# PharmPK Discussion - A question of clearance

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• On 2 Jan 2010 at 11:31:24, "J.H.Proost" (J.H.Proost.at.rug.nl) sent the message
`The following message was posted to: PharmPKDear Yaning,Thank you for your comments. As you might expect, I disagree at many  points."Then A/dT=V*K*C as long as you still agree dC/dT=K*C."I presume you mean 'dA/dT=V*K*C'. Until here we agree."As you can see, when you try to link dA/dT to C (the driving force), V  is always part of the proportionality constant, which shows the  dependence of the composite parameter CL=V*K on V. You can think of  dA/dT=V*K*C as the correct format for your first option or a fourth  option."I disagree. The proportionality constant is CL, of course. It is K that  is dependent on both CL and V. If you say that C is the driving force  (we agree!) and that dA/dt is the rate of elimination, then the only  meaningful view isdA/dt = CL * CI cannot see a different option.Please note that writingdA/dt = V * K * Cdoes not prove that dA/dt is dependent on V. As K = CL/V, V disappears  from the equation."If we apply this to an eliminating organ, such as liver, CL is  basically the so-called intrinsic clearance where V is the volume of the  liver and K is the composite rate constant that is dependent on the  enzyme concentration and a true rate constant as shown in your  derivation."Why do we need a 'composite rate constant' K for a liver? I don't  understand what it means. The same holds for 'a true rate constant'.  Please note that intrinsic clearance is different from the actual  hepatic clearance (as you describe later in your message). And what is  'the volume of the liver'? The total spatial volume, oe the water  content, or the apparent distribution volume of the liver, or something  else? And what do we learn from the rate constant obtained by dividing  intrinsic clearance by this volume? Let's try to make things clear and  simple, and avoid unnecessary parameters and assumptions."At an organ level, I think there should not be too much difficulty in  accepting that the intrinsic clearance is dependent on the size/volume  of the organ."Again, I don't agree. Of course, a larger organ will usually have a  large intrinsic clearance, but this does not imply that the intrinsic  clearance is proportional to the size or volume of the liver. This  requires an extra assumption, that is not needed in the usual clearance  approach. Clearance refers to the capacity of the whole liver, not to  some arbitrary fraction of it."Now we move to the whole body. We know the hepatic clearance is  CLh=Q*[Kliver*Vliver/(Q+Kliver*Vliver)] (simplified version from  Malcolm Rowland et al. Clearance Concepts in Pharmacokinetics,Journal of  Pharmacokinetics and Biopharmaceutics,1973, assuming the partition  coefficient in the original equation is 1) where Q is the blood flow  rate to liver (L/hr)."I don't have this paper at hand, but in their standard textbook  'Clinical Pharmacokinetics', Rowland and Tozer used a more rational  equation:CLbh=Q*[CLint*fub/(Q+ CLint*fub)]where CLbh is the hepatic blood clearance CLint is the intrinsic  clearance (i.e. the hypothetical clearance if fub = 1 and Q is  infinitely high) and fub is the fraction unbound in blood.The obvious reason for abandoning the earlier equation is its inability  to explain the influence of enzymatic capacity and plasma protein  binding on hepatic clearance."If I express Q as Q=Fliver*Vblood/Tcycle where Fliver is the fraction  of blood that goes to liver and Tcycle is the time it takes for the  blood to finish one cycle of circulation, then  CLh=Fliver*Vblood/Tcycle*[Kliver*Vliver/(Q+Kliver*Vliver)], which  shows the dependence of CLh on Vblood."I disagree. Liver blood flow Q is dependent on many factors including  cardiac output, arterial, portal and venous blood pressure, and  resistance of the hepatic blood vessels. Fliver is not a constant, but a  composite parameter, by definition equal to Q/CO (cardiac output. Tcycle  is not a constant, but a composite parameter, by definition equal to  Vblood/CO. Filling in these definitions in your equation results in Q=Q.  Physiologically there is no reason why Q is dependent on Vblood  (remember the example of extracorporeal clearance, see below). As a  consequence, there is no reason to assume that CLh is dependent on  Vblood. On the contrary, I cannot imagine a situation where CLh is  dependent on Vblood."Tcycle can depend on many factors such as cardiac function, rest or  not, etc."A simple hydrostatic reasoning will lead to the conclusion that Tcycle  is dependent on CO (pumping rate) and Vblood (circulating volume). As  stated above, Tcycle is by definition equal to Vblood/CO. Please note  the analogy with k = CL /V. Perhaps you may think that CO =  Vblood/Tcycle (analogous to: CL = V * k), but this makes no sense.  Tcycle and k are the dependent composite parameters."For any drug whose volume of distribution is dominated by the blood  volume (Vdrug~=Vblood) and elimination is mainly via liver, we can see  the dependence of CLh on Vdrug or Vblood."This conclusion has been refuted above."In your simple but uncommon example of extracorporeal circulation, you  increased Vblood but you also have to increase Tcycle in order to keep  CLh constant."Tcycle increases if Vblood increases. This is not an extra assumption,  but results from the fact that Tcycle = Vblood / CO.Besides, I fully agree that extracorporeal circulation is an uncommon  example, but it is a useful example to test the ability of  pharmacokinetic concepts. It simply refutes the 'rate constant'  approach."This does not show CLh is independent of Vblood because another factor  has to be changed simultaneously to make it look like independent."No, it's just the other way around. CLh is independent of Vblood. It  looks like dependent because another factor (K) changes simultaneously."From a rate constant point of view,  K=Fliver/Tcycle*[Kliver*Vliver/(Q+Kliver*Vliver)]. This composite rate  constant is also dependent on Vblood or Vdrug via Q."I don't understand what this K means. What can we learn from it? Why do  we need an additional parameter here?"In your example of drugs with high extraction in the liver, where  CLh=Q, the dependence of CLh on Vblood could not be more clear."Mechanistically, it cannot be true that Q is dependent on Vblood. Please  note that I don't say that Q cannot change as an indirect result of a  change of blood volume, e.g. by a change of blood pressure, CO, or  resistance."The same argument can be applied to GFR."GFR is not dependent on blood volume. GFR is a functional parameter of  kidney function, determined by several factors including blood pressure  and the functioning of the glomeruli. Please note that I don't say that  GFR cannot change as an indirect result of a change of blood volume,  e.g. by a change of blood pressure, CO, or resistance."Again, I am only pointing out certain scenarios where CL is not so  independent of V. When V is getting much larger than the blood volume,  the dependence becomes less."Even in the scenarios that V is close to blood volume, your arguments do  not hold, as pointed out above."After all, I don't mind using a composite parameter, whether it is K or  CL, to make decisions as long as it solves the problem."I'm afraid that using K produces more problems, instead of solving the  problem; please see my earlier message to Peter Mullen.best wishes for 2010,Hans ProostJohannes H. ProostDept. of Pharmacokinetics, Toxicology and TargetingUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlands`
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• On 3 Jan 2010 at 19:58:23, Peter W Mullen (pmullen.at.kemic.com) sent the message
`Dear Hans,I trust you've had a joyous Christmas holiday.In response to your posting of December 28th, I offer the following:My position (now repetitious :-( ) in this debate is that clearance  really offers little, if any, benefit over rate constants in practical  *classical* pharmacokinetic modeling applications. {In fact, Ke (or  T1/2) may have wider overall utility especially when one considers  multiple dosing calculations, etc.} Additionally, the assumption that  the use of clearance imbues a simple one, two or other *classical*  compartmental model (and yes, especially the intercompartmental transfer  process!) with meaningful "biological" characteristics is unrealistic to  say the least.  Applied to such structurally simple models, clearance is  mostly a "pharmacokinetic embellishment"! In *classical* pharmacokinetic  modeling it makes little difference whether a particular model is framed  in terms of a rate constant, or clearance, or (for that matter, if it  was possible) some "Thingy Parameter" (having units that work consistent  with the framing) considering the utter simplicity, biologically  speaking, of the models us`
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• On 4 Jan 2010 at 21:51:03, Nick Holford (n.holford.-at-.auckland.ac.nz) sent the message
`Hi,I think Peter Mullen's latest posting has pretty much confirmed that the  reason that the CL=K*V and K=CL/V view points of PK cannot be  distinguished is because they are just algebraic re-arrangements i.e.  reparameterizations. Thus they must  be indistinguishable and either  perspective will produce the same computational results.Let take a different viewpoint. Imagine a drug that is extensively bound  to skeletal muscle (but not to plasma proteins so we can ignore any red  herring phenomena related to plasma protein binding). Suppose that its  elimination is essentially all by glomerular filtration with no  secretion or absorption.Now think about two different biological scenarios:1. Imagine that one kidney is removed. or2. Imagine that both legs are amputated.What will happen to the mean residence time (MRT)?  (I've chosen MRT so  we don't get hung up with which half-life is involved if disposition  appears to be multi-exponential).From a clearance and volume viewpoint the clearance will be determined  by the kidneys and the apparent volume of distribution mainly by  skeletal muscle mass. With this perspective it is clear that scenario 1  will lead to a longer MRT because clearance is reduced and scenario 2  will lead to a shorter MRT because the volume of distribution is  reduced.What predictions would the rate constant believers make and why?NickWhat predictions`
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• On 4 Jan 2010 at 17:17:17, "J.H. Proost" (j.h.proost.-at-.rug.nl) sent the message
`The following message was posted to: PharmPKDear Peter,Thank you for your reply. I had a joyous Christmas holiday, and I'm  ready again to continue the 'clearance story'.A few comments on your comments:"My position (now repetitious :-( ) in this debate is that clearance  really offers little, if any, benefit over rate constants in practical  *classical* pharmacokinetic modeling applications. {In fact, Ke (or  T1/2) may have wider overall utility especially when one considers  multiple dosing calculations, etc.}"Daily dose is determined by clearance (not by rate constant, not by  volume), so clearance has the 'widest overall utility'. For the  'non-clearance absolutists': from the basic equation dA/dt = CL * C it  follows after integration over one dosing interval that in steady state  F*Dose = CL * Css."Additionally, the assumption that the use of clearance imbues a simple  one, two or other *classical* compartmental model (and yes, especially  the intercompartmental transfer process!) with meaningful "biological"  characteristics is unrealistic to say the least."On December 28 I wrote (you did not reply to this comment): Using  intercompartmental clearance is also much more 'biological' than the  rate constants approach. The transfer between compartments may be either  due to perfusion limitation (in this case the meaning of  intercompartmental clearance is the perfusion) or due to permeability  limitation; also in the latter case a single constant, intercompartmetal  clearance, for the 'diffusion coefficient' is more appropriate than two  rate constants (k12 and k12); is there any a priori reason why transport  constant in both directions would be different?"Applied to such structurally simple models, clearance is mostly a  "pharmacokinetic embellishment"!""You're joking now, I hope. If not, it is a rather presumptuous comment  on the clearance approach."In *classical* pharmacokinetic modeling it makes little difference  whether a particular model is framed in terms of a rate constant, or  clearance, or (for that matter, if it was possible) some "Thingy  Parameter" (having units that work consistent with the framing)  considering the utter simplicity, biologically speaking, of the models  used. (I know that you will not concur, but when applied to simple PK  models, clearance IS essentially "a mere number" albeit, a potentially  useful one.)"Yes, I agree as long as you don't want to do anything more than  presenting numbers. But this is not the merit of PK. PK should be used,  e.g. to rationalise dosing. Therefore we need models that can explain  and predict the concentration (and effec in PKPD) - time profile, also  in the case of altered conditions, e.g. displacement from tissue binding  (see below).In answer to my example of displacement from tissue binding sites you  wrote:"I'm afraid I don't fully appreciate the point you're trying to make  with this example.  