In order to be able to predict the effect of drugs used in anaesthesia accurately it is important to know not only the trends in concentration of the drug at the effector site (pharmacokinetics), but also the biological effects that it has on the patient (pharmacodynamics).
Pharmacokinetics can be described as the qualitative and quantitative study of the trends in the processes of absorption, distribution, metabolism and excretion (A-D-M-E) of a drug, or “what the body does to the drug”. Pharmacodynamics, on the other hand, is the study of “what the drug does to the patient”, or the desired (therapeutic) biological effects and the undesired (collateral/side) effects.
For non-anaesthetic drugs the trend in pharmacokinetics as a function of time can be described by a non-compartmental model (non-compartmental pharmacokinetics): the focus is on determining the total exposure of a patient to a drug (area under the curve – mean residence time; AUC – MRT) in relation to the drug’s absorption (bioavailability), its total capacity to distribute throughout tissues (volume of distribution at steady state; VDss) and the body’s capacity to metabolise and excrete it (clearance; CL). It is not, therefore, possible to determine the concentration of a drug in the plasma or tissues at every moment in time.
In contrast, when studying the pharmacokinetics of anaesthetics, a compartmental model is used (compartmental pharmacokinetics), in which the concentration as a function of time is calculated instant by instant using mathematical methods that describe both the distribution in the various body tissues and the elimination of the drug from the body. The compartments of distribution (central compartment – Vc or V1, rapidly equilibrating compartment for highly perfused organs - V2, slowly equilibrating compartment for poorly perfused organs - V3) are not associated with a real volume of distribution. They are only theoretical volumes that, through the use of mathematical equations, enable an estimate of the concentration of drug moment by moment after the administration of a given dose of the drug to a patient. The only calculated and real volumes are the central volume of distribution (VDc) and the total volume of distribution of the body at steady state (VDss).
The capacity of a drug to distribute in peripheral tissues is described with a constant of distribution that is named on the basis of the direction of movement (through a concentration gradient effect) of the drug. For example, the constant for the movement of a drug from the central compartment V1 to the peripheral compartment V2 is defined as K12, while the constant for the movement in the opposite direction is named K21. The polarity and the size of the molecules in the drug determine its volumes of distribution. Strongly polarised (and, therefore, poorly lipophilic) drugs, such as pancuronium, distribute very little or not at all into peripheral tissues (two-compartmental model of distribution), while the pharmacokinetics of almost all other drugs used in anaesthesia can be described using a three-compartmental model. For example, remifentanil (poorly liposoluble) has a very low V2 and V3, unlike fentanyl (very liposoluble) which has a large peripheral volume of distribution (V2 -V3). The tissue (peripheral) volume of distribution is also influenced by the haemodynamics of the patient, in relation to the amount of blood reaching the tissue (cardiac output) and the state of the microcirculation (vasoconstricted or vasodilated).
Pharmacokinetic and pharmacodynamic studies applied to anaesthetics also differ in other ways from the classical pharmacology used for antibiotics and other drugs. Indeed, with regards to the pharmacology of antibiotics, neither the researcher nor the clinician is interested in what happens in the first few minutes after the drug has been administered; the focus in this case is on how to optimise the patient’s profile of drug exposure over time (concentration of the drug in the plasma and tissues) in relation to the drug’s pharmacodynamic properties (concentration-dependent bactericidal action or time-dependent action). Most of the effect is, therefore, related to the determinants of the bioavailability of the drug, that is, its real absorption and the speed with which this occurs. In contrast, the fundamental knowledge concerning anaesthetics is what happens in the first few minutes (5-10 minutes) after the drug has been given, because this is the real determinant of its clinical effect. Studies of drug absorption are usually neglected in anaesthesia, since anaesthetics are administered intravenously and, therefore, have a theoretical absorption of 100%. It is the phase of rapid distribution (α) [9]from the blood to the tissues that determines the real appearance and disappearance of the desired effect (e.g., hypnosis, analgesia, or muscle relaxation).
The initial plasma concentration of an intravenously administered drug depends on its initial volume of distribution (apparent VD or central VD), that is, the amount of blood in which the drug is diluted, and is easily calculated as: dose of drug/volume of blood. All the variables that alter the subject’s circulatory volume can alter the initial VD of the drug, causing unexpectedly higher or lower plasma concentrations and, therefore, effects different from those foreseen. Anaesthetic drugs generally have a linear behaviour; for example, if the dose of the drug is doubled and the VD (volaemia) is kept the same, the plasma concentration is also doubled. If the initial concentration depends on the VD, the trend in concentration of the drug over time depends above all on the distribution into peripheral tissues (Kn.) and the body’s capacity to eliminate the drug (clearance). Clearance (CL) is a measure of the body’s capacity to eliminate an amount of drug per unit of time (volume/time). As far as concerns anaesthetic drugs, the fraction of drug eliminated is proportional to the fraction present in the blood (first-order elimination), thus the more drug there is in the blood, the greater the amount eliminated. In contrast, many other non-anaesthetic drugs (e.g. salicylic acid, aminophylline, phenytoin) have a fixed fraction of elimination (zero-order elimination): even if the concentration of the drug in the blood increases, the fraction eliminated remains the same.
As far as regards clearance, anaesthetic drugs can be divided into two classes. In “flow-dependent” clearance, an organ’s capacity to extract and metabolise the drug exceeds the amount of drug reaching the organ; the elimination capacity cannot be saturated and is relatively independent of the metabolic capacity of the organ. An example of this effect is that the metabolism of propofol is not altered in patients with liver failure. Many of the drugs used in anaesthesia belong to this class. Thus, the fraction extracted, and then excreted, by the organs metabolising the drug is proportional to volume of blood that arrives at the organ; for this reason if the perfusion of the organ increases/decreases, the fraction metabolised increases/decreases proportionally. In contrast, for drugs with a “capacity-dependent” metabolism (e.g. alfentanil), the theoretical metabolism by the organ is equal to or less than the fraction of drug that reaches it. In the case of impaired hepatic function, the metabolism is further limited and, therefore, easily saturated both because of diseases which limit its function (liver failure) and because the concentration of the drug exceeds the organ’s metabolic capacity. In this case the clearance is no longer proportional to the fraction of drug, but remains fixed. Each drug has its own metabolic pathway (Clhepatic, Clrenal, etc).
The total metabolic activity of the body is defined as the metabolic clearance (Clmetabolic), but this refers to the theoretical intrinsic capacity of the body, which can be modified by the dynamics of cardiovascular function that occurring during anaesthesia. Many of the drugs used in anaesthesia (e.g. alpha2 agonists, halogenates, propofol) can decrease hepatic blood flow and, therefore, reduce the elimination of the drugs, while hyperdynamic conditions, with an increase in cardiac output (e.g. during stimulation of the sympathetic system) may increase the elimination fraction. For drugs with “first order” elimination, the parameter that really indicates the fraction of drug eliminated is the elimination constant (Kel). Anaesthetics disappear from the plasma not other through clearance, but also because of distribution into tissues. This distribution is actually a form of clearance in that drug leaves the blood, even if only temporarily, and is called distribution clearance. The effects of a decrease in cardiac output on the distribution clearance vary according to the period of infusion considered. In the first phase of the infusion, a decrease in cardiac output causes an increase in the plasma concentration because of the decrease in the distribution of the drug into the tissues; with prolonged infusions, during which a complete equilibrium (steady-state) is reached in the distribution of the drug between the plasma and tissues the decreased cardiac output leads to a faster decrease in plasma levels at the end of the infusion.
Another important difference between the pharmacokinetics of anaesthetics and the classical pharmacological approach concerns the study of the half-life (t1/2), that is, the time required for the amount of drug in the body to decrease by 50%, which is considered a measure of the efficiency and speed of the metabolism of the drug. There are numerous reasons why the classic concept of half-life cannot be applied in anaesthesia; in fact, the decrease (offset) in the action of drugs is clinically evident already at reductions of 25-30%, and the time that it takes for 50% of the drug to be removed or all of it (5 half-lives) is sometimes of little interest. Another limitation is that the concept of half-life cannot be applied to prolonged infusions, in that it is related to a single bolus of the drug. Anaesthetic drugs are almost never given in a “single shot” and so the concepts of classical pharmacology are not applicable. For example, considering a 50% decrease in the concentration of fentanyl in the dog after either a single bolus dose which produces a plasma peak of 2 ng/ml (analgesic concentration) or when the infusion is given to keep the same plasma level for 1 hour, the 50% decrement time (disappearance of the analgesic effect) is 6 minutes for the bolus injection and almost 30 minutes for the infusion! This notable difference is due to the fact that the decrement (half-life) of the plasma concentration is strongly influenced by the distribution clearance. The longer the infusion time becomes, the more the distribution clearance decreases at the end of the infusion because the concentration gradient between the plasma and tissues decreases as the duration of the infusion increases. When an equilibrium is reached between the plasma and tissues, the “steady state” is reached, that is, the fraction of drug eliminated is the same as the dose of drug administered and the patient can only decrease the level of drug through metabolic elimination (clearance). For almost all the drugs used in anaesthesia of the dog, this equilibrium is reached only for infusions lasting more than 5 to 10 hours, depending on the properties of the specific drug,.
