Formulation of Compounds and Determination of Pharmacokinetic Parameters

Chapter 10

Formulation of Compounds and Determination of Pharmacokinetic Parameters R. M. Cozens

Introduction The ideal animal model of infection will provide data that allows the outcome of therapy in humans to be predicted. For a variety of reasons this ideal is difficult to attain; possible reasons include, among others, the different pharmacokinetics of compounds in animals and humans. It is well-established that pharmacokinetics of therapeutic agents is usually dependent on the species. Not only are there differences between animals and humans but there are also significant differences between a n i m a l s - - a fact made use of in making extrapolations from animals to humans, as will be described later. Pharmacokinetics in any species is governed by the physico-chemical properties of the drug. The processes of absorption and disposition can be influenced by the physiology and anatomy of the animal and also metabolism, which is often unpredictable (Williams, 1974; Dedrick and Bischoff, 1984). Although not often a concern in animal experiments, it is worth remembering that the age of the subject can also have a profound influence an the pharmacokinetic properties of a compound not only in humans but also probably in animals. The differences often observed between the pharmacokinetics of anti-infective agents in animals and humans means that efficacy data obtained in model infections is really only interpretable as a predictor of the clinical situation if the pharmacokinetics of the drug is taken into account. A number of studies have shown that with a knowledge of the pharmacokinetics in both humans and animals it may be possible to design treatment regimens in animals which result in at least an approximation of the pharmacokinetic profiles in humans (Gerber et al., 1986, 1991; Fltickiger etal., 1991; Lister and Sanders, 1995). There are a number of publications that deal with some of the issues surrounding the pharmacokinetics of anti-infectives in animals and the usefulness of pharmacokinetic data obtained in animals (Craig et al., 1988; Drusano, 1988; Mizen and Woodnutt, 1988; Dalhoff and Ullmann, 1990; Barza, 1993). The aim of this chapter is not to add to this debate but rather to describe some of the ways pharmacokinetic data can be obtained from animals and give some hints on how the data can be used to aid the design, interpretation and predictive value of efficacy experiments in Handbook of Animal Models of Infection ISBN 0-12-775390-7

animals. However, it is up to the experimenter to establish how useful the pharmacokinetic information is and how it can best be used in a particular situation. The determination of pharmacokinetic parameters and comparison between compounds and species only makes sense if the form in which the drug is presented is taken into account. The vehicle used to administer a drug, particularly via the oral route, can have a profound influence on the rate and extent of absorption. In animal studies, especially during the early evaluation of a new drug when optimized formulations are unavailable, it is often expedient to use formulations which may be quite different to those ultimately used during the clinical evaluation and use of the compound. This chapter will, therefore, also consider some of the formulations that can be used for the administration of anti-infective agents to animals.

Formulation of anti-infectives for administration to animals If animals are to receive a compound already available for human use, it may be possible to use the compound in its clinical formulation; indeed, this is probably desirable. However, care must be taken to ensure that excipients, are suitable for administration to animals and it must be remembered that it is seldom possible to give the dosage form directly to animals without some further preparation. For example, material presented in a capsule for human use must, in most cases, be removed from the capsule and dissolved or suspended in a vehicle for administration. In this section I have limited myself to discussing preparation of formulations from the pure active compound and to those procedures which can be carried out in a laboratory equipped with apparatus available to most microbiology laboratories. More advanced formulations, such as liposomes (Bakker-Woudenberg et al., 1993) or nanoparticles (Leroux et al., 1995, 1996), may certainly have a role to play in the evaluation of anti-infectives but are best prepared by specialists. Only injection and oral administration will be considered. Other routes of administration may be considered for particular situations. For example, lung infections Copyright 9 1999Academic Press All rights of reproduction in any form reserved

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may be amenable to therapy administered in an aerosol or skin infections may be treatable by a topical formulation. Such formulations require specialist knowledge and equipment to manufacture and use, and are beyond the scope of this chapter. There are obviously some formulations for oral administration and injection which also require specialist equipment such as milling apparatus. The production of these is probably best left to specialist formulation laboratories. Although those administering compounds to animals will occasionally need to call on specialist expertise to solve intractable formulation problems, much can be done using simple, readily available materials and equipment. Obviously, if the aim is to attempt to correlate pharmacokinetics with efficacy then the same formulations need to be used in both circumstances. This may seem trivial but as efficacy studies and pharmacokinetic studies are often performed in different laboratories or even different departments in an institution, some degree of agreement needs to be reached. It may be that a proposed excipient, while eminently suitable for efficacy experiments, may interfere with the analytical method employed. In what follows, a number of excipients are mentioned. Those mentioned are by no means exhaustive and information, such as composition, toxicity data, etc., on these and others can be found in the Handboo k of Pharmaceutical Excipients (Wade and Weller, 1994). For parenteral administration a useful handbook exists which gives details, including excipients, of injectable drugs (Trissell, 1992). This can provide useful starting points, particularly if compounds are congeners of those described in the handbook. It should be remembered that whatever excipients are included, they may not be pharmacologically inert. They may not only have direct effects on the animal but may also alter the basic pharmacokinetics of the compound (e.g. Sparreboom et al., 1996).

Parenteral administration

If the compound is sufficiently soluble in aqueous solvents, then a simple solution in a simple vehicle will be the most acceptable formulation. The formulation can be easily sterilized by filtration and will also be suitable for oral administration. Possible binding of the compound to the filtration equipment should be checked. If necessary the concentration in the filtrate should be determined to ensure accurate dosing. The best vehicle is physiologically neutral (neutral pH and isotonic); saline or phosphate buffered saline is the most common. Deviations from isotonicity or neutrality may lead to irritation at the site of injection and should therefore be kept to a minimum. Compounds which have poor aqueous solubility can often be administered as solutions in mixed-solvent systems. The compound may first be dissolved in a suitable organic solvent and then diluted with saline or phosphatebuffered saline (PBS). The amount of organic solvent in the final formulation should be kept to an absolute minimum. For example, dimethyl sulphoxide (DMSO) should be

R.M. Cozens

present at concentrations no higher than 10% v/v; ethanol, 10% v/v and benzyl alcohol, 6% v/v. Cyclodextrins (Duchene and Wouessidjewe, 1993; Loftsson and Brewster, 1996) have been used to solubilize compounds with poor water solubility. Cyclodextrins are a group of cyclical oligosaccharides consisting of 6 (0t-cyclodextrins), 7 (~-cyclodextrins) or 8 (7-cyclodextrins) glucose residues. The glucose residues may be derivatized to improve water solubility. The molecules form toroidal structures in aqueous solution. The interior of the torus is hydrophobic and can accommodate molecules of the correct size and hydrophobicity, forming a complex that is soluble in water. The choice of cyclodextrin will depend on the properties of the molecule of interest. On administration the compound is released from the complex. The potential problem with these molecules is that the rate of release of the active molecules may not be immediate, which may lead to atypical pharmacokinetic behaviour. These formulations can also be administered orally; however, it has been reported that cyclodextrins can influence the uptake of compounds and so may not play a simple carrier role. Any solution intended for intravenous formulation should be checked for the possibility that on addition to plasma the compound does not remain in solution. Precipitation of the compound in the circulation could result in misleading pharmacokinetic properties or even cause unnecessary suffering to the animal. Precipitation of the active ingredient is unlikely to occur if the formulation contains only water or aqueous solutions but may be a problem when organic solvents are employed. Suspensions should only be administered intravenously when they are well-characterized. This usually involves incorporation into liposomes or nanoparticles (Leroux et al., 1995), although simple suspensions can be employed. In general, particle sizes should be 100 }am or smaller. Suspensions can be contemplated for other parenteral routes (e.g. subcutaneous and intramuscular) but formulations used for these routes of administration must be welltolerated at the site of injection. These routes may lead to slower release of the compound into the circulation, although this cannot be assumed. For slow release, special formulations are required and these are best developed and produced by specialist formulation scientists and will not be considered further here.

Oral administration

Formulations for oral administration of compounds can vary from, for example, simple powder in gelatin capsules to complex mixtures designed to release the active ingredient in a particular portion of the GI tract (Leroux et al., 1996). Oral formulations must be designed to ensure accurate and reproducible dosing and to result in optimum absorption of the compound. The latter is easier said than done and optimization of a formulation will often require

FORMULATION OF COMPOUNDS AND DETERMINATION OF PHARMACOKINETIC PARAMETERS

specialist assistance. However, whenever a compound is administered orally and results in relatively poor plasma concentrations, which can be shown to be the result of poor absorption, it may be worthwhile trying another simple formulation before having recourse to complex, specialist formulations. As with intravenous administration, the easiest formulation is that in an aqueous vehicle. If the compound is soluble then often a simple solution in water is sufficient. Aqueous vehicles for oral administration need not be precisely physiological; however, if relatively large volumes are to be administered then extremes should be avoided. Suspensions can be readily administered by the oral route. There are two important factors to be considered if suspensions are used. First, the suspension should be homogeneous to ensure accurate and reproducible d o s i n g - - i t is impossible to administer an accurate and reproducible dose from a suspension which contains large clumps of material. Second, the particle size should be as small as possible and the particle size and distribution should be known if possible. As a minimum, microscopic examination of the suspension should be undertaken and particle size and distribution estimated. Generally compounds must be dissolved before they can be absorbed from the gastrointestinal tract. Particle size of poorly soluble compounds can markedly affect the rate of dissolution which, if too slow, can mean that a significant proportion of the compound will pass through the gastrointestinal tract before it has time to be absorbed. Micronized material (median particle size less than 10 lt.tm) can be obtained by wet or dry milling. Milling requires specialist equipment and often results in a loss of quite large amounts of compound. The nature of the solid must also be known; whether the compound is crystalline (and the form of the crystals) or amorphous can also affect dissolution rates and hence pharmacokinetic properties. The simplest suspensions are prepared in water containing an agent to increase the viscosity and thereby the physical stability of the suspension. Suitable agents are the chemically modified celluloses. Klucel H F (hydroxypropyl cellulose) at a concentration of 0.5% w/v is widely employed; the concentration can be increased if larger particles have to be kept in suspension. For some compounds it may be necessary to incorporate a wetting agent. Tween 80 at a concentration of0.1-1% is most suitable. Other wetting agents include the poloxamers (e.g. Pluronic), polyoxyethylene alkyl ethers (e.g. Brij), the polyoxyethylene castor oil derivatives (e.g. Cremphor), etc. The final step is sonication of the suspension to ensure homogeneity. It should be remembered that too powerful or too long exposure to ultrasound can actually result in the formation of large aggregates. The use of low-energy ultrasound baths is frequently sufficient to produce a finely divided, homogeneous suspension. In some cases the wetting agents may render the compound soluble. A procedure used frequently in our laboratories and found suitable for many compounds that are insoluble in water is detailed here.

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Compounds are dissolved in DMSO to a concentration of 20x the final concentration. The DMSO solution is slowly diluted 1 920 with 1% Tween 80 in water. Thorough vortexing and possibly light sonication (low-energy bath) produces a finely divided suspension of amorphous active ingredient. Subsequent crystal formation in this formulation cannot be excluded and it should therefore be prepared just before use. The universal solvent DMSO is very useful for preliminary formulations; however, it is recognized that DMSO may have a positive effect on oral absorption of drugs and this must be taken into account when comparing treatment with different agents which may be formulated differently. In some cases ethanol or other organic solvents can be used in place of DMSO in this formulation. Gelucires have proved to be useful for some compounds. Gelucires are polyglycerides which are manufactured in various grades having different melting points and dispersibility in water. The most useful is Gelucire 44/14 (the first number indicates the melting point and the second the dispersibility in water). The Gelucire is warmed to its melting point and the compound added. The compound may dissolve or be dispersed as a finely divided suspension. The melted Gelucire is then diluted with water and sonicated to produce a fine suspension. Alternatively, after the addition of the compound the Gelucire can be allowed to solidify and stored. Portions prepared in this way can be taken, water added and the suspension prepared as required. In the smaller species used in the majority of experiments in anti-infective research, it is not possible to administer the compound of interest in a solid form, although this can be easily achieved in larger species. However, using a suitable applicator, small hard-gelatin capsules with dimensions ca. 3 x 5 mm can be administered by gavage to rats. Following administration of the capsules it is important to administer water (ca. 1 ml) to ensure efficient disintegration of the capsule. Whichever formulation is chosen, it is usually preferable to prepare the material just before administration. If the chemical stability of the active ingredient and the physical stability (sedimentation and resuspension, growth of crystals, etc.) of the formulation are known then it may be possible to prepare larger batches of the formulation in advance. However, these properties are seldom known and can be difficult to determine and it is therefore preferable to use freshly prepared formulations.

Pharmacokinetics General considerations

The need for the evaluation of pharmacokinetics in the use of anti-infectives is apparent in such things as dose monitoring, dose adjustment in patients with underlying disease or when receiving therapy for underlying diseases when drug interactions may be an issue. Dose monitoring

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(Horrevorts and Mouton, 1993) is usually indicated when a drug has a narrow therapeutic window or shows large interindividual variation. In most instances these situations are not relevant to those investigating the effects of antiinfectives in animals. The need for pharmacokinetics in the laboratory situation is rather to aid interpretation of results and possibly to allow prediction to humans. Pharmacokinetic determinations may also be useful as a preliminary screen employed before investigations of efficacy are undertaken. If an oral therapy is proposed then a small pilot experiment can be used to demonstrate oral bioavailability before a time-consuming efficacy experiment is undertaken. There are four main species used for anti-infective research and it is expedient to consider only the determination of pharmacokinetic parameters in these, namely, the mouse, the rat, the rabbit and the guinea pig. As the methods for administration of the compounds to these species are well-known, only the collection of samples for analysis will be considered here. At this point it is sensible to consider experimental design. Before embarking on a pharmacokinetic experiment the method of analysis must be considered and some questions answered. Is whole blood or plasma or even serum to be analyzed? What anticoagulant should be used? Are any excipients likely to interfere with the analysis? How much sample is required? Once these questions have been answered then the next steps in the experiment can be planned. For how long will samples be collected? How many samples will be collected? The accuracy of the determination of the pharmacokinetic parameters is influenced by the number and frequency of samples. For example, an accurate terminal half-life can only be obtained when there are at least three (and preferably more) points on the linear portion of the curve. If a compound is rapidly absorbed and then excreted after oral administration then more early time points should be included. Conversely, for a compound which is absorbed slowly and has a long elimination half-life then more samples at later times are preferable. Given the limitations of the number of samples which can be taken from one animal it may be necessary to design an experiment in which not all animals are sampled at all time points. If a compound is being examined for which no pharmacokinetic information is available then a smaller pilot study may be useful to determine the times of sampiing and the number of samples that should be taken. Food can have an influence on the pharmacokinetics of orally administered compounds. Therefore, it must be decided whether the animals should have free access to food and water or whether they should be fasted. Clearly, if the intention is to use pharmacokinetics to aid planning and interpretation of efficacy experiments then the pharmacokinetic experiments will be done in animals held under the same conditions as those employed in the efficacy experiments. With rodents it is often difficult to ensure that all animals employed have the same nutritional status. This means that if the oral bioavailability of a compound is markedly affected by the presence of food then in animals

R.M. Cozens

that have free access to food and water there is often a larger degree of variation than would be found if the animals had been fasted.

Sampling from animals Mouse

Due to their small size and animal welfare considerations it is usually only possible to take one terminal blood sample from a mouse. Although it may be possible to take multiple samples via the tail vein, in most cases the volumes which can be taken are barely enough for one analysis. Similar and additional constraints apply to sampling from veins following surgical exposure. This means that experiments over a suitable time course require a number of animals and this can lead to data which can be rather variable. For this reason at each time point a suitable number of animals should be taken if variability is to be countered. A minim u m of four mice at each time has been found to be suitable in most cases. Some compounds may themselves have intrinsic variability due, for example, to having an absorption window or to being administered in poorly prepared formulations (see above). In the former case an increase in the number of animals at each time point should be considered, while in the latter the best solution would be to seek a better formu' lation. Samples are best collected under anesthesia from which the animals are not allowed to recover. Well-trained operators can retrieve at least 1 ml of blood from puncture of the inferior vena cava or directly from the heart. These two sites are probably the easiest from which to obtain blood which is uncontaminated with tissue fluid or other extraneous matter. The amount of blood or plasma required will of course depend on the method used for analysis. In some cases as little as 10 pl will be sufficient. With less sensitive methods then up to 1 ml (the maximum which can be guaranteed) may be required. Mice are frequently the first animal in which the efficacy of a new agent is investigated. As already mentioned above, in this situation it may be useful to obtain some basic knowledge of the pharmacokinetics of the compound before an efficacy experiment is undertaken. The small size of mice means that with very little compound some idea of oral bioavailability can be gauged. In the search for orally active human immunodeficiency virus 1 (HIV-1) protease inhibitors, we have routinely used mice in a pharmacokinetic screen (Alteri et al., 1993; Capraro et al., 1996; Cozens et al., 1996). Mice receive a standard oral dose of compound in a standard formulation. At 30, 60, 90 and 120 minutes after administration four mice are killed and plasma concentrations of the compound determined by high-performance liquid chromatography (HPLC). These experiments can be used to select compounds suitable for further evaluations. The time points chosen have been shown in most cases to encompass the

FORMULATION OF COMPOUNDS AND DETERMINATION OF PHARMACOKINETIC PARAMETERS

maximum plasma concentration. When starting with a new class of compounds it is worthwhile investigating tissue concentrations and trying to correlate plasma concentration with efficacy. Compounds which are quickly and extensively distributed may still be effective but have relatively low concentrations in the circulation. One example of this would be the situation of azithromycin (Girard et al., 1987, 1990), which is extensively and rapidly distributed to tissues. Once correlations have been obtained then it may be possible to select compounds for efficacy testing in vivo based on plasma concentrations attained in this simple model. Rat

For pharmacokinetic purposes, rats can be used in the same way as mice, however, their larger size does open some other possibilities. Sampling from the tail vein of a rat, particularly in older animals, is very difficult, if not impossible. There are two additional veins from which blood can be collected, namely the sublingual and penile veins (these veins are also found in mice but are usually so small that sampling is not practicable). While it is possible to remove several samples from a single animal via these routes the technique requires an anesthetic to be given to the animal and this may be avoided if the trouble is taken to implant catheters in suitable blood vessels. Implantation of a catheter in an artery is usually preferable to one in a vein as the sampling is then much more secure and the catheters are much less likely to become blocked. Standard surgical techniques can be employed to implant catheters in the jugular vein or carotid artery. However, in this position there can be interference with administration of the compounds by the oral route and a preferred vessel is the femoral vein or artery. This also has the advantage that the vessels are rather bigger than those in the neck and therefore the implantation is quicker and easier. If it is intended to administer the compound by the intravenous route then it is worth considering catheterization of both the femoral vein and artery: the latter is used to obtain the sample and the former to administer the compound. The use of suitable tethers, such as the Harvard swivel tether (Harvard Bioscience), will protect the catheter from the unwanted attentions of the rat and allow the possibility of sampling from an unanesthetized animal while allowing the rat almost full freedom of movement. With careful rinsing of the catheter with saline containing an anticoagulant it is easily possible to keep the rats for 48 hours after implantation of the catheter. As most single dose experiments will not last longer than 24 hours after administration of the drug, this length of time is adequate for most purposes. If it is intended to examine the pharmacokinetics after multiple administration, then it is probably better to perform the surgery on rats which have already received treatment rather than attempt to keep animals for several days with implanted catheters. Using these techniques it is poss-

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ible to take up to 4 ml of blood in a 24-hour period if the blood volume is replaced. Replacement of the blood volume can cause some small errors in the concentration in the circulation. Usually these are small; 4 ml of blood taken from a rat weighing 300 grams represents approximately 12% of the blood volume. The blood can be replaced with physiological saline in most cases. In special circumstances, for example when drug may partition strongly to erythrocytes, it may be desirable to use blood from donor animals. The need for this and the influence of blood volume replacement can be easily investigated in small pilot experiments in vivo or even in vitro. Not only the circulation of rats can be sampled m recently the pharmacokinetics and distribution of the antiviral penciclovir to the brain of rats has been studied (Borg and Stfihle, 1997). The authors used microdialysis to sample the unbound extracellular fraction of the drug in the brain. The basic technique of microdialysis has been described by Stfihle (1991, 1993). The technique is performed in anesthetized animals but has the advantagethat samples can be obtained without altering the volume of fluid in the sampling compartment and frequent samples can be obtained. The samples are also essentially free of protein and can be analyzed directly by HPLC. The technique is obviously not limited to rats or to the brain and could be adapted to other species and tissues. The oral administration of compounds can result in low plasma levels due not to poor absorption but rather to efficient first-pass extraction by the liver. An indication of the relative contributions of first-pass effects and absorption to plasma levels can be gleaned if samples are taken from the hepatic portal vein and the peripheral circulation. In anesthetized rats a cannula can be inserted into the hepatic portal vein and secured in place with veterinary cyanoacrylic glue m a procedure which ensures a maintained blood flow through the vein. A catheter implanted in the carotid or femoral arteries allows sampiing of the peripheral circulation. As the animals are anesthetized it is not possible to give the compound orally as stomach emptying and intestinal motility are invariably reduced by the anesthesia. Instead, the drug is given by intraduodenal injection, which has the added advantage that, if the concentrations in the peripheral circulation in this model are compared with those after administration by gavage, the possible effects of gastric instability can also be determined. A comparison of the concentrations of compound in the hepatic portal vein and in the peripheral circulation allows the relative contributions of absorption and first-pass effects to be assessed. The effects of first-pass extraction alone could be assessed if the compound were to be injected into the hepatic portal vein. Guinea pigs

Guinea pigs can be used in the same way as rats. This species has no easily accessible veins from which to remove

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blood, although marginal veins on the inside of the thigh, on the foot and ankle and the penile vein can be used by skilled operatives and other veins can be sampled after surgical exposure. This means that the use of indwelling catheters should be considered as the method of choice for this species. Rabbits