The net practical consequence of displacement of a  drug from tissue binding sites is complex and  would depend on many  factors including the initial extent of binding  (to both tissue and  plasma sites), the hepatic extraction ratio of the displaced drug, etc.  Why do you assume that drug elimination would not be affected?"Yes, in a 'rate constant' world this example is difficult to understand.  In the 'clearance' world, it is completely clear. Plasma protein binding  and hepatic extraction ratio are not relevant to answer the question.  Why would drug elimination be affected if clearance does not change?  This is not an assumption. Please note that, assuming unaltered dosing,  there is a temporary increase of drug elimination due to the temporary  increase of plasma concentration as a result of the reduced volume of  distribution; however, clearance remains constant, and in the new steady  state the average plasma concentration is the same as before the  administration of the displacer."Finally, concerning the "derivations" cited by both Yaing and me which  clearly indicate that CL = V*k, I notice that a rearrangement to k =  CL/V always occurs in your hands  :-) . I realize that you and others  will justify this on "biological" grounds but this tactic appears to be  an avoidance of the essential math underlying the clearance concept  merely to be consistent with the aforementioned "embellishment"."There is no tactic or avoidance here. The only reason that I always  write k = CL/V is to make clear that k is dependent on CL and V. What  is the essential math underlying the clearance? That is dA/dt = CL * C  and I never avoided this."I also notice that arguments in favour of clearance parameterization of  simple PK models are mostly illustrated from within the context of  multiple dosing (steady-state)."There is no multiple dosing in the argument that dA/dt = CL * C, which  is valid under all linear conditions."By the way, given a basic "graph paper exercise" how do YOU calculate  the clearance applicable to simple (e.g. mono-exponential decay after  bolus i.v. administration) single-dose, drug concentration-time data?"Either from Dose=CL*AUC, with AUC estimated by trapezoidal rule, if  necessary extrapolated using k (!), or from C0/k (!). Yes, I often use k  in its interpretation as the rate of plasma concentration decay dC/dt =  k * C. Please note that using k in this context does not mean that I  ignore the fact that k is dependent on CL and V.best wishes for 2010,Hans ProostJohannes H. ProostDept. of Pharmacokinetics, Toxicology and TargetingUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlands`
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• On 3 Jan 2010 at 19:44:24, Rostam Namdari (chista90.-a-.yahoo.com) sent the message
`The following message was posted to: PharmPKThediscussion on CL and K captured my attention for 2 reasons: 1)  scientificallyinteresting and 2) has become the lengthiest debate after the one I  generatedon half-life almost 10 years ago. As someone else also mentioned one of  themajor factors that some colleagues interpret CL is a dependent PK  parameter andV and K are independent parameters is the way this equation is written:  CL = Kx V. It is less confusing if is written as K = CL/V. I like to discuss  a side pointbut related to the topic which was raised by Andrew on his Dec 30/09  posting: "I saw yourreference to a probable increase in volume of distribution with age fordiazepam and it makes me ask the question of how this could actually  occurbecause the populations I am more familiar with tend to reduce body fat  withage, so you would expect a lipophilic molecule to find a smaller volume  of distribution.Hence, I'm bound to ask which population was in the study or studies  that youquoted."   Andrew, would you elaborate which population you are  referring to? elderly population?Klotzet al examined PK of diazepam (DZ) in 33 healthy adults with age ranging  from15 to 82 yr and observed linear increase in t1/2 from 20 h at 20 yr to  90 h at80 yr without seeing age-dependence for CL. They concluded that "it  appearsthen that the prolongation of t1/2 of DZ with age is preliminary  dependent onan increase in the initial distribution volume of the drug". This is not  astrong claim and perhaps they tried to put a fair balance on it by  saying appearsand preliminary. I found it difficult to examine the strength of this  claimsince they provided CL values for a subset of the study population (20  subjectsonly) but t1/2 values were provided the for all the 33 subjects. In  addition,they acknowledge that in 4 older subjects, a significant reduction in CLcontributed to the prolongation of t1/2 and speculated that this is due  to reductionin the hepatic extraction associated with an impairment of  drug-metabolizingenzyme. Nevertheless their observation is not without merit and I will  try toexplain why increase in Vd could result in longer t1/2 (which is not a  new conceptto you and perhaps the dispute is over the direction of change in body  fat). Bodyfat generally tend to increase with aging (I have a feeling you disagree  withthis) which could increase the Vd of lipophilic drugs like DZ and lead  to alonger t1/2. The other possibility is increase in tissue protein binding  which couldalso result in longer t1/2. Or alternatively combination of both. If  these are true then the frequency of CNS sideeffects in older subjects compared to younger subjects receiving the  same dose shouldbe higher; a significant increase in CNS side effects were noted between  theage of 40 and 70 (N. Engl. J. Med 288: 277-280).Rostam`
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• On 4 Jan 2010 at 20:40:18, Peter W Mullen (pmullen.aaa.kemic.com) sent the message
`The following message was posted to: PharmPKThis is a multi-part message in MIME format.Hi Hans,Here we go again...! :-)You wrote:> "Daily dose is determined by clearance (not by rate constant, not by> volume), so clearance has the 'widest overall utility'. For the> 'non-clearance absolutists': from the basic equation dA/dt = CL * C it> follows after integration over one dosing interval that in steady> state F*Dose = CL * Css. "Once again (here and later in your message) you're emphasizing dA/dt =CL * C and, to justify it, the steady-state situation (instead of of themore practical, dC/dt = ke * C as would be utilized upon firstinvestigating a drug (i.e. single dose administration). (Also, in thesingle dose situation, V, if known, amongst other considerations, wouldlikely be a determinant in choosing the dose.)> "On December 28 I wrote (you did not reply to this comment): Using> intercompartmental clearance is also much more 'biological' than the> rate constants approach. The transfer between compartments may be> either due to perfusion limitation (in this case the meaning of> intercompartmental clearance is the perfusion) or due to permeability> limitation; also in the latter case a single constant,> intercompartmetal clearance, for the 'diffusion coefficient' is more> appropriate than two rate constants (k12 and k12); is there any a> priori reason why transport constant in both directions would be> different? "Consistent with my previous comments, I would have to disagree. To useintercompartmental clearances instead of k12 and k21 (etc.) believingthat this approach is "much more 'biological'" is problematic. Why tryto be more "biological" in respect to transfer between compartments whenthese very "containers", simple as they are, hold little biologicalmeaning? (I know of no reason why, /a priori/, the intercompartmentaltransfer constants should be different, but I may be missing the pointof the question.)> ""Applied to such structurally simple models, clearance is mostly a> "pharmacokinetic embellishment"!"">> You're joking now, I hope. If not, it is a rather presumptuous comment> on the clearance approach. "Yes, it occurred to me (after I hit the send button...) that this turnof phrase might be considered presumptuous (or worse!). No offenseintended, but there is a grain of truth to the comment given theundeniable biological simplicity of the models so-embellished. :-)Re. your example of displacement from tissue binding sites:> "Yes, in a 'rate constant' world this example is difficult to> understand. In the 'clearance' world, it is completely clear. Plasma> protein binding and hepatic extraction ratio are not relevant to> answer the question. Why would drug elimination be affected if> clearance does not change? This is not an assumption. Please note> that, assuming unaltered dosing, there is a temporary increase of drug> elimination due to the temporary increase of plasma concentration as a> result of the reduced volume of distribution; however, clearance> remains constant, and in the new steady state the average plasma> concentration is the same as before the administration of the displacer."I doubt that clearance would be unaffected in the displacement situationyou mentioned! Assuming that both total and free plasma drugconcentrations increase, for a drug having mainly hepatic eliminationthe CL would likely INCREASE (since CL= fu*CLint). Moreover, regardlessof any change in CL or not, your ultimate decision making, as stated inyour previous message, was based on T1/2 (i.e. 0.693/ *ke*   :-) ). {AsI'm sure you know, whether the displacement is likely to be"significant" from a therapeutic (pharmacodynamic) standpoint requiresmore information about the hypothetical drug.}> ""By the way, given a basic "graph paper exercise" how do YOU> calculate the clearance applicable to simple (e.g. mono-exponential> decay after bolus i.v. administration) single-dose, drug> concentration-time data?">> Either from Dose=CL*AUC, with AUC estimated by trapezoidal rule, if> necessary extrapolated using k (!), or from C0/k (!). Yes, I often use> k in its interpretation as the rate of plasma concentration decay> dC/dt = k * C."I'm glad to hear it!> "Please note that using k in this context does not mean that I ignore> the fact that k is dependent on CL and V. "Somehow, that doesn't surprise me... :-)Cheers,- Peter*Peter W. Mullen, PhD, FCSFSKEMIC BIORESEARCH (**www.kemic.com* *)KentvilleNova Scotia, B4N 4H8Canada`
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• On 4 Jan 2010 at 20:37:27, Peter W Mullen (pmullen.-at-.kemic.com) sent the message
`Hi Nick,You wrote:"Let take a different viewpoint. Imagine a drug that is extensively  bound to skeletal muscle (but not to plasma proteins so we can ignore  any red herring phenomena related to plasma protein binding). Suppose  that its elimination is essentially all by glomerular filtration with no  secretion or absorption.Now think about two different biological scenarios:1. Imagine that one kidney is removed. or2. Imagine that both legs are amputated.What will happen to the mean residence time (MRT)?  (I've chosen MRT so  we don't get hung up with which half-life is involved if disposition  appears to be multi-exponential)....."This is a good nitty gritty question but it's not clear to me as to the  nature of the predictions you're seeking from the "non-absolutist"  community? Are you merely asking what they would predict in terms of the  direction of the MRT for each scenario? (In that regard, I would readily  agree with what you've already said in your posting.)Please clarify.Best regards and "Happy New Year",PeterPeter W. Mullen, PhD, FCSFSKEMIC BIORESEARCH (www.kemic.com)KentvilleNova Scotia, B4N 4H8Canada`
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• On 5 Jan 2010 at 19:48:07, Nick Holford (n.holford.-a-.auckland.ac.nz) sent the message
