Introduction

Good agreement between theoretical and experimental dissolution profiles were found when furosemide powders were dispersed by ultrasonication in a surfactant solutionfor all but the smallest of three batches of powder. The mean particle sizesfor the batches were 3, 10, and 19 mm when particle size was measured after sonication. Without sonication, the particle sizes were measured to be 108,38, and 27mm corresponding to the post sonicated measurements of 3, 10,and 19 mm, respectively. The relative order of the dissolution rates were also reversed before and after dispersion, indicating that comparing theoretical profiles with actual profiles would reveal the problem with agglomeration. For the smallest particle size batch of furosemide that did not agree well with the theoretically calculated dissolution rate, the drug particles were observed to agglomerate during dissolution, which would explain why the actual dis-solution rate was slower than predicted by the applications of trying to predict dissolution based on the Whitney theory, solubility, and drug particle size is to identify potential formulation problems, such as wetting and slow disintegration. This is accomplished by comparing the predicted dissolution profile with the actual profile of the formulation. If the actual dissolution profile of the dosage form is similar to that predicted by theory, one could reasonably conclude that the formulation was disintegrating rapidly and that the surface area of the released drug particles were well wetted. However, dissolution slower than predicted should be investigated to determine the cause. To this end, drug powder dissolution in the absence of excipients but with the judicial use of surfactants and agitation to promote wetting but not to increase solubility or reduce particle size can help establish problems with agglomeration and poor wetting. Dissolution profiles faster than expected might indicate a change in drug form, resulting in a higher solubility or an increase in drug surface area, either of which might occur due to formulation processing. The approach of using the dissolution theory described earlier to evaluatethe dispersion process for furosemide has been reported (20). Good agreementbetween theoretical and experimental dissolution profiles were found whenfurosemide powders were dispersed by ultrasonication in a surfactant solutionfor all but the smallest of three batches of powder. The mean particle sizesfor the batches were 3, 10, and 19 mm when particle size was measured aftersonication. Without sonication, the particle sizes were measured to be 108,38, and 27 mm corresponding to the post-sonicated measurements of 3, 10,and 19 mm, respectively. The relative order of the dissolution rates were alsoreversed before and after dispersion, indicating that comparing theoretical pro-files with actual profiles would reveal the problem with agglomeration. For thesmallest particle size batch of furosemide that did not agree well with thetheoretically calculated dissolution rate, the drug particles were observed to agglomerate during dissolution, which would explain why the actual dissolution rate was slower than predicted by theoryOne of the applications of trying to predict dissolution based on the Whitney theory, solubility, and drug particle size is to identify potential formulation problems, such as wetting and slow disintegration. This is accomplished by comparing the predicted dissolution profile with the actual profile of the formulation. If the actual dissolution profile of the dosage form is similar to that predicted by theory, one could reasonably conclude that the formulation was disintegrating rapidly and that the surface area of the released drug particles were well wetted. However, dissolution slower than predicted should be investigated to determine the cause. To this end, drug powder dissolution in the absence of excipients but with the judicial use of surfactants and agitation to promote wetting but not to increase solubility or reduce particle size can help establish problems with agglomeration and poor wetting. Dissolution profiles faster than expected might indicate a change in drug form, resulting in a higher solubility or an increase in drug surface area, either of which might occur due to formulation processing. The approach of using the dissolution theory described earlier to evaluatethe dispersion process for furosemide has been reported. Good agreement between theoretical and experimental dissolution profiles were found whenfurosemide powders were dispersed by ultrasonication in a surfactant solution for all but the smallest of three batches of powder. The mean particle sizesfor the batches were 3, 10, and 19 mm when particle size was measured aftersonication. Without sonication, the particle sizes were measured to be 108,38, and 27 mm corresponding to the post sonicated measurements of 3, 10,and 19 mm, respectively. The relative order of the dissolution rates were alsoreversed before and after dispersion, indicating that comparing theoretical profiles with actual profiles would reveal the problem with agglomeration. For the smallest particle size batch of furosemide that did not agree well with the theoretically calculated dissolution rate, the drug particles were observed to agglomerate during dissolution, which would explain why the actual dissolution rate was slower than predicted by theory Disintegration, wetting, and agglomeration should be understood and addressed by the formulator. If not, more variability in the in vitro/in vivo correlation is likely to result if a patient were to ingest something that might increase the wetting of a drug product that does not provide a surfactant itself. This would be analogous to adding a surfactant to the dissolution mediainstead of the formulation to achieve a desired dissolution profile. Again,theory can help the formulator identify potential dissolution problems. The ability of the theory presented herein to simulate a polydisperse powder under nonsink conditions, which has been shown in studies that carefully address wetting and dispersion, challenges the conventional wisdom of conducting dissolution under sink conditions. The following example will be based on the physical properties of digoxin, whose bioavailability has been shown clinically tobe dependent on its particle size (21). This dependency requires that drug particlesize be controlled so that dissolution and bioavailability is consistent from batch to batch of drug product. The question is whether to test dissolution under sink or non sink conditions. Hypothetically, let it be assumed that the drug particle size specificationcalls for the drug powder to have a geometric mean particle size of 10 mm and ageometric standard deviation of 2. Figure 3 compares the simulated dissolution profiles of a 1 mg dose of drug that has a solubility of 0.05 mg/mL, similar indose and solubility to digoxin. Profiles compare the simulated dissolution of a1 mg dose in 900 or 90 mL of water for drug powders with geometric meanparticle sizes of 10 and 20 mm, both with geometric standard deviations of2. In Figure 3, dissolution is expressed as mass dissolved as a function of timewith total dissolution occurring at the dose of 1 mg. The higher and lowersolid line profiles represent the dissolution of 10 and 20 mm powders, respectively, dissolving in 900 mL. The higher and lower dash line profiles representthe dissolution of 10 and 20 mm powders, respectively, dissolving in 90 mL.

