Local application: Here the drug is applied directly to the intended site of action and absorption into the bloodstream is unnecessary. This refers to the movement of the drug back and forth between the blood and various body tissues.
Blood Kidneys
LiverMuscle
- Pharmacokinetics
- Passive diffusion and other mechanisms by which drugs may cross biological membranes
- Rate of drug absorption and the Absorption rate constant (Ka)
- Bioavailability
In this chapter we will discuss the first phase of ADME – the entry of the drug into the bloodstream. The vessel that connects the gut to the liver is not an artery or vein; it is a “portal vessel” (the hepatic portal vessel – HPV in Figure 2-4).
THE BEST MASTER
However, a relatively polar drug such as digoxin is absorbed rather inefficiently and it is likely that a significant proportion of the dose will still be present when the GI contents reach the colon. Then the expanded colonic flora will have an opportunity to break down part of the dose.
IN THE NETHERLANDS
Salt factor
The salt factor is the proportion of the parent substance present in the salt, expressed on a weight/weight basis. In this chapter we will consider the factors that control the rate and extent of drug movement between the blood and tissues and introduce a new pharmacokinetic parameter - the Volume of Distribution.
The rate of distribution and compartments
BloodT1
One compartment model
The simplest model allows for immediate distribution of the drug throughout the blood (and perhaps to some extent into the tissues), but this is not followed by any further slow movement elsewhere. The drug is injected or absorbed into the blood and is immediately distributed throughout its range and eventually eliminated.
Two compartment model
For many drugs, blood flow is the critical factor, and for the remainder of this chapter we will focus solely on that, but remember that polarity can be an issue and we will return to this later. It is generally accepted that the rate of drug delivery to and removal from tissues is determined by blood flow.
The extent of distribution
The drug is injected or absorbed into the blood (part of the first compartment) and immediately spreads throughout this compartment. The result will depend on the relative binding affinity of the blood and the intracellular components.
Stomach
NH + 3 Lipid
- Volume of distribution
- Using the volume of distribution to calculate dose size
- Practice calculations
- Elimination rate constant and half-life
- Clearance
In (b), more of the drug has moved from the blood – this leaves a lower concentration – the calculated value of V is greater. Another way of expressing the rate of drug elimination is via the half-life – the time it takes for the blood concentration to decrease by 50%.
Liver
Practice calculations
Calculate its half-life in units of h. 6) The drug has a clearance of 12.5 ml/min and a volume of distribution of 12 liters. Calculate its elimination rate constant in units of h-1. 7) The drug has an average population clearance of 1.5 ml/min/kg of body weight.
Concentration versus time graph
The drug simply diffuses throughout its volume of distribution (V) and awaits its elimination as governed by the elimination rate constant (K). This calculation that the elimination rate will be 10 mg per hour is only true at the single point in time when the drug has just been injected.
Relationship between time and concentration
At any later time point, the amount of drug present will have decreased and the rate of elimination will also have decreased. After another half-life (point C on the graph), the body load is halved again to 25 mg and the elimination rate is now only 2.5 mg per hour, and so on.
Area Under the Curve (AUC)
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Practice calculations
Appendix 1
Appendix 2
In Section 6.1 we focus on data in the format typically found in clinical trials – blood concentrations measured at numerous time points. In this setting, it is unlikely that blood samples were taken at multiple times.
Analysis of clinical trials data
The first appendix of this chapter shows that plotting the data on semi-log graph paper leads to linearization. It is common to see pharmacokinetic data plotted as the log of concentration against time or (more likely) presented in a semi-log graph.
Analysis of data arising in a clinical setting
An Excel spreadsheet is available to automate the calculation of K and V from two drug concentration observations. Go to www.phrData.co.uk, then click on 'Pharmacokinetics' and then 'K and V from two points'.
Practice calculations
The Practice Calculations section in Chapter 13 (Section 13.2) invites you to reanalyze the data using a computerized approach. 2) A patient received a dose of 120mg of drug per bolus i.v. Blood samples were taken 2 and 12 hours after administration and found to contain 7.1 and 0.8 mg/L of drug, respectively.
Appendix 1
So if instead of plotting concentration, if we plot the natural logarithm of concentration against time, we should get a linear relationship. In the above discussion we have used natural logs, but in fact the data will also be linearized by using the better known base 10 logs; however, the course would change.
Appendix 2
Instead, we can use graph paper with a logarithmic vertical scale and plot the actual observed concentration directly.
The model to be considered
Drug concentrations in blood and the rest of the first compartment
There will be a marked disequilibrium between the compartments, and the rate of movement of the drug from compartment 1 to 2 will be much greater than in the opposite direction. Later (B) the concentrations in compartment 1 will have decreased and the concentrations in 2 will have increased and there will be a moment of equilibrium.
Determining how many compartments a drug occupies
The practical method of distinguishing a single-compartment drug is to inspect a semi-log plot of concentration versus time.
Drug concentration in the second compartment
We start with virtually no drug in the second compartment, but re-equilibration moves drug in – levels rise b). A short equilibrium - no net movement - at the peak of the curve levels do not rise. c) Re-equilibrium moves in reverse direction and drug leaves the second compartment - levels drop.
Two compartment systems and therapeutic drug monitoring for digoxin
The three stages of the process were characterized by (A) movement of drug from compartment 1 to 2, (B) no movement and finally (C) a return of drug to the first compartment. Blood samples for therapeutic drug monitoring of digoxin are normally taken at least 6 hours after administration.
The model to be considered
Concentration versus time curve during infusion
Finally, in (C), the body burden is increased enough that the rate of elimination matches that of infusion. Steady state' is the state where the rate of entry of the drug into the body balances with the rate of elimination and no further accumulation occurs.
Relationship between rate of infusion and concentration at steady state
This situation is referred to as 'Steady state', and the associated blood concentration is 'Concentration at steady state' or Css. Because the equation relating Css to Rinf is general, infusion offers a definitive method of measuring clearance.
Loading doses
The loading dose will eventually redistribute throughout the volume and drug concentrations will decrease. Alternatively, if we calculate the loading dose with just V1, then the initial concentration in the first compartment (including blood levels) must match the target concentration.
The accumulation period
Give a small, additional loading dose a short time into the infusion when the drop in concentrations is expected. Use a higher infusion rate than is normally required during the period when the dip would otherwise occur and then return to the normal rate for the remainder of the infusion.
Practice questions
Appendix
The situation to be considered
Concentration versus time curve
There is therefore enough drug in the gut to stimulate the absorption process (large arrow), but very little in the body to stimulate elimination (small arrow). In the early phase, the absorption rate exceeds that for elimination and blood levels rise.
Changing the rate of absorption
Then comes a period during which the amount remaining in the intestine is constantly decreasing and therefore the rate of absorption is also decreasing. So at the peak, most of the dose will be present in the body, giving a high peak.
Cmax and Tmax
A lower peak: If the drug is absorbed very quickly, most of the dose will enter the body within a short period of time and only a small portion of the dose will be eliminated in this short period of time. Which of the two patterns shown in Figure 9-3 is preferable depends on the therapeutic situation.
Determination of bioavailability for extravascular doses
So, oral bioavailability can be determined very simply as the ratio of the two AUCs. The result tells us the actual fraction of the oral dose that reaches the general circulation.
Trapezoidal rule – A practical method to measure AUC
We can therefore construct an additional trapezoid between the origin of the graph and the first observed concentration. This period can be identified by plotting the data semi-logarithmically and looking for a late period where the data points form an essentially straight line - 'Terminal linear portion'.
Practice question
For the data under consideration, the half-life of the extrapolated line is 2.25 hours (see Figure 9.7). In this case, the final blood sample contained very little drug and the tail made only a minimal contribution to total AUC.
Appendix
Pharmacokinetic accumulation and steady state
With the second interval marked (B), the body burden and the amount eliminated are higher, but the elimination still does not fully match the input dose and there is continuous accumulation. By the late interval (C), the body burden is high enough to increase the elimination rate to match the input dose and there is no further accumulation.
Multiple extravascular doses
Concentrations at steady state
For many drugs, a satisfactory clinical result can be achieved if we simply ensure that the average steady-state concentration (Css, av) is within a certain range. In the following example we will calculate peak and trough concentrations to see if a proposed regimen will produce a satisfactory pattern of blood concentrations.
Loading dose
The loading dose consists of an initial dose that is greater than the usual maintenance doses. If the loading dose is very large compared to the usual dose, it may be excessive and it will be necessary to achieve loading by increasing the size of the first two or three doses more moderately, rather than a single giant dose. give.
