Equations, Definitions and Laws

Question 1

Half-life with relation to time constant

Answer 1

T1/2 = τ.ln2

tau = time constant
Ln2 = 0.693

Can rearrange to find 𝞃 e.g. when finding clearance or Vd

𝞃 = T1/2 / In2 = T1/2 / 0.693

Question 2

T1/2 = τ.ln2

tau = time constant
Ln2 = 0.693

Answer 2

Elimination half-life, with relation to time constant

Can rearrange to find 𝞃 e.g. when finding clearance or Vd

𝞃 = T1/2 / In2 = T1/2 / 0.693

Question 3

Cl hepatic = HBF × ER liver

Where:
HBF = hepatic blood flow in ml.min-1
ER = extraction ratio

Answer 3

Hepatic clearance

Question 4

Hepatic clearance

Answer 4

Cl hepatic = HBF × ER liver

Where:
HBF = hepatic blood flow in ml.min-1
ER = extraction ratio

Question 5

pH = −log ([H+])

Answer 5

pH

Question 6

pH

Answer 6

pH = −log ([H+])

Question 7

pH = pKa + log ([A-]/[HA])

Answer 7

Henderson-Hasselbach

Used to predict the ratio of ionized to unionized form of a weak acid or a weak base.

For a weak acid, the ionized form is on top of the final part of the equation, but for a weak base the ionized form is on the bottom.

Question 8

Henderson-Hasselbach

Answer 8

pH = pKa + log ([A-]/[HA])

Question 9

kon [D][R] = koff [DR]

Answer 9

Law of mass action

The law of mass action states that the rate of a reaction is proportional to the concentration of the reacting elements.

What this means is that the population of drug molecules and receptor molecules will combine at a certain rate (kon), and then separate again at another rate (koff).

Question 10

Law of mass action

Answer 10

kon [D][R] = koff [DR]

The law of mass action states that the rate of a reaction is proportional to the concentration of the reacting elements.

What this means is that the population of drug molecules and receptor molecules will combine at a certain rate (kon), and then separate again at another rate (koff).

Question 11

KA = KON / KOFF

Answer 11

Affinity Constant

Reflects the strength of the drug-receptor bond

Question 12

Affinity Constant

Answer 12

KA = KON / KOFF

Reflects the strength of the drug-receptor bond

Question 13

KD = KOFF / KON

Answer 13

Dissociation constant

reflects the tendency the drug-receptor complex has to dissociate back to its drug and receptor components

Question 14

Dissociation constant

Answer 14

KD = KOFF / KON

reflects the tendency the drug-receptor complex has to dissociate back to its drug and receptor components

Question 15

V = (Vmax[S]) / (Km + [S])

Answer 15

Michaelis-Menten equation

Michaelis-Menten kinetics describe enzyme and substrate reactions which are weakly bonded and allow dissociation.

V is the velocity of the reaction.

Vmax is the maximum velocity of the reaction. This is reached when enzymes active sites have been saturated with substrate.

S is the substrate concentration.

Km is the Michaelis constant, specific to a single substrate-enzyme reaction. It is the concentration of substrate at which the velocity of the reaction is half of the maximum velocity, Km = ½Vmax

It is also the reciprocal of the enzymes affinity for a specific substrate. A small Km will have a high affinity for a substrate so less is required to reach ½Vmax at a faster rate - this is first order kinetics (i.e. non-saturated system)

Question 16

Michaelis-Menten equation

Answer 16

V = (Vmax[S]) / (Km + [S])

Michaelis-Menten kinetics describe enzyme and substrate reactions which are weakly bonded and allow dissociation.

V is the velocity of the reaction.

Vmax is the maximum velocity of the reaction. This is reached when enzymes active sites have been saturated with substrate.

S is the substrate concentration.

