Volume of distribution calculation

By definition, the systemic clearance of a drug is the product of the apparent volume of distribution, calculated by the area method, and the overall elimination rate constant ... 

In Eq. 13.30, evaluation of the expression Ki2+K2i)/a results in a number less than 1. Thus, volume of distribution at steady state is less than the apparent volume of distribution of drug in the body (l ss < Vi,)- This means that the volume of distribution at steady state (after elimination equilibrium has been established) has actually contracted in size when compared with the apparent volume of distribution of drug in the body, a volume of distribution calculated at an earlier time when distribution equilibrium had been reached. 

Tissue binding and drug distribution. Before examining the effect of tissue binding on the distribution of a drug, it is necessary to introduce the concept of apparent volume of distribution, calculated from the following expression. 

Lobell M and Sivarajah V. In silico prediction of aqueous solubility, human plasma protein binding and volume of distribution of compounds from calculated pKa and AlogP98 values. Mol Divers 2003 7 69-87. 

The area under the PCP concentration-time curve (AUC) from the time of antibody administration to the last measured concentration (Cn) was determined by the trapezoidal rule. The remaining area from Cn to time infinity was calculated by dividing Cn by the terminal elimination rate constant. By using dose, AUC, and the terminal elimination rate constant, we were able to calculate the terminal elimination half-life, systemic clearance, and the volume of distribution. Renal clearance was determined from the total amount of PCP appearing in the urine, divided by AUC. Unbound clearances were calculated based on unbound concentrations of PCP. The control values are from studies performed in our laboratory on dogs administered similar radioactive doses (i.e., 2.4 to 6.5 pg of PCP) (Woodworth et al., in press). Only one of the dogs (dog C) was used in both studies. 

A discussion of all the reasons for this phenomenon is beyond the scope of this chapter, but a simple example will illustrate the concept. Highly lipid-soluble drugs, such as pentobarbital, are preferentially distributed into adipose tissue. The result is that plasma concentrations are extremely low after distribution is complete. When the apparent volumes of distribution are calculated, they are frequently found to exceed total body volume, occasionally by a factor of 2 or more. This would be impossible if the concentration in the entire body compartment were equal to the plasma concentration. Thus, Vd is an empirically fabricated number relating the... 

Example. The biological half-life of procaine in a patient was 35 minutes, and its volume of distribution was estimated to be 58 L. Calculate the TCR of procaine. 

Example. Sulfadiazine in a normal volunteer had a biological half-life of 16 hours and a volume of distribution of 20 L. Sixty percent of the dose was recovered as unchanged drug in urine. Calculate TCR, RCR, and MCR for sulfadiazine in this person. 

A is a function of the two rate constants (ka and kei), the apparent volume of distribution (Vd), and the amount of drug absorbed (Dg). After ka and kei have been evaluated and A has been determined by extrapolation, a value for Vd can be calculated if it is assumed that Dg is equal to the dose administered, i.e., absorption is 100% complete. 

The volume of distribution is expressed as a fraction of the body weight, and the spreadsheet calculates Vd in liters using the subject weight in kilograms. 

Studies interested in the determination of macro pharmacokinetic parameters, such as total body clearance or the apparent volume of distribution, can be readily calculated from polyexponential equations such as Eq. (9) without assignment of a specific model structure. Parameters (i.e., Ah Xt) associated with such an equation are initially estimated by the method of residuals followed by nonlinear least squares regression analyses [30],... 

Methods for calculating volume of distribution (VD) can be influenced by renal disease. Of the commonly used terms (i.e., volumes of central compartment, terminal phase, and distribution at steady state [ Vss]), Vss is the most appropriate for comparing patients with renal insufficiency versus those with normal renal function because Vss is independent of drug elimination. 

The most important VD value for dictating the dosing regimen is the steady-state volume of distribution (VDSS). This volume represents the extent of distribution when the rate of transit to and from the tissues is equal. It is more representative of a time-averaged volume of distribution and its value will reside somewhere in between VDC and VDp. The steady-state VD is calculated from the mean-residence time (MRT). 

A recent variation on the prediction of human VD using allometric scaling involves the use of what has been termed "fractal volume of distribution (vf) [7], This refers to the VD value corrected to within the bounds of actual volumes within the body - in the case of human the upper and lower bounds would be 70 1 and plasma volume, respectively. Thus, even if a compound were to have a VDSS of 1000 1, its Vf would be 69.8 1. The authors of this approach have shown that Vf scales allometrically across species better than VD [8], with the explanation that body volume and body mass are exactly scaleable across species. Animal values for Vf are calculated from VD obtained from pharmacokinetic studies using the relationship ... 

