00 - Introduction and Physical Measures

• The functioning of biological systems is based on the principles of Physics and Chemistry.
  • Physics ⇔Physiology. They are highly connected.
• Physics enters clinical practice through several technologies and devices:
  • Diagnosis and Therapy
• Physics is a basic discipline, propedeutic to any other scientific discipline;
• It is useful for training, as it is the reference model for the scientific method.

Physics ⇔Physiology

Physics	Physiological Application
Kinematics & Mechanics	Musculoskeletal System (levers, torque, and movement)
Molecular Engines & Switches	Muscle contraction (myosin/actin) and cellular signaling
Gas & Fluid Physics	Mechanics of breathing (pressure gradients and flow)
Diffusion Laws	Transport across semipermeable membranes
Surface Tension	Respiratory system (alveolar stability and surfactants)
Fluid Mechanics	Hemodynamics (blood circulation and vascular resistance)
Osmotic Pressure	Renal function, filtration, and water balance
Thermodynamics	Metabolism and energy expenditure
Electricity & Electromagnetism	Nerve conduction and muscle contraction (action potentials)
Optics & Acoustics	Sensory organs (the eye and the ear)
Atomic Physics & Biophysics	Biochemical and molecular processes

Physics in clinics, diagnostics and therapy

• Laboratory analysis (sedimentation, centrifugation, electrophoresis)
• Radiological techniques:
  • X-ray, Computerized Axial Tomography (CT),
  • Positron emission tomography (PET),
  • Single photon computed tomography (SPECT).
• Diagnostic and therapeutic techniques based on electromagnetic fields:
  • electroencephalography (EEG),
  • electrocardiography (ECG),
  • defibrillator.
• Therapeutic applications of non-ionizing radiation:
  • Laser,
  • ultraviolet rays,
  • magnetotherapy.
• “Imaging” techniques: microscopy, fluoroscopy, mammography, absorbimetry and angiography.
• Diagnostic techniques based on magnetic resonance imaging:
  • Nuclear magnetic resonance (NMR),
  • functional magnetic resonance imaging (FMRi).
• Ultrasound: Ultrasound Techniques for Imaging and Fluximetry (Eco-Doppler)
• Radiotherapy: X, Gamma, and hadrontal sources

Many of the latest diagnostic techniques (brain MRi, molecular-level microscopy, lab-on-chip) have entered common medical practice (or at least in medical research) despite being based on very advanced physics (Quantum Mechanics, Microfluidics).

Interaction between Physics, Biology and Medicine is not a negligible aspect, in the next few years there will be a strengthening of this union in various fields (personalized medicine, transcriptomics, nanomedicine, bacterial and viral ecology, immunology, neuroscience, evolutionary biology).

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Physical quantities

Measurable, objective and repeatable quantities, to link the abstract concepts with the observed reality.

This link is given by the operational definition which indicates how the quantity in question should be measured.
The operational definition must necessarily indicate a practical or experimental method by which the result is achieved (for example, comparison with an appropriate standard).

Some definitions, such as length, could be given in a completely theoretical way (spatial extension), but this does not constitute an operative definition.

Classification of Physical Quantities

• fundamental: (e.g. space, time, mass, temperature)
• derived, obtained as a function of fundamental quantities: (speed, energy, magnetic field flux).

Every physical quantity is characterized by a specific dimensionality, given by the combination of fundamental quantities that compose it.

Only two physical quantities of the same species (homogeneous) can be compared to each other and therefore measured

Fundamental Quantities of the I.S.

Systems that assume certain quantities as fundamental and which express, compared to those, the others as derivatives.

International System (IS, or M.K.S.):

Physical size	Symbol	SI unit name	SI symbol
Length	$L$	meter	$m$
Mass	$M$	kilogram	$kg$
Time	$t$	second	$s$
Electricity	$I$	ampere	$A$
Temperature	$T$	kelvin	$K$
Quantity of substance	$n$	mole	$mol$
Luminous intensity	$I_v$	candela	$cd$

Powers: intervals of $10^3$

Power	Prefix	Symbol
$10^{15}$	Peta	$P$
$10^{12}$	Tera	$T$
$10^9$	Giga	$G$
$10^6$	Mega	$M$
$10^3$	Kilo	$k$
$10^{-3}$	milli	$m$
$10^{-6}$	micro	$\mu$
$10^{-9}$	nano	$n$
$10^{-12}$	pico	$p$
$10^{-15}$	femto	$f$

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Measure

Direct measurement: comparison with another quantity of the same species (unit of measure) and obtain the number (integer or decimal) which expresses how many times the unit of measure (or a part of it) is contained in the given size (es length).

Indirect measurement: the magnitude of interest is in mathematical relation with that actually measured (eg pressure, temperature, metabolism)

Measurement error

Each measure is affected by a error, related to the sensitivity of the instrument, random errors and systematic errors.