`Peter,I'm sorry my question was not clear enough so I will try again:Let take a different viewpoint. Imagine a drug that is extensively bound  to skeletal muscle (but not to plasma proteins so we can ignore any red  herring phenomena related to plasma protein binding). Suppose that its  elimination is essentially all by glomerular filtration with no  secretion or absorption.Now think about two different biological scenarios:1. Imagine that one kidney is removed. or2. Imagine that both legs are amputated.The question for the rate constant believers is what would you predict  will happen to MRT and how would you make that prediction from a rate  constant viewpoint?  (I've chosen MRT so we don't get hung up with which half-life is  involved if disposition appears to be multi-exponential)Nick`
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• On 5 Jan 2010 at 14:29:50, "J.H.Proost" (J.H.Proost.at.rug.nl) sent the message
`The following message was posted to: PharmPKDear Peter,You replied:"Once again (here and later in your message) you're emphasizing dA/dt =  CL * C and, to justify it, the steady-state situation (instead of of the  more practical, dC/dt = ke * C as would be utilized upon first  investigating a drug (i.e. single dose administration). (Also, in the  single dose situation, V, if known, amongst other considerations, would  likely be a determinant in choosing the dose.)"I did not justify 'my' equation dA/dt = CL * C with a steady-state  situation; I merely stated that this equation is valid under any  (linear) condition. The reason that I repeat this equation so often is  the fact that this is the basic of rational pharmacokinetics. It is  simply the definition of CL, using the notion that the rate of  elimination (amount/time) is proportional to the plasma concentration  (driving force), both for drugs renally filtered and for drugs  metabolised.'Your' equation dC/dt = ke * C is indeed more practical in the sense  that it is derivated more directly from observations of the plasma  concentration decay. In my view, that is the only 'more practical'  aspect, however."Consistent with my previous comments, I would have to disagree. To use  intercompartmental clearances instead of k12 and k21 (etc.) believing  that this approach is "much more 'biological'" is problematic. Why try  to be more "biological" in respect to transfer between compartments when  these very "containers", simple as they are, hold little biological  meaning? (I know of no reason why, /a priori/, the intercompartmental  transfer constants should be different, but I may be missing the point  of the question.)"In my opinion we should try to understand pharmacokinetics (or better,  PK-PD) from a physiological and anatomical starting point. This gives  the best chance to use PK (PKPD) for predictions. My counter-question  is: why should we NOT try to be more biological in respect to transfer  between compartments?The point of the question is: in the two-compartment model you get two  rate constants for transfer between the compartments, k12 and k21. The  values for these rate constants are different, suggesting that the  transport from 1 to 2 is governed by different 'rules' than transport  from 2 to 1. This may be so, e.g. in the case of active transport, but  in the 'normal' case there is no reason to assume that these transport  processes are really different. Also the question rises: are k12 and k21  independent? Your answer would probably be: Yes. My answer is No: both  k12 and k21 are related by a common intercompartmental clearance, i.e.  k12 = CL2/V1 and k21 = CL2/V2."No offense intended, but there is a grain of truth to the comment given  the undeniable biological simplicity of the models so-embellished. :-)"I don't see the grain. Of course we make our models as simple as  possible, but not more simple than minimally required. Using the  clearance approach is not for fun, not for embellishment. We use it for  a better understanding of PK."I doubt that clearance would be unaffected in the displacement  situation you mentioned! Assuming that both total and free plasma drug  concentrations increase, for a drug having mainly hepatic elimination  the CL would likely INCREASE (since CL= fu*CLint)."Please note that in my example it was tissue binding that was changing  by a displacement interaction. This implies that fu remains constant.""Moreover, regardless of any change in CL or not, your ultimate decision  making, as stated in your previous message, was based on T1/2 (i.e.  0.693/ *ke* :-) ). {As I'm sure you know, whether the displacement is  likely to be "significant" from a therapeutic (pharmacodynamic)  standpoint requires more information about the hypothetical drug.}"I fully agree that in real life we need more information about the  hypothetical drug to make a final judgement about the clinical  significance of the interaction. The main reason for this is that we  have to be sure that the interaction is indeed at the level of tissue  binding only. A PK model that can explain the effect of a change of  tissue binding quantitatively is more useful than a PK model that cannot  do this. Please note that I made two decisions: (1) daily dose should  not be change, because CL is unaffected, and (2) dosing interval may be  shortened because of the shorter half-life.best regards,Hans ProostJohannes H. ProostDept. of Pharmacokinetics, Toxicology and TargetingUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlands`
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• On 7 Jan 2010 at 13:50:53, Peter W Mullen (pmullen.at.kemic.com) sent the message
`Hi Hans,I've presented my position in our long-running "question of clearance"  debate and to avoid its further(!) repetition on PharmPK I am now bowing  out.I again thank you for participating. You are a knowledgeable and  gracious "opponent".Sincere best wishes,PeterP.S. Rate constants forever! :-)Peter W. Mullen, PhD, FCSFSKEMIC BIORESEARCH (www.kemic.com)KentvilleNova Scotia, B4N 4H8Canada`
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• On 11 Jan 2010 at 15:56:46, "J.H. Proost" (j.h.proost.-at-.rug.nl) sent the message
`The following message was posted to: PharmPKDear Peter,I'm sorry to hear that are bowing out. Indeed, repeating statements does not make sense, however, an open discussion on 'a question of clearance' is important. In fact, I didn't get a convincing rebuttal of my arguments. I still don't understand the reserve with respect to clearance.best regards,Hans ProostJohannes H. ProostDept. of Pharmacokinetics, Toxicology and TargetingUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlands`
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• On 12 Jan 2010 at 08:08:03, Nick Holford (n.holford.-at-.auckland.ac.nz) sent the message
`Johannes,Thanks for your very clear explanations of why clearance is preferable to rate constants for thinking about pharmacokinetic principles. I think it is now obvious that when it comes to solving PK math it makes no difference because simple algebraic re-parameterization has nothing to do with biology and pharmaocology.However, there have been no responses from the rate constant believers to my question on how to predict changes in MRT when either a kidney is remove or legs are amputated. Unless a convincing argument is given for making a prediction based on rate constants I think we can end this discussion by concluding that clearance is more useful than rate constants when it comes to understanding science.Best wishes,Nick-- Nick Holford, Professor Clinical PharmacologyDept Pharmacology & Clinical PharmacologyUniversity of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand[In the simplest case MRT = 1/k (or vice versa) so one kidney removed would k/2 or MRT x 2. In the case of amputation MRT might stay the same or change depending on the relative V1 versus Vss change. If Vss = CL x MRT and CL = V1 x k10 then MRT = Vss/(v1 x k10). If amputation doesn't change elimination, k10 is unchanged but MRT will depend on changes in the ratio of Vss to V1. Googling amputation and pharmacokinetics produced one reference involving propofol. MRT(normal patient) = 132 min, MRT(patient) = 145 min, ratio 1.1. Vss/V1 = 15.7 and 13.2, ratio = 1.2. Clearance ratio 1.25. Looking back at the PharmPK archives I found one mention in 2002 regarding amputation and changes in CLcr.http://www.boomer.org/pkin/PK02/PK2002076.htmlNick, do you have any more (recent) data?- db]`
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• On 12 Jan 2010 at 08:07:27, Des Williams (Des.Williams.at.unisa.edu.au) sent the message
`The following message was posted to: PharmPKDear AllI have very much enjoyed the continuing dialogue on clearance. Such debates can only help those involved or who read the arguments carefully to understand and consolidate understanding and confidence in the concepts discussed.I suspect that most pharmacokineticists and those applying the principles will very much favour clearance over rate constants (and I am very much one of those). Having said that, I think that those who have put forward the view that rate constants are sufficient or easier to work with have contributed to the scientific debate in a helpful manner. If we did not have these persons putting forward the opposing view, less of the good points supporting clearance concepts would have been made.Des--Des Williams, PhD, BPharm, FRACI, CChem Sansom Institute for Health Research, and School of Pharmacy and Medical Sciences University of South Australia North Terrace Adelaide`
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• On 11 Jan 2010 at 20:37:46, Peter W Mullen (pmullen.aaa.kemic.com) sent the message
`Hi Nick (& Hans),I promised (myself) that I would cease to participate in this debate as it was becoming very repetitious, but you guys make it sooo difficult! :-)Nick, I think David Bourne (in a P.S. to your posting) just answered your question re. rate constants and MRT in the context of kidney ablation and leg amputation.  I was thinking along essentially the same lines but never put pen to paper since it seemed so obvious I assumed that I was missing the point (which is why I sought clarification after your initial posting of this 'exercise'). (Admittedly, I still may be missing the point...!)I have absolutely no problem with the basic concept of clearance in pharmacokinetics. (It can even be useful :-) , particularly when applied at the organ level and, of course, it is a key and meaningful parameter in PBPK modeling.) However, regarding your conclusion "...that clearance is more useful than rate constants when it comes to understanding science", I present the following three questions:i) *Is understanding science really facilitated* by biasly rearranging the mathematics underlying clearance by always writing ke = CL/V when mathematical derivations clearly indicate that CL = ke*V? {CL = ke*V is a mathematical fact which no arbitrary pretense of invoking "physiology" will alter. A science without a firm, non-arbitrary mathematical foundation cannot aspire to be quantitative; it would merely be "stamp collecting" to (mis)quote Rutherford.}ii) *Is understanding science really facilitated* by parameterizing simple classical pharmacokinetic (e.g. two compartment) models with clearance (e.g. CL/V) instead of rate constants? (I have already referred to this approach as "pharmacokinetic embellishment". The expression, "applying lipstick to a pig", also comes to mind, although even the pig so-embellished isn't whole but merely an entity "comprised" of two interconnected containers!)iii) *Is understanding science really facilitated* by limiting the use of rate constants (or half-lives) when these may have greater overall utility than does CL in classical pharmacokinetics (as per multiple dosing calculations, etc. and, circuitously, in the actual calculation of CL itself!)?Finally, I'm somewhat surprised that you're presenting an exercise involving MRT given your admonition, early in this debate, about using SHAM (Shape, Height, Area, Moment) concepts. What could be more "SHAMFUL" than MRT? :-)BTW, if I don't respond to future postings on this topic it's only because I am actually living up to that commitment made in my previous posting!Regards,PeterPeter W. Mullen, PhD, FCSFSKEMIC BIORESEARCH (www.kemic.com)KentvilleNova Scotia, B4N 4H8Canada`
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• On 12 Jan 2010 at 17:05:44, Nick Holford (n.holford.at.auckland.ac.nz) sent the message