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Dissolution as Discussed

Table 3 shows how dissolution occurs as discussed earlier. For simplicity, the example of a polydisperse powder in Table 3 is made up of only three monodisperse fractions. In practice, more fractions would be needed to describe a more typical milled polydisperse drug powder. The simulation was done for 100 mg of drug with a solubility of 0.1 mg/mL dissolving in 1000 mL of water. With these par- ameters, the concentration of drug would be at the solubility when complete dissol- ution is reached. As can be seen in Table 3, the 100 mg of powder has an initial geometric mean of 25 mm containing most of the mass with smaller but equal amounts of mass at 6.25 and 100 mm. However, the 6.25 mm particle size fraction has the greatest number of particles and the most surface area per unit weight. In less than five minutes, the 6.25 mm particle size fraction has completely dissolved. The 25 mmparticle size fraction took slightly more than two hours to dissolve, with the size, mass, and surface area decreasing proportionately as determined by geo- metry and density. Only the number of particles remained constant until dissolution was complete. The largest particle size fraction starting at 100 mm dissolved the slowest because it had the smallest surface area and also because the two smallerparticle size fractions have dissolved more quickly, thereby reducing the concen-tration gradient environment for the remaining large particles. Even after 24hours, the largest particle size fraction did not completely dissolve.Evidence that dissolution occurs as described earlier can also be seen in theshape of actual dissolution data from a polydisperse powder. Figure 2 shows thepowder dissolution of hydrocortisone (17). Experimental measurement of theoriginal powder showed it had a geometric mean particle size of approximately36 microns with a geometric standard deviation of 2.4. Two simulations basedon the Noyes–Whitney theory are also shown. For one simulation, the powderwas treated as a polydisperse powder using 16 monosized fractions to describe it.The mass and size of drug particles in each fraction were calculated based on theexperimental data and the log-normal distribution function. For the other simu-lation, the powder was treated as a monodisperse powder with a size equivalentto the measured mean of 36 microns. The polydisperse simulation fitted the datamuch better than the monodisperse simulation as determined by the sumof residualssquared. Compared to the monodisperse simulation, the actual powder dissolvedmore quickly initially due to the presence of smaller particles with greater surfacearea, and slower later on, due to the presence of larger particles with lesssurface area. These phenomena, faster initial dissolution rate and slower final, aresimulated better by modeling the drug as a polydisperse powder. Excellent agree-ment has also been reported between observed and simulated dissolution data forcilostazol at each of three median particle diameters of 13, 2.4, and 0.22 mmwhen modeled as polydisperse particles versus monodisperse (19).Under certain special conditions, the described treatment of polydispersepowder dissolution would indicate that the mean particle size could increase; notbecause any particles were increasing in size, but because the smaller particles dis-solve first, skewing the particle size distribution toward larger particles. As can beseen in Table 3, the initial geometric mean particle size was 25 microns. However,at 24 hours, all particles in fractions 1 and 2 have completely dissolved, leavingonly particles in fraction 3. At that time, the particles in fraction 3 have gonefrom an initial value of 100 to 78.6 microns, leaving a mean particle size of 78.6microns that is greater than the initial geometric mean of 25 microns.

