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Mathematical Modeling and Its Application in Medicine

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

Deadline for manuscript submissions: closed (31 July 2022) | Viewed by 24053

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Special Issue Editors

Dr. Victoria López

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Guest Editor

Quantitative Methods Department, Colegio Universitario de Estudios Financieros (CUNEF), Leonardo Prieto Castro, 6, 28040 Madrid, Spain
Interests: computational mathematics; artificial intelligence; health; mathematical modelling; data analysis; computational neurocience; machine learning

Prof. Dr. Laureano González Vega

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Guest Editor

Quantitative Methods Department, Colegio Universitario de Estudios Financieros (CUNEF), Leonardo Prieto Castro, 2, 28040 Madrid, Spain
Interests: computer algebra; symbolic computation; computer aided geometric design; scientific computing; visualization and data science

Special Issue Information

Dear Colleagues,

This Special Issue aims to publish original research articles covering advances in mathematical modeling in medicine and healthcare. In particular, how to improve upon existing models or create new models, dynamics, and flow networks will be discussed, as well as applications in machine learning, algorithm design, and complexity optimization. Mathematical models in medicine and healthcare have gained a great deal of attention in recent years. On one hand, these models can be applied to analyze mood disorders (depression, bipolar, anxiety, etc.), neuro diseases (Alzheimer’s disease, Parkinson’s disease), and many other related issues. On the other hand, there are models to analyze thee behavior of a disease on the population. The application of these models can be used to detect the abovementioned issues at an early stage for better and effective treatment as well as to analyze the evolution of an issue along with the population. Advances in machine learning algorithms have recently seen a wide use of predictive systems and expert systems. In this way, this Special Issue focuses on the use of mathematical modeling and its application in medicine and other related areas.

Potential topics include but are not limited to:

Dynamic models;
Machine learning;
Flow networks;
Population models;
Network models;
Computational methods;
Algorithm complexity;
Information theory and estimation theory for computational neuroscience;
Medical aid systems;
Expert systems in medicine.

Dr. Victoria López
Prof. Dr. Laureano González Vega
Guest Editors

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Keywords

mathematics
modeling
medicine
healthcare
machine learning
data analysis

Published Papers (10 papers)

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Research

18 pages, 3679 KiB

Open AccessArticle

Multi-Scale Tumor Localization Based on Priori Guidance-Based Segmentation Method for Osteosarcoma MRI Images

by Baolong Lv, Feng Liu, Fangfang Gou and Jia Wu

Mathematics 2022, 10(12), 2099; https://0-doi-org.brum.beds.ac.uk/10.3390/math10122099 - 16 Jun 2022

Cited by 19 | Viewed by 1633

Abstract

Osteosarcoma is a malignant osteosarcoma that is extremely harmful to human health. Magnetic resonance imaging (MRI) technology is one of the commonly used methods for the imaging examination of osteosarcoma. Due to the large amount of osteosarcoma MRI image data and the complexity of detection, manual identification of osteosarcoma in MRI images is a time-consuming and labor-intensive task for doctors, and it is highly subjective, which can easily lead to missed and misdiagnosed problems. AI medical image-assisted diagnosis alleviates this problem. However, the brightness of MRI images and the multi-scale of osteosarcoma make existing studies still face great challenges in the identification of tumor boundaries. Based on this, this study proposed a prior guidance-based assisted segmentation method for MRI images of osteosarcoma, which is based on the few-shot technique for tumor segmentation and fine fitting. It not only solves the problem of multi-scale tumor localization, but also greatly improves the recognition accuracy of tumor boundaries. First, we preprocessed the MRI images using prior generation and normalization algorithms to reduce model performance degradation caused by irrelevant regions and high-level features. Then, we used a prior-guided feature abdominal muscle network to perform small-sample segmentation of tumors of different sizes based on features in the processed MRI images. Finally, using more than 80,000 MRI images from the Second Xiangya Hospital for experiments, the DOU value of the method proposed in this paper reached 0.945, which is at least 4.3% higher than other models in the experiment. We showed that our method specifically has higher prediction accuracy and lower resource consumption. Full article

(This article belongs to the Special Issue Mathematical Modeling and Its Application in Medicine)

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14 pages, 1100 KiB

Open AccessArticle

Modeling of Cerebral Blood Flow Autoregulation Using Mathematical Control Theory

by Alexey Golubev, Andrey Kovtanyuk and Renée Lampe

Mathematics 2022, 10(12), 2060; https://0-doi-org.brum.beds.ac.uk/10.3390/math10122060 - 14 Jun 2022