`The following message was posted to: PharmPKPeter W Mullen wrote:> Nick, I think David Bourne (in a P.S. to your posting) just answered your question re. rate constants and MRT in the context of kidney ablation and leg amputation.  I was thinking along essentially the same lines but never put pen to paper since it seemed so obvious I assumed that I was missing the point (which is why I sought clarification after your initial posting of this 'exercise'). (Admittedly, I still may be missing the point...!)  Thanks for pointing out David's PS. I didn't find an answer to my questions there.> I have absolutely no problem with the basic concept of clearance in pharmacokinetics. (It can even be useful :-) , particularly when applied at the organ level and, of course, it is a key and meaningful parameter in PBPK modeling.) However, regarding your conclusion "...that clearance is more useful than rate constants when it comes to understanding science", I present the following three questions:>> i) *Is understanding science really facilitated* by biasly rearranging the mathematics underlying clearance by always writing ke = CL/V when mathematical derivations clearly indicate that CL = ke*V? {CL = ke*V is a mathematical fact which no arbitrary pretense of invoking "physiology" will alter. A science without a firm, non-arbitrary mathematical foundation cannot aspire to be quantitative; it would merely be "stamp collecting" to (mis)quote Rutherford.} You can re-arrange the equations any way you like but it doesn't bias the numerical result.> ii) *Is understanding science really facilitated* by parameterizing simple classical pharmacokinetic (e.g. two compartment) models with clearance (e.g. CL/V) instead of rate constants? (I have already referred to this approach as "pharmacokinetic embellishment". The expression, "applying lipstick to a pig", also comes to mind, although even the pig so-embellished isn't whole but merely an entity "comprised" of two interconnected containers!) Simple classical = mathematical non-biological> iii) *Is understanding science really facilitated* by limiting the use of rate constants (or half-lives) when these may have greater overall utility than does CL in classical pharmacokinetics (as per multiple dosing calculations, etc. and, circuitously, in the actual calculation of CL itself!)?  Computations can be made easier sometimes by using rate constants. Computation isn't the science of biology and pharmacology.> Finally, I'm somewhat surprised that you're presenting an exercise involving MRT given your admonition, early in this debate, about using SHAM (Shape, Height, > Area, Moment) concepts. What could be more "SHAMFUL" than MRT? :-)I explained why I used MRT in the original posting...-- Nick Holford, Professor Clinical PharmacologyDept Pharmacology & Clinical PharmacologyUniversity of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand`
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• On 12 Jan 2010 at 16:58:43, Nick Holford (n.holford.aaa.auckland.ac.nz) sent the message
`David,I missed this because you buried it below my email signature.  But thanks to Peter Mullens (who decided to do a Lazarus act) I have now discovered it.Well - it seems you have made a prediction but I dont see the explanation. How do you EXPLAIN that if one kidney is removed then this would lead to k/2 (without invoking clearance)?I don't see the point of your question about recent data. This is armchair theoretical stuff :-)Nick>[In the simplest case MRT = 1/k (or vice versa) so one kidney removed would k/2 or MRT x 2. In the case of amputation MRT might stay the same or change depending on the relative V1 versus Vss change. If Vss = CL x MRT and CL = V1 x k10 then MRT = Vss/(v1 x k10). If amputation doesn't change elimination, k10 is unchanged but MRT will depend on changes in the ratio of Vss to V1. Googling amputation and pharmacokinetics produced one reference involving propofol. MRT(normal patient) = 132 min, MRT(patient) = 145 min, ratio 1.1. Vss/V1 = 15.7 and 13.2, ratio = 1.2. Clearance ratio 1.25. Looking back at the PharmPK archives I found one mention in 2002 regarding amputation and changes in CLcr.http://www.boomer.org/pkin/PK02/PK2002076.htmlNick, do you have any more (recent) data?- db]-- Nick Holford, Professor Clinical PharmacologyDept Pharmacology & Clinical PharmacologyUniversity of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand`
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• On 12 Jan 2010 at 14:24:18, Rostam Namdari (chista90.-at-.yahoo.com) sent the message
`The following message was posted to: PharmPKI think we all agree that both CL and K have their utility in PK. Peter is makinga very specific point that in the context of "classical PK" CL does not providea significant advantage over K but I do not think he is disputing the overallsuperiority of CL. There are certain situations where CL approach works better.For example:1)      Describing PK of metabolite. Hirt et al 2007 (BJCP, 65:4,548-557) study the effect of 2C19 polymorphism on nelfinavir to M8 Met in HIVPts. Since no urinary conc. data were available for M8 they re-parameterizedthe one comp PK model with an additional metabolite compartment using CL approachto describe the PK of nelfinavir and M8.2)      PK modeling of many botanical product with multiple secondary peaks(not a well distinguished terminal phase)3)      Dose adjustment for certain physiological changes or diseasestate when t1/2 does not change but Vd and CL changes in a manner leading tooverall exposure (AUC) change. I am familiar with preclinical example of this butdo not know a marketed drug that may behave like this and appreciate if someonecan provide an example.Rostam`
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• On 12 Jan 2010 at 17:25:11, Ayyappa Chaturvedula (ayyappach.-at-.yahoo.com) sent the message
`The following message was posted to: PharmPKCan somebody explain more on the plausible reasons where no changes in t1/2 but exposure (auc) changes are observed?Regards, Ayyappa Chaturvedula`
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• On 13 Jan 2010 at 16:12:32, Nick Holford (n.holford.-a-.auckland.ac.nz) sent the message
`The following message was posted to: PharmPKAyyappa Chaturvedula wrote:>> Can somebody explain more on the plausible reasons where no changes in t1/2 but exposure (auc) changes are observed?If clearance and volume change in similar proportions due to differences in extent of bioavailability or plasma protein binding then AUC (which is determined ONLY by clearance) will change and half-life will not change because it is a secondary parameter determined by the ratio of volume to clearance (and the magic number ln(2) (~=0.7)).-- Nick Holford, Professor Clinical PharmacologyDept Pharmacology & Clinical PharmacologyUniversity of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand`
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• On 14 Jan 2010 at 12:36:05, "J.H.Proost" (J.H.Proost.-a-.rug.nl) sent the message
`The following message was posted to: PharmPKDear Rostam,You wrote:> I think we all agree that both CL and K have their utility in PK.> Peter is making a very specific point that in the context of> "classical PK" CL does not provide a significant advantage over> K but I do not think he is disputing the overall> superiority of CL.In my opinion Peter (and Yaning) was disputing the overall superiority of CL, and that is the reason that I commented upon so many times. There is a superiority of CL. I have demonstrated that both theoretically (from the definition of clearance) and by examples ('should the dosing regimen be adjusted in the case of a displacement of tissue binding sites?'). Nick Holford added another theoretical example, and Les an example from real life. Peter and Waning did not provide a convincing rebuttal of these arguments. Instead, they repeated their arguments, or tried new arguments, without success, of course.Please note that there are situations where the rate constant approach is useful, and that in some situations the clearance approach might not be applicable. This is not where the debate is about. The essential point of the discusssion is on the question whether clearance is dependent on k and V, or whether the rate constant k is dependent on CL and V. This is not a chicken-and-egg question.best regards,Hans ProostJohannes H. ProostDept. of Pharmacokinetics, Toxicology and TargetingUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlands`
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• On 14 Jan 2010 at 12:42:23, "J.H.Proost" (J.H.Proost.-at-.rug.nl) sent the message
`The following message was posted to: PharmPKDear Nick,You wrote to Ayyappa Chaturvedula:> If clearance and volume change in similar proportions due to > differences in extent of bioavailability or plasma protein bindingI hope that you mean that in this sentence 'clearance' refers to the 'oral clearance' (terrible term), i.e. CL/F, and 'volume' to V/F.If not, we have to start a new discussion ...[Yes, that had me worried too, I misread the AUC comment and nearly misspoke ;-). Of course in this example, k10 doesn't change and AUC is proportional to F and AUC is inversely proportional to oral clearance (CL/F) - db]By the way, thanks to your support in the 'defense of the clearance approach'!best regards,Hans ProostJohannes H. ProostDept. of Pharmacokinetics, Toxicology and TargetingUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlands`
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• On 14 Jan 2010 at 12:47:17, "J.H.Proost" (J.H.Proost.at.rug.nl) sent the message
`The following message was posted to: PharmPKDear David,In your added comment to the message by Nick you wrote:>In the case of amputation MRT might stay the same or change depending>on the relative V1 versus Vss change. If Vss = CL x MRT and CL = V1 x>k10 then MRT = Vss/(v1 x k10). If amputation doesn't change>elimination, k10 is unchanged but MRT will depend on changes in the>ratio of Vss to V1.I disagree. In the case of amputation of one leg, one would expect adecrease of V, likely both V1 and Vss. However, there does not seem tobe an a priori reason that clearance would be affected. So, since MRT= Vss/CL, I would expect a decrease of MRT.In your reasoning, you say that no change in elimination would notaffect k10. It is clearance that is not expected to change. This is aclassical example where the rate constant approach fails (and I'mquite sure that this is the reason for Nick's question).>Googling amputation and pharmacokinetics produced one reference>involving propofol. MRT(normal patient) = 132 min, MRT(patient) = 145>min, ratio 1.1. Vss/V1 = 15.7 and 13.2, ratio = 1.2. Clearance ratio>1.25. Looking back at the PharmPK archives I found one mention in>2002 regarding amputation and changes in CLcr.The clearance ratio is 1.25. Whether of not this is due to theamputation (I would not expect), this would contribute to a lower MRT.If MRT is indeed increased, this would imply that Vss is increased.Quite strange. Do all ratio's refer to amputation / normal ?[The reference is athttp://www.springerlink.com/content/av8hf1pj4xv7j7pt/fulltext.pdfJ. Anesth (2003) 17:147-148 - db]best regards,Hans ProostJohannes H. ProostDept. of Pharmacokinetics, Toxicology and TargetingUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlands`
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• On 14 Jan 2010 at 15:48:23, "J.H.Proost" (J.H.Proost.-at-.rug.nl) sent the message
