Research

16 pages, 819 KiB

Open AccessArticle

Comparison of Non-Newtonian Models of One-Dimensional Hemodynamics

by Gerasim Vladimirovich Krivovichev

Mathematics 2021, 9(19), 2459; https://0-doi-org.brum.beds.ac.uk/10.3390/math9192459 - 02 Oct 2021

Cited by 7 | Viewed by 1491

The paper is devoted to the comparison of different one-dimensional models of blood flow. In such models, the non-Newtonian property of blood is considered. It is demonstrated that for the large arteries, the small parameter is observed in the models, and the perturbation [...] Read more.

The paper is devoted to the comparison of different one-dimensional models of blood flow. In such models, the non-Newtonian property of blood is considered. It is demonstrated that for the large arteries, the small parameter is observed in the models, and the perturbation method can be used for the analytical solution. In the paper, the simplified nonlinear problem for the semi-infinite vessel with constant properties is solved analytically, and the solutions for different models are compared. The effects of the flattening of the velocity profile and hematocrit value on the deviation from the Newtonian model are investigated. Full article

(This article belongs to the Special Issue Mathematics in Biomedicine)

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29 pages, 1584 KiB

Open AccessArticle

A Comprehensive Review on Seismocardiogram: Current Advancements on Acquisition, Annotation, and Applications

by Deepak Rai, Hiren Kumar Thakkar, Shyam Singh Rajput, Jose Santamaria, Chintan Bhatt and Francisco Roca

Mathematics 2021, 9(18), 2243; https://0-doi-org.brum.beds.ac.uk/10.3390/math9182243 - 12 Sep 2021

Cited by 34 | Viewed by 4879

Abstract

In recent years, cardiovascular diseases are on the rise, and they entail enormous health burdens on global economies. Cardiac vibrations yield a wide and rich spectrum of essential information regarding the functioning of the heart, and thus it is necessary to take advantage [...] Read more.

In recent years, cardiovascular diseases are on the rise, and they entail enormous health burdens on global economies. Cardiac vibrations yield a wide and rich spectrum of essential information regarding the functioning of the heart, and thus it is necessary to take advantage of this data to better monitor cardiac health by way of prevention in early stages. Specifically, seismocardiography (SCG) is a noninvasive technique that can record cardiac vibrations by using new cutting-edge devices as accelerometers. Therefore, providing new and reliable data regarding advancements in the field of SCG, i.e., new devices and tools, is necessary to outperform the current understanding of the State-of-the-Art (SoTA). This paper reviews the SoTA on SCG and concentrates on three critical aspects of the SCG approach, i.e., on the acquisition, annotation, and its current applications. Moreover, this comprehensive overview also presents a detailed summary of recent advancements in SCG, such as the adoption of new techniques based on the artificial intelligence field, e.g., machine learning, deep learning, artificial neural networks, and fuzzy logic. Finally, a discussion on the open issues and future investigations regarding the topic is included. Full article

(This article belongs to the Special Issue Mathematics in Biomedicine)

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15 pages, 6820 KiB

Open AccessArticle

Application of Hyperelastic Nodal Force Method to Evaluation of Aortic Valve Cusps Coaptation: Thin Shell vs. Membrane Formulations

by Yuri Vassilevski, Alexey Liogky and Victoria Salamatova

Mathematics 2021, 9(12), 1450; https://0-doi-org.brum.beds.ac.uk/10.3390/math9121450 - 21 Jun 2021

Cited by 6 | Viewed by 1721

Abstract

Coaptation characteristics are crucial in an assessment of the competence of reconstructed aortic valves. Shell or membrane formulations can be used to model the valve cusps coaptation. In this paper we compare both formulations in terms of their coaptation characteristics for the first [...] Read more.

Coaptation characteristics are crucial in an assessment of the competence of reconstructed aortic valves. Shell or membrane formulations can be used to model the valve cusps coaptation. In this paper we compare both formulations in terms of their coaptation characteristics for the first time. Our numerical thin shell model is based on a combination of the hyperelastic nodal forces method and the rotation-free finite elements. The shell model is verified on several popular benchmarks for thin-shell analysis. The relative error with respect to reference solutions does not exceed 1–2%. We apply our numerical shell and membrane formulations to model the closure of an idealized aortic valve varying hyperelasticity models and their shear moduli. The coaptation characteristics become almost insensitive to elastic potentials and sensitive to bending stiffness, which reduces the coaptation zone. Full article

(This article belongs to the Special Issue Mathematics in Biomedicine)

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15 pages, 2910 KiB

Open AccessArticle

Generation of Virtual Patient Populations That Represent Real Type 1 Diabetes Cohorts

by Sayyar Ahmad, Charrise M. Ramkissoon, Aleix Beneyto, Ignacio Conget, Marga Giménez and Josep Vehi

Mathematics 2021, 9(11), 1200; https://0-doi-org.brum.beds.ac.uk/10.3390/math9111200 - 25 May 2021

Cited by 8 | Viewed by 2717

Abstract

Preclinical testing and validation of therapeutic strategies developed for patients with type 1 diabetes (T1D) require a cohort of virtual patients (VPs). However, current simulators provide a limited number of VPs, lack real-life scenarios, and inadequately represent intra- and inter-day variability in insulin [...] Read more.

