# PHYSICS AND STATISTICS

## Learning outcomes of the course unit

The course of Applied Physics and Statistics has been designed to convey knowledge and understanding of basic physics principles and to introduce the student to the basics of statistical thinking and its application in practice.

The topics are geared to concrete analysis and research problems and deal in particular with situations and cases drawn from the medical literature.

The course will provide the necessary tools, mathematical, statistical and physical, to address issues of increasing complexity preparatory to other major disciplines of the degree course, such as Chemistry, Biology, Physiology, Biochemistry, etc.. , which are based on physical phenomenology and make frequent use of statistical analysis.

The course will also provide the conceptual basis for understanding a number of major technologies that with increasing frequency are used in medicine, such as: centrifuges, endoscopes, microscopes, transducers for

ultrasound equipment, laser systems, radiology equipment and NMR, radiation detectors, etc. In this sense, the module also aims to develop the students' attitude towards independent study and continuing education on the application of physical techniques to diagnosis and therapy in medicine.

As its final, but perhaps most important, goal, the course has been designed to stimulate students to become more familiar with certain common concepts, that are not always sufficiently explained in previous study, such as: mechanical action between bodies in contact, exertion and energy in action, dynamic aspects resulting from elastic force and impact, friction and thermal and thermodynamic aspects, static and dynamic properties of gaseous and liquid fluids, light and its manifestations, including in relation to the structure of the eye and its physical defects, fundamentals of electrical, magnetic and nuclear phenomena, the laws that govern potential and current, electromagnetic and nuclear radiation, detection and control.

Special emphasis will be put also on statistical reasoning, interpretation and decision-making process. We will insist more on the conceptual understanding that the mechanical calculation, especially in light of the wide range of software available for analysis. The theory will be made explicit by means of practical exercises and teaching cases, therefore, the ultimate goal of the course is that the student learn "how to do" as well as knowing.

## Course contents summary

PHYSICS:

The course of Applied Physics will deal with the most important aspects of basic physics, from the definition of the main physical quantities and measure systems up to the more complex content that are the basis of diagnostic imaging and radiation therapy.

The course will cover the fundamental principles of mechanics, fluid dynamics, electromagnetism, thermology, waves and optics.

Applications and consequences on human body physiology and medicine will be stressed. In particular, deeper insights will be provided into biomechanics, blood circulation, the use of radiations in diagnosis and therapy.

STATISTICS:

The first part of the course will introduce the basics of statistical planning and experimental design.

Principles of probability and combinatorial analysis needed later in the course will be introduced, as well as the major probability distributions. This includes the binomial distribution, the Poisson distribution, the Normal and standard Normal distribution.

The second part of the course will address the methods of descriptive statistics. It will be shown how to recognize the type of data and how to summarize them in appropriate indicators.

The student will learn how to calculate measures of location (mean, median, mode), variability (variance, standard deviation), the coefficient of variation (CV), quantiles and their use.

In the final part of the course the general principles of statistical inference will be introduced.

The student will face the concepts of sampling distribution, type I and II error, power of a statistical test and operating curve.

The following methods will then be explained:

parametric tests - Student's t test, ANOVA 1 and 2 classification criteria.

non-parametric tests: - Wilcoxon test, Mann-Whitney, Kruskal-Wallis, Friedman test, median test, chi-square test, Fisher's exact test.

## Course contents

Physics

Physical quantitites and their measurement: Measurement of a physical quantity - Dimensions and units – Errors - Mean value - Standard deviation and sampling approximation -Vector quantities.

- Fundamentals of dynamics: Principles of dynamics - Energy, work and power - Weight force - Theorem of the kinetic energy - Conservative force fields - Potential energy - Conservation of mechanical energy - Center of mass and its properties - Conservation of the quantity of motion - Moment of force - Overview of rigid body motion - Levers and the human body – Balance - Elastic phenomena, Hooke’s law and elasticity modules - Flexure and torsion - Elasticity of blood vessels and bones.

- Waves and acoustics: Wave motion, wave equation and characteristic parameters - Interference and beats - Stationary waves - Resonance - Diffraction and Huyghens principle - Sound and its characteristics - Intensity, sensation, Weber-Fechner law - Doppler effect - Ultrasound and its application in the biomedical field

- Hydrostatics and hydrodynamics: Pressure, Pascal and Archimedes - Atmospheric pressure and Torricelli’s barometer - Arterial pressure and its measurement - Surface tension and Laplace’s formula - Capillarity and Jurin’s law - Gaseous embolism - Pipe flow capacity - Ideal liquid and Bernouilli’s theorem -Implications for blood flow - Real liquids and viscosity - Laminar motion and Poiseuille’s theorem - Hydraulic resistance - Stokes’ equation and sedimentation speed - Turbulent regime and Reynolds number - Overview of cardiac work.