`The following message was posted to: PharmPKDear Peter,Yes, 'you guys make it sooo difficult'! I'm not able to answer soshort and sharp as Nick (thanks Nick!), but it may be helpful to add afew sentences.>(Admittedly, I still may be missing the point...!)Indeed, see my reply to David. This is a typical case where the rateconstant approach fails, similar to my examples of extracorporealcirculation and change in tissue binding (without a seriously commentor rebuttal from your side).> i) *Is understanding science really facilitated* by biasly>rearranging the mathematics underlying clearance by always writing ke>= CL/V when mathematical derivations clearly indicate that CL = ke*V?Which mathematical law or axioma indicates that CL = ke*V? I havenever found anything like that.>A science without a firm,>non-arbitrary mathematical foundation cannot aspire to be>quantitative; it would merely be "stamp collecting" to (mis)quote>Rutherford.}And what about a life science without a firm, non-arbitrary biologicalfoundation?> ii) *Is understanding science really facilitated* by parameterizing>simple classical pharmacokinetic (e.g. two compartment) models with>clearance (e.g. CL/V) instead of rate constants? (I have already>referred to this approach as "pharmacokinetic embellishment". The>expression, "applying lipstick to a pig", also comes to mind,>although even the pig so-embellished isn't whole but merely an entity>"comprised" of two interconnected containers!)I have explained earlier (again, without a serious comment or rebuttalfrom your side) that the biological interpretation of a twocompartment model using the clearance approach is simple,straightforward and mechanistically logical, and indeed by definitiontoo simple to describe the real situation exactly. In contrast, therate constants approach is almost purely mathematical.> iii) *Is understanding science really facilitated* by limiting the>use of rate constants (or half-lives) when these may have greater>overall utility than does CL in classical pharmacokinetics (as per>multiple dosing calculations, etc. and, circuitously, in the actual>calculation of CL itself!)?Again, I have argued that clearance has a much greater overall utilitythan the rate constant approach, including multiple dosing calculation(again, without a serious comment or rebuttal from your side).> BTW, if I don't respond to future postings on this topic it's only>because I am actually living up to that commitment made in my>previous posting!Of course, but there is no need to repeat your arguments: please giveme a rebuttal of my arguments, without empty statements on stampcollecting, embellishment, lipstick and pigs.best regards,Hans ProostJohannes H. ProostDept. of Pharmacokinetics, Toxicology and TargetingUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlands`
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• On 14 Jan 2010 at 12:53:02, "Wang, Yaning" (Yaning.Wang.aaa.fda.hhs.gov) sent the message
`The following message was posted to: PharmPKDear Hans:I would recommend you read one more time the fundamentals ofMichaelis-Menten equation athttp://en.wikipedia.org/wiki/Michaelis-Menten_kinetics and the originalpaper by MalcolmRowland et al. (Clearance Concepts in Pharmacokinetics,Journal ofPharmacokinetics and Biopharmaceutics,1973) who started the concept ofclearance. Combining these two sources of information, you willunderstand what are the true primary parameters that will determine theso called intrinsic clearance (Clint) as you quoted fromCLbh=Q*[CLint*fub/(Q+ CLint*fub)]) in 'Clinical Pharmacokinetics' byRowland and Tozer. I disagree with your explanation of "The obviousreason for abandoning the earlier equation is its inability to explainthe influence of enzymatic capacity and plasma protein binding onhepatic clearance". The authors just used a composite parameter Clint toreplace the original equation that shows what factors determine Clint(km*Ve*Kp). Plasma protein binding was simply added to the originalequation because the original derivation was using free concentration.The role of enzymatic capacity is contained in km*Ve*Kp. If you link kmto the Michaelis-Menten equation derived on wiki website, you canclearly see the role of enzyme concentration. Actually, in yoursimplified derivation on 12/17/2009, you already showed the dependenceof CL on k' (a rate constant independent of the enzyme concentration),C_e (the enzyme concentration), and V. To link your derivation toRowland's equation, CL=Clint, k'*C_e=km, V=Ve*Kp. I think this is a muchbetter understanding of the science or physiology than just callingClint or CL a "primary" parameter.Best regards,Yaning"The contents of this message are mine personally and do not necessarilyreflect any position of the Government or the Food and DrugAdministration."Yaning Wang, Ph.D.Team Leader, PharmacometricsOffice of Clinical PharmacologyOffice of Translational ScienceCenter for Drug Evaluation and ResearchU.S. Food and Drug Administration`
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• On 15 Jan 2010 at 10:14:25, Nick Holford (n.holford.-at-.auckland.ac.nz) sent the message
`Yaning,You are just doing algebraic manipulations of symbols. Re-parameterization of the model does not change anything.Intrinsic clearance has a biological meaning that describes the overall elimination function of an organ. Consider the case for the liver --  the naive assumption that enzyme activity is uniformly distributed per unit volume of the organ is often made and used with the activity per unit volume and the organ volume to predict intrinsic clearance.But this uniform activity assumption ignores what is really known about the biological structure e.g. the liver clearly has structure and does not have uniform enzyme activity plus elimination may be by biliary excretion in addition to enzymatic metabolism. Thus organ volume is not a fundamental part of the definition of intrinsic clearance but merely a first-order approximation used to make a guess at the value of intrinsic clearance from in vitro measurements.By the way, it would be helpful if you defined your symbols. I dont understand this:CLint= km*Ve*KpNick`
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• On 14 Jan 2010 at 20:05:22, "Wang, Yaning" (Yaning.Wang.-a-.fda.hhs.gov) sent the message
`The following message was posted to: PharmPKNick:Those equations are not re-parameterization of the model if you followthe derivations for Michaelis-Menten equation athttp://en.wikipedia.org/wiki/Michaelis-Menten_kineticsand the originalderivation for clearance by MalcolmRowland et al. (Clearance Concepts in Pharmacokinetics,Journal ofPharmacokinetics and Biopharmaceutics,1973). Yes, the liver wassimplified to be a uniform organ with uniform enzyme activity todemonstrate the quantitative relationship between Clint and some morefundamental factors. Do you think just calling Clint a primary parameteris reflecting the true physiological structure of the liver and thepotential multiple elimination pathways in a quantitative way?km, Ve and Kp are the original parameters used in Rowland paper todescribe the first-order elimination rate constant from the  eliminatingorgan, volume of the eliminating organ and the apparent partitioncoefficient of drug between the eliminating organ and the emergentvenous blood. So the original equation for CL isCL=Q*km*Ve*Kp/(Q+km*Ve*Kp) in Rowland paper where Q is the blood flow tothe eliminating organ.Yaning"The contents of this message are mine personally and do not necessarilyreflect any position of the Government or the Food and DrugAdministration."Yaning Wang, Ph.D.Team Leader, PharmacometricsOffice of Clinical PharmacologyOffice of Translational ScienceCenter for Drug Evaluation and ResearchU.S. Food and Drug Administration`
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• On 15 Jan 2010 at 17:32:33, Nick Holford (n.holford.-a-.auckland.ac.nz) sent the message
`The following message was posted to: PharmPKYaning,Thanks for making me go and re-read a couple of very influential earlypapers about the theory of pharmacokinetics.Wang, Yaning wrote:>> Those equations are not re-parameterization of the model if you follow> the derivations for Michaelis-Menten equation at> http://en.wikipedia.org/wiki/Michaelis-Menten_kinetics> and the original derivation for clearance by Malcolm> Rowland et al. (Clearance Concepts in Pharmacokinetics,Journal of> Pharmacokinetics and Biopharmaceutics,1973). Yes, the liver was> simplified to be a uniform organ with uniform enzyme activity to> demonstrate the quantitative relationship between Clint and some more> fundamental factors.Wagner (1973) describes the Michaels-Menten model in the paper precedingthat of Rowland et al. (1973)dConc/dt = Vm/(Km+Conc) *  Concwhere Vm is a proportionality factor for unit concentration of e.g.enzyme,  as used in the wikipedia derivation, and Km is theMichaelis-Menten constant. Note how confusing it was in Rowland (1973)to use km to indicate a first-order rate constant!.I will use Vmax to refer to the proportionality factor for the wholebody so that we then get this expression for whole body elimination rate:dA/dt=Vmax/(Km + Conc) * ConcWhen Conc -> 0 then Vmax/(Km+Conc) -> clearanceso we can then see:dA/dt = Clearance *  ConcClearance (CL) is the proportionality factor (for the whole body ororgan) between the physicochemical driving force ( 'activity') forchemical reactions i.e. concentration,  and the rate of elimination (dA/dt).The Rowland et al. (1973) paper gives no fundamental meaning to thefirst order rate constant (unfortunately named 'km') and in fact this kmis nothing more than clearance per unit volume of organ where VE is thephysical volume of the eliminating organ in Eqn 2. i.e. from the wholeorgan perspective km=CL/VEThe Rowland paper goes on to say that the left hand expression of Eqn 2describng the elimination rate:km * Kp * VE * Co  (which could also be written CL * Kp * Co)for a non-reabsorbed renally eliminated drug reduces to:CL,R * Ci = GFR * fu * Ciwhich defines renal clearance, CL,R:CL,R = GFR * fu for  renal clearance with respect to whole  bloodorCL,R,u = GFR for unbound drug renal clearance.Kp=organ to blood partition coefficient; Co = blood conc leaving organ;Ci= blood conc entering organ; fu=fraction unbound; GFR=glomerularfiltration rateNotice how renal clearance, CL,R, is now directly related to whole organbiological function (GFR) without any need for a rate constant.Wang, Yaning asked:> Do you think just calling Clint a primary parameter> is reflecting the true physiological structure of the liver and the> potential multiple elimination pathways in a quantitative way?This question is a trick because it confounds the structure of the liver(volume) with the elimination pathways (clearance).  I will ignore theconfounding of structure and answer just with respect to elimination :-)The essential property of clearance is that it describes the whole bodyor whole organ elimination properties without any assumption about thebody or organ structure i.e. there is no need to introduce simplifyingassumptions requiring uniform clearance per unit physical volume. If forexample the liver volume changed but there was no change in themetabolic enzyme activity then clearance would not change. But theclearance/unit volume would change i.e. the first-order rate constant(km) would change. Introducing volume into the system just confounds thedescription of the true elimination process.In Rowland et al. 1973 the summary ends with: "The virtue of using clearance, instead of half-life, as a correlativeparameter between these systems is stressed".The systems were a perfusion representation and a compartmentalrepresentation of an isolated perfused liver.  So please note, that evenin 1973, Rowland was advocating the use of clearance instead of rateconstants for understanding pharmacokinetics.Thus the answer to your question about elimination by the liver is YES! Wagner JG. Properties of the Michaelis-Menten equation and itsintegrated form which are useful in pharmacokinetics. 207-46. 1973;1:103-121 Rowland M, Benet LZ, Graham GG. Clearance concepts in pharmacokinetics.207-46. 1973;1:123-136> km, Ve and Kp are the original parameters used in Rowland paper to> describe the first-order elimination rate constant from the  eliminating> organ, volume of the eliminating organ and the apparent partition> coefficient of drug between the eliminating organ and the emergent> venous blood. So the original equation for CL is> CL=Q*km*Ve*Kp/(Q+km*Ve*Kp) in Rowland paper where Q is the blood flow to> the eliminating organ.>> Yaning>--Nick Holford, Professor Clinical PharmacologyDept Pharmacology & Clinical PharmacologyUniversity of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand`
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• On 15 Jan 2010 at 15:00:30, Rostam Namdari (chista90.aaa.yahoo.com) sent the message
`The following message was posted to: PharmPKDearHans, thank you for your reply. Just to focus on particular aspects (e.g.,adjusting dosing regimen) of demonstrating CL advantage under certain physiologicalor disease conditions (e.g., change in plasma protein levels due to aging ordisease) can you or other colleagues provide one or two examples of marketeddrug products that drug exposure changes significantly with progression of diseasebut t1/2 remains constant? I apologize if this is repeat question and suchexamples were provided earlier; I missed the early part of this debate.Rostam`
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• On 16 Jan 2010 at 13:14:13, Nick Holford (n.holford.at.auckland.ac.nz) sent the message
