PKQuest

Each of the following Sections are relatively self-contained and can be read as independent topics, for example, as a supplement to material in a PK course.  Some of the material is at a general introductory level that should be useful to a student with a limited background, while other material is more advanced and primarily of interest only to research investigators.  In the following, a brief synopsis of each section is presented.

Section 2.  Compartment Modeling:  Clearance and Volume of Distribution.  This provides a general introduction to the use of simple PK compartment modeling.  It begins with an introductory level discussion of material that should be fundamental for anyone studying PK.  This approach is then illustrated by a specific, and clinically important, PKQuest example of using a 2-compartment model to determine the human endogenous albumin synthesis rate and the total amount of albumin in the blood and whole body compartment. This example is highly quantitative and could be skipped by general readers.

Section 3.  Non-compartmental PK:  Steady state clearance (Cl_ss), volume of distribution (V_ss) and bioavailability.   This section describes material that represents the essence of the subject of pharmacokinetics.  The discussion is at a level that is somewhat more quantitative then the typical textbook with a focus on the assumptions required for the validity of the fundamental Cl_ss and V_ss relationships – areas that are skipped in some textbooks.   For example, the V_ss relation is only strictly valid if the blood is sampled from the artery. A rigorous derivation of the Cl_ss and V_ss relations is also provided.  Two examples using PKQuest to determine Cl_ss and V_ss with actual clinical data (albumin and amoxicillin) are discussed.  These examples help to flesh out some of the subtleties and limitations of these relations and should be of value to the beginning student. The PKQuest example files also provide a template that allows the student to easily substitute their own PK data and determine Cl_ss and V_ss. The amoxicillin example uses a PBPK model to estimate the error in the V_ss estimate if the antecubital vein is used as the sample site versus arterial sampling (the theoretically required sample site).  The section concludes with a detailed, step by step exercise for determining the PK of morphine-6-glucuronide.  It emphasizes the practical problems that are presented when using real clinical data that has limited precision.     

Section 4.  Physiologically based pharmacokinetics (PBPK):  Tissue/blood partition coefficient; toxicological and other applications.    This section provides a general introduction to the PBPK modeling approach.  It describes the mathematical blood/tissue exchange model, its assumptions, and how the body tissue organs are combined to produce a complete whole animal model.  It directs special attention to the difficult problem of accurately estimating the tissue/blood partition coefficient (K_B) and how this limits the applicability of the PBPK approach for the great majority of drugs that are weak acids or bases with partition coefficients that cannot be accurately predicted, a priori. There are two drug classes that are exceptions to this rule: the extracellular solutes and the highly lipid soluble solutes. The K_B for these two classes can be predicted a priori and their PBPK analyses are described in separate sections. It provides a brief overview of the PBPK software routines that are available.  This material does not require any special background and it is intended to provide students an introduction to the PBPK modeling approach and its strengths and weaknesses.  These concepts are then illustrated with 4 specific PBPK examples using PKQuest that cover the gamut of experimental situations that students might face:  Example1) PBPK modeling of human thiopental PK, a weak  acid that requires input of previous measurements (rat) of the K_B of each of the PBPK model organs.  Example 2) PBPK model of rat antipyrine PK. Although the focus in this book is on human PK, this example describes the modifications required to apply PKQuest to non-humans.  Example 3)  Describes how the user can model the intestinal input to a PBPK model, in this case, for amoxicillin.  Example 4) Once a PBPK model is developed, one can determine blood concentrations for arbitrary inputs, in this case, oral amoxicillin, 3 times/day.

Section 5. Extracellular Solutes: The pharmacokinetics of the interstitial space.  Because this drug class cannot enter cells, the primary tissue binding that determines the tissue/blood partition coefficient (K_B) is the binding to interstitial and plasma albumin.  Since this can be directly predicted from the known interstitial and plasma albumin concentrations and the drug albumin binding constant (determined from the plasma “free fraction”), its K_B can be accurately predicted.  Thus, the PK of this drug class can be accurately modeled using the PBPK approach with only one or two adjustable parameters. This section begins with a brief review of the PK of extracellular drugs, including a table summarizing the extracellular volume and albumin concentration of the different organs.  It ends with a PKQuest example describing the PBPK modeling of amoxicillin. 

Section 6.  Capillary Permeability Limitation.  This is a specialized topic that is probably not of interest to introductory students.  It focuses on a subject that is almost never discussed in PK textbooks:  the capillary permeability limitation of tissue/blood exchange.  The section begins with a discussion of the highly protein (albumin) bound extracellular solutes and describes why they are permeability limited.  It ends with a PKQuest PBPK example for Dicloxacillin, using human PK data, quantifying the permeability limitation and its clinical importance.

