Simplifying Clinical Pharmacokinetics with Professor Leslie Benet | Emery Pharma Speaker Series

If we give an oral dose and we calculate the average time that the drug's in the systemic circulation, it will be equal to the average time that the drug is in the circulation if we gave an IV dose. Because the body doesn't like xenobiotics getting into it. So we have efflux transporters in the intestine and there are two efflux transporters, P glycoprotein and bcrp. Breast cancer resistant protein. And what do they do? They pump the drug back into the intestinal lumen.

Hello everyone. And I just have to say Professor Les Bennett needs no introduction. Thank you for joining us for the Emory Pharma Speaker Series. It is my absolute pleasure to introduce today's esteemed speaker, Professor Les Bennett. Professor Bennett is a renowned scientist and professor at the University of California, San Francisco with groundbreaking contributions to pharmacokinetics, biopharmaceutics, drug delivery and pharmacodynamics. His extensive work has earned him a prominent place as one of the most highly cited pharmacologists in the world with over 33,000 citations of his peer review publications and impressive 55,000 citations on Google Scholar. Since his last presentation here at emory back in 2023, he has published seven additional papers on these concepts. Today he will provide an update on his latest findings and we're excited to hear from. His presentation today is called Simplifying the Application of Clinical Pharmacokinetics. Please join me in extending a warm welcome to Professor Elias Bennett.

Thank you Benjamin, and it is my pleasure to be once again here at Emory and to be able to update the material that I presented about 13 months ago. Give me a little recent history. As Benjamin said, we published seven papers since that time, since mid-2022, including the summary presented in my Emory talk in November of 2023, which was available on YouTube and still available. My laboratories published seven papers demonstrating how adaption of basic principles from physics allows for the derivation of all clinically relevant pharmacokinetic equations that are applicable to making drug dosing decisions without relying on differential equations as summarized here. I'm going to briefly talk about the following outcomes that have resulted. The first paper in 2022 published in Pharmacology and Therapeutics, the review of the application of Kirchhoff's Laws, where we considered that where we recognized that what had been considered the well stirred model of hepatic clearance was derived independent of any mechanistic assumptions and the transporter effects are considered as the difference between influx and efflux. Similar to what is seen in the kidney. This was followed up in 2023 in a paper in AAPS Journal where the primary take home from that paper introducing the concepts of clearance entering and clearance leaving for in series processes. Probably the most important paper is this early 2024 paper in AAPSJ where we explained why systemic bioavailability values can be greater than one actually a no no in pharmacokinetics and be statistically significantly different than bioavailability measures from drug and unchanged drug in the urine and that in turn reflects in statistically significant renal clearance values depending on route of administration. Again a no no in the basic concepts of pharmacokinetics. That was followed up by a paper in European Journal of Pharmaceutical Sciences showing that all mechanistic models of hepatic elimination, including the extended clearance model lead to KPU values. Now KPU is the unbound liver concentration divided by the unbound systemic concentration. All of those mechanistic models by definition cannot give a value of KPU greater than one and for no reason whatsoever appear to be a function of hepatic bioavailability. Later in 2024 in Journal of Controlled Release we demonstrated that slow controlled delivery of high hepatic clearance drugs could offer significant clinical advantage and that formulators could dictate the in vivo systemic clearance as the clearance from their dosage form which be independent of the drug characteristics and independent of the patient characteristics. A completely new hypothesis then our work is extremely controversial and attracted people who said we were wrong. But those papers were published after just our first two papers and we showed in this paper in Drug Metabolism and disposition earlier in 2000, later in 2024 what the error was in those papers and what the major error was that we had made for the past 50 years from the mechanistic model that I was the author of the first paper on that in our hepatic elimination we did not allow liver blood flow to have an effect of clearance within the liver, which is just not possible. Then the last paper published just a few months ago in Frontiers in Pharmacology was a mini review emphasizing the application to enzymatic and transporter hepatic processes as well as the deficiencies of the extended clearance model. Now there is an eighth paper that was submitted now more than six weeks ago to Drug metabolism and disposition, which again takes a very, very controversial position redefining the Michaelis Menten kinetics analysis and derivation in all kinds of fields drug metabolism, pharmacology, biochemistry, chemistry and pharmacokinetics. What we showed was that we could derive the Michaelis Menten equation independent of the steady state or quasi steady state assumptions, the criteria that has been assumed in enzyme kinetics for the past hundred years. And we showed that Vmax and KM for a high clearance sexual metabolism drug like