Km is the Michaelis constant, specific to a single substrate-enzyme reaction. It is the concentration of substrate at which the velocity of the reaction is half of the maximum velocity, Km = ½Vmax

It is also the reciprocal of the enzymes affinity for a specific substrate. A small Km will have a high affinity for a substrate so less is required to reach ½Vmax at a faster rate - this is first order kinetics (i.e. non-saturated system)

Question 17

Hepatic Extraction Ratio

Answer 17

HER = (Ci - Co) / Ci

Question 18

HER = (Ci - Co) / Ci

Answer 18

Hepatic Extraction Ratio

Question 19

Renal excretion = (glomerular filtration + tubular secretion) - reabsorption.

Answer 19

Renal excretion

Question 20

Renal excretion

Answer 20

Renal excretion = (glomerular filtration + tubular secretion) - reabsorption.

Question 21

Volume = Dose/Concentration

Answer 21

Volume of distribution

Question 22

Volume of distribution

Answer 22

Volume = Dose/Concentration

Question 23

Clearance = Volume of distribution / 𝜏

Answer 23

In a single-compartment model, can calculate clearance from values Vd and time constant

Question 24

Single compartment model clearance using Vd and time constant

Answer 24

Clearance = Volume of distribution / 𝜏

Question 25

Loading dose

Answer 25

Loading Dose = Volume of distribution X Target concentration

Question 26

Loading Dose = Volume of distribution X Target concentration

Answer 26

Loading dose

Question 27

BF = AUCpo / AUCiv

Answer 27

Bioavailability
Absolute bioavailability compares a drug with it’s IV form
Relative bioavailability compares drugs with no IV form - compares it’s formulations against each other

Question 28

Single compartment model

Clearance =
Volume of distribution x Elimination rate constant (K)

Answer 28

“That volume of plasma from which drug is completely removed in unit time. The product of volume of distribution and rate constant for elimination (Vd.k)”
OR
“The ratio of volume of distribution to time constant (Vd/τ)”

Question 29

“That volume of plasma from which drug is completely removed in unit time. The product of volume of distribution and rate constant for elimination (Vd.k)”
OR
“The ratio of volume of distribution to time constant (Vd/τ)”

Answer 29

Single compartment model

Clearance =
Volume of distribution x Elimination rate constant (K)

Question 30

Clearance of oral drugs

Answer 30

Clearance = dose x (BF/AUCpo)

Question 31

Clearance = dose x (BF/AUCpo)

Answer 31

Clearance of oral drugs

Question 32

Clearance of IV drugs (multicompartmental)

Answer 32

Clearance = Dose / AUC

Question 33

Clearance = Dose / AUC

Answer 33

Clearance of IV drugs (multicompartmental)

Question 34

Rate of elimination

Answer 34

Rate of elimination (mg/min) = [plasma drug (mg/ml)] x Clearance (ml/min)

Question 35

Rate of elimination (mg/min) = [plasma drug (mg/ml)] x Clearance (ml/min)

Answer 35

Rate of elimination

Question 36

Critical temperature

Answer 36

The temperature above which a substance can only exist as a gas, irrespective of how much pressure is applied.

Below their critical temperature they exist in both the liquid and gas forms and are termed vapours.

In any liquid some molecules will have sufficient energy to leave and become a vapour by evaporation. Therefore a vapour is the gas phase of a substance at or below its critical temperature.

Question 37

Boiling point

Answer 37

The temperature at which saturated vapour pressure is equal to atmospheric pressure.

At the boiling point, adding heat does not increase the temperature, but it provides the latent heat of vaporisation which leads gas molecules to evaporate from the liquid phase.

Question 38

When atmospheric pressure is equal to the saturated vapour presssure of a substance, what happens to the substance?

Answer 38

It boils

Question 39

Saturated Vapour Pressure (SVP)

Answer 39

The pressure exerted by the vapour phase of a substance when in equilibrium with the liquid phase.

At any given temperature, there will be a dynamic equilibrium where the number of molecules entering the liquid phase equals those leaving it and the vapour is therefore saturated - the saturated vapour pressure (SVP, Fig 1).

This is because at the surface of a liquid some molecules of the substance have enough energy to escape and evaporate. This process uses energy; the latent heat of vaporisation. In a closed container the pressure of the container wall forces some molecules back into the liquid phase, setting up an equilibrium between the liquid and vapour phase.