Section 7.  Highly lipid soluble solutes (HLS): Pharmacokinetics of volatile anesthetics, persistent organic pollutants, cannabinoids, etc.   This is the other drug class for which the tissue/blood partition coefficient (K_B) can be predicted from first principles, allowing successful PBPK modeling with a minimum of adjustable parameters.  The K_B of these drugs is dominated by the tissue/blood lipid partition, which can be predicted from measurements of tissue and blood lipid and the drug’s oil/water partition (P_L/W).  The section describes how PKQuest can be used to accurately describe human volatile anesthetics PK, with no adjustable parameters (their clearance can be predicted from alveolar ventilation).  This discussion of how the PK of anesthetics can be predicted just using their water/air, olive oil/air, and blood/air partition coefficients should be of particular interest to students with an interest in these drugs (eg, nurse anesthetists, anesthesiology fellows, etc.).   This PBPK method is both more general and more accurate with fewer adjustable parameters than the compartmental modeling approach that is the standard in the anesthesiology field. Since the PBPK model depends crucially on the value(s) of the adipose blood flow, special attention is devoted to describing how PKQuest was used to determine what is, currently, the best available measurement of the heterogeneity of human adipose blood flow.  The section ends with three PKQuest examples:  Example 1) the short term (3 hours) human PK of isoflurane, sevoflurane and desflurane.  Example 2) the long term (5 days) human PK of  isoflurane, sevoflurane and desflurane. During these long term experimental measurements, the PBPK parameters change as the patients wake up from the anesthesia and become ambulatory, and this section describes how PKQuest can be used to accommodate changing parameters.  Example 3) applies this same model to cannabinol, a non-volatile, highly lipid soluble drug.

Section 8.  Persistent organic pollutants (POP): why are they “persistent”?   The POPs (eg, dioxins, PCBs, DDT) represent a special class of the highly lipid soluble drugs discussed in the previous section.  They are of interest to students in a large range of fields and most of this section is written at a general introductory level. Pharmacokinetic modeling and prediction is especially important for these compounds because experimental human PK measurements are limited because of their long lifetimes (years).  For such an important drug class, there is a surprising lack of coverage in the standard PK textbook and what is available is inaccurate. This section looks in detail at the question of why these POPs have such long lifetimes?  It explains that the usual explanation (high lipid partition) is incorrect and, instead, it results simply from their very low metabolic rates.  There is a detailed PKQuest example illustrating that, as the metabolic rate falls to very low values, the human PK can be accurately described by a simple 1-compartment model characterized just by its volume and clearance and the details of the peripheral PBPK tissue-blood exchange become irrelevant. There is also a PKQuest example that describes in detail the quantitative measurement of the previously unrecognized adipose/blood diffusion limitation that develops for the POPs with very high lipid partition.  This last example is of interest only for a limited set of investigators.

Section 9.  Deconvolution: a powerful, underutilized tool.  Deconvolution is a general PK approach that is discussed only briefly in most PK textbooks. It provides, for most drugs, the best approach for quantitating PK inputs such as the intestinal absorption of oral drugs or from dermal patches.  Most of this section could serve as a stand-alone introduction to this topic.  The most limiting aspect of the subject is that, without the appropriate software, it has no practical value.  PKQuest has been designed to make deconvolution simple and versatile, with 6 different deconvolution routines that can be selected.  The strengths and weaknesses of the different routines are explained and illustrated with three PKQuest examples using clinical human PK data (oral absorption of amoxicillin and nitrendipine and fentanyl absorption from a dermal patch).  It ends with an exercise that takes the student through the individual steps for determining the intestinal absorption of propranolol.

Section 10. Intestinal absorption rate and permeability, the “Averaged Model” and first pass metabolism.   This section describes a specialized application of the deconvolution technique that provides a direct estimate of the human intestinal epithelial permeability of drugs.  It uses a new approach (“Averaged model”) that I recently developed and applied to 90 drugs with a wide range of PK properties.  The first part of this section is focused on the details of the “Averaged model” approach, and could be skipped by most students.  However, the remainder of this section discusses a large range of topics related to intestinal absorption (bioavailability, first pass metabolism, mucosal permeability, dependence on octanol/water partition, caco-2 monolayer measurements, etc.) that would could serve as an in depth introduction to intestinal drug absorption.  It concludes with four PKQuest examples that illustrate different aspects of intestinal absorption:  Example 1)  Propranolol, a drug with a very high first pass metabolism.  Example 2) Acetaminophen, a drug with a very high absorption rate that is limited by luminal unstirred layer diffusion.  Example 3)  Risedronate, a drug with a very low absorption  rate that is limited by the small intestinal transit time.  Example 4) Acetylcysteine, a weak acid that is absorbed only in the proximal small intestine which has relatively acid pH.

Section 11.  Non-linear pharmacokinetics -  Ethanol first pass metabolism.     Although this is a topic that is rarely addressed in PK textbooks, students should be aware of the importance of the standard, and usually unrecognized, assumption that the PK are linear.  This is dramatically illustrated by the set of publications by Lieber and colleagues that they interpreted as indicating that that there was a large first pass gastric ethanol metabolism that was clinically important in determining human blood alcohol levels and was widely covered by the popular press. In fact, as was first pointed out be Levitt and Levitt, gastric ethanol metabolism is negligible and this conclusion is an artifact of erroneously assuming that ethanol PK is linear. The classical PK clearance is not a valid descriptor of the PK if it is non-linear.  PBPK modeling is probably the best approach for handling this situation, allowing direct modeling of the nonlinearity.  This section focuses on the concept of “bioavailability” (the main emphasis of Lieber and colleagues) and illustrates that the usual definition is not applicable to the non-linear situation.  A new and rigorous definition of the non-linear bioavailability has been implemented in PKQuest and applied to oral ethanol. The first part of this section provides a general introduction to non-linear PK that should be of interest to students.  The four PKQuest examples provide detailed analyses of human experimental ethanol PK and are of interest primarily to investigators specifically involved with ethanol PK.