Assignment Group 4.docx

TOPIC: BIOLOGICAL HALFLIFE AND VOLUME OF DISTRIBUTION

GROUP 4 HAFSA SHAHID

06331513005

SAMAN SHAHJEHAN

06331513014

HASSAN SALEEM BUTT

06331513023

MASOOMA NAQVI

06331513034

NISHAT SALEEM

06331413039

SUBMITTED TO : MA’AM GUL SHEHNAZ SUBMISSION DATE : 5TH NOVEMBER 2018

CONTENTS 1) Biological half life • Introduction • Pharmacokinetic parameters for determination of half life • Method of determination • • • • •

Types of half life Two-Compartment Model Clinical applications Application of short Half life Drug Therapy Consideration

2) Volume of distribution • • • • • • • • •

Introduction Drug distribution and Volume of distribution Assessment of Volume of distribution Models to explain Volume of distribution Types of Volume of distribution Methods of determination of volume of distribution Factors which Influence the Volume of Distribution Applications of Volume of Distribution Conclusion

Saman shahjehan (06331513014)

Biological half life Definition This is the period of time required for the concentration or amount of drug in the body to be reduced by one-half. 

We usually consider the half life of a drug in relation to the amount of the drug in plasma.

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A drug's plasma half-life depends on how quickly the drug is eliminated from the plasma. A drug molecule that leaves plasma may have any of several fates.

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It can be eliminated from the body, or it can be translocated to another body fluid compartment such as the intracellular fluid or it can be destroyed in the blood.

Pharmacokinetic parameters for determination of half life 

Volume of distribution

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Clearance

1) Clearance The removal of a drug from the plasma is known as clearance 

Clearance is not an indicator of how much drug is being removed; it only represents the theoretical volume of blood which is totally cleared of drug per unit time. Because clearance is a first-order process, the amount of drug removed depends on the concentration.

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Clearance can be thought of as the proportionality constant that makes the average steady-state drug level equal to the rate of drug administration. Clearance (rate out) can be calculated from the dose (rate in) and average steady-state concentration: Cl = (Dose / interval) / Cpss ave

 Half life of drug is inversely proportional to the clearance So, more the clearance of a drug, shorter is the half life. 2) Volume of distribution. The distribution of the drug in the various body tissues is known as the volume of distribution.  Half life of a drug is directly proportional to the volume of distribution. 

When the drug is absorbed and reaches the plasma, it is distributed to the tissues. Some drugs have high volume of distribution and are distributed to various tissues, mostly adipose tissue. More time is required for their elimination, thus have greater half life.

Both of these pharmacokinetic parameters are important in determining the half life of a drug. symbol to represent the half-life: t½ Half life = 0.693 x Vd/ total body clearance

Method of determination Experimentally the half life can be determined by giving a single dose, usually intravenously, and then the concentration of the drug in the plasma is measured at regular intervals.

The concentration of the drug will reach a peak value in the plasma and will then fall as the drug is broken down and cleared from the blood.

The time taken for the plasma concentration to halve is the half life of that drug. Examples Some drugs like ibuprofen have very short half lives, others like warfarin and digoxin, take much longer to eliminate from the plasma resulting in a long half life. So drugs like ibuprofen that are cleared from the blood more rapidly than others need to be given in regular doses to build up and maintain a high enough concentration in the blood to be therapeutically effective. As repeated doses of a drug are administered its plasma concentration builds up and reaches what is known as a steady state. Steady state This is when the amount of drug in the plasma has built up to a concentration level that is therapeutically effective and as long as regular doses are administered to balance the amount of drug being cleared the drug will continue to be active.  

The time taken to reach the steady state is about five times the half life of a drug. Drugs like digoxin and warfarin with a long half life will take longer to reach a steady state than drugs with a shorter half life.

Types of half life 1) Alpha half life The rate of decline in plasma concentrations due to the process of drug redistribution from the central to the peripheral compartment •

Alpha half life =plasma/distribution half life Most of the drugs have alpha half life and remain in the plasma.

2) Beta half life The rate of decline due to the process of drug elimination due to metabolism. Beta half life =tissue/elimination half life • Drugs having beta half life have two half lives, one in the plasma and one in the tissues. They are highly distributed drugs. Their total time of elimination is more.