The presence of the large blood vessels on the ears of rabbits means that blood collection from this species is relatively easy even in conscious animals. No special preparation is required. In some experiments it may be possible to insert a catheter into the vessel which remains in place throughout, but this is probably not necessary. Other species

Although other species are not so often employed for efficacy studies a knowledge of the pharmacokinetics in larger animals such as dogs or monkeys can be useful to aid extrapolations of animal data to the situation in humans (see below). The larger species present no particular problems. Experienced operatives using trained dogs can administer compounds and obtain many blood samples from an individual animal with the minimum of stress to the animal. The dog opens up several opportunities which are not possible in smaller animals. Recently, Sagara and coworkers (Sagara et al., 1994), used pentagastrin and atropine sulphate to regulate the gastrointestinal physiology in dogs. Much of the differences in oral absorption between species depends on the rate of movement of drugs through the gut (intestinal motility and gastric emptying) and differences in gastric pH. These can be regulated by the coadministration of pentagastrin and atropine sulphate. A cautionary note is necessary; the co-administration of any compound can affect the pharmacokinetics of the compound under study and the extent of any influence should be determined in control experiments. Another possibility is to investigate regiospecific absorption of the drug. This information can be useful to optimize formulations, particularly if slow-release formulations are contemplated. Kwei et al. (1995) have used beagle dogs fitted with chronic cannulas allowing direct administration of drug solutions to specific regions of the gastrointestinal tract to investigate the differences in absorption in different portions of the gut of an HIV-protease inhibitor. Dogs and other larger species have the advantage that they can be reused. Interindividual variation can be considerable for some compounds. In dogs cross-over experimental designs can be contemplated. The only prerequisite is that sufficient time is left to ensure that essentially all the compound administered in the first use is eliminated (including metabolites) before the animals are reused. Such experiments get around the problem of interindividual variation and are recommended whenever possible.

R.M. Cozens

Methods of analysis

For the investigation of new agents the choice falls between microbiological or other biological assay and HPLC. Other techniques, such as radioimmunoassay, which may be considered are compound-specific, would only be used on a case-by-case basis and usually will only be available for compounds already in clinical use or those in an advanced stage of development. Microbiological assays for antibacterials are well-defined and can quite quickly be established for a new compound. Other biological assays for other antiinfectives can be foreseen but are usually only developed on a case-by-case basis. Therefore for anti-infectives as a whole HPLC is probably the method of first choice. There are two main weaknesses of HPLC: cost and the need for experienced operators to establish suitable methods. Microbiological assay has the advantage that it is relatively cheap and should be able to be established quickly in any microbiology laboratory. The two main strengths of HPLC is that it is specific, and can often be adapted to measure both parent compound and any potential metabolite, and has the potential to be more sensitive. The main weakness of microbiological assay is that it lacks specificity. If a compound were metabolized to an active metabolite then it would not be possible accurately to measure the concentration of the parent in a microbiological assay. The method is also relatively insensitive. Here a word of caution is needed. Often analysts strive for increased sensitivity. While in some cases this may be desirable, allowing smaller sample volumes to obtain the same data, in many cases it may not be necessary. If it is only required to know how long a compound is present at a level above the minimal inhibitory compound (MIC) then it is not necessary to strive to obtain a method which can detect and quantitate amounts severalfold less than the MIC. Recent developments in mass spectrometry allied to HPLC mean that mass selective detectors are now available to all; hitherto liquid chromatography/mass spectrometry was a technique which required extensive practical and theoretical knowledge. HPLC allied to mass spectrometry has the possibility of improving sensitivity and selectivity, allowing quicker method development. Mass selective detection may also allow the simultaneous determination of compounds in a mixture (Berman et al., 1997; Olah et al., 1997). This opens up the possibility of administration of a carefully selected mixture to an animal and determination of individual compounds in the circulation. The savings in time and animals could be considerable and the method has much to commend it as a screening system. However, interaction of compounds can cause profound mutual changes in pharmacokinetic properties and therefore results should be interpreted with caution, and certainly the pharmacokinetics of interesting compounds repeated in subsequent experiments in which the compound is given alone. The most difficult part of analysis by H P L C is the development of suitable methods. As already stated, the use of mass selective detectors may help in this regard. For screen-

FORMULATION OF COMPOUNDS AND DETERMINATION OF PHARMACOKINETIC PARAMETERS

ing purposes it is often possible to establish generic methods which can be used by all compounds of a particular class. The aim here is not necessarily to obtain the highest sensitivity; however, the method should be adequately sensitive, selective and the work-up of samples relatively easy. For more advanced pharmacokinetic experiments then the method used for screening may need to be altered to increase sensitivity. There are any number of different methods for sample preparation and chromatography. Even for one compound a review of the literature will reveal many methods, all of which could be used. The choice of method will often be dictated by one's own experience and knowledge as well as access to particular equipment. Klassen and Edberg (1996) have recently reviewed some of the methods for the analysis of antibacterials in body fluids and the reader is referred to this chapter and to the extensive literature for details of methods for individual compounds.