The concept of context-dependent decrement time (CSDT) or context-dependent half-life [16], which is currently widely used in anaesthesia, helps the clinician to predict the duration of the effects of a drug used in an infusion. The CSDT is a parameter calculated starting from the pharmacokinetic characteristics of the drug and takes into consideration the context (duration of infusion and plasma levels reached) and the decrease that the clinician considers most useful in order to predict the disappearance of the clinical effects of a drug. If, for example, it is considered that extubation of dogs receiving a propofol infusion usually occurs at a decrement of about 25% compared to the concentrations used in surgical anaesthesia, then the extubation of the patient can be predicted on the basis of the duration of the infusion. The same calculations are also applicable to drugs used in inhaled anaesthesia.
The aim of every anaesthetist is (or should be) to be able to predict the effects of drugs administered to a patient (pharmacodynamics). However, in order to do this it is not sufficient to know the changes in the plasma concentration of drugs over time (pharmacokinetics), but also the fraction of the drug that really reaches the site where the drug has its biological effect (e.g. the brain for hypnotic drugs). In order to determine this, a model of the distribution of the drug must be calculated, relating the plasma with the effector site by a distribution constant (Ke0). The rate of entry/exit of the drug to/out of the effector site is the real determinant of the appearance/disappearance of the clinical effect. Instead, the dose reached at the effector site determines the intensity of the effect. Although the equilibrium constant (Ke0) is known for may drugs used in human anaesthesia, in veterinary medicine only the constant for propofol in dogs is known.
The clinical effect is also related to the pharmacodynamic properties of the drug and the characteristics of its receptor binding. When a drug is able to bind to a receptor and generate a biological effect it is called an “agonist”. An agonist is defined as “pure” when its binding with the receptor causes the maximal biological response, and “partial” when it causes on a submaximal response. Antagonists are drugs that bind to receptors, but that are not in themselves able to induce a biological response. With regards to the affinity of a drug for a receptor, the molecules can be divided into competitive antagonists, which compete with an agonist for the same receptor or can be displaced from the receptor because they are only weakly bound (reversible competitive antagonism) and non-competitive antagonists, which bind to the same receptor site as the agonist with a strong bond (covalent), or to a different site of the same receptor and cannot, therefore, be displaced by the agonist. In this case the non-competitive antagonism is irreversible. The effects of a drug also depend on the interaction of other pharmacodynamic characteristics. The main ones in clinical use are:
- Specificity: the capacity to cause a desired effect compared to an undesired one;
- Efficacy: this is the maximum response produced by a drug and depends on the number of drug- receptor complexes formed and on the efficiency with which the activated receptor produces a cellular action;
- Potency: this is a measure of how much drug is necessary to produce a given response. It depends strongly on the properties of affinity, that is, the characteristics of the bond between the drug and the receptor.
The potency of a drug is very often confused with its clinical efficacy; stating, for example, that buprenorphine (a partial agonist) is about 30-60 times more potent than morphine (a pure agonist) does not mean that buprenorphine provides more analgesia than morphine, but only that its range of clinically effective doses is about 30-60 times lower. The potency of a drug concerns only its dose and must not be confused with efficacy!
The study of pharmacokinetic constants in anaesthesia is not an abstract concept, but has a concrete influence on both the infusion of intravenous drugs and the administration of inhaled drugs.
Factors that influence the half-life (t1/2) of a drug
t1/2 = 0.693 x VD / CL (CL = Vd x Kel)
in other words, the more that a drug distributes into tissues and the less that remains available to be metabolised, since this process occurs in proportion only to the plasma fraction. For example:
·remifentanil (very low VD and high Kel): short half-life
·fentanyl (high VD and average Kel) = long half-life
Is the volume of distribution or clearance more important when calculating CSDT?
Considering two different types of drugs such as fentanyl (high VD and average Kel) and alfentanil (low VD and low Kel), it can be noted that these have two different behaviours depending on the duration of the infusion.
For short-lasting infusions (< 2 hours) fentanyl has the same or slightly lower CSDT. For longer infusion times (> 2 hours) alfentanil has a shorter CSDT. Thus, when giving a short-lasting infusion it is more important to have a drug with a good Kel and a good distribution clearance, while for protracted infusions, it is better to have a drug with the lowest possible VD and VDss. This prevents accumulation of the drug in the tissues and the redistribution of the drug from the tissues into the plasma, which delays the decrement in the drug in the terminal stage of the drug’s elimination (γ phase).
An integrated study of the pharmacokinetics and pharmacodynamics of anaesthetic drugs is not, therefore an abstract, theoretical exercise, but of practical use in the daily administration of such drugs and aids more precise prediction of the appearance and disappearance of the biological effects of the drugs. The differences between the compartmental pharmacology of anaesthetic drugs and classical non-compartmental pharmacology are notable and of such importance to make the former almost a discipline of its own.
Graphic examples of pharmacokinetics/pharmacodynamics
Interactive Clinical Pharmacology]
Simulation Portfolio - University of Florida
Pharmacokinetics/pharmacodynamics equations
Pharmacokinetic Software for Research and Education