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Mathematical Models: Perspectives of Mathematical Modelers and Public Health Professionals
This chapter describes mathematical epidemiology from the perspectives of mathematical modelers and public health professionals. The mathematical...
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Mathematical models of leukaemia and its treatment: a review
Leukaemia accounts for around 3% of all cancer types diagnosed in adults, and is the most common type of cancer in children of paediatric age...
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Pessimistic multigranulation rough bipolar fuzzy set and their application in medical diagnosis
Multigranulation rough sets have recently attracted a lot of attention, and numerous multigranulation rough set models have been created from...
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Recent Development of Medical Shape Analysis via Computational Quasi-conformal Geometry
Medical analysis is closely related to mathematics in many aspects. Over the past decades, mathematicians have designed numerous mathematical models...
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Variational Models and Their Combinations with Deep Learning in Medical Image Segmentation: A Survey
Image segmentation means to partition an image into separate meaningful regions. Segmentation in medical images can extract different organs,...
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Mathematical Model of Building a Neural Network for Diagnosing Circulatory Disorders
AbstractA mathematical model of building a neural network for diagnosing circulatory disorders in the vessels of a human’s circulation is considered....
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Models of Solid Mechanics in the Problems of Ophthalmology
AbstractThis paper presents a very brief review of models constructed in cooperation with ophthalmologists, namely, for the change in the...
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Mathematical Modeling of the Functioning of Conditioned Reflexes
The basic principles and approaches to mathematical modeling of conditioned reflexes in a human or animal on the basis of the developed mathematical...
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A mathematical model of the human heart suitable to address clinical problems
In this paper, we present a mathematical model capable of simulating the human cardiac function. We review the basic equations of the model, their...
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Pattern recognition in data as a diagnosis tool
Medical data often appear in the form of numerical matrices or sequences. We develop mathematical tools for automatic screening of such data in two...
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Mathematical Model of COVID-19 Progression: Prediction of Severity and Outcome
AbstractThe objective of the study is to develop a method that enables to predict disease severity at the moment of admission to an intensive care...
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Variational Models and Their Combinations with Deep Learning in Medical Image Segmentation: A Survey
Image segmentation means to partition an image into separate meaningful regions. Segmentation in medical images can extract different organs,...
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Deep Learning for Ill Posed Inverse Problems in Medical Imaging
Recently, with the significant developments in deep learning (DL) techniques, solving underdetermined inverse problems has become one of the major...
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A Mathematical Model of the Disruption of Glucose Homeostasis in Cancer Patients
In this paper, we investigate the disruption of the glucose homeostasis at the whole-body level by the presence of cancer disease. Of particular...
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Deep Learning Techniques for Medical Image Segmentation and Object Recognition
Segmentation of a target object in the form of closed curves has many potential applications in medical imaging because it provides quantitative...
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Numerical Methods for Diagnosis and Therapy Design of Cerebral Palsy by Bilevel Optimal Control of Constrained Biomechanical Multi-Body Systems
In this chapter, we describe how to use mathematical optimization for diagnosis and treatment planning of cerebral palsy. We give background...
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Sensor Fault Diagnosis and Tolerant Control Based on Belief Rule Base for Complex System
This paper develops a new fault diagnosis and tolerant control framework of sensor failure (SFDTC) for complex system such as rockets and missiles....
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The role of A\(\beta \) and Tau proteins in Alzheimer’s disease: a mathematical model on graphs
In this Note we study a mathematical model for the progression of Alzheimer’s Disease in the human brain. The novelty of our approach consists in the...
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Mathematical Analysis of Diagnosis Rate Effects in Covid-19 Transmission Dynamics with Optimal Control
Many countries around the world are trying to fight Covid-19, and their main methods are lockdown, quarantine, isolation, and awareness programs to...
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Clifford Convolutional Neural Networks: Concepts, Implementation, and an Application for Lymphoblast Image Classification
This chapter presents the basic concepts of convolutional neural network (CNN) models on Clifford algebras, referred to as Clifford CNNs. The basic...