ethanol. What's published is not correct because hepatic blood flow is not considered. And then we showed it is impossible to derive a clearance equation for saturable kinetics that includes hepatic blood flow when you use differential equations. So in addition to these eight published papers, there's three further papers that are in process. One is talking about renal clearance and applying to metformin and looking at these basic concepts. And I will talk about that in this talk. And the second is explaining and predicting increased dose predicted pharmacodynamic effects for extended versus immediate release dosage forms. If you look in the literature, there is data out there showing that for the same dose of an extended release formulation, you can get better effects than an immediate release formulation. And we can explain that and what you're presenting. And then finally, the deficiencies of the extended clearance model. So we developed this new methodology for simply deriving clinical pharmacokinetic equations. The 11 manuscripts listed on the three previous slides describe the value of the adapted Kirchhoff's Law's approach to simply derive all of the clearance relationships that those clearance terms are then multiplied by measured systemic concentration, determine the rate of drug elimination and that rate of drug elimination then defines the rate of drug administration. These outcomes are then used to make clinical decision for drug dosage regimens and adjustments of dosing regimens in disease states, changes related to pharmacogenomics, changes related to physiology and drug drug interactions to obtain systemic exposure that maximizes efficacy and minimizes toxicity. In many cases, the new methodology just provides a simpler approach to the clearance equations that we have routinely used in clinical drug dosing for the last 75 years. But in more than a few instances, the new methodology corrects inaccuracies that have been universally accepted for this past century. That is for as long as pharmacokinetics has been taught and practiced. So in the following slides, the approach to implementing and teaching the new methodology is presented in 2022. In that first paper, we recognized that adaption of the laws first proposed by Gustav Kirchhoff in 1857 to derive measures of resistance and conductance and electrical circuits for parallel and in series processes would allow determination of the equations for total clearance in pharmacokinetics and total rate constants. In chemistry, biochemistry, enzymology and pharmacokinetics independent of differential equations. And this was part of the topic that I presented 15 months ago in applying and teaching clinical pharmacokinetics. It is not necessary from now on to review the electrical circuit implications or even to further review refer to Kirchhoff's laws. Thus, we will proceed and refer to these relationships as equations defining total clearance and total rate constants for parallel and in series rate defining processes. So now what must be taught, what must be taught and understood are the definitions of parallel, the definition of in series and the definition of a rate defining process. For parallel processes, total clearance is equal to the sum of the parallel rate defining processes as given in equation one, where you add the rate defining parallel processes to get the total clearance. But for in series, the inverse of the total clearance equals the sum of the inverse of each of the in series rate defining processes. A parallel clearance process is one that has no effect on any other clearance processes. For example, in the liver there are two elimination metabolism and biliary excretion. The value of the metabolism clearance has no effect on the measurement of the biliary elimination clearance and vice versa. Therefore, they're parallel processes. So to get total clearance, you add the two of them together. Total body clearance for the great majority of drugs is the sum of hepatic clearance and renal clearance. The measurement of renal clearance does not affect the measured hepatic clearance and vice versa. So to get total body clearance, you add hepatic clearance and renal clearance. In series processes follow one another and the first process can affect the measured value of the next in series process. For example, in a series of metabolic steps, in a series of metabolic CEPs from the parent compound to metabolite 1, then to metabolite 2. If the metabolic clearance of the parent compound, the metabolite 1, is very slow, clearance of metabolite 1 to metabolite 2 will be rate limited by the parent clearance. It will also be very slow. In the liver or the kidney, drug clearance can be rate limited by organ blood flow and can never be greater than the rate of blood flow to the liver or the kidney. So no matter how fast in vitro the kidney or the liver can clear the drug in vivo, it can never be faster than that first step blood flow that gets it to the organ of elimination. Okay, so that's parallel and in series processes. What is a rate defining process? So clearance equations can be simply derived independent of differential equations by the appropriate summation of parallel and in series rate defining processes and the definition of a rate defining clearance is it is a parameter defining the elimination process where it is possible under certain conditions that the total clearance will be equal to this value and when it is equal to that value, it can be experimentally measured. And third, for in series process, it must be a positive value. For example, again for a very high hepatic clearance drug, total hepatic clearance would equal hepatic blood flow and you can