Two-Compartment Model: Relation Between Distribution and Apparent (Beta) Half-Life The distribution half-life of a drug is dependent on the type of tissues the drug penetrates as well as blood supply to those tissues. In addition, the capacity of the tissue to store drug is also a factor. Distribution half life is generally short for many drugs because of the ample blood supply to and rapid drug equilibration in the tissue compartment. However, there is some supporting evidence that a drug with a long elimination half-life is often associated with a longer distribution phase. It is conceivable that a tissue with little blood supply and affinity for the drug may not attain a sufficiently high drug concentration to exert its impact on the overall plasma drug concentration profile during rapid elimination. In contrast, drugs such as digoxin have a long elimination half-life, and drug is eliminated slowly to allow more time for distribution to tissues. Human follicle-stimulating hormone (hFSH)injected intravenously has a very long elimination half-life, and its distribution half-life is also quite long. Drugs such as

lidocaine, theophylline, and milrinone have short elimination half-lives and generally relatively short distributional half-lives.In order to examine the effect of changing k (from 0.6 to 0.2 h−1) on the distributional (alpha phase) and elimination (beta phase) half-lives of various drugs, four simulations based on a twocompartment model were generated (Table 5-8). The simulations show that a drug with a smaller k has a longer beta elimination half-life. Keeping all other parameters (k12, k21, Vp) constant, a smaller k will result in a smaller a, or a slower distributional phase.

Nishat Saleem (06331413039 )

CLINICAL APPLICATION In clinical research, the half-life is needed and used to determine how long after the dosing of the test agent that one is required to take blood samples so that the area under the time course curve (AUC) represents the true time course of the drug. In general, agents with very short t ½ ’s will require an intravenous infusion to maintain the continued presence of the drug. Examples include lidocaine and dopamine. Other agents with a short half-life are knowingly given at intervals longer than 5 times their plasma t ½, either because the continued presence of the drug is not required for receptor activity or because the effect of the drug outlasts the plasma concentration. The organic acid antibiotics fall into the former group. The later group is large and brings up the concept of an effect (efficaciousness) half-life.

APPLICATIONS OF SHORT HALF LIFE What usually happens is that it is noticed that a drug with a relatively short half-life is still able to produce an effect long after it is supposedly eliminated (which would be 5 times the plasma half-life). It is presumed that the drug is acting intracellularly and either remains partly bound to the receptor long after most of the extracellular drug has been eliminated or the drug is a “hit -and -run” type which alters a receptor such that the effect remains long after the drug is gone. The reason it is important to always be on the lookout for this phenomenon is that it is far easier for patients to take a drug once or twice a day than three of four times a day.

ELIMINATION FATE A drug's plasma half-life depends on how quickly the drug is eliminated from the plasma. A drug molecule that leaves plasma may have any of several fates. It can be eliminated from the body, or it can be translocated to another body fluid compartment such as the intracellular fluid or it can be destroyed in the blood. The removal of a drug from the plasma is known as clearance and the distribution of the drug in the various body tissues is known as the volume of distribution. Both of these pharmacokinetic parameters are important in determining the half life of a drug.

LENGTH OF TIME OF THE EFFECT The elimination half-life is a useful pharmacokinetic parameter as it provides an accurate indication of the length of time that the effect of the drug persists in an individual. It can also show if accumulation of the drug is likely to occur with a multiple dosing regimen. This is helpful when it comes to deciding the appropriate dose amount and frequency.

RATE OF DRUG ELIMINATION Along with other pharmacokinetic data and values about the individual patient, the half-life can help health practitioners to estimate the rate at which a drug will be eliminated from the

body, and how much will remain after a given time period. From this information, appropriate decisions to promote patient health outcomes can be made.

DOSAGE REGIMEN DESIGN When doctors write prescriptions for medications, they don't just jot down the name of a drug on a little blue pad and send their patients off to the pharmacy. Included on the prescription are details about how much of the medication to take at one time (the dose) and at what intervals. These instructions, which are very important for making certain the drug is both effective and safe, are based in part on the half-life of the medication being prescribed.

INDIVIDUALIZATION OF DOSAGE It's important to note that the expected half-life of a drug will vary from person to person, depending on factors such as age, weight, genetics, and even specific health issues. For example, the half-life of acetaminophen (the active ingredient in Tylenol, another non-narcotic pain relief medication), can be significantly affected by a person's liver function since acetaminophen is primarily processed through the liver.

MULTIPLE DOSING During multiple dosage, elimination half life does have value in predicting the rate and relative extent of drug accumulation, as well as the rate of washout after termination of treatment. Clinicians should consider volume of distribution and clearance, in addition to elimination half, when evaluating the pharmacokinetic properties of drugs.

ACHIEVING A STEADY STATE The goal of any medication that will need to be taken on an ongoing basis, such as an antidepressant, is to get it to a "steady state"—in other words, to the point at which the amount that goes into the body is equal to the amount that's eliminated. Interestingly, no matter what the half-life of a medication is, it takes about four times that amount of time for the concentration of the drug to reach a steady state in the body. This means that if you begin taking a medication with a half-life of 24 hours, after four days, or on the fifth day, the rate of intake of the drug will approximately equal the rate of elimination. If the halflife is 12 hours, you'll reach steady state at the beginning of the third day (after 48 hours).

APPLICATION IN ATHLETICS

Published half-life data is usually determined by measuring the decrease in parent drug in serum or plasma. In the anti-doping world, the serum half-life is of limited value in determining how long a substance stays in the body because it does not reflect the presence of metabolites (break-down products from the parent drug). These metabolites are often what is measured in anti-doping tests and the serum half-life does not necessarily reflect urine concentrations which is the main sample of choice in anti-doping testing. Furthermore, the half-life can vary greatly between individuals and is specific for each medication. It can be dose-dependent and affected by other factors such as accumulation in adipose tissue. Marijuana is an example of a drug that is excreted in the urine over a prolonged period that could take weeks or months, depending on the route of administration, to clear completely from an athletes’ body. Aspirin on the other hand, is an example of a rapidly excreted drug, and could clear completely from an athletes’ body within hours. Athletes are strictly responsible for what is found in their body at the time of a drug test. Understanding clearance times of medications, which is the time it takes for the medication, and its metabolites, to be completely eliminated from the body, becomes essential. This is especially important if the athlete is prescribed a medication that is prohibited only incompetition and they are going to be competing soon. If an athlete uses the medication out-ofcompetition and it is still present in their body when tested at a competition, they may be held responsible for an anti-doping rule violation. A physician or pharmacist should be able to assist in predicting clearance times for medications. However, USADA cannot predict the clearance time for any medication for any particular individual. If an athlete needs to use a substance prohibited in-competition and they are close to competition time, they are strongly encouraged to contact USADAs Drug Reference Department to learn if they need a Therapeutic Use Exemption (TUE).

DRUG THERAPY CONSIDERTAION The half life is an important concept for clinicians:   

When treating infections, the antibiotic needs to be present long enough and at a high enough dose to kill the infection When taking a sleeping medication, you want it to work only so long that you wake up refreshed, not groggy When being treated for blood pressure problems (Hypertension) or cholesterol problems (Hyperlipidemia) you'd like the medication to work all day.

Some medical conditions will either shorten or prolong the half life of a medication, which is important for the clinician to consider, to avoid over or under dosing.

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Kidney disease will reduce the excretion of medications that are primarily eliminated through the kidney, allowing it to increase in the blood. This is predictable and should be taken into consideration by the clinician Certain medications interfere with the metabolism of other medications, either by speeding up, or slowing down, the metabolism. The clinician has the information to know what does what to what, to avoid this problem. Certain foods can interfere with metabolism of medication. Grapefruit and grapefruit juice can cause problems with this, and the clinician may tell one to avoid this food.

WHY HALF LIFE MATTERS Drugs with a longer half-life take longer to work, but on the positive side, they take less time to leave your bloodstream. On the flip side, those with a short half-life become effective more quickly but are harder to come off of. In fact, drugs with very short halflives can lead to dependency if taken over a long period of time. A drug's half-life is an important factor when it's time to stop taking it. Both the strength and duration of the medication will be considered, as will its half-life. This is important because you risk unpleasant withdrawal symptoms if you quit cold turkey. Withdrawal symptoms are caused by quickly getting off of some types of medication. When you are being weaned from this type of medication, the drug's half-life will be considered so that those with a longer half-life will take longer to come off of. Medication side effects occur usually when the blood level of the drug is not in its steady state. That's why it's important to follow the dosage and duration recommendations to the letter. Otherwise, the body will react and the effect of the drug will be either toxic, as in more than intended, or not therapeutic, as in ineffective for treatment. One impact of half-life is found in the SSRI antidepressants. People taking SSRIs with short half-lives are much more likely to experience SSRI discontinuation syndrome. People taking an SSRI with a long half-life such as Prozac need to wait far longer between stopping Prozac and starting a new antidepressant, such as an MAOI.

Masooma Naqvi (06331513034)

VOLUME OF DISTRIBUTION INTRODUCTION Definition : It is defined as ; "Fluid volume that would be required to contain the amount of drug present in the body at the same concentration as in the plasma."

DESCRIPTION According to its definition the volume of distribution (Vd) is not a physical space but a dilution space which may also be called an apparent volume. The volume of distribution of a drug gives the information about the distribution of that drug in the body. The Vd is calculated as the ratio of the dose present in the body and its plasma concentration , when the distribution of the drug between the tissues and the plasma is at equilibrium. Accordingly, a drug that accumulates in tissues as e.g. fat tissue, will have a relatively low plasma concentration with regard to the administered dose, and consequently, the calculated Vd will be high.

DRUG DISTRIBUTION AND VOLUME OF DISTRIBUTION  Drugs with a very small Vd Drugs with a very small Vd (<10 L) are mainly confined to the intravascular fluid, thus the blood, corresponding to roughly twice the plasma volume. This may occur for two reason 1. The molecule is too large to leave this compartment. 2. The molecule binds preferably to plasma proteins (e.g. to albumin) and much less to tissue proteins. Competition for plasma protein binding sites can occur between such drugs or with endogenous substances.

 Drugs with a relatively small Vd Some drugs cannot enter cells because of their low lipid solubility. These drugs are distributed throughout the body water in the extracellular compartment and have a relatively small Vd (12-20 L).

 Drugs with a high Volume of distribution Drugs that accumulate in organs either by active transport or by specific binding to tissue molecules have a high volume of distribution, which can exceed several times the anatomical body volume. Therefore, Vd should not be identified too closely with a particular anatomical compartment. Lipid-soluble drugs are stored in fat. Bone is a reservoir for drugs such as tetracycline and heavy metals.

Following are the values of Vd for different drugs

ASSESMENT OF VOLUME OF DISTRIBUTION Volume of distribution is determined as ;

A= amount of drug in the body C= plasma concentration All the volumes of distribution correspond to the ratio of an amount (A) of drug in the body at a given time (At), and plasma (blood) concentration (C) at that time Most importantly, the Vd is determined in conditions under which the drug distribution between the plasma and the tissues is at equilibrium. By definition a Vd should only be regarded as a proportionality constant (parameter) between a plasma concentration and the

corresponding amount of drug in the body. This proportionality constant having a volume for dimension has been termed volume of distribution.

MODELS TO EXPLAIN VOLUME OF DISTRIBUTION There are several models to explain the volume of distribution i.e 1. The Bathtub Model of Volume of Distribution The bathtub model provides a physical model to explain how physical factors can influence the volume of distribution. For example there is no loss of water from the bathtub. By putting a known amount of drug (the dose) into the bathtub and measuring the concentration it is easy to calculate the volume of distribution. It is common to distinguish 3 physical volumes based on anatomical and physiological concepts. Very large molecules (proteins) or blood components (blood cells) will largely be confined to the vascular volume. This vascular volume consists of the total blood volume, the fluid component defined by plasma and the cellular component defined largely by red blood cells. Molecules which can leave the vascular space but do not cross cell membranes easily (e.g. highly ionised molecules) will mainly be in the extracellular compartment. Molecules which can readily cross cell membranes may share the same physical volume as water

Bathtub model for volume of distribution

2. The bathtub with sponge model of volume of distribution. Apparent volume of distribution does not necessarily correspond to any physical compartment because of binding to tissues, binding to plasma proteins, preferential partitioning into fat or adsorption onto bone. The apparent volume of distribution will be large when there is extensive binding to tissue proteins. Some drugs may have a large apparent volumes because of partitioning rather than binding to tissues. Partitioning into fat can make the apparent volume of distribution larger in obese people. Some drugs adsorb to bone e.g. tetracycline and bisphosphonates. Tetracycline causes teeth staining in children. Bisphosphonate adsorption can be beneficial in osteoporosis by reducing bone breakdown. Some poisonous substances e.g. radioactive caesium, are adsorbed to bone and can cause bone cancer. All these substances will have relatively large volumes of distribution.

The bathtub with sponge model of volume of distribution.

3. The bathtub with red herring model of volume of distribution. Plasma protein binding is another major reason why the apparent volume of distribution does not correspond to a physical volume. But binding to plasma will lead to a smaller apparent volume. Drugs bind to proteins like albumin and α1-acidglycoprotein. Because they bind to plasma proteins they are extracted from plasma and included in drug concentration measurements. This gives a misleading impression of the volume of distribution and this phenomenon can be thought of as a ‘red herring’. When a sample of bathwater is removed it also takes ‘red herrings’ with it. The concentration of drug will be higher in the sample than in the rest of the bath water because of the higher concentration of drug bound to the ‘red herrings’. The ‘red herring’ effect is caused by drug binding to plasma proteins. A higher concentration in the sample leads to a lower apparent volume of distribution.

The bathtub with red herring model of volume of distribution

DIFFERENT TYPES OF VOLUME OF DISTRIBUTION It is clear that timing plays a major role in this, because the measured drug concentration will vary depending on the rate and extent of absorption. Even with IV administration there is going to be some delay. A discussion of the volume of distribution as dose divided by concentration meets with a limitation of the multi compartment model, which is the assumption that the drug is distributed equally and instantly throughout the compartment. In reality, drug concentration in the sample will vary over time because it takes time for the drug to distribute around the body, and a concentration taken within minutes of administration will be very different to the concentration taken many hours later. Clearly these will produce completely different Vd values.

Following are the types of volume of distribution ;

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Initial volume of distribution Vinitial Extrapolated volume of distribution Vextrap Non Compartmental volume of distribution Varea Steady state volume of distribution Vss

1) Initial volume of distribution Vinitial Consider if you measure the Vd of the central (intravascular) compartment. It is possible to calculate this soon after a drug is administered intravenously, by extrapolating an imaginary line from plasma concentration measurements, extended to time zero. You need to extrapolate this line because under no realistic circumstances could you ever actually measure the concentration at time zero.

So, by this method, you measure the volume of initial dispersion of the drug. This volume is usually called either Vinitial, or Vc, and it represents the behaviour of the drug during the first rapid phase of distribution through the central compartment. It is generally determined by the degree of protein binding. Drugs which are highly protein-bound will have a larger Vinitial if you intend to measure free drug levels.

2) Extrapolated volume of distribution ( Vextrap ) If you completely ignore the distribution of the drug into the tissues your volume of distribution estimate is going to be inaccurate for the purpose of determining such things as loading doses. The alternative approach is to ignore everything but the tissue distribution. This method takes the slow late stages along the concentration/time curve (the terminal elimination phase) and extrapolates a line of best fit from them.

Obviously this is going to be a massive overestimate for many drugs, particularly if they are drugs which disperse extensively into the tissues. Your (time=0) concentration estimate will potentially be a very low value, producing an unreasonably large Vd estimate. One could potentially use the Vextrap value to identify drugs which have so much tissue distribution that clearance by dialysis is near-impossible.

3) Non Compartmental volume of distribution Varea The Vinitial value and the Vextrap value both focus on the drug distributing into some compartment volume (be it central or peripheral). Neither give a good estimate for the "ideal" volume of distribution, one which you could reliably use to calculate your loading doses. Varea is an attempt to get around the errors of focusing on just one compartment at a time. It uses a non-compartmental pragmatic model, easily calculated from serial concentration measurements.

where AUC is the area under the concentration-time curve and the "β" terminal elimination time constant is the slow exponential rate of decline at the latter stages of a drug's tenure in the body.

You take the whole concentration/time curve, integrate the area under it (AUC) and use this to establish the "true" volume. This gives a better (smaller) Vd estimate than Vextrap but is still frequently incorrect if there is significant distribution around compartments. The Varea equation assumes that the rate of the concentration decline during the terminal elimination phase is the average rate of clearance for the entire duration of the dose, and that this rate remains constant. Practically, clearance is almost never constant and is usually concentration-dependent ("first order") which means that using the "β" terminal elimination time constant will always yield an underestimate of the "time=0" intercept and therefore an overestimate of the Vd. This problem also limits the utility of Varea in altered clearance states. For instance, for a renally cleared drug Varea measured in a patient with renal failure will always be smaller (because the slope of the β terminal elimination rate will be near-horisontal). But this will not represent any sort of change in the drug's distribution.

4) Steady state volume of distribution ( Vss ) As mentioned above, the Varea method assumes some sort of linear rate of drug clearance. So, it's clearly going to be useless in situations where the clearance rate is zero, or appears to be zero- for example, in renal failure, in the context of an intravenous drug infusion or when the drug has long-term regular administration. Fortunately the real or apparent absence of clearance makes Vd calculations much easier:

The point of intersection hardly matters any more. Nobody needs to draw any intercept lines. Vss describes the volume of distribution during steady state conditions, i.e. when there is a stable drug concentration. It is always going to be slightly lower than Varea because of the effect of clearance on the β terminal elimination time constant.

Of all the volumes of distribution, Vss is probably the most useful for calculating the loading dose. The loading dose, after all, is the dose you wish to give in order to achieve a desired (steady state) drug concentration. With the simplicity of the steady state model, the dose is calculated as (Vss × Css) where Css is the desired steady-state concentration.

Hafsa Shahid (06331513005)

METHODS OF DETERMINITION OF VOLUME OF DISTRIBUTION As the plasma concentration can be measured in different situations [just after an intravenous (i.v.) drug administration, during the phase of drug distribution, during the terminal phase of drug disposition or at equilibrium], several Vd are needed because the proportionality ratio between the amount of drug in the body and the plasma concentration will have different values according to the state of drug disposition. Figure 4 gives the four possibilities, with Vc being the initial volume of distribution, Vss, the appropriate volume of distribution when plasma concentrations are measured in steady- state conditions, and Varea or Vz (formerly termed Vdb), the appropriate Vd when plasma concentration is measured in pseudo-equilibrium conditions. When plasma concentration is measured during the drug distribution phase, the ratio of the drug amount over the plasma concentration is not a parameter but a time dependent variable. THE INITIAL (VC) AND THE TERMINAL (VAREA OR VZ) VOLUMES OF DISTRIBUTION AFTER INTRAVENOUS BOLUS DRUG ADMINISTRATION Just after an i.v. drug administration, plasma concentration is maximal (C0). Before any drug elimination or distribution, the amount of drug in the body is by definition equal to the administered dose, and the plasma concentration is C0. Applying the definition of a Vd, the initial volume of distribution (Vc) is

This equation assumes that C0 corresponds to an initial plasma concentration resulting from a total drug mixing in blood before any drug elimination or distribution, which is generally an unrealistic assumption. It is estimated by extrapolation to time zero of the drug disposition curve . In the framework of a compartmental analysis, the initial volume of distribution is termed volume of the central compartment and is obtained by mean of Eq

where Yi are intercepts of the different phases of the kinetic disposition obtained by fitting the plasma drug concentration vs. time profile. Therefore, Vc can be viewed as the apparent volume from which drug elimination occurs because kidney and liver, the two main clearing organs, belong to the central compartment

Compartmental model and the volume of distribution of the central compartment.

The figure shows the correspondence between a tricompartmental model (right) vs. the physiological and anatomical reality (left). The classical 2 or 3 compartmental mammillary models are a simplistic representation of the body in 2 or 3 well-stirred compartments. The mammillary topography is due to the anatomy of the cardiovascular system, which irrigates different organs in a parallel pathway (rather than sequentially). The central compartment corresponds to blood and all organs, which are in rapid equilibrium with blood (lungs, kidney and liver). The kidney and liver being the two most important clearing organs, drug elimination occurs from the central compartment (according to a first-order rate constant noted K10), and the volume of the central compartment (Vc) can be viewed as the apparent space from which drug elimination occurs. It is the reason why body clearance can be estimated by the product of K10 and Vc. The peripheral compartment corresponds to organs for which the rate of equilibrium with blood is slower, the number of required peripheral compartments being indicated by the data itself .