Accumulation stage
It takes a period equal to three or four elimination half-lives of the drug to reach steady state (or thereabouts). Doctors' lives would be much easier if they used a competing drug with a shorter half-life and thus faster accumulation and without the need for a loading dose.
Extent of fluctuation in drug concentrations
The two traces in Figure 10.9 model the same total daily dose of drug, but in one case (solid line) we have suppressed fluctuation by giving the drug four times daily, and in the other (dashed line) we have used a slow release form and only needed to give the drug twice a day. We can suppress fluctuations in concentration either by increasing the dose split or by using a slow-release dosage formulation.
Practice questions
Both methods achieve a very similar envelope of concentrations, but twice-daily dosing is easier to follow from a patient perspective. The highest concentrations should be between 5 and 10 mg/L - the lowest concentrations should be less than 1 mg/L. The answers are available at the back of the book.
Appendix
This chapter describes a situation where many of the assumptions made in previous chapters break down.
Considering drug metabolism as an enzyme catalysed reaction
Consequently, only the highlighted area in the lower left corner of Figure 11-3 is clinically relevant. As a result, most drugs never reach a significant degree of saturation of the enzymes and the relationship between elimination rate and concentration is essentially linear.
Exceptions to linearity
Ethanol in doses high enough to cause noticeable effects will fully saturate liver enzymes. There is evidence of some enzyme saturation with theophylline, but the effect is quite small, and for practical clinical purposes its kinetics are treated as linear.
Effect of non-linearity on the relationship between dose and drug concentration
Clinical significance of non-linear kinetics
From part (d) of Figure 11.6 it is clear that a doubling in dose would achieve far more than a doubling in blood levels. General pharmacokinetics assumes first-order drug elimination, where the elimination rate constant is a valid concept.
Non-linear kinetics and drug development
Because the elimination rate constant is closely related to half-life and clearance, these two parameters also cease to apply. This chapter briefly introduces an alternative method for determining pharmacokinetic parameters such as elimination rate constant and clearance from experimental data.
The case for non-compartmental methods
This chapter is relevant to the drug development process; it is very unlikely to have any application in clinical practice. This account is not intended to provide full coverage of non-compartmental analysis; however, it should make you aware of the availability of an alternative methodology.
Calculation methods
This is reflected in the fact that more than 200 of the 1,200 employees at FOSS work with Research and Development in Scandinavia and the USA. Note that in the above calculation of the elimination rate constant and clearance, no account was taken of how many compartments the drug occupied.
More complex situations
Some of them will be eliminated fairly soon after injection, while others will survive longer.
Least squares fitting
The initial state of the skin mentioned in the box above is shown in Figure 13.2. 6JGFGUKIPQHGEQHTKGPFN[OCTKPGRQYGTCPFRTQRWNUKQPUQNWVKQPUKUETWEKCNHQT/#0&KGUGN6WTDQ 2QYGTEQORWGPEKGUCTGQHHGTGFYKVJVJGYQTNFOUNCTIGUITVCCPIKWPQGQTNFOUNCTIGUITVCCPIKWP QOVQM9RGTGPIKPGGVWRHTQPV. The graph has not changed radically from Figure 13.2, but the fit of the curve to the points looks slightly better.
Practice question
The material in this chapter relates primarily to clinical practice rather than drug development.
Clearance of creatinine and various drugs
In summary – Serum creatinine must ultimately be related to weight, sex, age and creatinine clearance. Once the two equations were established, it was possible to estimate creatinine clearance in new patients, knowing their sex, age, weight and serum creatinine concentration.
Digoxin dosing
Creatinine clearance then provides a good estimate for the renal clearance of drugs such as aminoglycosides and digoxin. Creatinine clearance' calculates creatinine clearance using the Cockcroft and Gault equation and - 'Digoxin dosing' calculates digoxin total body clearance and also Css,av for a given dosing.
Practice questions
TwoPointsAnalysis.xlsx (Chapter 6) K and V from two observed concentrations CalculateAUC.xlsx (Chapter 9) Trapezoidal rule for AUC. DigoxinDosing.xlsx (Chapter 14) Digoxin Clearance and Dosing Source is www.phrData.co.uk and click on 'Pharmacokinetics'.