Value for XdT

Value for XdT is used for each particle size fraction. In summary, simulation of the dissolution of a polydisperse powder is accomplished by treating it as a collection of monosized fractions. At time zero, dissolution is the fastest because there is the most surface area and the con- centration gradient is the greatest. Using the Runge–Kutta numerical method and Equations 21 and 22, the amount of drug that has dissolved from each particle size fraction is calculated, and after each step of the simulation, Equations 23 and 24 are used to sum up all the contributions from each particle size fraction. The total amount of dissolved drug from all fractions is then used during the next step of the numerical method so that each particle size fraction is dissolving against the same concentration gradient. Dissolution slows with time because the surface area and concentration gradient are getting smaller. Typically, milled drug powders are distributed lognormally by mass about some geometric mean particle size. This means that one can find a collection of particles of similar size that are smaller than the mean particle size and another collection of particles of similar size that are larger than the mean particle size, both collections of which are roughly equivalent in mass. However, since both collections are approximately equal in mass, the collection of smaller particles is made up of more particles and represents more surface area than the larger col- lection. As a result, the collection of smaller particles will dissolve faster and completely dissolve before the larger collection. Both the number and particle size distribution will change during the dissolution of a polydisperse powder, whereas only the particle size would change within each monosized fraction until complete dissolution was reached. At that point, the number within the frac- tion would become zero. It is uncertain at what particle size one would be able to say that a particle is no longer a solid and that complete dissolution had occurred. However, particles calculated in the size range of molecular dimensions could probably be con- sidered as completely dissolved. In computer simulation, without some statement as to when solid particles are completely dissolved, the calculated particle size will continue to decrease until the lower numerical limit of the computer system is reached. In agreement with the model described earlier for a polydis- perse powder, it has been shown that during dissolution, the number of particles in a smaller particle size fraction decreased more rapidly relative to larger particle size fractions.

Mass of Solid Drug

Xs is the mass of solid drug remaining at any time t, D is the drug diffusion coefficient, S is the drug surface area, h is the hydrodynamic diffusion layer thick- ness, Cs is the drug solubility, Xd is the mass of dissolved drug at any time t, and V is the volume of fluid in which the drug is dissolving. In trying to solve the earlier equation, it should be noted that the drug surface area would not remain constant as drug dissolves after being released from typical dosage forms. The amount of dissolved drug would also not be constant. As a result, the rate of dissolution is continually changing. Dissolution testing is typi- cally done under sink conditions; therefore, the Xd/V term is small compared to Cs so that former can be ignored. However, in trying to establish a mechanistically based in vitro/in vivo correlation, the assumption that sink conditions would exist in the GI tract is an especially bad one for poorly soluble drugs. Also, as will be shown, testing dissolution under sink conditions is not necessary and can make instrumental analysis of dissolution more difficult. What is required is a numerical solution of the Noyes–Whitney equation to make the application of the theory as general as possible by eliminating the need to make frequently bad assumptions in order to solve the equation analytically. The following approach has been previously described (15,16). If one assumes that a drug particle has certain geometry, then surface area can be expressed in terms of drug mass if the drug density is known. The simplest geometry to use is spherical, although other geometries could be used. However, for the following derivations, spherical geometry will be assumed. The surface area at any given time can then be expressed by the following. where rt is the drug particle radius at any time t, and N0 is the number of drug par- ticles present initially. It will be shown later how one could handle a polydisperse drug powder, but for now, it will be assumed that all drug particles are exactly the same size and that they will all dissolve at the same rate. If this were the case, then the number of drug particles would not change with time until they completely dissolved at which time the number of particles would be zero. The number of drug particles present initially can be calculated by dividing the initial mass of drug or dose by the mass of one drug particle. Figure 1 shows the numerical calculation of XS and Xd with time based on Equations 19 and 20, respectively. Because the simulation is for a closed system, the two curves representing XS and Xd are symmetric. This would not be the case if one were to simulate drug dissolving in the GI tract while drug absorp- tion was occurring. Equations 19 and 20 are only able to handle a single particle size. To expand the application to polydisperse powders, it will be assumed that a poly- disperse powder can be simulated as a collection of monodisperse powder In solving these equations numerically using the Runge–Kutta method, the values of XSi and Xdi are calculated at each step of the numerical method, the size of which can be selected as a trade-off between accuracy favored by smaller step sizes versus speed of calculation for larger step sizes. A typical step size would be approximately one second. After each step, the amount of solid and dissolved drug from each particle size fraction i would be totaled as follows.

