Mathematics in health care with applications

The Author aims to show how mathematics can be useful in supporting key activities in a hospital, including: noninvasive measurement of a patient’s status (see chapter 1), evaluation of quality of services (see chapter 2), business and clinical administration (see chapter 3), and diagnosis and prognosis (see chapter 4). Such applications suggest the development of innovative projects to improve health care processes, services and systems. In this way, mathematics can be a very important tool for technological and societal development

A derivative-free approach for a simulation-based optimization problem in healthcare

Hospitals have been challenged in recent years to deliver high quality care with limited resources. Given the pressure to contain costs,developing procedures for optimal resource allocation becomes more and more critical in this context. Indeed, under/overutilization of emergency room and ward resources can either compromise a hospital's ability to provide the best possible care, or result in precious funding going toward underutilized resources. Simulation--based optimization tools then help facilitating the planning and management of hospital services, by maximizing/minimizing some specific indices (e.g. net profit) subject to given clinical and economical constraints. In this work, we develop a simulation--based optimization approach for the resource planning of a specific hospital ward. At each step, we first consider a suitably chosen resource setting and evaluate both efficiency and satisfaction of the restrictions by means of a discrete--event simulation model. Then, taking into account the information obtained by the simulation process, we use a derivative--free optimization algorithm to modify the given setting. We report results for a real--world problem coming from the obstetrics ward of an Italian hospital showing both the effectiveness and the efficiency of the proposed approach

Functional balance at rest of hemispheric homologs assessed via normalized compression distance

Introduction: The formation and functioning of neural networks hinge critically on the balance between structurally homologous areas in the hemispheres. This balance, reflecting their physiological relationship, is fundamental for learning processes. In our study, we explore this functional homology in the resting state, employing a complexity measure that accounts for the temporal patterns in neurodynamics. Methods: We used Normalized Compression Distance (NCD) to assess the similarity over time, neurodynamics, of the somatosensory areas associated with hand perception (S1). This assessment was conducted using magnetoencephalography (MEG) in conjunction with Functional Source Separation (FSS). Our primary hypothesis posited that neurodynamic similarity would be more pronounced within individual subjects than across different individuals. Additionally, we investigated whether this similarity is influenced by hemisphere or age at a population level. Results: Our findings validate the hypothesis, indicating that NCD is a robust tool for capturing balanced functional homology between hemispheric regions. Notably, we observed a higher degree of neurodynamic similarity in the population within the left hemisphere compared to the right. Also, we found that intra-subject functional homology displayed greater variability in older individuals than in younger ones. Discussion: Our approach could be instrumental in investigating chronic neurological conditions marked by imbalances in brain activity, such as depression, addiction, fatigue, and epilepsy. It holds potential for aiding in the development of new therapeutic strategies tailored to these complex conditions, though further research is needed to fully realize this potential

THE ENEL SMART GRID TEST SYSTEM: A REAL-TIME DIGITAL SIMULATOR-BASED INFRASTRUCTURE

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Measuring and benchmarking the quality of two different organizational ways in delivering infant vaccination

Introduction: The aim of this study was the quality of service evaluation of two different organizational ways in delivering infant vaccination according to a Regional Vaccination Plan. Materials and Methods: Eleven vaccination centres were selected in two Local Health Units (ASLs) belonging to the Regional Health Service of the Lazio Region, Italy. The services offering paediatric vaccinations for children under three years of age, delivered with the need for an appointment (VACL) or else without an appointment (VACP), were investigated. The quality aspects under evaluation were communicational efficiency, organisational efficiency and comfort. Three steps are necessary to quantify the overall quality of service. Step 1 involves different stakeholders and the elicitation of best and worst feasible performance conditions for the ASLs when delivering VACP/VACL services (i.e., subjective data collection). Step 2 consists in the observation of current performances of the selected vaccination centres (i.e., objective data collection). Step 3 involves the combination of all data. Benchmarking between VACP and VACL, i.e., two different organisational ways in delivering infant vaccination, can be performed as a result of the probabilistic meaning of the evaluated scores. Results: An expert of vaccination services, i.e., a virtual combination of patients, doctors and nurses, claims the quality of service delivery of the ASLs under investigation with probability 78.03% and 69.67% for VACL and VACP, respectively. In other words, for short, the quality scores of the ASLs were 78.03% for VACP and 69.67% for VACL. Furthermore our results show how to practically improve the current service delivery