Cited by 2 | Viewed by 1531

Abstract

A mathematical model of cerebral blood flow in the form of a dynamical system is studied. The cerebral blood flow autoregulation modeling problem is treated as a nonlinear control problem and the potential and applicability of the nonlinear control theory techniques are analyzed in this respect. It is shown that the cerebral hemodynamics model in question is differentially flat. Then, the integrator backstepping approach combined with barrier Lyapunov functions is applied to construct the control laws that recover the cerebral autoregulation performance of a healthy human. Simulation results confirm the good performance and flexibility of the suggested cerebral blood flow autoregulation design. The conducted research should enrich our understanding of the mathematics behind the cerebral blood flow autoregulation mechanisms and medical treatments to compensate for impaired cerebral autoregulation, e.g., in preterm infants. Full article

(This article belongs to the Special Issue Mathematical Modeling and Its Application in Medicine)

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9 pages, 569 KiB

Open AccessArticle

Adsorption of Cisplatin Molecules in Nanoporous Inorganic Materials as Drug Delivery Vehicles

by Mansoor H. Alshehri

Mathematics 2022, 10(7), 1018; https://0-doi-org.brum.beds.ac.uk/10.3390/math10071018 - 22 Mar 2022

Cited by 1 | Viewed by 1310

Abstract

The use of nanoparticles as anticancer cargo systems for drug delivery is a promising modality, as they avoid the known toxicity of anticancer drugs on healthy cells by the delivery of multiple drugs to the target cells. Here, the adsorption behavior of cisplatin drug molecules in two different inorganic materials, silica and metallic gold, is investigated mathematically. The 6–12 Lennard-Jones potential, together with the continuum approximation, is adapted to calculate the molecular interatomic energies between molecules. For each material, the relation between the pore radius ℓ and the minimum energy is determined, and the results indicate that the minimum energy occurs when the radii are

ℓ = 5.3

and

ℓ = 4.7

Å for the silica and gold nanopores, respectively. The method is promising for applications in the design of novel nanocapsules for future targeted drug and gene delivery. Full article

(This article belongs to the Special Issue Mathematical Modeling and Its Application in Medicine)

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19 pages, 928 KiB

Open AccessArticle

A Model for Brucellosis Disease Incorporating Age of Infection and Waning Immunity

by Cyrille Kenne, Gisèle Mophou, René Dorville and Pascal Zongo

Mathematics 2022, 10(4), 670; https://0-doi-org.brum.beds.ac.uk/10.3390/math10040670 - 21 Feb 2022

Cited by 2 | Viewed by 1873

Abstract

This paper proposes a model for brucellosis transmission. The model takes into account the age of infection and waning immunity, that is, the progressive loss of immunity after recovery. Three routes of transmissions are considered: vertical transmission, and both direct and indirect routes of horizontal transmission. According to the well-posedness results, we provide explicit formulas for the equilibria. Next, we derive the basic reproduction number

R_{0}

and prove some stability results depending on the basic reproductive number. Finally, we perform numerical simulations using model parameters estimated from biological data to confirm our theoretical results. The results of these simulations suggest that for certain values of parameters, there will be periodic outbreaks of epidemics, and the disease will not be eradicated from the population. Our results also highlight the fact that the birth rate of cattle significantly influences the dynamics of the disease. The proposed model can be of a good use in studying the effects of vaccination on the cattle population. Full article

(This article belongs to the Special Issue Mathematical Modeling and Its Application in Medicine)

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16 pages, 4167 KiB

Open AccessArticle

A Mathematical Model for Controlling Exchanged Spinor Waves between Hemoglobin, Tumor and T-Cells

by Massimo Fioranelli, Alireza Sepehri, Maria Grazia Roccia, Aroonkumar Beesham and Dana Flavin

Mathematics 2021, 9(24), 3310; https://0-doi-org.brum.beds.ac.uk/10.3390/math9243310 - 19 Dec 2021