Sophisticated Models

The MAD analysis is mathematically simple, which is part of its appeal. However, more sophisticated models involve differential equations that do not necessarily have analytical solutions and, therefore, need to be solved numeri- cally. The mathematical model to be presented as follows has the ability to simu- late the kinetics of a polydisperse crystalline powder. This has wide applicability In Vitro Release and Biopharmaceutics Classification 9 because of the prevalence of immediate-release dosage forms containing drug as a crystalline powder. One of the assumptions of the model is that the crystalline drug particles are completely wetted and dispersed initially. The model does not describe the kinetics of wetting. However, by comparing theoretical simulations of the dissol- ution rate with actual dissolution from the dosage form, one can gain insight into the extent that wetting is slowing the rate of dissolution. Validating and refining the model requires powder dissolution data that is independent of the effects of dispersion and wetting since this is an assumption of the model. This may require developing an experimental technique that uses a surfactant at a concentration that will not enhance solubility but will improve wetting. The technique may also require a brief period of vigorous mixing to achieve dispersion and wetting. High-quality data is required to validate dissol- ution theory as well as gain insight into some of the more elusive aspects such as how to handle hydrodynamics. One of the goals of this chapter is to convince the reader that dissolution can be explained and predicted based on theory and that this is worthwhile in terms of shortening the time it takes to develop drug products. Perhaps the most dramatic way would be to show that, based on the solubility and permeability of a drug candidate, inherent absorption would never be good enough to allow the drug to become a product. Knowing this, project teams could decide whether to drop drug candidates and pursue others, or to commit resources in an attempt to over- come the solubility issue and accept the higher development cost and risk of failure in doing so. For the formulator, however, not knowing the effect of particle size on dissolution rate and absorption or whether poor disintegration or wetting is affecting the dissolution rate can lead to costly delays in development that could require the need to repeat toxicological and clinical studies. Although the Biopharmaceutics Classification System (BCS) (13), discussed later, and MAD analysis are useful and attractive because of their simplicity, both are limited in terms of guidance that might be extracted from solubility, per- meability, dissolution, and other pharmacokinetic data. Neither can describe the kinetics of absorption leading to insight into the effects of drug particle size and hydrodynamic conditions that would lead to a mechanistically based in vitro/in vivo correlation. They would also not allow one to make a rational estimation as to when dissolution samples should be taken and whether the dissolution test would be discriminating to significant differences in dosage forms. To do this, a more sophisticated model is needed such as the one described subsequently. The dissolution rate of crystalline drug is proportional to its solubility, surface area, and diffusion coefficient. It is also dependent on the hydrodynamic conditions, but in a less well understood way. These relationships can be summar- ized in a Noyes–Whitney (14) type equation.

