Equations, Definitions and Laws Flashcards
Half-life with relation to time constant
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
T1/2 = τ.ln2
tau = time constant
Ln2 = 0.693
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
Cl hepatic = HBF × ER liver
Where:
HBF = hepatic blood flow in ml.min-1
ER = extraction ratio
Hepatic clearance
Hepatic clearance
Cl hepatic = HBF × ER liver
Where:
HBF = hepatic blood flow in ml.min-1
ER = extraction ratio
pH = −log ([H+])
pH
pH
pH = −log ([H+])
pH = pKa + log ([A-]/[HA])
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.
Henderson-Hasselbach
pH = pKa + log ([A-]/[HA])
kon [D][R] = koff [DR]
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).
Law of mass action
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).
KA = KON / KOFF
Affinity Constant
Reflects the strength of the drug-receptor bond
Affinity Constant
KA = KON / KOFF
Reflects the strength of the drug-receptor bond
KD = KOFF / KON
Dissociation constant
reflects the tendency the drug-receptor complex has to dissociate back to its drug and receptor components
Dissociation constant
KD = KOFF / KON
reflects the tendency the drug-receptor complex has to dissociate back to its drug and receptor components
V = (Vmax[S]) / (Km + [S])
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)
Michaelis-Menten equation
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)
Hepatic Extraction Ratio
HER = (Ci - Co) / Ci
HER = (Ci - Co) / Ci
Hepatic Extraction Ratio
Renal excretion = (glomerular filtration + tubular secretion) - reabsorption.
Renal excretion
Renal excretion
Renal excretion = (glomerular filtration + tubular secretion) - reabsorption.
Volume = Dose/Concentration
Volume of distribution
Volume of distribution
Volume = Dose/Concentration
Clearance = Volume of distribution / 𝜏
In a single-compartment model, can calculate clearance from values Vd and time constant
Single compartment model clearance using Vd and time constant
Clearance = Volume of distribution / 𝜏
Loading dose
Loading Dose = Volume of distribution X Target concentration
Loading Dose = Volume of distribution X Target concentration
Loading dose
BF = AUCpo / AUCiv
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
Single compartment model
Clearance =
Volume of distribution x Elimination rate constant (K)
“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)”
“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)”
Single compartment model
Clearance =
Volume of distribution x Elimination rate constant (K)
Clearance of oral drugs
Clearance = dose x (BF/AUCpo)
Clearance = dose x (BF/AUCpo)
Clearance of oral drugs
Clearance of IV drugs (multicompartmental)
Clearance = Dose / AUC
Clearance = Dose / AUC
Clearance of IV drugs (multicompartmental)
Rate of elimination
Rate of elimination (mg/min) = [plasma drug (mg/ml)] x Clearance (ml/min)
Rate of elimination (mg/min) = [plasma drug (mg/ml)] x Clearance (ml/min)
Rate of elimination
Critical temperature
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.
Boiling point
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.
When atmospheric pressure is equal to the saturated vapour presssure of a substance, what happens to the substance?
It boils
Saturated Vapour Pressure (SVP)
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.
Latent Heat of Vapourisation
The energy required for molecules in a substsance to escape the surface and evaporate
Critical Pressure
The critical pressure of a substance is the pressure required to liquefy a gas at its critical temperature.
Meyer-Overton Hypothesis
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.
Ideal volatile anaesthetic
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
Filling ratio (in context of gas storage)
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.
Concentration effect of Nitrous Oxide
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.
Second Gas effect of Nitrous Oxide
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.
MAC
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.