Pharmacokinetic parameters

A full treatise on pharmacokinetics is well beyond the scope and space limitations of this chapter. Pharmacokinetics is a science in itself and several monographs serve to introduce the reader to the basic and more advanced concepts. The book by Rowland and Tozer (1995) has become a standard reference work for those involved in pharmacokinetics, although other volumes are also useful for a less comprehensive coverage (for example, Krishna and Klotz, 1990). Here I will only discuss some of the key pharmacokinetic parameters which pertain to studies in animals (there are several pharmacokinetic parameters which are relevant in the clinical situation but which have little use in experimental infection models). Knowledge of this will aid in planning of experiments, interpretation of data (particularly where compounds are to be compared) and may allow some degree of prediction to the clinical situation. There are five key parameters: elimination halflife, apparent volume of distribution, total plasma clearance, absolute bioavailability (relative bioavailability can also be useful) and free fraction of drug. All of these, with the exception of free fraction of drug, can be determined by measurement of plasma concentrations after administration of the drug. At this point it is worth considering in what other compartments, beyond the circulation, concentrations of an anti-infective should be measured. There is still much debate about the relative merits of measuring concentrations in organs or tissue fluid as opposed to the circulation. Some points in the debate can be gleaned from a number of reviews which have appeared over the past few years (Carbon, 1990; Barza, 1993). Clearly, to exert its effect an anti-infective needs to be present in the same space as the target organism. Whether concentration in the circulation is sufficiently predictive of the concentration in tissue fluid probably needs to be determined for each compound,

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although it is probable that at equilibrium mean concentrations of unbound drug in plasma and tissue fluids are equal (Barza, 1993). There are several ways in which antibiotic concentrations can be determined in tissue fluids and these have been comprehensively reviewed by Bergeron and Brousseau (1986) in the first edition of this handbook. Although there are a few well-known exceptions, most bacterial infections are extracellular. Therefore in most cases intracellular concentrations of drug are not relevant. However, the observation that drug taken up into phagocytic cells can be targeted to the site of infection (Gladue et al., 1989) means that even here there may be a rationale to measure intracellular concentrations. In the case of antivirals there is clearly a need in many cases for the drug to enter the cell. Here then intracellular concentrations may be the most relevant. The measurement of concentrations in organs is most easily accomplished in homogenates of the organ. Contamination of the organ with blood will lead to some error unless a correction is made for the blood content of the organ. However, in those circumstances in which the drug concentration in the organ equals or is higher than that in the circulation then clearly the content of the organ per se must be higher than the concentration in the circulation, indicating uptake into the organ from the circulation. Elimination kalf-life

The elimination half-life is the time it takes the drug concentration during the elimination phase to decrease by 50%. Half-life can be estimated from the linear terminal portion of the log plasma concentration/time curve or it can be calculated: t~

=

0.693 x Vd

=

0.693 K

where, Vd is the apparent volume of distribution (see below), CI is the total plasma clearance (see below) and K is the elimination rate constant. This parameter is probably the most readily understood of the pharmacokinetic parameters. It can be used to predict suitable dosing intervals; as a starting point a drug could be administered once every half-life. It can also be used to predict the time required for a steady-state situation to be attained during multiple dosing or even continuous intravenous infusion and will also allow the differences between peak and trough concentrations during the steady state to be estimated. It can also be used to calculate a so-called accumulation factor: R

1 (3-K'C -

where I: is the dosing interval. This accumulation factor can in turn be used to calculate, in conjunction with a known maintenance dose, the loading dose required to bring plasma concentration to the required level immediately. However, loading doses are, it seems, seldom used in animal models.

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Apparent volume of distribution This is a proportionality constant that indicates the volume into which the given dose of a drug distributes, assuming its concentration in that volume to be the same as that in the plasma.