For example, a length is expressed by a number that expresses its relation to another socket as a unit of measurement (meters or centimeters) ± an error (absolute or relative)

• Absolute error: deviation from the “true measure”
  • $\Delta x=x-x_m$
• Relative error: ratio between absolute error and “true measure”
  • $E_{rel}=\frac{\Delta x}{x_m}$, possibly expressed as a percentage

es. $l=34.5m\pm 0.2m$ ~ $l=34.5m\pm 0.2\%$

Fundamental quantities IS

• meter:
  • distance traveled by light in vacuum over a period of 1/299 792 458 s.
• kilogram:
  • mass of a cylinder with a height and diameter of 0.039 m of a platinum-iridium alloy deposited at the International Bureau of Weights and Measures
• second:
  • duration of 9 192 631 770 periods of the radiation corresponding to the transition between two hyperfine levels, from (F = 4, MF = 0) to (F = 3, MF = 0), of the fundamental state of the cesium-133 atom.
• ampere:
  • intensity of electrical current that, if maintained in two parallel linear conductors, of infinite length and negligible cross section, placed one meter away from each other in the vacuum, produces between them a force equal to 2 ×10−7 newton per meter of length.
• kelvin:
  • 1/273.16 of the thermodynamic temperature of the triple point of water.
• mole:
  • amount of substance of a system that contains a number of interacting units equal to the number of atoms present in 12 grams of carbon 12 (NA = 6.02·1023).
• candle:
  • light intensity, in a given direction, of a source emitting a monochromatic radiation of frequency equal to 540 ×1012 hertz and of radiant intensity in that direction w/ 683 watt per steradian.

Some lengths

Object / Distance	Length Equivalence (m)	Scale Category
Distance Earth to Andromeda (M31)	$2\times 10^{22}$	Galactic
Diameter of the Milky Way	$8\times 10^{20}$	Galactic
Distance Earth to Proxima Centauri	$4\times 10^{16}$	Interstellar
Distance Earth to Sun (1 AU)	$1.5\times 10^{11}$	Solar System
Earth Radius (average)	$6.37\times 10^6$	Planetary
Thickness of paper	$1\times 10^{-4}$	Macroscopic
Diameter of a Red Blood Cell	$8\times 10^{-6}$	Cellular
Diameter of a Virus	$1\times 10^{-7}$	Molecular/Viral
Diameter of an Ion Channel	$1\times 10^{-9}$	Nanoscale
Diameter of an Oxygen Atom	$1\times 10^{-10}$	Atomic
Diameter of a Proton	$2\times 10^{-15}$	Subatomic
Classical Radius of the Electron	$2\times 10^{-22}$	Quantum

Times

Event / Duration	Time Interval (s)	Scale Category
Life of an unstable particle	$10^{-23}$	Subatomic
Life of a radioactive particle	$10^{-22}$ to $10^{28}$	Nuclear
Light travel (1 meter)	$0.3\times 10^{-8}$	Light-speed
Cellular action potential	$3\times 10^{-3}$	Physiological
Heartbeat	$1\times 10^0$	Biological
One day	$1\times 10^5$	Planetary
One year	$3\times 10^7$	Planetary
Average human lifespan	$2\times 10^9$	Biological
Humans on the planet (Total time)	$1\times 10^{14}$	Anthropological
Age of Earth	$1\times 10^{17}$	Geological
Age of Universe	$1\times 10^{18}$	Cosmological

Masses

Object	Mass (kg)	Scale Category
Electron	$10^{-30}$	Subatomic
Proton / Neutron	$10^{-27}$	Subatomic
DNA Molecule	$10^{-17}$	Molecular
Bacteria	$10^{-15}$	Microscopic
Fly	$10^{-5}$	Macroscopic
Human Being	$10^2$	Biological
Earth	$6\times 10^{24}$	Planetary
Sun	$2\times 10^{30}$	Stellar
Galaxy	$1\times 10^{41}$	Galactic

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Derived quantities

• Volume = $L\ast L\ast L=m^3$
• Speed = space/time → $v=m/sec$
• Density = mass/volume → $\rho =kg/m^3$

Homogeneity principle of physical equations

Physical laws are in general algebraic relationships between a quantity and a combination of other quantities.

Example:

Direct or inverse proportionality relationships. Equality is introduced through a proportionality constant that depends on the measurement system adopted.

$y=\frac{h}{x}$ → $y=h\times x$

Principle of homogeneity:

the terms of an equation must have the same units of measurement.

$F=G\frac{m_1{m}_2}{r^2}\to G=\frac{F{r}^2}{m_1{m}_2}\to [G]=\frac{N{m}^2}{k{g}^2}$

Physical constants

Constant	Symbol	Value	Unit
Light speed in vacuum	$c$	$3\times 10^8$	${\text{m s}}^{-1}$
Electron charge	$e$	$1.6\times 10^{-19}$	$\text{C}$
Electron mass	$m$	$9.1\times 10^{-31}$	$\text{kg}$
Proton mass	$M$	$1.67\times 10^{-27}$	$\text{kg}$
Planck’s constant	$h$	$6.6\times 10^{-34}$	$\text{J s}$
Avogadro number	$N_0$	$6.02\times 10^{23}$	${\text{mol}}^{-1}$
Perfect gas constant	$R$	$8.3$	${\text{J K}}^{-1}{\text{mol}}^{-1}$
Boltzmann constant	$k=R/N_0$	$1.38\times 10^{-23}$	${\text{J K}}^{-1}$
Faraday constant	$F=N_{0}e$	$96487$	${\text{C mol}}^{-1}$
Dielectric constant (vacuum)	${\epsilon }_0$	$8.86\times 10^{-12}$	${\text{C}}^2{\text{N}}^{-1}{\text{m}}^{-2}$
Gravitational constant	$G$	$6.67\times 10^{-11}$	${\text{N m}}^2{\text{kg}}^{-2}$
Magnetic permeability (vacuum)	${\mu }_0$	$1.25\times 10^{-6}$	${\text{kg m C}}^{-2}$
Stefan-Boltzmann constant	$\sigma$	$5.67\times 10^{-8}$	${\text{W m}}^{-2}{\text{K}}^{-4}$
Wien constant	$k_w$	$2.897\times 10^{-3}$	$\text{m K}$
Mechanical equivalent of heat	$J$	$4.18$	${\text{J cal}}^{-1}$