The solid state of matter has a definite volume and shape and particles are packed closely together and are incompressible. Within this tight lattice, there is enough thermal energy to produce vibration of particles.

Liquids however have a volume but no definite shape. These particles are less tightly packed together. Although there is free movement within the volume, they are incompressible.

Gases, however, have no finite shape or volume and particles are free to move rapidly in a state of random motion. They are compressible and are completely shaped by the space in which they are held. Vapours exist as a gas phase in equilibrium with identical liquid or solid matter below its boiling point.

The most prevalent state of matter in the universe is plasma which is formed by heating atoms to very high temperatures to form ions.

Small measurement units are denoted by the following SI mathematical prefixes:

1 deci = 0.1
1 milli = 0.001
1 micro = 0.000001
1 nano = 0.000000001
1 pico = 0.000000000001
1 femto = 0.000000000000001 (used to measure red blood cell volume)
1 atto = 0.000000000000000001

The total body water content of a 70kg man is (70 × 0.6) = 42 litres. For a woman, the calculation is (70 × 0.55) = 38.5 litres.

For a man, it is subdivided into:

Extracellular fluid (ECF) = 14L (1/3)
Intracellular fluid (ICF) = 28L (2/3).

The ECF volume is further divided into:

Interstitial fluid = 10.5 litres
Plasma = 3 litres
Transcellular fluid (CSF/synovial fluid) = 0.5 litres.

Directly measured fluid compartments:

Heavy water (deuterium) can be used to measure total body water content, which is freely distributed.
Albumin labelled with a radioactive isotope or using a dye called Evans blue can be used to measure Plasma volume . They do not diffuse into red blood cells.
Radiolabelled (Cr-51) red blood cells can be used to measure total erythrocyte volume.
Inulin as the tracer can be used to measure ECF volume as it circulate freely in the interstitial and plasma volumes.

Indirectly measured fluid compartments:

Total blood volume can be calculated with the level of haematocrit and the volume of total circulating red blood cells.
ICF volume can be calculated by subtracting ECF volume from total blood volume.

The following units are derived SI units of measurement.

Energy or work: kg.m2.s-2
The Joule (J) is the energy transferred to an object when a force of one newton acts on that object in the direction of its motion through a distance of one meter or N.m.

Power: kg.m2.s-3
The Watt (W) = rate of transfer of energy or Joule per second J/s.

Force: kg.m.s-2
One Newton (N) which is the international unit of measure for force = 1 kilogram meter per second squared. 1 Newton of force is the force required to accelerate an object with a mass of 1 kilogram 1 meter per second per second.

Volt: kg.m2.s-3.A-1
The volt (V) is defined as the potential difference across a conductor when a current of one ampere dissipates one watt of power or W/A.

Pressure: kg.m-1.s-2
A pascal (Pa) is force per unit area or N/m2.

The amount of oxygen carried by 100 ml of blood is called the arterial oxygen content (CaO2)and is normally 17-24 ml/dL and can be determined by this equation:

CaO2 = oxygen bound to haemoglobin + oxygen dissolved in plasma

CaO2 = (1.34 × Hgb × SaO2 × 0.01) + (0.003 × PaO2)

where:

1.34 = Huffner’s constant (D) – Huffner’s constant does not change and its magnitude relatively small.
Hgb is the haemoglobin level in g/dL and SaO2 is the percent oxyhaemoglobin saturation of arterial blood
PaO2 is (0.0225 = ml of O2 dissolved per 100 ml plasma per kPa, or 0.003 ml per mmHg).

Quantitatively, the amount of oxygen dissolved in plasma is 0.3 mL/dL.

Henry’s law states that at constant temperature, the amount of gas dissolved at equilibrium in a given quantity of a liquid is proportional to the pressure of the gas in contact with the liquid.

Given a haemoglobin concentration of 15 g/dL and a SaO2 of 100% and a PaO2 of 13.3 kPa, the amount of oxygen bound to haemoglobin is 20.4 mL/100mL.

Cardiac output is an important determinant of oxygen delivery but does not influence the oxygen content of blood.

Charles’ Law states that there is a direct correlation between temperature and volume, where pressure and amount gas are constant. As temperature increases, volume also increases.

Boyle’s Law states that Pressure is inversely proportional to volume, assuming that temperature and amount of gas are constant. As volume increases, pressure decreases. In Dalton’s law of partial pressure, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressure of the gases in mixture.

According to Henry’s Law for concentration of dissolved gases, at a constant temperature, the amount of a given gas that dissolves in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid. An equivalent way of stating the law is that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.

Gay-Lussac’s Law states that the pressure of a given mass of gas varies directly with the absolute temperature of the gas, when the volume is kept constant. This law is very similar to Charles’ Law, with the only difference being the type of container. Whereas the container in a Charles’ Law experiment is flexible, it is rigid in a Gay-Lussac’s Law experiment.

The magnitude of x determines the rate of change of x. First-order drug kinetics is a good example. Most drugs’ plasma levels are controlled by an exponential process. The rate of change in drug metabolism is proportional to the current plasma concentration (so-called non-linear kinetics).

A tear-away function is just one type of exponential relationship (y = ex), in which e is Euler’s number, x is the power, and e is the base. Natural logarithms rely on Euler’s number.

Euler’s number is a mathematical constant, not a mathematical principle. It’s referred to as an irrational number. This is a number that cannot be expressed as a simple fraction or a ratio.

A line or curve that acts as the limit of another line or curve is known as an asymptote. A washout exponential curve, for example, where the value y represents the plasma concentration of a drug in a single compartment model against time on the x axis. This descending curve approaches but never touches the x axis. This curve is asymptotic to the x axis, which is the curve’s asymptote. An asymptote isn’t just a characteristic of exponential curves.

Smallest drops reach not only the upper but also the lower respiratory tracks. As a result, the ultrasonic nebulizer is most efficient for the therapy of pulmonary diseases and stands out as a robust and reliable support within the clinical setting.

Bernoulli’s principle states that as the speed of a moving fluid increases, there is a simultaneously decrease in static pressure or a decrease in the fluid’s potential energy.
This is seen in the simultaneous increase in speed and kinetic energy and fall in pressure that causes entrainment of large volumes of air into a flow of 100% oxygen in the nozzle of HAFOE masks.

The reduction in fluid pressure that happens when a fluid flows through a constriction in a tube is the Venturi effect.

When a flow of gas or liquid attaches itself to a nearby surface and remains attached even when the surface curves away from the initial direction of flow, this is the Coanda effect.

The branch of engineering and technology that is concerned with the building of devices that use the flow and pressure of a fluid for functions usually performed by electronic devices is Fluidics . Fluidic logic is used to power some ventilators.

The branch of engineering that utilises pressurised gases is Pneumatics.