`The following message was posted to: PharmPKRostam,Rostam Namdari wrote:>  can you or other colleagues provide one or two examples of marketed> drug products that drug exposure changes significantly with progression of disease> but t1/2 remains constant? I apologize if this is repeat question and such> examples were provided earlier; I missed the early part of this debate.  I assume you are referring to examples not due to the trivial cases explained by changes in plasma protein binding or extent of bioavailability.If so then what a strange question!  Given that clearance and volume are determined by quite different things  then if such an example exists it must be rather rare because it would require exactly the same change in both clearance and volume in order for the exposure to change (which is due to clearance alone) and half-life to remain the same.Can you explain why you are looking for such an example?Nick-- Nick Holford, Professor Clinical PharmacologyDept Pharmacology & Clinical PharmacologyUniversity of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand`
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• On 17 Jan 2010 at 15:30:34, Peter W Mullen (pmullen.-at-.kemic.com) sent the message
`Hi Rostam,You wrote:"...can you or other colleagues provide one or two examples of marketeddrug products that drug exposure changes significantly with progression of diseasebut t1/2 remains constant?"One possible example is propofol in burn patients. (In patients AUC was approximately half while V and CL were both slightly more than double compared to controls; T1/2 was the same in both groups. See Han et al., J. Clin. Pharmacol. 49, 768-772, 2009.)Regards,PeterPeter W. Mullen, PhD, FCSFSKEMIC BIORESEARCH (www.kemic.com)KentvilleNova Scotia, B4N 4H8Canada`
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• On 18 Jan 2010 at 23:43:58, "Wang, Yaning" (Yaning.Wang.aaa.fda.hhs.gov) sent the message
`The following message was posted to: PharmPKNick:I think the derivation for Michaelis-Menten equation athttp://en.wikipedia.org/wiki/Michaelis-Menten_kinetics is not like whatyou described: "Vm is a proportionality factor for unit concentration ofe.g. enzyme,  as used in the wikipedia derivation". Vm itself is acomposite parameter depending on a proportionality factor (a rateconstant, k2 on wiki website) and the enzyme concentration ([E]0 on wikiwebsite). When you convert dConc/dt to dA/dt by multiplying both sidesby the volume (of the organ), Vmax=k2*[E]0*Ve, which clearly shows whatfactors determine this composite parameter. Even Km is a compositeparameter that depends on three rate constants as shown on the wikiwebsite. When you call clearance {CL=Vmax/(Km+Conc)} as theproportionality factor, you are ignoring the more fundamental factorsthat determine Vmax and Km. I disagree "Introducing volume into thesystem just confounds the description of the true elimination process".In fact, introducing volume precisely explains how Vmax (in your dA/dTform) depends on the size of the eliminating organ and why a largersubject has a larger Vmax. When a person donates part of the liver(lower Ve) AND uses an enzyme inducer (higher [E]0), Vmax can remain thesame and therefore CL remains the same. Are you considering this personis physiologically same as another person with full liver and no inducer(assuming equal size between these two persons)?Even for renally eliminated compounds (simple filtering mechanism), Ican apply the same concept. In that case, k2 is the same for allcompounds, [E]0 can be considered as the function of each nephron (e.g.the enlargement of remaining glomeruli in situations of nephron loss canbe considered the same as a higher enzyme concentration in the liver),Ve can be considered as the number of nephrons. Then the eliminatingcapacity of the kidney can be evaluated based on two factors: thefunction of each nephron ([E]0) and the number of nephrons (Ve).Notice all my discussions above are limited to the organ level todemonstrate the composite nature of Vmax (and intrinsic clearance). Whenwe go to the whole body level, another factor, blood/plasma flow rate tothe eliminating organ (Q), has to be added to the overall equation,CL=Q*Clint/(Q+Clint), which makes the whole body clearance a "more"composite parameter. However, this was considered an advantage ofclearance concept because it can relate the whole body clearance to theblood/plasma flow rate to the eliminating organ. In the renal case,people can directly link CL,R,u=GFR mainly because there is a convenientway to calculate or approximate GFR (GFR=glomerular filtration rate).However, the underlying equation CL=Q*Clint/(Q+Clint) can still beapplied to renal clearance GFR=Q*Clint/(Q+Clint) to understand what canlead to a lower than normal GFR, namely Q and other factors affectingClint. I can apply similar equation to Clint (k2*[E]0*Ve) to link thefunction of average individual nephron and the number of nephrons to theintrinsic eliminating capacity of the kidney, where k2*[E]0 is same askm in the liver case (linear PK), a rate constant reflecting thefraction of drug eliminated per unit of time at the organ level. Justbecause GFR can be directly measured as a composite parameter to inferCL,R,u does not mean GFR is not dependent on some rate constant itself."The contents of this message are mine personally and do not necessarilyreflect any position of the Government or the Food and DrugAdministration."Yaning Wang, Ph.D.Team Leader, PharmacometricsOffice of Clinical PharmacologyOffice of Translational ScienceCenter for Drug Evaluation and ResearchU.S. Food and Drug Administration`
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• On 19 Jan 2010 at 14:59:43, "J.H.Proost" (J.H.Proost.-at-.rug.nl) sent the message
`The following message was posted to: PharmPKDear Yaning,You wrote to Nick:"When you convert dConc/dt to dA/dt by multiplying both sides by the volume (of the organ), Vmax=k2*[E]0*Ve, which clearly shows what factors determine this composite parameter."I think we agree here that Vmax is a composite parameter. However, as I have indicated earlier, there is nothing 'primary' to the rate constant k2. You may express the maximum conversion rate per molecule enzyme, per cell, per mg protein, per ml, per organ or per universe, I don't see why one is more fundamental than the other.In pharmacokinetics, there is obviously a very good reason to express Vmax per whole body, or per organ, since one is interested in the capacity of the whole body, or the organ, to convert the drug."When you call clearance {CL=Vmax/(Km+Conc)} as the proportionality factor, you are ignoring the more fundamental factors that determine Vmax and Km."A strange reasoning. The same applies to Vmax and Km itself. And I think that Nick and I did not say that clearance is a fundamental parameter, independent of anything else. On the contrary, clearance is a composite parameter reflecting the elimination capacity of the whole body, irrespective of the volume of distribution, or whatever other volume."I disagree "Introducing volume into the system just confounds the description of the true elimination process". In fact, introducing volume precisely explains how Vmax (in your dA/dT form) depends on the size of the eliminating organ and why a larger subject has a larger Vmax."This applies only if the system is homogeneous, as Nick and I have explained. And the system is not homogeneous, so this approach simply doesn't explain anything."When a person donates part of the liver (lower Ve) AND uses an enzyme inducer (higher [E]0), Vmax can remain the same and therefore CL remains the same. Are you considering this person is physiologically same as another person with full liver and no inducer (assuming equal size between these two persons)?"Of course this depends on many factors, but if (1) the clearance of the two persons was the same before the changes in one person, (2) liver blood flow is not changed, or if the extraction ratio is low, and (3) the fraction of liver removed is balanced by the increased enzyme activity, i.e. Vmax (expressed per whole body(!)) remains the same, the clearance in both persons would be the same, and both persons would require the same dose (assuming the same pharmacodynamics)."Even for renally eliminated compounds (simple filtering mechanism), I can apply the same concept. In that case, k2 is the same for all compounds, [E]0 can be considered as the function of each nephron (e.g. the enlargement of remaining glomeruli in situations of nephron loss can be considered the same as a higher enzyme concentration in the liver), Ve can be considered as the number of nephrons. Then the eliminating capacity of the kidney can be evaluated based on two factors: the function of each nephron ([E]0) and the number of nephrons (Ve)."I really don't understand this comparison. You are talking about k2, E[0], and Ve, i.e. the factors determining Vmax (in your view), i.e. the enzyme capacity of the liver, a nonlinear process. The filtration process in the kidneys is linear, and not related to enzymes or whatever chemical process. I don't see the correlation."Notice all my discussions above are limited to the organ level to demonstrate the composite nature of Vmax (and intrinsic clearance). When we go to the whole body level, another factor, blood/plasma flow rate to the eliminating organ (Q), has to be added to the overall equation, CL=Q*Clint/(Q+Clint), which makes the whole body clearance a "more" composite parameter."Don't forget plasma protein binding, so clearance is even 'more composite'!"However, the underlying equation CL=Q*Clint/(Q+Clint) can still be applied to renal clearance GFR=Q*Clint/(Q+Clint) to understand what can lead to a lower than normal GFR, namely Q and other factors affecting Clint. I can apply similar equation to Clint (k2*[E]0*Ve) to link the function of average individual nephron and the number of nephrons to the intrinsic eliminating capacity of the kidney, where k2*[E]0 is same as km in the liver case (linear PK), a rate constant reflecting the fraction of drug eliminated per unit of time at the organ level."If you are talking about active secretion in the proximal tubules, I agree with your first sentence. But according to your second sentence, you are talking about glomerular filtration. In your equation, Clint would be the GFR if the blood flow through the kidneys (or glomeruli?) is very high. But I don't think that GFR is a function to renal blood flow according to GFR=Q*Clint/(Q+Clint). I'm quite sure that GFR is dependent on many factors, including renal blood flow, but not following this simple equation, not even as an approximation.Again, the second sentence is completely incomprehensible for me. I really don't see your point. Why are you making life so difficult, instead of the simple argument that GFR is the amount of plasma filtered per unit of time, and that all small molecules present in that amount, and not bound to proteins or blood cells, are present in the filtrate."Just because GFR can be directly measured as a composite parameter to infer CL,R,u does not mean GFR is not dependent on some rate constant itself."What is the point you want to make here? I fully agree that GFR is a composite parameter, depending on many underlying processes; unless you are at the scale of quantum mechanics, everything is a composite parameter. With some imagination, I might even consider that GFR is dependent on some rate constant. But this rate constant is definitely not a rate constant that is linked to GFR and the volume of distribution.On the other hand, there does not seem to be much debate about GFR being the primary measure of renal function, and that this is primarily because of the observation that the renal excretion of many compounds, both endogenous and drugs, is dependent of GFR, and in most cases close to proportional to GFR. The fact that GFR can be estimated is of course important from a clinical point of view, not from a mechanistic point of view.best regards,Hans ProostJohannes H. ProostDept. of Pharmacokinetics, Toxicology and TargetingUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlands`
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• On 20 Jan 2010 at 10:14:52, Nick Holford (n.holford.-a-.auckland.ac.nz) sent the message