Viewed by 2167

Abstract

To date, it is known that tumor cells respond to attacks of T-cells by producing some PD-1/PD-L1 and other connections. Unfortunately, medical methods for preventing these connections are expensive and sometimes non-effective. In this study, we suggest a new way for reducing these connections by producing some noise in the exchanged information between tumor cells, T-cells, hemoglobin, and controller cells such as those of the heart or brain. In this model, we assume that human cells use spinor waves for exchanging information because the velocity of exchanged information between two spinors, which are located a large distance apart, exceeds the velocity of light. In fact, two spinors could send and receive information from each other instantaneously. In this hypothesis, the DNAs within heart cells, brain cells or any controller are built from some spinors such as electrons, and by their motion, some waves are generated. These spinor waves are received by iron atoms and multi-gonal molecules within hemoglobin and other spinors within the blood vessels. The hemoglobin molecules are located on some blood cells, move along the blood vessels and pass on their information to cells, proteins and RNAs. The spins of the spinors within the hemoglobin and also the spins of the charges and ions within the blood vessels are entangled and could transmit any information between cells. Thus, when a tumor is formed, its spinor waves change, and are transmitted rapidly into the heart cells, brain cells and other controller cells. The heart, brain or other controller cells diagnose these quantum waves, and by using the entanglement between the spinors within the blood vessels and the hemoglobin, send some messages to the T-cells. These messages are received by tumor cells and they become ready to respond to attacks. To prevent the reception of information by tumor cells, we can make use of some extra cells or hemoglobin, which interact with spinors and hemoglobin around tumor cells and produce some noise. Science quantum spinor waves are minute and have minor power and intensity; we cannot detect them by our present electronic devices and for this reason, we suggest using biological cells. This is a hypothesis; however, if experiments show its validity, some types of cancers could be cured or controlled by this method. We formulate the model by considering quantum entanglement between spinors within biological systems. By changing any spin within this system, all spins change and consequently, information is transmitted immediately. Then, we add new spinors to this system mathematically, and show that this causes the correlations between the initial spinors to reduce. Thus, the spinors of the extra hemoglobin or cells could act like noise, and prevent reception of real information by tumor cells. Full article

(This article belongs to the Special Issue Mathematical Modeling and Its Application in Medicine)

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34 pages, 3099 KiB

Open AccessFeature PaperArticle

Expert System to Model and Forecast Time Series of Epidemiological Counts with Applications to COVID-19

by Beatriz González-Pérez, Concepción Núñez, José L. Sánchez, Gabriel Valverde and José Manuel Velasco

Mathematics 2021, 9(13), 1485; https://0-doi-org.brum.beds.ac.uk/10.3390/math9131485 - 24 Jun 2021

Cited by 5 | Viewed by 2792

Abstract

We developed two models for real-time monitoring and forecasting of the evolution of the COVID-19 pandemic: a non-linear regression model and an error correction model. Our strategy allows us to detect pandemic peaks and make short- and long-term forecasts of the number of infected, deaths and people requiring hospitalization and intensive care. The non-linear regression model is implemented in an expert system that automatically allows the user to fit and forecast through a graphical interface. This system is equipped with a control procedure to detect trend changes and define the end of one wave and the beginning of another. Moreover, it depends on only four parameters per series that are easy to interpret and monitor along time for each variable. This feature enables us to study the effect of interventions over time in order to advise how to proceed in future outbreaks. The error correction model developed works with cointegration between series and has a great forecast capacity. Our system is prepared to work in parallel in all the Autonomous Communities of Spain. Moreover, our models are compared with a SIR model extension (SCIR) and several models of artificial intelligence. Full article

(This article belongs to the Special Issue Mathematical Modeling and Its Application in Medicine)

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17 pages, 606 KiB

Open AccessArticle

A Comparative Study between Discrete Stochastic Arithmetic and Floating-Point Arithmetic to Validate the Results of Fractional Order Model of Malaria Infection

by Samad Noeiaghdam, Aliona Dreglea, Hüseyin Işık and Muhammad Suleman

Mathematics 2021, 9(12), 1435; https://0-doi-org.brum.beds.ac.uk/10.3390/math9121435 - 20 Jun 2021

Cited by 16 | Viewed by 1538

Abstract

The researchers aimed to study the nonlinear fractional order model of malaria infection based on the Caputo-Fabrizio fractional derivative. The homotopy analysis transform method (HATM) is applied based on the floating-point arithmetic (FPA) and the discrete stochastic arithmetic (DSA). In the FPA, to [...] Read more.

ε

. Because in real life problems we do not have the exact solution and the optimal value of

ε

, we need to introduce a new condition and arithmetic to show the efficiency of the method. Thus the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library are applied. The CESTAC method is based on the DSA. Also, a new termination criterion is used which is based on two successive approximations. Using the CESTAC method we can find the optimal approximation, the optimal error and the optimal iteration of the method. The main theorem of the CESTAC method is proved to show that the number of common significant digits (NCSDs) between two successive approximations are almost equal to the NCSDs of the exact and approximate solutions. Plotting several graphs, the regions of convergence are demonstrated for different number of iterations k = 5, 10. The numerical results based on the simulated data show the advantages of the DSA in comparison with the FPA. Full article

(This article belongs to the Special Issue Mathematical Modeling and Its Application in Medicine)

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21 pages, 2500 KiB

Open AccessArticle

Using a Modified VIKOR Technique for Evaluating and Improving the National Healthcare System Quality

by Sun-Weng Huang, James J. H. Liou, Hai-Hua Chuang and Gwo-Hshiung Tzeng

Mathematics 2021, 9(12), 1349; https://0-doi-org.brum.beds.ac.uk/10.3390/math9121349 - 11 Jun 2021

