Mathematical methods in medicine: neuroscience, cardiology and pathology

Abstract

The application of mathematics, natural sciences and engineering to medicine is gaining momentum as the mutual benefits of this collaboration become increasingly obvious. This theme issue is intended to highlight the trend in the case of mathematics. Specifically, the scope of this theme issue is to give a general view of the current research in the application of mathematical methods to medicine, as well as to show how mathematics can help in such important aspects as understanding, prediction, treatment and data processing. To this end, three representative specialties have been selected: neuroscience, cardiology and pathology. Concerning the topics, the 12 research papers and one review included in this issue cover biofluids, cardiac and virus dynamics, computational neuroscience, functional magnetic resonance imaging data processing, neural networks, optimization of treatment strategies, time-series analysis and tumour growth. In conclusion, this theme issue contains a collection of fine contributions at the intersection of mathematics and medicine, not as an exercise in applied mathematics but as a multidisciplinary research effort that interests both communities and our society in general. This article is part of the themed issue ‘Mathematical methods in medicine: neuroscience, cardiology and pathology’.

Loss of adaptive capacity in asthmatic patients revealed by biomarker fluctuation dynamics after rhinovirus challenge

“…Over the past decades a considerable research effort has been invested into mathematically analyzing the fluctuation behavior of physiologic time series with the aim of characterizing the normal homeokinetic variability of physiologic systems (Garfinkel, 1983; Glass and Mackey, 1988; Goldberger et al, 2000; Glass and Kaplan, 1993; Amigó and Small, 2017). One of the most counterintuitive findings has been that both excessive and too little variation are indicative of pathological modifications and aging (Que et al, 2001; Goldberger et al, 2002 and references therein).…”

Neuroscience without borders: Preserving the history of neuroscience

“…A second way that the history of neuroscience can aid neuroscience research is in its interdisciplinary nature (Barbara, 2016). Many publications in the history of neuroscience note the importance of interdisciplinary collaborations from the 19th century (Berlucchi, 1999) to the neuroscientific advances of the 1950s and 1960s (Shepherd, 2010) and the present day (Amigó & Small, 2017;Derry, Schunn, & Gernsbacher, 2005). Neuroscience research involves partnerships between universities and industry, and benefits from knowledge of fields outside of neuroscience.…”

“…Individual scientists have given their perspectives on large-scale collaborations vs. single-lab, hypothesis-driven science (Fairhall et al, 2016). Neuroscience involves a variety of disciplines including neuroanatomy, neurochemistry, neurophysiology, neuropharmacology, neurology, psychiatry, molecular biology, biochemistry, physics, cell biology, developmental biology, evolution, physics, chemistry, engineering, computer science, ethology, psychology, and neuroeconomics (Amigó & Small, 2017). While the term "neurologia -neurology" originates from Thomas Willis (Cerebri Anatome, 1664), the term "neuroscience" itself was coined by Francis O. Schmitt in the 1960s in order to embrace in a single word the variety of disciplines converging on the study of brain functions (Shepherd, 2010).…”

Hybrid Model for Time Series of Complex Structure with ARIMA Components

“…The examples are the problems of the recognition of anomalies in geophysical monitoring data, such as the detection of magnetic and ionospheric storms [1][2][3][4], earthquakes [5,6], tsunamis [7,8], geological anomalies [9] and other catastrophic natural phenomena. The need to detect anomalies often arises in the medical field, for example, to detect and to identify clinical conditions of patients [10]. An important property of such methods is their ability to adapt, providing the possibility to detect and identify rapid changes in the system or object state, indicating anomaly occurrences.…”