- Thermology and thermodynamics: Thermal dilation -Temperature and heat - Laws of gas and absolute temperature - Equation of state of ideal gases and approximation for real gases - Overview of the kinetic theory of gases - Specific heats –Change of state and latent heat - Heat propagation mechanisms -First and second principle of thermodynamics -Thermal machines and efficiency - Entropy and disorder.

- Optics: Reflection and refraction - Total reflection and optical fiber - Optical system, focus and dioptric power - Spherical diopter - Thin lenses, mirrors and image construction - Compound microscope - Resolution strength - The eye as a dioptric system - Principal ametropies of the eye and their correction using lenses - Wave theory of light - Laser light.

- Electricity, magnetism and electrical current: Electrical charges and Coulomb’s law - Electrical field - Work of the electrical field and electrostatic potential - Dipolar field - Overview of muscle fiber and electrocardiogram - Gauss’s theorem and its applications - Faraday cage - Electrical capacity and capacitor - Current intensity - Overview of the electronic structure of insulators, metallic conductors and semi-conductors - Ohm’s law - Series and parallel resistors – Electromotive force - Thermal effect of current - Electrical conduction in liquids - Passing of current in the human body -Thermoionic and photoelectric effects - Magnetic field and its action on current and magnets - Biot-Savart law - Ampere’s theorem of circulation - Solenoid - Electromagnetic induction - Self-induction – Alternating voltage and current - Impedance -Electromagnetic waves.

- Radiation: Structure of the atom and nucleus - Quantum numbers, electronic orbitals and transitions - Unstable isotopes and alpha, beta, gamma radiation - Law of radioactive decay and half-life - Radiation detection - Biomedical applications of radioisotopes - X-rays (production, properties and absorption mechanisms in the matter) - Radiological image - Overview of computerised axial tomography (CAT) and radiofrequency (NMR) imaging techniques- Overview of radiation safety.

Statistics

Introduction: medical statistics and related disciplines. Logic and statistical planning. Overview of combinatorial analysis: permutations, arrangements, combinations. Applications. Overview of probability calculations: simple and compound probability, Bayes theorem.

Odds. Odds ratios. Likelihood ratios.

## Recommended readings

FISICA:

Giambattista, McCarthy Richardson, Richardson: Fisica Generale,Ed. McGraw-Hill (Milano).

Bersani, Bettati, Biagi, Capozzi, Feroci, Lepore, Mita, Ortalli, Roberti, Viglino, Vitturi:

Fisica biomedica, Ed. Piccin Nuova Libraria (Padova).

Scannicchio: Fisica Biomedica, Ed. EdiSES (Napoli).

STATISTICA:

1) Appunti delle lezioni

2) Stanton A. Glantz : Statistica per discipline Bio-mediche - ed. McGraw-Hill

3) Sidney Siegel, N. John Castellan Jr. : - Statistica non parametrica - ed. McGraw-Hill

4) Risorse e link da Internet

## Teaching methods

Physics

During classroom lectures, the topics contained in the program of the module will be illustrated and commented. Emphasis will be posed on the applications to biology and medicine of basic physics principles, with examples of how such principles can lead to quantitative predictions on physiological and pathological phenomena.

In selected cases, the demontration of basic physics principles will be illustrated, with the aim to introduce the students to the practice of logical thinking and experimental approach.

Statistics

During classroom lectures, the topics contained in the program of the module will be illustrated and commented. At the end of each topic classroom exercises explaining the application of the theory in practice will follow. The formal procedure and the step by step execution of the necessary calculations will be described. Both manual solution and computer calculation will be shown.

The students will be particularly encouraged to use the open source statistical system "R" and the free software package Epi Info.

## Assessment methods and criteria

The achievement of the objectives of the module will be assessed through a written examination, mainly consisting in open questions on the topics of the course. This will allow to ascertain the knowledge and the

understanding of both the theoretical bases and their consequences.

The written examination will include the resolution of problems, to assess the achievement of the ability to apply the acquired knowledge to a simulated biological or medical situation. All parts of the written exam will be equally weighted in the final evaluation.