Normalized compression distance to measure cortico-muscular synchronization

The neuronal functional connectivity is a complex and non-stationary phenomenon creating dynamic networks synchronization determining the brain states and needed to produce tasks. Here, as a measure that quantifies the synchronization between the neuronal electrical activity of two brain regions, we used the normalized compression distance (NCD), which is the length of the compressed file constituted by the concatenated two signals, normalized by the length of the two compressed files including each single signal. To test the NCD sensitivity to physiological properties, we used NCD to measure the cortico-muscular synchronization, a well-known mechanism to control movements, in 15 healthy volunteers during a weak handgrip. Independently of NCD compressor (Huffman or Lempel Ziv), we found out that the resulting measure is sensitive to the dominant-non dominant asymmetry when novelty management is required (p = 0.011; p = 0.007, respectively) and depends on the level of novelty when moving the nondominant hand (p = 0.012; p = 0.024). Showing lower synchronization levels for less dexterous networks, NCD seems to be a measure able to enrich the estimate of functional two-node connectivity within the neuronal networks that control the body

Design and development of a database for the administration and supply of vaccines for COVID-19 on the Italian territory

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MATEMATICA PER LA SANITA' CON APPLICAZIONI

The Author aims to show how mathematics can be useful in supporting key activities in a hospital, including: noninvasive measurement of a patient’s status (see chapter 1), evaluation of quality of services (see chapter 2), business and clinical administration (see chapter 3), and diagnosis and prognosis (see chapter 4). Such applications suggest the development of innovative projects to improve health care processes, services and systems. In this way, mathematics can be a very important tool for technological and societal development.This thesis is a collection of health care applications of mathematical methods and models from various disciplines of mathematics. In this way, the Author intends to show the necessity and benefits of multidisciplinary knowledge as well as the importance of an attitude to drive innovation by means of mathematical tools, using probability calculus, numerical analysis, operations research, and other methods. The integration of mathematics and real-life problems can be very effective. Advanced mathematics tools allow problems to be solved in innovative ways. From a theoretical point of view, each application may suggest if and how (in what direction) the theory on which it is based can be extended. This effort can result not only in the publication of scientific papers but also in the awarding of grants to continue such research activities. This thesis is a proof of these claims. It is structured as stand-alone chapters that share a common structure: an introduction, background and algorithms sections and a target application.QOLITY Design (www.qolitydesign.com

Measuring the quality of health-care services: A likelihood-based fuzzy Modeling approach

We face the problem of constructing a model which is suited for an effective evaluation of the quality of a health-care provider: to this purpose, we focus on some relevant indicators characterizing the various services run by the provider. We rely on a fuzzy modeling approach by using the interpretation (in terms of coherent conditional probability) of a membership function of a fuzzy set as a suitable likelihood

Functional Source Separation-Identified Epileptic Network: Analysis Pipeline

This proof-of-concept (PoC) study presents a pipeline made by two blocks: 1. the identification of the network that generates interictal epileptic activity; and 2. the study of the time course of the electrical activity that it generates, called neurodynamics, and the study of its functional connectivity to the other parts of the brain. Network identification is achieved with the Functional Source Separation (FSS) algorithm applied to electroencephalographic (EEG) recordings, the neurodynamics quantified through signal complexity with the Higuchi Fractal Dimension (HFD), and functional connectivity with the Directed Transfer Function (DTF). This PoC is enhanced by the data collected before and after neuromodulation via transcranial Direct Current Stimulation (tDCS, both Real and Sham) in a single drug-resistant epileptic person. We observed that the signal complexity of the epileptogenic network, reduced in the pre-Real, pre-Sham, and post-Sham, reached the level of the rest of the brain post-Real tDCS. DTF changes post-Real tDCS were maintained after one month. The proposed approach can represent a valuable tool to enhance understanding of the relationship between brain neurodynamics characteristics, the effects of non-invasive brain stimulation, and epileptic symptoms