Cited by 11 | Viewed by 2295

Abstract

The effectiveness of the national/regional healthcare system is one of the keys to prevent the spread of COVID-19. In the face of this unknown pandemic, where the healthcare system should continue to be promoted and improved are crucial decision issues. In the past, most studies have used the subjective opinions of experts for analysis and decision-making processes when investigating complicated decision-making problems. However, such decision-making processes are easily influenced by experts’ preferences. Therefore, this research proposes a soft computing technology that integrates CRiteria Importance Through Intercriteria Correlation (CRITIC) with the modified VlseKriterijumska Optimizacija I Kompromisno Resenje in Serbian, meaning multicriteria optimization and compromise solution (modified VIKOR) technique to reduce the impact of expert preference. In order to cope with the fact that COVID-19 has spread globally and to discover problems quickly and effectively, this study uses the global health security (GHS) index as the evaluation framework and conducts overall discussions in 195 countries/regions around the world. It is verified that the technology of soft computing can be used for continuous promotion and improvement of the national/regional healthcare system. This technology facilitates decision makers to know the gap of performance between the current healthcare system and the aspiration level. Finally, based on these gaps, we provide management advice to help improve these systems. Full article

(This article belongs to the Special Issue Mathematical Modeling and Its Application in Medicine)

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18 pages, 1702 KiB

Open AccessArticle

Personalized Characterization of Emotional States in Patients with Bipolar Disorder

by Pavel Llamocca, Victoria López, Matilde Santos and Milena Čukić

Mathematics 2021, 9(11), 1174; https://0-doi-org.brum.beds.ac.uk/10.3390/math9111174 - 22 May 2021

Cited by 11 | Viewed by 2502

Abstract

There is strong clinical evidence from the current literature that certain psychological and physiological indicators are closely related to mood changes. However, patients with mental illnesses who present similar behavior may be diagnosed differently, which is why a personalized study of each patient is necessary. Following previous promising results in the detection of depression, in this work, supervised machine learning (ML) algorithms were applied to classify the different states of patients diagnosed with bipolar depressive disorder (BDD). The purpose of this study was to provide relevant information to medical staff and patients’ relatives in order to help them make decisions that may lead to a better management of the disease. The information used was collected from BDD patients through wearable devices (smartwatches), daily self-reports, and medical observation at regular appointments. The variables were processed and then statistical techniques of data analysis, normalization, noise reduction, and feature selection were applied. An individual analysis of each patient was carried out. Random Forest, Decision Trees, Logistic Regression, and Support Vector Machine algorithms were applied with different configurations. The results allowed us to draw some conclusions. Random Forest achieved the most accurate classification, but none of the applied models were the best technique for all patients. Besides, the classification using only selected variables produced better results than using all available information, though the amount and source of the relevant variables differed for each patient. Finally, the smartwatch was the most relevant source of information. Full article

(This article belongs to the Special Issue Mathematical Modeling and Its Application in Medicine)

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27 pages, 715 KiB

Open AccessArticle

Patients’ Prioritization on Surgical Waiting Lists: A Decision Support System

by Fabián Silva-Aravena, Eduardo Álvarez-Miranda, César A. Astudillo, Luis González-Martínez and José G. Ledezma

Mathematics 2021, 9(10), 1097; https://0-doi-org.brum.beds.ac.uk/10.3390/math9101097 - 13 May 2021

Cited by 9 | Viewed by 2670

Abstract

Currently, in Chile, more than a quarter-million of patients are waiting for an elective surgical intervention. This is a worldwide reality, and it occurs as the demand for healthcare is vastly superior to the clinical resources in public systems. Moreover, this phenomenon has worsened due to the COVID-19 sanitary crisis. In order to reduce the impact of this situation, patients in the waiting lists are ranked according to a priority. However, the existing prioritization strategies are not necessarily systematized, and they usually respond only to clinical criteria, excluding other dimensions such as the personal and social context of patients. In this paper, we present a decision-support system designed for the prioritization of surgical waiting lists based on biopsychosocial criteria. The proposed system features three methodological contributions; first, an ad-hoc medical record form that captures the biopsychosocial condition of the patients; second, a dynamic scoring scheme that recognizes that patients’ conditions evolve differently while waiting for the required elective surgery; and third, a methodology for prioritizing and selecting patients based on the corresponding dynamic scores and additional clinical criteria. The designed decision-support system was implemented in the otorhinolaryngology unit in the Hospital of Talca, Chile, in 2018. When compared to the previous prioritization methodology, the results obtained from the use of the system during 2018 and 2019 show that this new methodology outperforms the previous prioritization method quantitatively and qualitatively. As a matter of fact, the designed system allowed a decrease, from 2017 to 2019, in the average number of days in the waiting list from 462 to 282 days. Full article

(This article belongs to the Special Issue Mathematical Modeling and Its Application in Medicine)

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