MAD Analysis Results

Although the MAD analysis provides a simple and valuable approach to under- stand and act on solubility and permeability data, much more can be done with regard to modeling dissolution and absorption, and at the same time, incorporat- ing pharmacokinetic concepts, such as metabolism, excretion, and distribution of drug in and out of tissues. By taking a more comprehensive approach to modeling the whole process, commonly referred to absorption, distribution, metabolism, and excretion (ADME), dissolution can be correlated to blood plasma concen- trations and, therefore, Cmax and area under concentration time curve (AUC). In developing an in vitro/in vivo correlation, a mechanistically based approach will be described. This approach is distinct from perhaps the more common and traditional empirical approach. With the empirical approach, dosage forms are made with varying dissolution rates, the resulting dosage forms are dosed in the clinic to determine plasma concentrations, and finally, the plasma concentrations are correlated with the dissolution rates. This approach does not require a mechanistic explanation of the result. Its limitation is that it does not provide a mechanistic framework to predicting outcomes across chemical structures and, therefore, may not be applicable to the development of future drugs. The goal of the mechanistic approach is to predict the outcome before doing the experiment through a fundamental understanding of the dynamics of dissolution, ADME. It is not suggested that the mechanistic approach will eliminate the need to do empirical experiments or eliminate the need to validate predicted outcomes through experimentation. However, as the science progresses, it is certainly a goal of the industry to predict outcomes to increase its success rate by eliminating ill conceived clinical studies, and a fundamental understanding of the ADME processes hold promise to this end. Predicting dissolution falls under the realm of the formulation scientist, whereas methods to predict drug metabolism, toxicity, and efficacy generally do not. However, incorporating key aspects from all disciplines into the decision of what makes a successful drug product is likely to increase the quality of drug candidates. Here again, a mechanistically based approach holds the promise of wider applicability across diverse chemical structures and therapeutic areas. Mathematical models help bring the important parameters from each discipline together in a way so that more rational decisions can be made. As stated before, solubility and permeability are key parameters for the physical scientist working on dosage form development. Scientists involved in drug metabolism typically contribute estimates of drug clearance rates and volumes of distribution. Combining these two disciplines allows the prediction of drug plasma concen- trations and whether or not the dose–exposure relationship will be linear or not. Although it is beyond the scope of this chapter, toxicologists and biological and clinical scientists can then review the predictions to see if projected plasma concentrations meet the needs for toxicological and clinical evaluation. This would ideally occur in project team meetings with representatives present from all disciplines.

MAD Calculations

Table 1 shows MAD calculations for several marketed drugs. An attempt was made to find literature values for solubility in the pH range of 6 to 7 to reflect conditions in the small intestine. Only one significant figure is shown for solubility, absorption rate constant, and MAD values due to the large degree of uncertainty associated with trying to assign numbers to parameters in an in vivo situation. Typical doses can also vary due to the size, age, sex, and genetics of the patient. However, inspection of Table 1 shows that for drugs that made it into the market as conventional products, namely atenolol, digoxin, furosemide, naproxen, and propranolol, the typical dose is below the MAD number that would be calculated based on the solubility of the drug at pH values expected to be found in the small intestine. For cyclosporine and griseofulvin, the dose is greater than the MAD number, and it is generally known among formulation scientists that extensive work has been carried out on the development of dosage forms to improve the absorption of cyclosporin and griseofulvin. The absorption rate constant for griseofulvin was assumed to be at the high end of the range. Even so, the MAD number is less than the dose. This demonstrates that, in some cases, only solubility needs to be measured to determine a likely problem with absorption. Both nifedipine and carbamazepine are borderline cases where the doses of the immediate-release dosage form are similar to the MAD. However, based on the commercially available dosage forms, the need for solubility-enhancing formulations to improve the bioavailability for nifedipine or carbamazepine does not appear as critical as for cyclosporine and griseofulvin. The intent of the MAD analysis summarized in Table 1 is to demonstrate that the degree of dif- ficulty in developing a commercial dosage form with regard to absorption can be estimated in a relatively straightforward manner. Inspection of Table 1 indicates that although atenolol has the lowest absorption rate constant, it has a high MAD number. Table 2 shows the predicted percent of dose absorbed for solution doses for various values for the absorption rate constant. For a drug with a low absorption rate constant like atenolol, nothing can be done to improve the percent of dose absorbed without altering the charac- teristics of the intestinal membrane. However, as long as solubility does not prevent the entire dose from dissolving, increasing the dose will continue to increase the absolute amount of drug absorbed, even while the percent of dose absorbed remains the same. While some may view incomplete absorption due to low permeability unfavorably, it does not present an obstacle to increasing absorption as long as solubility does not limit absorption.