Preclinical testing and validation of therapeutic strategies developed for patients with type 1 diabetes (T1D) require a cohort of virtual patients (VPs). However, current simulators provide a limited number of VPs, lack real-life scenarios, and inadequately represent intra- and inter-day variability in insulin sensitivity and blood glucose (BG) profile. The generation of a realistic scenario was achieved by using the meal patterns, insulin profiles (basal and bolus), and exercise sessions estimated as disturbances using clinical data from a cohort of 14 T1D patients using the Medtronic 640G insulin pump provided by the Hospital Clínic de Barcelona. The UVa/Padova’s cohort of adult patients was used for the generation of a new cohort of VPs. Insulin model parameters were optimized and adjusted in a day-by-day fashion to replicate the clinical data to create a cohort of 75 VPs. All primary and secondary outcomes reflecting the BG profile of a T1D patient were analyzed and compared to the clinical data. The mean BG 166.3 versus 162.2 mg/dL (

p

= 0.19), coefficient of variation 32% versus 33% (

p

= 0.54), and percent of time in range (70 to 180 mg/dL) 59.6% versus 66.8% (

p

= 0.35) were achieved. The proposed methodology for generating a cohort of VPs is capable of mimicking the BG metrics of a real cohort of T1D patients from the Hospital Clínic de Barcelona. It can adopt the inter-day variations in the BG profile, similar to the observed clinical data, and thus provide a benchmark for preclinical testing of control techniques and therapy strategies for T1D patients. Full article

(This article belongs to the Special Issue Mathematics in Biomedicine)

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18 pages, 1387 KiB

Open AccessArticle

Skewness-Kurtosis Model-Based Projection Pursuit with Application to Summarizing Gene Expression Data

by Jorge M. Arevalillo and Hilario Navarro

Mathematics 2021, 9(9), 954; https://0-doi-org.brum.beds.ac.uk/10.3390/math9090954 - 24 Apr 2021

Cited by 5 | Viewed by 1850

Abstract

Non-normality is a usual fact when dealing with gene expression data. Thus, flexible models are needed in order to account for the underlying asymmetry and heavy tails of multivariate gene expression measures. This paper addresses the issue by exploring the projection pursuit problem [...] Read more.

Non-normality is a usual fact when dealing with gene expression data. Thus, flexible models are needed in order to account for the underlying asymmetry and heavy tails of multivariate gene expression measures. This paper addresses the issue by exploring the projection pursuit problem under a flexible framework where the underlying model is assumed to follow a multivariate skew-t distribution. Under this assumption, projection pursuit with skewness and kurtosis indices is addressed as a natural approach for data reduction. The work examines its properties giving some theoretical insights and delving into the computational side in regards to the application to real gene expression data. The results of the theory are illustrated by means of a simulation study; the outputs of the simulation are used in combination with the theoretical insights to shed light on the usefulness of skewness-kurtosis projection pursuit for summarizing multivariate gene expression data. The application to gene expression measures of patients diagnosed with triple-negative breast cancer gives promising findings that may contribute to explain the heterogeneity of this type of tumors. Full article

(This article belongs to the Special Issue Mathematics in Biomedicine)

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11 pages, 381 KiB

Open AccessFeature PaperArticle

Impact of Regional Difference in Recovery Rate on the Total Population of Infected for a Diffusive SIS Model

by Jumpei Inoue and Kousuke Kuto

Mathematics 2021, 9(8), 888; https://0-doi-org.brum.beds.ac.uk/10.3390/math9080888 - 16 Apr 2021

Viewed by 1563

Abstract

This paper is concerned with an SIS epidemic reaction-diffusion model. The purpose of this paper is to derive some effects of the spatial heterogeneity of the recovery rate on the total population of infected and the reproduction number. The proof is based on [...] Read more.

