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.

The formula for calculating air: oxygen entrainment ratio is given as :
100% − FiO2 = air/oxygen entrainment ratio
Since FiO2 − 21% and the entrainment ratio is already known. Substituting the values in the equation: x = FiO2.

100 − x = 9
x − 21
100 − x = 9(x − 21)
100 − x = 9x − 189
10x = 289
x = 289/10
x = 28.9%

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.

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.

Since the gas is less dense at higher altitudes, the density of a gas influences flows when passing through the orifice. Due to this reason, for a given flow rate, the bobbin will not be forced as far up the rotameter tube.

At higher altitudes, the volume of a fixed mass of gas increases, and therefore the molecules of gas are widely spaced resulting in a decrease in density with an increase in altitude.

Viscosity is simply termed as friction of gas. The viscosity of a gas is important only at low flow rates when the flow characteristic of the gas is laminar.

Charle’s law stated that the volume occupied by a fixed amount of gas is directly proportional to its absolute temperature (T) provided the pressure remains constant.

Boyle’s law for a fixed amount of gas at constant temperature, the pressure (P) and volume (V) are inversely proportional.

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

In the Child-Pugh classification system, the following 5 components are determined or calculated in order:

Ascites

Grade of encephalopathy

Serum bilirubin (?mol/L)

Serum Albumin (g/L)

Prothrombin time or INR

Raised liver enzymes are not the component of the classification system.

pH is the negative log to the base 10 of hydrogen ion concentration:

So, what power produces the answer?

pH = – log10 [H+]

Making [H+] the subject:

[H+] = 10-pH

Substituting, [H+] = 10-7

One nanomole = 1 x 10-9 or 0.000000001

10-7 = 1x 0.0000001 or 10 x 0.00000001 or 100 x 0.000000001

100 nanomole