Vd= D C where D is the dose and C the concentration in plasma at zero time (determined by extrapolation). In animal studies this parameter has only one u s e ~ t o calculate a loading dose to attain a target steady-state concentration. Dose = Vd • Css where Css is the target steady state concentration. The volume of distribution can be useful to indicate which compounds may have better tissue distribution. All other factors being equal, then a compound with the greater tissue distribution will have the greater volume of distribution. However, as the volume of distribution also reflects distribution of fat-soluble compounds into fat deposits and binding to tissue components, not much about tissue distribution can be concluded in the absence of additional information.

Total plasma clearance Clearance is defined as the portion of the distribution volume which is totally cleared of drug per unit time:

CI=

D AUC

where D is the dose and A UC is the area under the whole of the concentration/time curve (calculated by the trapezoidal rule). The area under the curve represents an important parameter which is easily derived from the concentration-time curve. Total clearance is the sum of all the routes of clearance; renal clearance and hepatic clearance are usually the main routes of elimination but other minor routes are recognized and may in some cases be significant. Clearance can be used to determine the average steady-state concentration of a drug during multiple dosing and similarly, when a steady-state concentration is required, then it can be used to calculate the rate of dosing. While probably not of relevance to the subject of this book, a knowledge of the two major components of total clearance may also provide insight into the processes by which a drug is eliminated in an animal, and which may be significantly different in humans.

Absolute bioavailability The absolute bioavailability is most often applied to oral administration where it is defined as follows:

F - AUC~ X D~.v. A UCi.v. Doral By definition, intravenous administration results in 100% bioavailability. Similarly, bioavailability from other routes of administration can be calculated. The relative bioavailability is used to compare compounds given by the same route or possibly to compare the same compound given in different formulations. The use of computer programs can expedite the calculation of these parameters. There are several programs which can calculate the parameters based on a non-compartmental procedure or data can be used to construct a compartmental model from which the parameters are calculated. However, all the parameters are easily calculated with the aid of graph paper and a hand-held calculator.

Free fraction of drug Generally only drug which exists free in the plasma is able to exert its pharmacological effects or even to be metabolized or excreted; it is therefore important to know the amount of drug which is free to exert its pharmacological action. Usually determination of plasma concentrations is designed to measure the total drug in the circulation, i.e. bound and unbound; this is mainly because it is the easiest way to proceed. However, the determination of the concentration of only the free fraction may provide more meaningful information. It is important to recognize that the relative amounts of proteins in the circulation, and therefore the degree of protein binding, can change under certain disease states (Zini et al., 1990). Particularly if protein binding is high, drugs administered simultaneously can, by competition for binding sites, cause mutual changes in the unbound fraction.

Interspecies scaling Although the pharmacokinetic differences between animals do not make life easy for those involved in the in vivo evaluation of anti-infectives, the differences can in some cases be used to extrapolate to the human situation. It has been noted that certain physiological processes can change in proportion to the size of the animal. These changes can be reflected in the dependence of certain pharmacokinetic parameters on the size of the species, a fact that can be used for predicting human pharmacokinetics from pharmacokinetic data collected in small animals. Prediction of pharmacokinetics in humans from data from animals relies on general allometric relationships that link physiology and anatomy with body weight (Boxenbaum, 1982; Boxenbaum and Ronfield, 1983). In some cases pharmacokinetic parameters are better related to other variables such as brain weight or maximum life span potential (Mahmood, 1996; Mahmood and Balian, 1996). Unfortunately, application of these principles is

FORMULATION OF COMPOUNDS AND DETERMINATION OF PHARMACOKINETIC PARAMETERS

limited to compounds for which the route of elimination and route and extent of metabolism (no metabolism is preferable) are the same in all species. In addition, firstorder pharmacokinetics is an additional prerequisite. Usually, the relationships do not hold for absorption of drugs from the gastrointestinal tract; due to variations in gastrointestinal physiology (pH, gastrointestinal tract motility, etc.) rather than differences in the movement of compound across the gut wall. Thus a potentially useful method is limited by a variety of preconditions and it is up to the experimenter to determine experimentally if interspecies scaling could be of use in a particular situation. Lastly, even if the preconditions are met there is no guarantee that the predictions obtained will survive clinical scrutiny. In conclusion, pharmacokinetics of anti-infectives in animals can be used as an aid to the design and interpretation of efficacy experiments, can allow prediction to the human situation, particularly if the human pharmacokinetics is known, and is essential for the development of suitable formulations. Pharmacokinetic data should always be interpreted with due regard to the formulation in which the compound is administered. Which pharmacokinetic parameters can or should be determined will depend on the particular situation: the compound under study, the route of administration, the site of infection, the species under study, etc. Much useful information can be obtained if, at a minimum, concentrations in the circulation are determined and the basic pharmacokinetic parameters are calculated.

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