measure that clearance will be blood flow in a series of metabolic reactions mentioned above. The clearance for the parent drug could be the rate limiting defining process for all the subsequent metabolic steps and you can measure that process. Understanding these definitions is essential in the application of this new methodology. For in vivo drug disposition. There are many processes affecting a drug that are not rate limiting processes. The critical aspect of the approach is that only rate defining processes can be combined to determine the overall elimination clearance. Passive permeability, no matter how slow, cannot be a rate defining process. For elimination clearance will never equal passive permeability. When hepatic basolateral transporters affect permeability and active influx is greater than efflux, this can be a rate defining process, but not when efflux is greater than influx. When hepatic clearance can never be defined in terms of permeability, when the measured efflux is greater than influx, because then this is a negative value. There's another very useful relationship to be applied and taught for the derivation of in series processes that came from that second paper in 2023. One over the clearance total for in series process is equal to the sum of one over the clearance of the rate defining entering processes plus one over clearance of the rate defining leaving processes. Where the first term after the equal sign relates to the processes delivering the drug to the site from which elimination occurs, while the second term after the equal sign relates to processes eliminating drug from this site. So just as this methodology can be applied to total clearance equations, it can also be applied to derivation of total rate constants. In equation 4, parallel rate constants are added together in equation 5. In series rate constants, the sum is the inverse and in equation 6, the sum of the total in series is the rate constants entering plus the rate 1 over the rate constants leaving. All of this relates to exposure because exposure is what defines how we dose drugs. The extent of exposure as measured by the systemic area under the concentration time curve is the drug characteristic that relates overwhelmingly to measures of drug efficacy and toxicity. There are some exceptions for which this relationship cannot be defined. Usually for drugs with high variability in pharmacokinetics or pharmacodynamics and for a few drugs the rate of exposure is clinically relevant, but these are minor exceptions. Thus, in utilizing and teaching clinical pharmacokinetics, the emphasis should be on dosing a drug to achieve the correct exposure. So for linear systems, two pharmacokinetic parameters govern exposure. Exposure is area under the curve, clearance and bioavailability and so area under the curve for a single dose from time zero to infinity or at steady state, the area during a dosing interval will be the bioavailability multiplied by the dose divided by clearance. Now, using these definitions and principles above will begin to derive the pharmacokinetic equations beginning with IV bolus, where bolus means instantaneous IV dosing, where by definition IV bolus bioavailability is one. Based on the principles presented in the previous slides, we begin to simply derive clearance equations independent of differential equations. Many of the clearance equations will be identical to that taught by traditional methods, but more simply derived without mechanistic assumptions. However, in several cases, the derivations of clearance equations from rate defining parallel in series process provide previously unrecognized relationships. The following material is dense, but please recognize that my goal in this one hour talk is to cover all of the three equations necessary to apply clinical pharmacokinetics. So I'm taking a whole course and putting it one hour. But there is one thing that I have not will not address. So the only methodology not presented here is how to predict accumulation and determine the appropriate dosage regimens at steady state when adjusted dosing due to changes in pharmacokinetics such as due to drug interactions, changes in clearance due to disease state and other pharmacogenetic and physiologic variables which is very poorly now addressed. But we can do it. I just don't have the time in this talk to talk about it. So let's start out with renal clearance following an IV Bose There are IV bolus dose. There are three rate defining processes that can affect renal clearance based on equation three. Equation three was clearance entering and clearance leaving. There is one rate defining entering clearance, renal blood flow and two rate defining leaving clearance glomerular filtration which is the fraction unbound in the blood fub multiplied by the glomerular filtration rate. That's one of the leaving processes and the other is the difference between tubular secretion and tubular reabsorption. These two rate defining clearances are. These rate defining leaving clearances are in parallel since the value of the clearance by filtration has no effect on the value of the transporter clearance and vice versa. Thus, we can immediately write down, following an iv, the renal clearance equation. Although PAH elimination is recognized as the exogenous gold standard for evaluating renal plasma flow, it was not clear until we derived equation 8 how it could be used in deciding clinical dose adjustments. It is not possible using differential equations to include renal blood flow in solving for renal clearance. So people measure pah, but how do you use it in terms of making drug dosing decisions? Here's the equation again. Ignoring qh, as is routinely done in renal clearance analysis, leads to mischaracterizing the importance of the difference between secretory and reabsorptive clearances. For example, let's look at the drug Metformin considered by the International Transporter Consortium as the model victim drug for characterizing drug drug interactions related to renal secretion. Because there are two transporters that affected OACT and mate. If you just look in the literature, what's the renal clearance of metformin? It's about 530mils per minute in healthy young people with GFR of 120mils per minute. And it's not protein bound. Now if you ignore renal blood flow and calculate from equation 8, not including the QR term, then you would get the secretion minus reabsorption being 410 mils per minute. But when you include the blood flow in there, the actual value of secretion minus clear reabsorption is 903. So we're more than half underestimating the actual effect of the transporter effects. The field has been significantly under predicting the magnitude of transporter clearances for many relatively high renal clearance drugs like metformin. How do we actually do make decisions on dosing drugs in patients with impaired renal function? So for almost all drugs following linear pharmacokinetics, dosing adjustments in patients with decreased renal function are determined solely based on changes in GFR from all of the terms in the equation. We make the total decision based on gfr. This approach assumes that the fractional decrease in renal filtration clearance is equivalent to the fractional decrease in the transporter effect and the fractional decrease in renal blood flow. This assumption is based on an observation in 1960 called the Bricker Intact Nephron hypothesis, which proposes that if one portion of a Nephron is damaged such that its function is impaired or lost, the function of all other segments of that Nephron and QR are also equally Reduced changes in fraction unbound are not considered since as we showed in this 2002 paper, these would only be relevant for a high clearance drug given iv, where elimination of unchanged drug is significant and no such predominantly renal eliminated drugs were identified like that. So in essence we don't even use this equation in making any decisions about dosing in renal failure. It's all based on gfr. But here's the equations and we can go back and look at the various aspects of what's affecting it. Actually, Bricker never considered hepatic blood flow, but he has to make that same assumption, that blood flow goes down when renal function goes down. And it does. But is it equivalent? I don't know, nobody's ever looked at it. But let's go to hepatic clearance, which is the major problem that we usually are trying to define. For an IV bolus dose, there are four rate defining processes that affect hepatic clearance. Based again on equation three, clearance, leaving clearance, entering. There are two potential rate defining entering clearances, hepatic blood flow, which blood flow gets the drug to the liver, and the potential of a basolateral hepatic transporter affecting how the drug gets into the liver, influx minus efflux. So those are the two entering clearances. The two rate defining leaving clearances are the ones I've already talked about, metabolism and biliary excretion, which are in parallel. So I can then immediately write down the hepatic clearance equation as given in equation 9. Generally, the parallel metabolic and biliary excretion clearances are combined. So just total liver metabolism and the extent of protein binding is taken into consideration, resulting in intrinsic clearances. So equation 9 is usually rewritten as equation 10. So here's the equation. When a patobasalater transporter is not clinically relevant, only passive permeability is present. But passive permeability is not a rate defining process. And so that term actually drops out of equation 10. Then when we solve equation 10, dropping out this middle transporter term, this is the equation we get. Equation 11, which we have thought for the past 75 years, is the well stirred model, which I was the author of the first paper that said that. But no mechanistic assumptions concerning metabolic and biliary excretion clearance were made in deriving equation 11. Consistent with the fact that the only, the only thing we can measure are systemic concentrations, we can't measure what goes on inside the liver. So when hepatobasalatotransporter is clinically relevant, it is usually Assumed that blood flow is much greater than the two other rate defining terms. And so the qh term drops out of the equation and we get equation 12. So basically one can readily see in the two equations equation 11 when the transporters aren't there, equation 12 when blood flow is not there, when one of the parameters is much greater than the other parameter, that much greater parameter will drop out. However, equations 11 and 12 define clearance at all the intermediate conditions. Okay, so I've derived hepatic clearance. I divide renal clearance very simply without differential equations for IV bolus dose. But that isn't the way we usually give drugs. We usually give drugs by oral routes or some other administrative route. Up till now we've only been considering IV bolus dosing. But the great majority of clinical pharmacokinetic data are following oral or other dosing routes. Im subq. And now we need to go back to a concept called mean residence time. So what is mean residence time? It's the average time a drug is measurable in the systemic circulation. And those concepts, first developed in 1979 allow simple analysis of the data. Equation 13 said if we give an oral dose and we calculate the average time that the drug's in the systemic circulation, it will be equal to the average time that the drug is in the circulation. If we gave an IV dose plus the average absorption time, mean mt, the total mean residence time of the system is equal to the mean residence time following an IV bolus dose plus the mean absorption time. Now, these mean residence time are actually the inverse of a rate constant. So we could say there's one rate constant that describes best elimination, average elimination following an oral dose, one rate constant that best describes elimination following an IV dose and one rate constant that describes the rate of absorption. Equation 14 is an in series process for rate constants. In fact, we've been using this approach since 1979. But not realizing we were using it, one can see that equation 14 is applicable of in series processes for determining the total rate constant of a system as we defined earlier. So here it is in terms of rate constants. And we can now solve for this K system. Oral dose is given by equation 15. So if K absorption is much greater, if the absorption rate is much greater than the elimination rate, this term becomes zero, becomes very small, and the K system for the oral dose will be the same as the K system for the IV dose. But if K absorption is a small number compared to the system, IV bolus dose elimination, what is called the flip flop models, where elimination is slower Absorption is slower than elimination, then we do not get the same rate constants. So only if K absorption is significantly greater than K system IV bolus will the terminal concentration time curve have the slope of the IV bolus time curve. And in most cases this will be true. But frequently the absorption rate constant can be very slow, often deliberately for controlled release dosage forms. And equation 15 mathematically explains the flip flop model. It explains why when absorption is very slow, the terminal rate constant is the absorption rate constant. And while when absorption is very fast, why, the terminal rate constant is the same rate constant following the IV bolus. But we don't make drug dosing decisions based on rate constants, we make them on clearance values. So the equivalent of equation 14 in terms of clearance is one over the clearance system, one over the system clearance following an oral dose, one over the system clearance following An IV dose, plus one over the clearance from the absorption site. Now, this is a new concept that has never been considered before. We've talked about the rate constant from the absorption site, but there ought to be a clearance from the absorption site too. Simply, we could just say it's the product of the rate constant times the volume of distribution, not of the systemic circulation, but of the gut compartment. So solving equation 16, we then get this relationship again, where we have to look at the two clearances, and only if clearance from the absorption site is significantly greater than clearance from the IV bolus with a clearance measured following oral dosing equal the clearance following IV bolus. Now, this goes against everything that has been taught in pharmacokinetics since Professor Dost first talked about absorption rate constants. And in most cases it's true. But frequently the clearance from the absorption site can be very slow, often deliberately for controlled release dosage forms. We'll return to the implications of equation 17 after discussing bioavailability. Here's the schematic of the gut and the liver. We give a drug gets into the intestinal lumen. And because drugs are lipophilically and they're in a water environment, they get absorbed into the lipophilic intestinal epithelia where they can be metabolized. If they get through that, they get into the portal vein, they get into the liver where they can be metabolized or excreted in the biliary excretion, and then we get the total bioavailability. Bioavailability and oral dose is the fraction of an oral dose that reaches the systemic circulation intact. And it's going to be the product of the Fraction of the dose absorbed, faabs, the fraction of those that gets through the gut intact and the fraction of dose that gets through the liver intact. Equation 18. So basically here's that drug into the intestinal lumen. It gets absorbed because it's lipophilic. But in addition to metabolism, we have another protective mechanism in the gut because the body doesn't like xenobiotics getting into it. We have efflux transporters in the intestine. There are two efflux transporters, P glycoprotein and bcrp, breast cancer resistant protein. And what do they do? They pump the drug back into the intestinal lumen. That F absorbed is just not what goes in, but the effect of the transporters also. Then the F got is from the metabolism in the FH, the metabolism in the intestine, which is primarily cytochrome P453A4, a little bit of 2C9, some UGTs, which is going to be important for our naloxone, but not necessarily orally and for those of the enzymes in the intestine. Okay, return to equation seven. So here we said AUC for a single dose and let's talk about a single oral dose. Now is going to be the oral dose, bioavailability times the dose divided by clearance. And if we give an IV dose by definition F equals one and we can measure AUC and then we can calculate the value of clearance. Dose divided by AUC will be clearance. Then if we also give an oral dose, we can calculate F because we know clearance. And if we assume clearance hasn't changed, then we'll be able to calculate F once knowing total clearance and now measuring renal clearance, we can also determine hepatic clearance because.