SVP increases with an increase in temperature, i.e. as temperature increases the energy of the molecules causing more to evaporate. The converse is also true.

Removing molecules from the vapour phase results in a shift in the equilibrium favouring movement of molecules out of the liquid phase; this increases the initial rate of vaporisation but indirectly results in lowering the temperature, a fall in SVP, and ultimately reduces vaporisation rate.

SVP is an indication of the degree of volatility, i.e. the higher the SVP the more readily the agent will vaporise. Note that SVP increases with increasing temperatures so standard temperatures are used in definitions.

Question 40

Latent Heat of Vapourisation

Answer 40

The energy required for molecules in a substsance to escape the surface and evaporate

Question 41

Critical Pressure

Answer 41

The critical pressure of a substance is the pressure required to liquefy a gas at its critical temperature.

Question 42

Meyer-Overton Hypothesis

Answer 42

inhalational agents must work non-specifically on the lipid rich neuronal cells of the central nervous system. They also proposed that potency increases with oil:gas solubility.

Question 43

Ideal volatile anaesthetic

Answer 43

Physical properties:

Liquid at room temperature (so easy to store and handle)
Stable at room temperature
Stable in light
Non-flammable
Inert when in contact with metal, rubber and soda lime
Inexpensive (can be used in low-income settings)
Environmentally safe
Low latent heat of vapourisation
High saturated vapour pressure (for easy vaporisation)

Pharmacological properties:

Pleasant smell
No respiratory irritation or depressant effect (avoiding coughing or breath holding on induction)
Low blood:gas partition coefficient (so fast onset/offset)
Potent, with a low MAC and high oil:gas coefficient (so no supplemental anaesthesia is required)
Minimal metabolism (avoiding toxic metabolites)
Excretion via the lungs
Cardiovascular stability
Analgesia properties
Non-epileptogenic
No increase in intracranial pressure

Question 44

Filling ratio (in context of gas storage)

Answer 44

The filling ratio is the ratio of the mass of liquid in the cylinder compared with the mass of water that the cylinder can hold. In temperate regions this is 0.75, while in the tropics it is 0.67.

This is due to the ambient temperature increasing beyond the critical temperature of N2O (36.5C) - the canisters must therefore be less full to avoid exploding.

Question 45

Concentration effect of Nitrous Oxide

Answer 45

During induction of anaesthesia using HIGH concentrations of N2O the initial transfer across the alveolar membrane and absorption in the blood is high.

This occurs while a significantly smaller volume of N2 enters the alveoli from the blood, causing a reduction in total volume of the alveolus. Decreasing the alveolar volume leads to a concentration of the remaining gases in the alveolus and an increase in their partial pressures.

This results in a disproportionate rate of rise of FA/FI.

Question 46

Second Gas effect of Nitrous Oxide

Answer 46

The increased alveolar partial pressure of the inhaled anaesthetic drug, from both the concentration effect and the increased delivery from the dead space, leads to a higher FA/Fi ratio and induces a faster onset of anaesthesia.

Question 47

MAC

Answer 47

Minimum alveolar concentration

Minimum alveolar concentration (MAC) is the alveolar concentration of a gaseous volatile agent needed to ensure that 50% of a test population at sea level does not respond to a standard surgical skin incision. This is a proxy for the suppression of spinal cord reflexes and it cannot be assumed to ensure a lack of awareness.

The partial pressure of the agent determines the MAC but at 1 atmosphere, the concentration in kPa and the partial pressure in kPa are virtually the same at 101.325 kPa and 100 kPa respectively.

MAC is additive within the group of inhalational agents, so a mixture of agents with a cumulative alveolar concentration of 1 MAC has the same effect as 1 MAC of a single agent. This is most commonly seen with the use of nitrous oxide but also apples to Xenon, e.g. If 60% nitrous oxide (MAC 105%), is added to a volatile agent, the volatile agent required is reduced by 57%.

MAC is age-dependent and has a peak value at 6 months of age, a smaller peak in the mid-teens and then declines 10% per decade after the age of 40. Therefore, a 90-year-old patient has a MAC that is 50% less than a young adult.