THE ERRONEOUS COMPUTATIONS OF VAREA FOR EXTRAVASCULAR ROUTES The computation of Varea requires two major assumptions: (i) the dose which gains access to the systemic circulation should be accurately known and (ii) the terminal phase during which Varea is computable should be a pure elimination phase. When Varea is computed after extra-vascular drug administration and when the amount of drug that gains access to the systemic circulation is unknown, what is actually estimated is Varea/F, not Varea which can be calculated from the following equation ;

Where F is the bioavailability factor from 0 to 1. If F is unknown (no i.v. study), Varea/F is at best of little value because Varea/F cannot be used to compute the actual amount of drug in the body after an extra-vascular administration. STEADY-STATE VOLUME OF DISTRIBUTION (VSS) As Varea relies on total body clearance, Varea is not an appropriate Vd in those situations for which clearance is null or apparently null. This is the case during i.v. infusion, once the steadystate condition has been reached and the rate of drug input exactly compensates for the rate of drug elimination. Under these con- ditions, the system behaves equivalently to a closed system (no input and no output), i.e. as having a null clearance. In this circumstance, the use of Varea overestimates the total amount of drug in the body and the appropriate Vd to be selected will be the so-called Vss with following equation

Vss is a clearance independent volume of distribution that is used to calculate the drug amount in the body under equilibrium conditions, i.e. during a drug i.v. infusion and also during multiple drug administration once the steady-state conditions are achieved. Vss can be derived using different approaches (compartmental, statistical moments, …). For a classical mammillary compart- mental model, Vss is given by Equation

where K1j and Kj1 represent the distributional rate constants such as K12, K21, K13, K31, etc. of the general mammillary model. Vss can also be derived using the statistical moments approach described by Benet and Galeazzi.

where AUMC is the area under the first moment of the disposition curve, Cl the plasma clearance, and MRT the mean residence time in the system.

Vss can also be computed during a multiple dosing regimen, but in this situation Eqn 15 will overestimate the true Vss and corrections are required. When data are obtained in steady-state conditions, Vss is given by following Equation;

Here are the dosing interval, the area under the first moment curve within a dosing interval at steady-state, the area under the plasma concentration time curve within a dosing interval at steady-state, and the area under the plasma concentration curve from the last dose to infinity, respectively. DIFFERENCES BETWEEN VAREA AND VSS For all drugs, Varea is higher than Vss but generally, the difference remains small. The difference between Varea and Vss can be very large, however, if a large fraction of the drug is eliminated before reaching pseudo-equilibrium. This is the case for aminoglycosides when considering the very late terminal phase .The difference between Varea and Vss derives from the difference between pseudo-equilibrium and equilibrium conditions. In pseudoequilibrium conditions, plasma drug concentrations decrease because the drug is continually removed from plasma at a rate proportional to plasma clearance.In contrast, in equilibrium conditions, plasma concentration is constant because the rate of drug elimination is compensated by the rate of drug input in the body (clearance is apparently null). Thus, all things being equal (i.e. for the same total amount of drug in the body), plasma concentration will be systematically lower in pseudo- equilibrium conditions than in equilibrium conditions. Therefore, when establishing the correlation between the same amount of drug in the body with plasma concentration, the proportionality constant should be higher in the pseudoequilibrium state (Varea) than in the equilibrium state (Vss), and Vss can be viewed as the limit of Varea when the clearance tends towards zero. The impact of clearance on Varea explains why Varea decreases when renal insufficiency exists. It would be errone- ous to explain this decrease as an altered drug distribution. For instance, the pharmacokinetics of gentamicin was inves- tigated in the horse before and after the occurrence of nephrotoxicity. Varea was reduced by 36%, i.e. a reduction proportional to that of body clearance (40%) whereas, as expected, the reduction of Vss was more limited.

Hafiz Hassan Butt (06331513023)

Factors which Influence the Volume of Distribution Patient factors could include age, gender, muscle mass, fat mass and abnormal fluid distribution (oedema, ascites, pleural effusion). The drug factors would include tissue binding, plasma protein binding and physicochemical properties of drug (size, charge, pKa, lipid solubility, water solubility)

 Measurement and pharmacokinetic modelling of Vd 1) Timing of measurements Depending on when the measurements are taken, the Vd will be different (i.e. it will correspond to Vinitial if the measurements are taken too early, and Vextrap if they are taken during the elimination phase). 2) Pharmacokinetic model Vinitial, Vextrap, Varea and Vss are various ways to estimate the Vd of a drug from empirical measurements. All of these methods will yield slightly different results or, occasionally completely different results. 3) Free vs. total drug levels In highly protein bound drugs, the calculated volume of distribution for the "total" drug levels will be totally different to the Vd calculated for the free drug. Total Vd will correspond to the Vd of the binding protein rather than the drug itself.