`Yaning,Johannes has responded very well to the points you raised (thank you!).I want to add for emphasis that I see the key issue here is about scaling the parameter describing drug elimination e.g. clearance or Vmax.You have chosen to believe that elimination should be scaled by some volume e.g. the apparent volume of distribution.Johannes and I (and perhaps others) choose to believe that elimination should express the whole body  elimination process without confounding it with volume of distribution.I prefer this belief because I know that the biological determinants of elimination and distribution are not identical so it is simpler for me to understand if I deal with each of them separately. Even when they are highly correlated e.g. by body size, it is very clear that the relationship is not identical. The rate constant viewpoint has no explanation for why half-lives tend to be shorter in smaller subjects  but this is simple to explain by considering how clearance and volume vary with size.So perhaps we can agree it is a matter of belief (like religion) and leave it there.Nick`
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• On 19 Jan 2010 at 23:44:47, "Masoud Jamei" (masoud.jamei.-a-.gmail.com) sent the message
`The following message was posted to: PharmPKDear AllDuring this discussion the liver well-stirred model was few times mentionedin different shapes and I would like to draw your attention to the followingarticle discussing the correct equation:Yang J, Jamei M, Yeo KR, Rostami-Hodjegan A and Tucker GT (2007) Misuse ofthe well-stirred model of hepatic drug clearance. Drug Metab Dispos35:501-502.Which is freely available fromhttp://dmd.aspetjournals.org/content/35/3/501.full.pdf+htmlKind RegardsMasoud`
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• On 19 Jan 2010 at 22:38:58, "Walt Woltosz" (walt.aaa.simulations-plus.com) sent the message
`The following message was posted to: PharmPKDear Hans,In your reply to Yaning you said:"I really don't understand this comparison. You are talking about k2, E[0],and Ve, i.e. the factors determining Vmax (in your view), i.e. the enzymecapacity of the liver, a nonlinear process. The filtration process in thekidneys is linear, and not related to enzymes or whatever chemical process.I don't see the correlation."In fact, the filtration process in kidneys can be quite nonlinear. Bothinflux and efflux transporters exist in kidney, and generally such transportis saturable. See for example:Hill et al, DMD 30:13-19 (2002)in which the authors found, "Coadministration of probenecid resulting inreducing the renal clearance from 15.7 L/h (262 mL/min), a value exceedingthe glomerular filtration rate, to 7.5 L/h, a value equal to glomerularfiltration rate, suggesting complete inhibition of tubular secretion ...."Best regards,WaltWalt WoltoszChairman & CEOSimulations Plus, Inc. (NASDAQ: SLP)42505 10th Street West[When replying to PharmPK messages please make sure you don't have 'PharmPK' at the start of your new subject. I have my mail client set to filter messages starting with PharmPK into my archive folder and I may miss them. Thanks - db]`
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• On 20 Jan 2010 at 17:31:28, markus.weiss.at.novartis.com sent the message
`Dear Walt,I'm not sure about your statement on non-linearity of filtration:         "In fact, the filtration process in kidneys can be quite nonlinear. Both       influx and efflux transporters exist in kidney, and generally such transport       is saturable." My understanding is, that filtration is always linear (except in case of saturable protein binding that changes the free fraction with plasma concentration). Renal CL will of course be nonlinear as soon as saturable active transport processes contribute.Best regards, MarkusH Markus Weiss, PhDNovartis Institutes for BioMedical Research Translational Sciences - DMPK CHBS, WSJ-210.4.25Novartis Pharma AG, Werk St. JohannCH-4057 Basel, Switzerland`
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• On 20 Jan 2010 at 09:20:31, "Walt Woltosz" (walt.-a-.simulations-plus.com) sent the message
`he following message was posted to: PharmPKMarkus,Oops - you're correct, of course. I had in mind total renal clearance anddidn't stop to think that I was saying filtration!Thanks for the correction.Best regards,WaltWalt WoltoszChairman & CEOSimulations Plus, Inc. (NASDAQ: SLP)42505 10th Street WestLancaster, CA  93534-7059U.S.A.`
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• On 22 Jan 2010 at 11:11:39, Rostam Namdari (chista90.-at-.yahoo.com) sent the message
`The following message was posted to: PharmPKNick,you asked: "Can you explain why you are looking for such an example?" Tofurther demonstrate advantage of CL in adjusting dosing regimen under certainphysiological or disease conditions when, t1/2 does not change but AUC changessignificantly. I am trying to create a hypothetical example here: Drug A hasMEC=10 ng/mL, MTC= 600 ng/mL and following PK parameters under a typical (mild/moderate)version of disease X: Cmax=400 ng/mL, C trough=10 ng/mL, AUC=150 ng.h/mL,t1/2=~2 h, Vz=10 L/kg and CL=4 L/h/kg and in a severe version has Cmax=1200ng/mL, C trough ng/mL, AUC=400 ng.h/mL, t1/2=~2 h, Vz=4 L/kg and CL=1.5L/h/kg.Rostam`
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• On 25 Jan 2010 at 21:33:24, "Roger W. Jelliffe" (jelliffe.-a-.usc.edu) sent the message
`Dear All:             Let us return once again to the question of kel and clearance. I would like to respond to several recent comments. It is disappointing to hear some of the discussants trying to "get away from theoretical arguments and deal with real data". Really now, if we don't have theory, what do we have, after all? Isn't that what we, as scientists, are really trying to develop - a firm theory that helps us explain, predict, and control drug behavior? What about other theories, such as those of quantum mechanics and Einstein? Once we can construct them, we have a firm foundation and rationale for our actions. We have had so many words about this issue that some theory might, after all, be helpful. It was Kurt Lewin, I think, who said, "there is nothing as practical as a good theory".             Why shouldn't we base our discussion on theoretical arguments? If we don't do this, what basis do we have for what we actually do, and what is our  scientific rationale for our actions?  Let's look at the data, and the theory, that will help us evaluate the utility of K and Cl. In my view, K and Cl are both equally useful. The beauty is in the eye of the beholder. No one is more "biologically relevant" than the other, unless someone thinks so. Then that is a belief, not a fact. No one is more "orthogonal" than the other. That depends upon the particular model parameter values. The correlation between Cl and V simply depends on the model parameter values one is dealing with. By itself, Cl is no more orthogonal than K with respect to V. The result presented,  Corr(CL&V)=0 gets one's attention. Is this real or an accident? Answer - an accident of the values for V, CL and K that were used. In an earlier discussion, the model used was ln(y)= ln(1/V) - Kt + noise Alan says it is straightforward to calculate analytically the formula for the asymptotic covariance matrix between CL and V.  The off-diagonal term, Corr(CL&V), is exactly Corr(CL&V)= -((1/4)*V-CL)*V  The stated parameter values were V=1, K=0.25, which implies CL=V*K=0.25 and Corr(CL=0.25&V=1)=0  But what if K=0.35?  Fixing V=1, Alan shows a short table for CL vs.Corr(CL&V)      CL         Corr(CL&V)   0.0500   -0.2000    0.1500   -0.1000    0.2500         0    0.3500    0.1000    0.4500    0.2000    0.5500    0.3000    0.6500    0.4000    0.7500    0.5000    0.8500    0.6000    0.9500    0.7000    So the correlation between Cl and V simply depends on the model parameter values one is dealing with. By itself, Cl is no more orthogonal than K with respect to V. In addition, it is clear, as described by David Bayard, that "a fundamental property of the maximum likelihood estimator is the result that the maximum likelihood estimate of a function of the parameters can be computed by taking the function of the maximum likelihood estimates of the parameters. This property is known as the principle of invariance" [1]. Because of this, the MLE estimation of  = (K, V) gives exactly the same result as the MLE estimation of g() = (Cl, V). If you estimate it in clearance form (Cl,V) and then convert it to elimination form (K,V), you get the same estimate as if you had originally estimated it in elimination form. And vice versa.               The examples of losing a kidney or losing 2 legs are interesting examples. I am not sure what they settle. If you lose 2 legs you lose volume. Renal perfusion probably stays the same, though. Lose a kidney and you lose renal elimination - that is intuitive. For a drug eliminated from the body only by glomerular filtration, for example, th`
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• On 27 Jan 2010 at 13:08:50, andrew sutton (drandrewsutton.-at-.googlemail.com) sent the message
`The following message was posted to: PharmPKThank you Roger for such a clear and erudite exposition of the issues.I do so much agree that we need to explain real clinical orphyiological findings such as the discovery of increased volume ofdistribution in ICU patients. I presume that the role of (typicallygenerous in ICUs)  IV hydration regimes was eliminated from the listof causes.The one thing I would question is whether removal of one kidneyactually halves renal elimination. It assumes that the capacity ofboth kidneys has been reached and that there is no compensatorymechanism such as increased renal perfusion to the remaining kidneywhen one is removed.  Otherwise there must be implications forvolunteer kidney donors that are not widely known, when I think theyshould be.Kindest regardsAndrew`
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• On 28 Jan 2010 at 12:40:28, "J.H.Proost" (J.H.Proost.at.rug.nl) sent the message
`The following message was posted to: PharmPKDear Roger,Thank you for your thoughful comments. I fully agree with your pleafor theory and theoretical arguments. But I have still a few comments.> In my view, K and Cl are both equally useful. The beauty is in the> eye of the beholder. No one is more "biologically relevant" than> the other, unless someone thinks so. Then that is a belief, not a> fact.Over the last two months I have given several arguments why clearanceis more "biologically relevant" than elimination rate constant. Thisis not a belief, and it is not a fact. It follows from sound theory.All arguments in favor of K by Peter Mullen and Yaning Wang wererefuted by Nick Holford or by me. Do you have an argument why K is 'asbiologically relevant' as clearance?> No one is more "orthogonal" than the other.I agree. Please note that I stated this explicitly in my message ofDecember 9 to David. Your numerical example is a nice illustration ofmy theoretical view in that message.> If you lose 2 legs you lose volume. Renal perfusion probably> stays the same, though.OK, but the question was also: what changes, CL, K, CL and K, or none?I would like to hear your opinion.Your examples on TDM of antiobiotics and digoxin are important 'goldenclassics', and are highly appreciated. I have one comment to:> Further, using this model, it is clear that quinidine does not> reduce the clearance of digoxin - it simply reduces the uptake in> the peripheral compartment, raising the serum concentrations, and> resulting in a smaller apparent volume of distribution in the> central compartment.In many handbooks it is stated that quinidine reduces both clearance(by competition of active secretion in the proximal tubules) andvolume of distribution of digoxin (by displacement from tissue bindingsites). I don't have primary references for this statement, which maybe a wrong interpretation of data. But your reasoning does not seem tobe correct: if the steady state serum concentration of digoxin raisesafter administration of quinidine, clearance is reduced, irrespectiveof any change in distribution.best regards,Hans ProostJohannes H. ProostDept. of Pharmacokinetics, Toxicology and TargetingUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlands`
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• On 29 Jan 2010 at 03:21:29, Peter W Mullen (pmullen.-at-.kemic.com) sent the message
`Hi Hans,In your message to Roger Jelliffe you wrote:"Over the last two months I have given several arguments why clearance is more "biologically relevant" than elimination rate constant. This is not a belief, and it is not a fact. It follows from sound theory.All arguments in favor of K by Peter Mullen and Yaning Wang were refuted by Nick Holford or by me. ..."I'm compelled to respond to your assertion that: "All arguments in favor of K by Peter Mullen and Yaning Wang were refuted by Nick Holford or by me."  You have overestimated - perhaps not surprisingly - the merit of your arguments in this debate by using the verb "refute". 'A more accurate statement would be: "All arguments in favor of K by Peter Mullen and Yaning Wang were *debated* by Nick Holford or by me.'Also, I'm pleased to see that we at least agree that the statement, "clearance is more "biologically relevant" than elimination rate constant" is *not* a fact.We all know that drugs are eliminated (or "cleared") from the body. Whether we use "rate constants" or "clearance" or, as I've said previously, a conceivable ""Thingy Parameter" (having units that work consistent with the framing)" to describe this process matters little. Of course, in the initial assessment of single dose pharmacokinetic data, everyone (even you!) readily appreciates the practical utility of the rate constant(s). Then, having a value for ke at hand, one, if so inclined, could also determine a value for clearance applicable to the data using the essential (and ke-dependent) equations CL = Dose/AUC or CL = V * ke. :-)Best regards,PeterPeter W. Mullen, PhD, FCSFSKEMIC BIORESEARCH (www.kemic.com)KentvilleNova Scotia, B4N 4H8Canada`
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• On 29 Jan 2010 at 14:03:32, "Lu, Chuang" (Chuang.Lu.-a-.MPI.com) sent the message
`The following message was posted to: PharmPKDear Peter,You wrote: "in the initial assessment of single dose pharmacokinetic data, everyone (even you!) readily appreciates the practical utility of the rate constant(s). Then, having a value for ke at hand, one, if so inclined, could also determine a value for clearance applicable to the data using the essential (and ke-dependent) equations CL = Dose/AUC or CL = V * ke. :-)"I am a scientist with no PK background and the only class I ever took was the 5-days UCSF training, so forgive me if my comments are pre-mature.If we have a drug that has tight tissue-binding, in this case, say get into RBC and barely come out. After dosing, during the early time frame, say 0-4 hours, metabolic clearance plays an important role because there are some drugs in the plasma. After that period, the plasma concentration becomes very low and the elimination rate depends on the rate of the drug come out of RBC to plasma.If we apply the clearance concept, we are use Dose/AUC(0-infinity) regardless what happened in the biological system.If we apply ke, I guess the ke = f(k (liver), k (kidney), k (tissue binding and release), k (x) ...). To be more clearer ke = f(x,y,z...).The ke concept is not wrong, but it would be hard to apply. If our body is a well stirred one-compartment and the drug follows first order reaction, then apply ke would be fine. This, again, get back to some previous comments that link intrinsic clearance directly to in vivo clearance without acknowledge the complexity of the biological systems.ChuangChuang Lu, Ph.D.Associate DirectorDMPK, Drug Safety and DispositionMillennium, The Takeda Oncology Company35 Landsdowne StreetCambridge, MA 02139`
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• On 29 Jan 2010 at 18:15:45, Peter W Mullen (pmullen.aaa.kemic.com) sent the message
`Dear Chuang,Thank you for your comments and hypothetical example of a drug extensively bound to RBCs. You raise some interesting and important points.As you point out, if the overall elimination in your example still appeared to be first order, there is no reason why the rate constant approach should be considered less preferable than that of clearance. In such a case, neither clearance (total) nor ke would be revealing of the underlying complexities to which you have alluded. However, if the concentration-time plot did reveal such underlying "goings-on" then a focus on clearance, as you imply, enables one to avoid the issue(s) and "look the other way"! :-)In the assessment of single-dose data, a rate constant emphasis readily reveals potential complexities underlying distribution and/or elimination. Calculating Dose/AUCinf, however, reveals little since, to state the obvious, AUC can be estimated for practically any concentration-time plot regardless of how "contorted" it might appear.Best wishes,PeterPeter W. Mullen, PhD, FCSFSKEMIC BIORESEARCH (www.kemic.com)KentvilleNova Scotia, B4N 4H8Canada`
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• On 29 Jan 2010 at 18:31:55, Peter W Mullen (pmullen.aaa.kemic.com) sent the message
`The following message was posted to: PharmPKDear Roger,You wrote:> It is disappointing to hear some of the discussants trying to "get away from theoretical arguments and deal with real data". Really now, if we don't have theory, what do we have, after all? Isn't that what we, as scientists, are really trying to develop - a firm theory that helps us explain, predict, and control drug behavior? What about other theories, such as those of quantum mechanics and Einstein? Once we can construct them, we have a firm foundation and rationale for our actions. We have had so many words about this issue that some theory might, after all, be helpful. It was Kurt Lewin, I think, who said, "there is nothing as practical as a good theory".Your thoughtful comments deserve a proper considered response but at least for now, I wish merely to say: *HEAR, HEAR*!Best regards,Peter*Peter W. Mullen, PhD, FCSFSKEMIC BIORESEARCH (**www.kemic.com* *)KentvilleNova Scotia, B4N 4H8Canada`
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• On 31 Jan 2010 at 01:14:08, Dimiter Terziivanov (terziiv.-a-.yahoo.com) sent the message
`Dear Hans, I read with interest your note to Roger Jelliffe's arguments and I have to confess  that I was a little bit confused because of your statement: "Over the last two months I have given several arguments why clearance is more "biologically relevant" than elimination rate constant. This is not a belief, and it is not a fact. It follows from sound theory..."I am now asking myself "Where the sound theory comes from if not from facts? Is the sound theory some knowledge a priori defined without factual basis? Is clearance, as more "biologically relevent" than Ke, a self-evident proposition?" As educated in Aristotle's scientific tradition I am accustomised to use in my scientific reasoning inductive and deductive method. I think that our knowledge begins with experience. According to Wikipedia "In the most basic sense a scientific fact is an objective and verifiable OBSERVATION".In my understanding that means that we observe and record natural fact(s) and after analyzing this (these) fact(s) we build up some theory, right or wrong. If the statement that "clearance is more "biologically relevent" than Ke" is not a belief nor a fact, what is this statement itself? ;-)) Kind regards, Dimiter--Dimiter Terziivanov, MD,PhD,DSc, Professor,Pharmacology and Clinical Pharmacology,Medical Faculty, University of Sofia "St. Kliment Ohridski",1 Koziak str, 1407 Sofia,`
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• On 1 Feb 2010 at 13:39:39, "J.H. Proost" (j.h.proost.aaa.rug.nl) sent the message
`The following message was posted to: PharmPKDear Dimiter,Thank you for your interesting remarks.>If the statement that "clearance is more "biologically relevent" than Ke">is not a belief nor a fact, what is this statement itself? ;-))I will try to give a very short and very simplified explanation aboutobservations and PK theory. Of course observations are the starting pointfor all theory. In the early days of pharmacokinetics it was observed thatthe concentration profile plotted on a logarithmic scale against timeresulted often in a straight line. The slope was called elimination rateconstant (k). The logical explanation for this is that drug elimination is alinear process, i.e. that the rate of elimination is dependent on theamount, or concentration, of drug present. This is often the case forenzymatic processes, and also for a filtration process, where the rate ofmetabolism and filtration are proportional to drug concentration, assupported by many observations and underlying theory. The proportionalityconstant is denoted clearance. This may be called the 'pharmacokinetictheory', based on observations.Interestingly, from a historical point of view, rate constants (k) camebefore clearance. This is likely due to the early observations of thestraight line with slope k, whereas in the 1970-ties the clearance approachemerged, on the analogy of renal clearance and GFR. It took some time, evenfor the early promotors of clearance, that clearance was recognized as thecapacity of the body to eliminate drugs. This may be partly due to thesomewhat clumsy early definition of clearance as the ('apparent', 'virtual')volume of plasma that is completely cleared from the drug per unit of time.We don't need this anymore, using the above 'pharmacokinetic theory' basedon observations.best regards,Hans ProostJohannes H. ProostDept. of Pharmacokinetics, Toxicology and TargetingUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlands`
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• On 1 Feb 2010 at 13:41:11, "J.H. Proost" (j.h.proost.at.rug.nl) sent the message
`The following message was posted to: PharmPKDear Peter,You are right that the verb "refute" was too strong, and  *debated* islikely the better verb here. The reason that I was used this strong verb isnot (or not only) that I have overestimated the merit of my arguments, butrather the lack of response from your side with respect to both my argumentsin favor of the clearance approach, and my argument in disfavor of the rateconstant approach.You understand that I will not stop in replying to:> Then, having a value for ke at hand, one, if so inclined, could also> determine a value for clearance applicable to the data using the essential> (and ke-dependent) equations CL = Dose/AUC or CL = V * ke. :-)Again, CL is independent on k (ke, K). k is dependent on CL and V. This isnot a fact, nor a belief. It is the consequence of the most generaldefinition of clearance as the proportionality constant in the relationshipbetween rate of elimination and concentration (dA/dt = CL * C), andtherefore it is the characteristic proporties of the drug eliminatingcapacity of the body, independent of the volume of distribution.best regards,Hans ProostJohannes H. ProostDept. of Pharmacokinetics, Toxicology and TargetingUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlands`
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• On 1 Feb 2010 at 11:50:07, Dimiter Terziivanov (terziiv.aaa.yahoo.com) sent the message
`Dear Hans, Thank you for the clarification. I respect your preference to clearance concept and all supporting arguments as well. In early 80-ies I thought, as a physician, that clearance concept is more understandable for physicians and will substitute for Ke which appears to be more abstract. Twenty years later I think that, irrespective of my own epistemological considerations, any substitution is misleading.Kind regards, Dimiter--Dimiter Terziivanov, MD,PhD,DSc, Professor,Pharmacology and Clinical Pharmacology,Medical Faculty, University of Sofia "St. Kliment Ohridski",1 Koziak str, 1407 Sofia, Bulgaria`
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• On 2 Feb 2010 at 09:17:30, "J.H.Proost" (J.H.Proost.aaa.rug.nl) sent the message
`The following message was posted to: PharmPKDear Dimiter,Thank you for your commments. But what do mean with the phrase "any substitution is misleading". Substitution of k or substitution of CL or both? In my view the substitution of the ratio CL/V by k is a valid substitution, and not "misleading".best regards,Hans ProostJohannes H. ProostDept. of Pharmacokinetics, Toxicology and TargetingUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlands[Hans, I was talking about analysis of urine data this morning, in class. I started to wonder what information you get from urine data alone. Remember, no sticking in needles and collecting blood - db]`
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• On 3 Feb 2010 at 02:18:33, Dimiter Terziivanov (terziiv.at.yahoo.com) sent the message
`Dear Hans,Many thanks for your note. I was a little bit vague. I agree that the substitution of the ratio CL/V by k is a valid one. I had in mind conceptual substitution.Kind regards,Dimiter`
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