Benchmark Calculation

This provides a useful benchmark calculation that includes the key parameters that are generally recognized as limiting absorption: solubility in the GI tract and the intrinsic absorption rate constant specific to drug in solution. Other attractive features of the MAD number are that it is expressed in units of mass, facilitating communication among scientists with diverse backgrounds involved in pharmaceutical research, and the MAD number is dose-independent. This is particularly useful in early drug discovery and development because the clinical dose is unknown. The simplicity and pertinence of the MAD analysis in the drug discovery/early development phase has lead to its growing acceptance (12). The other key parameter for absorption is solubility. Given everything else the same, dissolution rate will increase with solubility. Given two drugs with the same absorption rate constant, the one with the greater solubility will have a greater MAD. In measuring solubility, using a fluid that is closer to real GI fluid rather than plain water is likely to give a more accurate prediction of the MAD. Likewise, using a dissolution media that more closely mimics GI fluid is more likely to result in a meaningful in vitro/in vivo correlation between dis- solution and absorption. TheMAD number is intended to give a “ballpark” estimate of how much drug one might expect to be absorbed if a plug of fluid with a volume expected to be found in the GI tract were to be saturated with drug, and that the drug in solution could exit the plug at a rate determined by the absorption rate constant for a period of time that the plug would typically reside in the small intestine. The typical fluid volume and GI residence time could evolve, as experience and data become available, but, for example, let them be 250 mL and three hours, respectively. In general, if the pro- jected clinical dose were below the MAD number, then drug absorption should not be a limiting factor in determining clinical efficacy. However, if the projected clinical dose were above the MAD number, limited absorption would be likely. The same could be said for projected doses for toxicological studies, and the volume and residence time could be scaled to a particular animal. The MAD number could also be used in early drug discovery to rank order candidates with regard to their ease of development. Given similar potency, a compound with a larger MAD number would have a greater dose/exposure range in which to establish safety and efficacy. Toxicity and clinical studies that show a plateau in exposure as a function of dose can be used to validate the predictive value of the MAD number.

Crystalline Powder

In reality, most dosage forms are tablets containing a crystalline powder of the drug substance. Unlike a solution dose, the amount of drug dissolved in the intestine will increase with time, as the dosage form disintegrates and releases crystalline drug particles. There are no simple pharmacokinetic equations to describe this process. Solution dosage forms of the same drug are unlikely to show differences in the rate and extent of absorption and, therefore, are likely to be bioequivalent. Solution dosage forms will present the total dose in the form of drug that can be absorbed (in solution) with the amount of drug in the lumen falling exponentially, as drug is absorbed at the same rate. However, immediate-release solid dosage forms are likely to have slightly different rates of disintegration due to the choice of tablet excipients and the manufacturing process and potentially larger differences in dissolution rate depending on the drug particle size and the efficiency of wetting provided by the formulation. There is a mechanistically based theory to describe the kinetics of dissolution that will be discussed, and it will be shown how dissolution theory can be used to determine if the combined effect of disintegration and wetting are having a significant impact on drug absorption. Before getting into the more sophisticated treatment of dissolution, the absorption rate equation discussed earlier provides the starting point for a very simple and useful analysis of situations that might present difficulties in drug absorption. Recalling Equation, the integration of this equation over a specified period of time gives the mass of drug absorbed from the GI tract. If nothing limited the amount of drug that could be administered as a solution to the GI tract, then there would be no limit to the amount of drug that could be absorbed. However, drug solubility presents a limit to the amount of drug that can exist as a solution in the GI tract. Any solid crystalline drug administered would continue to dissolve unless its concentration equaled its solubility. At this point, no further drug would dissolve until some of the drug in solution was absorbed. If enough solid drugs were administered so that the rate of dissolution was equal to the rate of absorption, a temporary steady state would exist where the concentration of drug in the GI tract would It can be seen that if enough solid crystalline drug is given so that the rate of dissolution can match the rate of absorption to keep the concentration of drug in the GI tract at its solubility, the rate of absorption becomes constant. If equation is integrated over the typical residence time, that drug would remain in the small intestine tr, with this integration called the maximum absorbable dose (MAD) (11), a simple calculation is the result.

Characterize Permeability

There are several techniques to characterize permeability before going into human clinical studies, including rat intestinal perfusions, Caco-2 permeability (1), and parallel artificial membrane permeability assay (PAMPA) (2). However, one should be careful in considering whether the values are useful inan absolute sense or only in a relative sense. Clinically determined human absorption rate constants serve as a good reality check for comparison. There are a largenumber of clinical studies that have been done, which include some estimate ofthe absorption rate constant (3). The upper end of the range appears to be in theneighborhood of 0.1 min21, placing the shortest absorption half-life around sevenminutes. Although there might be reports of individual patients having highervalues, it would be rare that population averages exceed this value. Typically,if an intravenous dosing leg of a clinical study has been done in addition to anoral leg, then an observed absorption rate constant can be determined aftercorrecting for bioavailability. As a word of caution, some reported absorptionrate constants might be smaller than the true intrinsic absorption rate constantsdue to the influence of dosage form disintegration and drug dissolution. Correctingobserved absorption rate constants for the effect of dissolution was part of themotivation for the author of this chapter in developing more sophisticated dissolution models so that surrogate methods could be validated against a moreaccurate data base of clinically determined absorption rate constants.As mentioned earlier, one of the most direct methods for evaluatingpermeability is the isolated perfusion of the human intestine. Becausesome of this data will be used in this chapter, it is worthwhile to compare thismethod and its results with the traditional way of determining the absorptionrate constant from pharmacokinetic data.Given an estimated radius of the human small intestine of 1.75 cm, the surfaceto volume ratio is approximately 1.1. Permeability is typically in units of cm/sec,whereas absorption rate constants are generally reported in units of reciprocalminutes or hours. Permeability can be easily converted to an absorption rateconstant by multiplying its value by the surface to volume ratio and convertingto desired units of time. Using propranolol as an example, its human intestinalpermeability was reported as 3.8781024 cm/sec. This calculated absorption rate constant using permeability from human intestinal perfusion experiments compares well with the value of 0.025 min21 reported independently from a pharmacokinetic study.It should also be noted that the absorption rate constant as presented earlierhas only been shown in one direction: from the lumen to the blood. In general,drugs with solubilities in the mg/mL range will exist in the mg/mL range inthe GI tract. Blood concentrations are generally in the mg/mL range. Therefore,the reverse absorption rate constant would have to be approximately 1000-foldhigher to be significant. If the drug is poorly soluble, in the mg/mL range,blood concentrations are likely to be in the ng/mL range. Again, the reverserate would have to be 1000-fold higher to be comparable to the forward rate.For the remainder of this chapter, the reverse rate will be ignored while acknowledging that this assumption is open to debate.

ABSORPTION

Absorption is important to discuss with regard to dissolution because in vivo, dissolution occurs in a permeable GI tract, whereas dissolution testing is usually done in an impermeable glass vessel. Characterizing absorption using parameters such as an absorption rate constant or permeability provide an essential link between dissolution and what happens to the drug once it has been absorbed, and necessary to establish a predictable in vitro/in vivo correlation. Absorption is an area of common interest to both formulation and pharmacokinetic scientists because it affects the decisions that both groups make. In Equations 2 and 3, drug absorption was characterized as drug leaving the GI lumen. This is a common way to study absorption. For example, both rat and human intestinal perfusion experiments have been used to characterize absorption by isolating a segment of the intestine and using the difference in drug concentration entering and leaving the segment to calculate an absorption rate constant or permeability. When done properly to ensure that drug degradation or water absorption and secretion are not affecting the results, characterizing absorption in this way is a reliable method. Another method to study absorption would be to use drug blood concentrations after intravenous and oral dosing to calculate an absorption rate constant. This method is more complicated because metabolism must be taken into account. For example, it would be possible for a drug to be completely absorbedacross the GI membrane, but entirely metabolized by the liver before reaching thesystemic circulation. Unless all drug metabolites were traced, one might erroneously assume that because the drug itself was not detected in the blood, thatabsorption had not occurred. This situation is important to recognize so that aformulation group does not waste time attempting to improve absorption whenmetabolism is the real problem.Throughout this chapter, both the term absorption rate constant andpermeability will be used interchangeably. The term permeability has the advantage that it is shorter and perhaps more descriptive. Both absorption rate constantsand permeability are not like other physical parameters that might be found in thescientific literature. Their values have a rather large degree of error typical of pharmacokinetic parameters and may vary in the GI tract due to positionalchanges in anatomy and environmental conditions. The term absorption rateconstant has been criticized because the name implies something that it is not.However, in practice, permeability is also usually treated as if it were a constant.The absorption rate constant has the advantage of having the characteristics of afirst-order rate constant. Given its value, one can quickly take the natural logarithm of two and divide it by the absorption rate constant to calculate an absorptionhalf-life. In effect, permeability is usually converted to a first-order rate constant for calculations that require the calculation of mass of drug absorbed.