 Properties of the drug 1) Molecule size The larger the molecule, the harder it will be for it to passively diffuse out of the central compartment, and therefore the smaller the Vd. 2) Molecule charge Highly ionised charged molecules will have higher water solubility, and may even be trapped in the central compartment by electrostatic factors which keep them bound to proteins with corresponding charge.

3) pKa pKa determines the degree of ionisation and therefore influences lipid solubility. 4) Lipid solubility Lipid solubility is one of the major determinants of Vd; highly lipid-soluble drugs will have the highest Vd values because of the low fat content of the bloodstream. 5) Water solubility Highly water-soluble drugs will have difficulty penetrating lipid bilayer membranes and generally tent do have smaller volumes of distribution, essentially being limited to extracellular water.

 Properties of the patient's body fluids 1) pH pH interactes with the drug's pKa to influence the degree of lipid solubility. pH also influences the degree of protein binding (a good exmaple of this is ionised calcium) 2) Body water volume Dehydrated patients will have drug levels concentrated in the plasma just as all dissolved substances are concentrated by loss of water. 3) Protein levels For highly protein-bound drugs, lower serum protein levels will result in a higher free (unbound) drug fraction. This may have little effect on the Vd as calculated from total drug concentration, but if you are measuring free drug levels it will make the Vd appear smaller. 4) Displacement Drugs may be displaced from their protein and tissue binding sites by the effects of pH or by competition from other drugs/substances (eg. urea). Displaced drugs mayl redistribute into plasma, decreasing the calculated Vd.  Effects of physiology and pathological states 1) Age As an old professor of mine had put it, babies are grapes and the elderly are raisins. As you age, body water content decreases, shrinking the Vd of water-soluble drugs. Muscle mass also decreases, and so tissue binding diminishes. 2) Gender Female Vds tend to be higher than male Vds due to the generally higher body water content

3) Pregnancy Both the body water and the body fat content increases, and therefore the Vd increases for most drugs. Not to speak of the possible distribution into amniotic fluid and foetus. 4) Oedema Oedema represents increased body water and this influences water-soluble substances; Vd for these will increase 5) Ascites / effusions Just as in oedema, large fluid collections may sequester water soluble drugs and act as reservoirs.  Effects of apparatus 1) Adsorption on to apparatus Dialysis filters and ECMO circuits tend to adsorb drugs in an unpredictable fashion, resulting in an apparent increase in the volume of distribution. 2) Volume expansion In the context of bypass circuits and other large extracorporeal machinery, there may be 2000-2500ml of additional extracorporeal fluid, which will change the volume of distribution (particularly for drugs which are largely confined to the central compartment)

Applications of Volume of Distribution 1) Loading dose can be estimated

2) Clearance can be calculated

Cl = Vd / kel 3) Total amount of drug present in the body can be determined

Conclusion 1. Low molecular weight drugs have high Vd 2. Pharmakokinetics is the study of rates of absorbtion, distribution, metabolism and excretion of drug. 3. We use different compartmental models to explain these parameters 4. Apparent volume of distribution is thus explained using Compartment models 5. It is the volume that would be required to contain all drug in the body if it was distributed at concentration measured in the plasma.

REFERENCES       

Essentials of Medical Pharmacology, 7th Ed. KDT Textbook of Biopharmaceutics and Pharmacokinetics 1st Ed. Subramnayam https://derangedphysiology.com/main/cicm-primary-exam/requiredreading/pharmacokinetics/Chapter%202.0.2/volume-distribution https://synapse.koreamed.org/Synapse/Data/PDFData/1179TCP/tcp-24-74.pdf https://www.nottingham.ac.uk/nmp/sonet/rlos/bioproc/halflife/index.html https://www.news-medical.net/health/What-is-the-Half-Life-of-a-Drug.aspx Applied biopharmaceutics and pharmacokinetics by shargel and Yu,s seven edition