Ideal for studying the dose-response relationship for QT interval prolongation taking into account all the pharmacological properties of a compound The dog model is one of the most widely used anesthetized rabbits (especially female rabbits) have also been proposed for high sensitivity It provides complementary information with respect to in vitro tests (activity of metabolites, measurement of plasma drug concentrations, calculation of the volume of distribution) Possibility to induce experimental TdP... 

The plasma concentration at when divided by the dose gives an estimate of distribution volume that can be used to calculate dosing for fast equilibrating drug, in particular, such as anesthetics. This distribution volume term often proves more useful than the traditional central volume of distribution or the steady-state distribution volume. 

Figure 2.4. In vivo measurement of blood-brain barrier (BBB) permeability, (a) Internal carotid artery perfusion technique (i) in the rat. Other branches of the carotid artery are ligated or electrically coagulated (o, occipital artery p, pterygopalatine artery). The external carotid artery (e) is cannulated and the common carotid artery (c) ligated. Perfusion time may range from 15 s to 10 min, depending on the test substance. It is necessary to subtract the intravascular volume, Vo, from (apparent volume of distribution), to obtain true uptake values and this may be achieved by inclusion of a vascular marker in the perfusate, for example labelled albumin. Time-dependent analysis of results in estimates of the unidirectional brain influx constant Ki (pi min which is equivalent within certain constraints to the PS product. BBB permeability surface area product PS can be calculated from the increase in the apparent volume of distribution Vd over time. Capillary depletion, i.e. separation of the vascular elements from the homogenate by density centrifugation, can discriminate capillary uptake from transcytosis. (b) i.v. bolus kinetics. The PS product is calculated from the brain concentration at the sampling time, T, and the area under the plasma concentration-time curve, AUC.

An extensive retrospective analysis [11] examined various scahng approaches to the prediction of clinical pharmacokinetic parameters. In this analysis the most successful predictions of volume of distribution were achieved by calculating unbound fraction in tissues (/(,) of animals and assuming this would be similar in man. Volume of distribution was then calculated using measured plasma protein binding values and standard values for physiological parameters such as extracellular fluid and plasma volumes. The equation used was as follows ... 

The concentration (c) of a solution corresponds to the amount (D) of substance dissolved in a volume (V) thus, c = D/V. If the dose of drug (D) and its plasma concentration (c) are known, a volume of distribution (V) can be calculated from V = D/c. However, this represents an apparent volume of distribution (Vapp), because an even distribution in the body is assumed in its calculation. Homogeneous distribution will not occur if drugs are bound to cell membranes (5) or to membranes of intracellular organelles (6) or are stored within the latter (7). In these cases, Vapp can exceed the actual size of the available fluid volume. The significance of Vapp as a pharmacokinetic parameter is discussed on p. 44. 

The pharmacokinetic information that can be obtained from the first study in man is dependent on the route of administration. When a drug is given intravenously, its bioavailabihty is 100%, and clearance and volume of distribution can be obtained in addition to half-life. Over a range of doses it can be established whether the area under the plasma concentration-time curve (AUC) increases in proportion to the dose and hence whether the kinetic parameters are independent of dose (see Figure 4.1). When a drug is administered orally, the half-life can still be determined, but only the apparent volume of distribution and clearance can be calculated because bioavailability is unknown. However, if the maximum concentration (Cmax) and AUC increase proportionately with dose, and the half-life is constant, it can usually be assumed that clearance is independent of dose. If, on the other hand, the AUC does not increase in proportion to the dose, this could be the result of a change in bioavailability, clearance or both. 

The units of volume of distribution are those of volume (i.e. litres) and can be adjusted for, say, body weight. The two main uses of volume of distribution are in the calculation of loading doses for rapid onset of drug effect, and in understanding changes in half-life (see below). 

Calculation of bioavailability requires a comparison of the AUcs following a non-intravenous and an intravenous dose, after correction for dose size. Without knowing the bioavaUabU-ity, only apparent clearance and volume of distribution can be calculated, and the ability to make predictions from these values is very limited. 

Distribution - Following IV injection, the calculated volume of distribution (Vdgs)... 

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