Papers (8 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI