Prof. Leslie Benet - UCSF: The explanation for WHY when bioavailability calculation exceed unity?

Foreign. I'm very excited to introduce our guest speaker today, Dr. Les Bennett. Dr. Bennett is a former professor of mine from UCSF and we're so honored to have him here at Emory Pharma with us today. Dr. Bennett is a distinguished professor, researcher, thought leader, recognized globally for his contributions in the field of pharmacokinetics and drug metabolism. Over his decades long career, he's had over 600 publications, he's written many books, and he's been granted over 10 patents in the areas of pharmacokinetics, biopharmaceutics, drug delivery. Dr. Bennett has actually been listed as one of the most highly cited pharmacologists worldwide. Google's Scholar credits him with over 50,000 citations. So we're really excited to have him here today. I know that everyone is going to really enjoy his presentation. He has a lot of interesting information to share and with that I'll hand it over to Dr. Bennett.

Okay, thank you Anna, and thanks Ron, for arranging it and thank you all for putting up with it today. So this is cutting edge stuff that may be difficult to necessarily understand. So let's start with a little preface. Over the past two years, my colleagues and I have made a major discovery recognizing that a well known principle of physics can be applied to deriving chemical, kinetic and drug pharmacokinetic relationships independent of differential equation approaches, allowing very simple predictions of the parameters relating measured amounts or concentrations to rates of reaction. However, as yet, few scientists accept this discovery and it's really anathema. If anathema means I hate it, it's anathema to many leading scientists, particularly in the field of pharmacokinetics. Probably because the discovery concludes that many of the basic pharmacokinetic principles that we have taught and utilized for the past 50 years may not be right. Thus, leading scientists publish theoretical arguments of the deficiencies of our approach, but they never consider the extensive experimental data published that can be explained by our approach, previously believed to be only the results of poor and unreliable experimental procedures. It's quite controversial. Start with some very basic principles and can I convince you of the benefits of our discovery? I presented this Talk at the FDA on March 6th and I presented it to a number of companies and it is slowly perking through. So let's go back to very basic principles. Rates of reaction. So rates of reaction are derived and we're only going to talk about first order processes following equation one. So the outcome, the flux, what happens or the current is J, what drives it is F and K is the proportion of the coefficient of proportionality that determines the magnitude of the flux response to the input force. Now back in physics, we see this relationship for fixed law of diffusion, for Ohm's law of electric current, for heat transfer relationships, drag force on falling objects. But when we apply it to chemical rates of reaction, it's easy to see what it is. So the outcome, the flux is the rate of reaction. What drives it is the amount that's there driving it. And the coefficient of proportionality is a rate constant. So we take a rate constant times an amount, tells us how much is reacted in a particular time. We can use this and derive it during differential equations. And that's what we've done up till now for the past hundred years, including the rate constants and the amounts driving the reaction. So here we are that chemical rate of reaction. And now let's go though to in vivo pharmacology and pharmacokinetics. So what's the equivalent of equations one and two? So we're still trying to understand the rate of reaction, what happens to the drug and where it goes. But our driving force is not the amount anymore, it's a concentration. And the coefficient of proportionality is now clearance. So clearance times the concentration gives us the rate of reaction, clearance units of volume per time of flow. So how do you get clearance? How do we get clearance for any drug? The only way that we can get clearance for a drug is by equation 4. The amount eliminated divided by the exposure driving that elimination. The exposure in the patient driving the elimination is clearance. So if we give an IV bolus dose, then all of it's eliminated. We measure the area under the curve, overall time, and then we can get clearance. And that's all clearances in the literature come from this. So why do we have to measure concentrations and determine clearance in pharmacology, pharmacokinetics and clinical medicine? Three reasons. First, in a patient, it's the only thing we can get. Systemic concentrations are the only convenient and easily measurable drug related parameter that we can get, but system. Second, for the very great majority of drugs, systemic exposure can be related to efficacy or toxicity. Too much exposure, toxicity, too little exposure, not efficacious. And so it's exposure that gives us efficacy and toxicity. And when we make adjustments, well, we need to do that for the initial approval studies that a drug company does. It shows the exposure, what's the right dose to get the right exposure. And then if we have a disease state or we have to make a change due to pharmacogenomics or physiology or drug, drug interactions. All of those dose adjustments are based on exposure, change exposure, we change the dose to make sure that the patient isn't toxic and remains efficacious. And the third reason is just because of what I said, we can have this relationship. So here are three reaction rates, general chemistry, pharmacokinetics. And we might be able to believe that all we need to do to convert equation two to equation three is to divide the amount by the volume of distribution and multiply the rate constant times the volume of distribution. And then we change amount in the concentrations and the rate constant in clearance, and we get some volume of distribution of drug in the systemic fluids. And this is what we do, and this is what we've done since the initiation of pharmacokinetics. But I'm going to say here for the first time, this can be wrong. Something that we've always believed is true, but it could be wrong. But let's review a little history first. That sort of gets back to the kind of stuff you guys do. The pharmacokinetics timeline and the bioanalytical method. So you couldn't have pharmacokinetics before we had bioanalytical methods. So we had to be able to measure drugs before we could do pharmacokinetics. So initially, if we go Back to the pre1960s, our only analytical instrument was a spectrophotometer. And it wasn't sensitive enough to measure systemic concentrations. But we collect drug in urine and we could evaporate off the fluid. We could get the really high concentrations. The original pharmacokinetic studies were all done with urine data because the amount in the urine relates to the rate constants, not the clearance, but to the rate constants. All pharmacokinetics was based on these rate constants. And that's what we got from differential equations. The big advance in terms of relationship to pharmacokinetics was gas liquid chromatography, because it was the first methodology that would now allow us to measure concentrations of drugs in biological fluids. But even then when we did that, we didn't know anything about clearance in those days. So we just got rate constants. We used it to get rate constants for drugs in the body. Now free post 1973. Now we had terrific methodologies. HPLC, LC MS, your Orbitrap for 800,000, $900,000. Okay, so now we can measure anything, right? And we also understand the relevance of clearance. So we Know that we need to get that exposure and divide it by the amount eliminated to get clearance. And we can do it. So why did I present this timeline? To remind you that all of the basic principles of pharmacokinetics, principles of drug elimination and absorption, were defined in terms of rate constants and differential equations. Before we recognized that to make pharmacokinetics clinically relevant, we had to find elimination in terms of clearance, not rate constants. Those rate constant derivations were all based on differential equations, the same thing we learned in chemistry. So last year we presented a new derivation of the equation relating organ clearance to organ blood flow, intrinsic clearance and fraction unbound of drug eliminated by metabolism or biliary excretion. It's a paper that appeared in Pharmacology and Therapeutics entitled the review of the application of Kirchhoff's laws to series and parallel flows to Pharmacology Defining organ Clearance. Now, you all learned Kirchhoff's laws in your first physics class and you've all completely forgotten. Everybody learned Kirchhoff's laws and we'll come back to what it was. So this was a joint project. I needed some real good chemistry expertise. And I worked together with Ken Dill, a member of the National Academy and his lab at sunny Stony Brook to do this understanding of what was going on, because we didn't understand it either. So let's go back and look at what Kirchhoff did. In 1857, just after I was born, Gustav Kirchhoff first developed his laws to describe the motion of electricity from Ohm's law. And he said, I can define the motion of electricity in conductors in one paper, and in another paper he can define it in wires. Since then, Kirchhoff's laws have been applied to all kinds of physics processes, but not pharmacology until our publication. So the take home relevance in our paper is that when two or more rate defining processes are in parallel, the total value of the reaction parameter is equal to the sum of those rate defining processes. Equation 5. If I have two parallel clearances, I add them together to get the total clearance. But if I have processes in series, the inverse of the total reaction parameter is equal to the sum of the inverse of the rate defining parameters. This is what Kirchhoff developed in terms of how you take physical principles and he applied it to electricity and resistors and conductors. So in the last slide I did it clearance, but it can also be done with rate constant. So in fact that's how it was always done in chemistry. So 2 in parallel rate defining processes, the total rate constant is going to be the sum of those two or more rate defining processes in series. The inverse is going to add together to get the inverse of the total rate. So what's a rate defining process? So a rate defining clearance or a rate defining constant is a parameter describing the elimination process. What is possible under certain conditions, the total clearance or total rate constant can equal this value. So Kirchhoff didn't talk about rate defining processes, it's less Bennett. For example, a rate declining process for hepatic elimination could be hepatic blood flow. So if we have a very high clearance drug, the clearance can't be any more than the delivery blood flow. So blood flow is going to be a rate defining process in terms of clearance. Let's talk about in chemistry, a rate defining process, a metabolic reaction occurring in a beaker. Let's say the first step is very, very slow and you're going to go to metabolite two, metabolite three. But all of those processes are going to be very slow because the rate defining process will be the first step. Very simple stuff that we learn from chemistry. So understanding this definition is essential in applying Kirchhoff's laws. The critical aspect of this approach is that only rate defining processes can be combined to determine the overall rate constant for elimination or clearance. Passive permeability. No matter how slow it is, elimination is never going to be passive permeability, no drug, it's elimination as a function of passive permeability. It's going to be something else, metabolism, something else. Okay, so you have to have a positive process to be a rate defining process. So what's the advantage of the Kirchhoff law's approach? So rates of reaction are divided by this first order process. As we shown, the flux or the current is equal to the product of the driving force, coefficient of proportionality and the driving force. And so today the only methodology available to determine the coefficients of proportionality, clearance in pharmacokinetics and rate constant chemistry is to solve differential equations for first order process. But application of Kirchhoff's laws allows one to solve for clearance in pharmacokinetics, an overall rate constant in chemistry, independent of differential equations directly by considering only parallel and in series rate defining processes. So let's consider a parallel process in human drug clearance. So a drug gets eliminated in the liver, it can two ways. It can get eliminated, it can be metabolized, it can be excreted in the bile. But the clearance of metabolism doesn't Affect the clearance of biliary excretion. The clearance parameter for biliary excretion doesn't affect metabolism. So the total intrinsic clearance of the liver is going to be the sum of those two. They're in parallel. Let's look in the kidney. What are the things that can happen in the kidney to get renal elimination? Well, you can filter the drug through the glomerulus. And the other way you can have transporter effects. Drug could be transported into the tubule or transported back out. It's going to be the difference between those two. Those are the two rate defining processes in the kidney. Now what do we do in differential equations and what you were taught if you learned anything about clearance, Renal clearance, this is the equation you get from differential equations. The fraction unbound times gfr that gives you the clearance of filtration. But to get this secretion and reabsorption, we have to put in a whole bunch of things that we can't measure. You can't measure the fraction unbound in the tubule, you can't measure the renal secretion, you can't measure the passive reabsorption, you can't measure the active reabsorption. But this is the equation we use. So neither equation 9 or 10 are new, but I just wrote them based on Kirchhoff's laws for measurable parallel processes. I didn't have to derive them in differential equations. So let's take a moment to further consider that approach to renal clearance. Kirchhoff's law has two rate defining processes, filtration and the difference between clearance and reabsorption. So what can we actually measure when we derive renal clearance Using differential equation? We, we must include that unmeasurable tubular drug concentration and infection unbound. But we can only measure two things or three things. So we can measure renal clearance, the amount eliminated divided by the exposure. We can measure the fraction unbound in plasma. And we can measure glomerular filtration rate, GFR using creatinine clearance or something like that. So we can get clearance filtration. So what do we learn if the renal clearance is equal to the filtration clearance transporter processes are not relevant. If the renal clearance is greater than the filtration, we must have had active secretion more than reabsorption. If renal clearance is less than clearance filtration, then we must have had active reabsorption being greater than secretion. This is all we can learn. We don't need this complicated differential equation to do it. We can simply get the clinically relevant parameters from just saying. Okay, here's what renal clearance is in terms of Kirchhoff's loss. Okay, so let's go to in series processes. Something in series means I'm going to enter and I'm going to leave. Okay, enter has to come before leaving. And so when we talk about the liver, what's entering, blood flow, what's leaving, fub clearance, intrinsic metabolism, biliary excretion times a fraction unbound. Those are the two processes in series. The entering and leaving to give us the hepatic clearance. And when I solve equation 12, I get equation 13, which is a very familiar equation because it's the equation we think is the well stirred model. A paper I was on, the original paper that said it was back in 1973, but I derived equation 13 making no assumptions related to mechanistic characteristics of hepatic elimination. Equation 13 is organ model independent. And now we understand why all steady state clearance data appear to fit the well stirred model. Because in fact equation 13 is not the well stirred model. It's a model independent relationship in terms of blood flow and elimination. Therefore, there's no value to predicting whole body clearance values utilizing different mechanistic models of hepatic organ elimination, as is presently implosed in some physiologic based pharmacokinetic processes. So why is this anathema to all of my colleagues? It basically says hundreds of papers talking about parallel tube dispersion models are all completely useless. They don't tell you anything that this is the model independent relationship. So this is really anathema. Now let's go on to some other in series examples published in this paper earlier this year in AAPS Journal. The use and advantages of Kirchhoff's laws versus differential equations in pharmacology, pharmacokinetics and even chemistry. So let's see how we would solve for the mean residence time of metabolite 2 in a chemistry in vitro incubation metabolic experiment. We would put drug D in the beaker. Okay, so we have a beaker and its volume of distribution is 200 mils. And we put 90 micromoles of drug into it. It's a beaker and we got enzymes in that beaker. And this drug gets metabolized from drug to metabolite 1. So we can find out that rate constant by looking at the disappearance. We can find out what KD is by looking at the disappearance. Now this is an in vitro study. I can then take metabolite 1 and put it into the beaker and find out what its rate of elimination is. I can put metabolite 2 into the beaker and look at what its rate constant of elimination is. So I know all the numbers, but what I want to know is what does M2 look like in terms of its overall rate constant, its mean residence time in this reaction. So what do I have to do? I have to derive the equation for M2 and I need three differential equations to do that. And when I do it, I get this equation using Laplace transforms and input and disposition functions. So I get this very complicated equation, three differential equations, but I know all the numbers, so I put them all in there. So now what I want to know is what's the mean residence time of metabolite 2, in other words, the overall rate constant of metabolite 2. I can calculate mean residence time by just taking the coefficients and dividing them by the exponent squared, which gives me area under the moment curve divided by the coefficients divided by the exponents, which gives me AUC. I put all the numbers in 25 hours. So in this reaction when I put drug into the beaker, the mean residence time of metabolite 2 in that beaker is going to be 25 hours. Now let's look at the Kirchhoff's law approach to the same thing. Kirchhoff's law says these are in series processes, you just add up the inverses. So 1 over the M2 measured elimination rate constant is going to be the inverse of the three rate defining processes which I have here. I put in the numbers 25 hours. So I didn't need to do all of that. Complicated differential equations. Kirchhoff's law is immediately in chemistry, allows me to find out what the rate constant is without solving differential equations. Okay, now let's get to the topic of the talk. Why can we get bioavailability greater than 1? What I did was have my postdoc Dr. Wakuda search all the literature to find published studies, peer reviewed published studies where bioavailability was greater than one, both in animals and in humans. Now this is really not easy to do because people don't put in their title that I got a bioavailability greater than 1, which is impossible according to our present theory. So he had to do a huge amount of work searching all the literature to find this. But here's 34 examples that we found where the numbers were greater than 0.02. Now right now what our field says is these are all bad experiments because you can't have bioavailability greater than 1 according to our present theory. So there has to be experimental errors and there's all kinds of stuff saying why these papers might be experimental errors, but the ones in red may not be experimental errors because there's some statistical data here that says this is significant and I believe in statistics. So in this paper of 1D amino 8 arginine vasopressin, the authors found that the renal clearance following the sub Q dose is 76% of the renal clearance following the IV dose. Now, you were taught if you learned any of this, that renal clearance is independent of the route of administration. This turned out to be significant. In this paper of the sodium fluoride, the ratio was 1.23 and it turned out not to be statistically significant. P is 0.055. But the authors hadn't gone back and calculated the renal clearances of the subjects. So I went back and calculated because the data was all there, the renal clearances of the subjects. And in a paired T test, the renal clearance oral versus IV differed with a P of.007. That's highly statistically significant. This study with cimetidine, they did find that the bioavailability 1.11 was statistically significant. I also went back and calculated the renal clearances highly different 0.002 in this levotera sita, this antiepileptic drug. Okay, they didn't give enough data that I can do the statistics. They reported the mean 1.09, but they also reported the 90% confidence interval. 90% confidence interval 1.05 to 1.13. This has to be statistically significant. And here's another one. Hydroxyurea, different renal clearances, p less than 0.01. And here's a paper where the ratio is 0.05, but it turns out, in fact it's statistically significant. In the paper, they say because the variability is so low, this is statistically significant. There's some data out there that all my colleagues ignore because it doesn't fit our theory. Present theory, but I don't ignore data. I always go back and look at experimental data. So until now, no explanation for these bioavailabilities being greater than 100 when you use systemic concentrations. And each of these papers, because they wanted to get them published, so they had to say, okay, yeah, we got this number greater than one, but it's probably because of some errors. And here's the errors, analytical problems. They didn't go to Emory. So biliary cycling binding to the apparatus, different studies don't give the same results. High urine flow rates give you the wrong renal clearance. High variability, lack of statistical validation, saturation of elimination. All of those papers that I listed there have some explanation about why the values aren't real, even though their data said it was. So do we believe these explanations and the reason they look for them is because they got a value that nobody would believe? Maybe. Yes, there are definitely some papers there that that is lousy. But certainly some know the ones I showed you in red on the last slide. We make no assumptions as the validity of all the studies. We only list those published in the literature. However, as a consultant to the industry over the years, I am aware of many more studies, both in humans and animals, following Oral and IV studies yielding dose corrected AUC greater than 1. But they never get published because there's no explanation for the results. When I presented this data at the FDA, one of the FDA scientists said in his PhD studies he was looking at lymphatic absorption and he carried out all these studies on lymphatic absorption in rats. None of that data was in his published. None of that data was in his thesis. Why? Because all of the bioavailabilities came out greater than one. So he couldn't believe any of it and he left it all out. Ah, fantastic. I never thought of lymphatic absorption. Sure, we'll come back to it. Could there be another explanation? So let's see how we in pharmacokinetics deal with absorption. So here's a simple model. Drug at the absorption site gets absorbed into the body, can be excreted or metabolized. So what do we do? We do a differential equation for the amount of drug in the body. What comes in minus what goes out. That's our differential equation. And then we have to put in something for the absorption site. So we take the differential equation for the absorption site and we put that in. And where did this come from? Professor Dost in 1940s was the first person to say this is how we'll solve for this. But look at the assumption we're making here. We're making the assumption that what drives the absorption site is only the available drug. Of course, not all the drug in the gut is driving the absorption and that f happens after absorption. It's the metabolism in the gut, metabolism in the liver. But that's what we do. So we then derive solve the differential equations for the amount of drug in the body from this equation. Substituting that in, we get two exponentials very simple relationship, but we have to change it to concentrations because that's what we measure. So we put in a volume and distribution and then we integrate that so we can get the exposure. And when we integrate the equation, we get the area under the curve is the available dose divided by KD V body. If we give the drug IV and we solve it, we only have one differential equation. When we solve it, we get the amount in the body is from the oral dose. We got the amount in the body is F dose. KDV body from the IV dose we get this. Basically, this is how we do bioavailability. Basically, we say for the last 70 years that absorption has no effect on measured clearance. Therefore, giving an IV bolus and an oral dose of a drug to a patient, we can determine bioavailability. And that's how we do it. Let's look at Kirchhoff's laws. Kirchhoff's law says what we do is we take these in series, the entering and the leaving. So what's the entering? Clearance from the gut. Something we've never talked about before. We've talked about rate constant from the gut. We've never talked about clearance from the gut. But when we do clearances, that's the parameter we have to put in. And what's the clearance of the drug elimination? It's going to be the clearance from the IV bolus. Now let's solve for that equation. What we get total body clearance is equation 15. And what it says is, although we teach that following oral dosing, absorption has no effect on the clearance measure, this is really only true when clearance gut is much bigger than clearance IV bolus. Because if clearance gut is much bigger than clearance IV bolus, that term drops out and we get clearance IV bolus. But if clearance gut is not much bigger than IV bolus, it says it affects the total clearance. Again, anathema to our field. Well, let's go back to something else we've been doing for a long time. We've been doing mean residence time concepts since the 1970s. And Yamaoka et al said, if I take the mean residence time of an IV bolus dose and I take the mean absorption time, that'll be the mean residence time if I gave the drug orally, and mean residence times are just the inverse of the rate constants. So in fact, we've been using Kirchhoff's laws for 40 years. We just didn't realize we were doing it in series things. So the theoretical basis of Kirchhoff's laws is mean Resonance time concepts. Now let's solve for the rate constant and we get the equation that says the rate constant, terminal rate constant following an IV bolus dose is not going to be the rate constant finding an IV bolus dose, unless the absorption rate constant is much greater than that, then this term drops out. But if the absorption is not much bigger, then what happens? Well, we know that there are situations like that, flip flop models or even controlled release dosage forms where we change the delivery so that the absorption rate is very slow. So if the absorption rate is very slow, the terminal rate constant is not going to be the rate constant from the IV bolus. It's going to be the slowest step, which would be absorption. And so all pharmacokinetic textbooks talk about the potential for flip flop. In other words, the slowest step is not elimination, the slowest step is absorption. Now, if we compare the two equations, how do we get the rate constant equation to the clearance equation? Well, we have to take each of the rate constants and multiply by its volume of distribution. So to change the absorption rate constant into a gut clearance, we got to multiply by V gut. Now, V gut has no physiologic significance, just like all pharmacokinetic volumes of distribution have no physiologic significance. It just says if I measure in the fluid, what's the apparent volume of distribution? Because drug distributes all over the place in the body, drug will distribute all over the place in the gut. So we can get the right rate constant all the time using differential equations. But we can't get the right clearance if we have more than one site. Because when we do differential equations, we can only put in one volume. We don't make drug dosing decisions based on rate constants. We make drug dosing divisions based on clearances. So the argument, if you want to argue against this, what do you have to say? You have to say, yes, the absorption rate constant in the flip flop model can be the rate limiting step for elimination of drug from the systemic circulation. But no, clearance of drug from the gut cannot be the rate limiting step. That's what you have to say. That's what we intrinsically have been saying, although we don't realize it. So basically, here's what really happens. And well, why can't we get this? Why when we do simulations, we never get this curve. We only see this curve when we do actual studies. So why do we get AUC greater than 1? So these experiments are not, these measurements are not a function of experimental error they result from having to assume in differential equation derivations that the volume distribution for the different processes are the same. So why can't we see this if we do a simulation? Well, we can't do a simulation because when we derive the differential equation, we can only put in one volume. And what we're saying is, no, gut clearance is not that volume. It's a different volume. And that's why we get sometimes these weird results. Now, we don't get it most of the time because most of the time absorption is faster than elimination. But a lot of times it isn't. Here's something else. What about this phenomenon? And I've already talked to you about it. When bioavailability determined by comparison of dose corrected urinary excretion, unchanged drug is less than bioavailability determined by aucs. So some of that data that I showed you, when they looked at the systemic concentrations, they got a bioavailability greater than 1. But when they looked at urinary bioavailability, it was less than 1. Here's some data. So here are the cimetidine, fluoridine, endoprofen, where it's greater, but we can see other cases where it's different. Now, a lot of times these differences aren't statistically significant, but in some of the times they are statistically significant. So let's take a look at what goes on here with cimetidine. So the area under the curve from the systemic concentrations was 1.12 bioavailability, but the urinary data set is only 0.6. That's a big difference. And it's highly, statistically Significantly different in 16 pairs measurements, 0.001 renal. This bioavailability is very different. So if I go back to the equations and Ron has these slides, you can all look if you want to, because it gets a little complicated here. When I calculate clearance after oral dosing, it's one over clearance entering, one over clearance leaving. And I can solve for clearance after oral dosing because it's the amount eliminated divided by the exposure driving that elimination. Well, what's the amount eliminated? Well, the real amount eliminated is the urinary F from the urine times the dose. So I can calculate clearance after oral dosing to be 30 liters per hour. Now, from this equation, if I can get clearance after oral dosing, and if I also give the drug iv, which these studies did in catal, a clearance iv, I can now calculate clearance gut. So here's a clearance gut that is 78.6 and clearance IV is 48.5. So yeah, absorption is faster than elimination, but not much faster. It has to be much faster for clearance to come out to be the IV clearance. So basically what happens, here's the simetidine. It's 1.6. So many of these studies the clearance on the gut versus clearance IV are really big. 98, 7.8, 7.5, 11. But in some of them, 1.6, 2.6, 4.1. So maybe in those studies our assumptions are wrong because clearance in the gut is not much greater, even though most of the time it's much greater. So again, let's go back and return to the cimetidine analysis. So why is the urinary ratio significantly smaller than the systemic AUC ratio? Because renal clearance was different. In this cimetidine study, the oral renal clearance was only 61% of the IV renal clearance highly statistically significant. But we've been taught that's impossible. But this is the experimental data and it's highly significant. We can't say, oh, okay, yeah, I'll believe it. Even though it's highly statistically significant, I don't believe it because it doesn't go with my theory. Something wrong with the theory. So measures of renal clearance support the Kirchhoff's Law's approach. Here's where we showed with the sodium fluoride, with the cimetidine, with the vasopressin, with the hydroxychloroquine, these are getting significantly different renal clearances. When you've always been taught that renal clearance is independent of route of administration, it's not. But the only way we can see this is with Kirchhoff's laws. You can't see it with differential equations because you can only put one volume term in the differential equations. Slow clearance from the absorption site will increase AUC as predicted by the Kirchhoff's law of derivation. I'm not going to go through the sodium fluoride example also. So the major take home message Differential equation derivations in pharmacokinetics will only be valid for determining clearance following an IV bolus dose. But until today you had no other way of getting these derivations. Until I showed you I can get them with Kirchhoff's laws. And I don't have to use differential equations. So even when the components of hepatic and renal clearance are evaluated, only equation 11 is operable. Differential equation derivations in chemistry are valid for determining rate constants. Why? Because everything in chemistry happens in a beaker they all have the same volume of distribution. A beaker is not a biological system where drugs go to different places. Some in the fluid, some in the lipid soluble environment that we've ignored. And organ clearance determining using measured systemic concentrations give you this equation which is independent of any mechanism, thus was previously believed to be the well stirred model is the correct equation for defining organ clearance independent of mechanistic models of organ elimination. So what are the regulatory implications and what are the implications in terms of therapy? From what I've just taught you, nothing. So from a regulatory and a clinical dosing perspective, these findings are negligible. Bioequivalence is based on matching AUCs, doesn't base matching on F, you base, you match AUCs, that's how you show bioequivalence. You don't have to give an IV dose to show bioequivalence. When you make dose adjustments therapeutically, you're based on auc. You don't care what the AUC is. You give the dose and you have a drug interaction the AUC change, you change the dose unless it's a wide therapeutic index. So the most relevant result of our finding with respect to F is the recognition that dose corrected AUC ratios can be greater than 1 and there can be large differences between the ratios AUC and U and urinary measurement. But these aren't experimental errors. This is valid data. And so the FDA scientist who told me about the lymphatic absorption, I said let's go back and look at all your data. I can now explain all your results. Let's go back and do it and we'll follow up with him and see if he can do that. But from a pharmaceutical company. What are the implications? Well, first one is the same one that I said before. These differences may not be experimental errors, but there's something really interesting here. A previously unrecognized result is dose corrected pharmacodynamics from an oral IM or sub Q dose may be greater than an IV dose because you can get a bigger area under the curve if clearance gut is close to clearance iv. So in fact you can have better effects. And from a PBVK perspective, the result relevant result is that the prediction of affin food effects are presently not based on sound theoretical approaches. Food effect studies never consider that the volume of distribution in the gut may have changed. Nobody's ever thought about that. But these can be corrected. But let's go back to why I went to the FDA and wanted to talk to them and they wanted to talk to you. A previously unrecognized result is a dose corrected. Pharmacodynamic effect from an oral IM or sub Q dose may be greater than from an IV dose. And actually any way that we deliver drugs slowly, we might be able to get better pharmacodynamics. Who has that data? Only the fda, but nobody's ever looked for it in the fda. But they've got all the data from those studies. Those AUCs were there, they just weren't analyzed. And the pharmacodynamics were there because that's what they had to do to show that their drug works. So what I asked the FDA do is to go back. I don't care what data they look at, but look and see if you can find in fact where there's pharmacodynamic differences that are better for giving a controlled release dosage form or lymphatic absorption dosage form or even slow release IV dosage forms. I have some clues. I have a paper abstract that we've submitted for CPT next April because I've looked at a bunch of data and I think there's data out there, the Salazar Pro data that I was looking at in terms of renal, I think the semiglutides are seeing their effects better than IV in the semi glutides. If you go back and look at the data, it obviously shows that you get better effects of giving the drug once a month than giving the same dose every day or every week basically. So if you're giving it once a month, you had to have slower absorption. So I think that data has it many cancer drugs, there's data out there showing controlled release, weekly monthly dosing versus daily dosing, you get better effects. Nobody's ever thought about why, but now I have the explanation or potential explanation and short IV infusions versus long IV infusions. Now again, this last one is really you were taught if you went to school that okay, one way to get clearance is amount eliminated divided by exposure. But another way to get clearance is going to steady state. And looking at the steady state concentration times clearance equals radian. And that doesn't change. But it does change. There's a whole bunch of data in the literature shows that some if you have a drug that has high clearance like lidocaine or oxycodone, if you give those drugs by very long infusions, clearance changes because rate in is getting slow. So I think there's a potential, some really potential ways of making better drugs by making a controlled release dosage form. So not only does our controlled release dosage form give more convenience, it actually gives better pharmacodynamics. But nobody's ever thought about it before. But I think it's potentially something very useful. So this is too controversial to ever get any outside funding. I have to fund it all myself through people contributing and this fund at ucsf. And I had to deal with. To learn this stuff. I had to go with people who were electrical engineers because they use Kirchhoff's Laws. And. And I had to go with people with physiological, basic stuff to. To make sure that I understood what was going on with Kershaw Law. Said, you can get slides from me or you can get them from Ron, if you're interested. So thank you for taking the time to listen.