This paper is concerned with an SIS epidemic reaction-diffusion model. The purpose of this paper is to derive some effects of the spatial heterogeneity of the recovery rate on the total population of infected and the reproduction number. The proof is based on an application of our previous result on the unboundedness of the ratio of the species to the resource for a diffusive logistic equation. Our pure mathematical result can be epidemically interpreted as that a regional difference in the recovery rate can make the infected population grow in the case when the reproduction number is slightly larger than one. Full article

(This article belongs to the Special Issue Mathematics in Biomedicine)

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14 pages, 635 KiB

Open AccessArticle

Tropical Balls and Its Applications to K Nearest Neighbor over the Space of Phylogenetic Trees

by Ruriko Yoshida

Mathematics 2021, 9(7), 779; https://0-doi-org.brum.beds.ac.uk/10.3390/math9070779 - 05 Apr 2021

Cited by 5 | Viewed by 1819

Abstract

A tropical ball is a ball defined by the tropical metric over the tropical projective torus. In this paper we show several properties of tropical balls over the tropical projective torus and also over the space of phylogenetic trees with a given set [...] Read more.

A tropical ball is a ball defined by the tropical metric over the tropical projective torus. In this paper we show several properties of tropical balls over the tropical projective torus and also over the space of phylogenetic trees with a given set of leaf labels. Then we discuss its application to the K nearest neighbors (KNN) algorithm, a supervised learning method used to classify a high-dimensional vector into given categories by looking at a ball centered at the vector, which contains K vectors in the space. Full article

(This article belongs to the Special Issue Mathematics in Biomedicine)

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12 pages, 3252 KiB

Open AccessArticle

Study of Reversible Platelet Aggregation Model by Nonlinear Dynamics

by Grigorii A. Vasilev, Aleksandra A. Filkova and Anastasia N. Sveshnikova

Mathematics 2021, 9(7), 759; https://doi.org/10.3390/math9070759 - 01 Apr 2021

Cited by 2 | Viewed by 2013

Abstract

Blood cell platelets form aggregates upon vessel wall injury. Under certain conditions, a disintegration of the platelet aggregates, called “reversible aggregation”, is observed in vitro. Previously, we have proposed an extremely simple (two equations, five parameters) ordinary differential equation-based mathematical model of the [...] Read more.

Blood cell platelets form aggregates upon vessel wall injury. Under certain conditions, a disintegration of the platelet aggregates, called “reversible aggregation”, is observed in vitro. Previously, we have proposed an extremely simple (two equations, five parameters) ordinary differential equation-based mathematical model of the reversible platelet aggregation. That model was based on mass-action law, and the parameters represented probabilities of platelet aggregate formations. Here, we aimed to perform a nonlinear dynamics analysis of this mathematical model to derive the biomedical meaning of the model’s parameters. The model’s parameters were estimated automatically from experimental data in COPASI software. Further analysis was performed in Python 2.7. Contrary to our expectations, for a broad range of parameter values, the model had only one steady state of the stable type node, thus eliminating the initial assumption that the reversibility of the aggregation curve could be explained by the system’s being near a stable focus. Therefore, we conclude that during platelet aggregation, the system is outside of the influence area of the steady state. Further analysis of the model’s parameters demonstrated that the rate constants for the reaction of aggregate formation from existing aggregates determine the reversibility of the aggregation curve. The other parameters of the model influenced either the initial aggregation rate or the quasi-steady state aggregation values. Full article

(This article belongs to the Special Issue Mathematics in Biomedicine)

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22 pages, 754 KiB

Open AccessArticle

Global Hypothesis Test to Compare the Predictive Values of Diagnostic Tests Subject to a Case-Control Design

by Saad Bouh Regad and José Antonio Roldán-Nofuentes

Mathematics 2021, 9(6), 658; https://0-doi-org.brum.beds.ac.uk/10.3390/math9060658 - 19 Mar 2021

Cited by 1 | Viewed by 1925

Abstract

Use of a case-control design to compare the accuracy of two binary diagnostic tests is frequent in clinical practice. This design consists of applying the two diagnostic tests to all of the individuals in a sample of those who have the disease and [...] Read more.

Use of a case-control design to compare the accuracy of two binary diagnostic tests is frequent in clinical practice. This design consists of applying the two diagnostic tests to all of the individuals in a sample of those who have the disease and in another sample of those who do not have the disease. This manuscript studies the comparison of the predictive values of two diagnostic tests subject to a case-control design. A global hypothesis test, based on the chi-square distribution, is proposed to compare the predictive values simultaneously, as well as other alternative methods. The hypothesis tests studied require knowing the prevalence of the disease. Simulation experiments were carried out to study the type I errors and the powers of the hypothesis tests proposed, as well as to study the effect of a misspecification of the prevalence on the asymptotic behavior of the hypothesis tests and on the estimators of the predictive values. The proposed global hypothesis test was extended to the situation in which there are more than two diagnostic tests. The results have been applied to the diagnosis of coronary disease. Full article

(This article belongs to the Special Issue Mathematics in Biomedicine)

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