QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Full Text (PDF) Submit a response Alert me when this article is cited Alert me when eLetters are posted Alert me if a correction is posted Services Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Yang, J. Articles by Tucker, G. T. Search for Related Content PubMed PubMed Citation Articles by Yang, J. Articles by Tucker, G. T.

LETTER

Misuse of the Well-Stirred Model of Hepatic Drug Clearance

Simcyp Limited, Blades Enterprise Centre, Sheffield, United Kingdom (J.Y., M.J., K.R.Y., A.R.-H., G.T.T.); and Academic Unit of Clinical Pharmacology, Pharmacokinetics and Pharmacogenetics Group, University of Sheffield, United Kingdom (A.R.-H., G.T.T.)

(Received October 17, 2006; accepted December 15, 2006)

(1)

This assumes that the drug is distributed instantly and homogenously throughout liver water and that the unbound concentrations in plasma and liver water are identical. Effectively, this means that drug distribution into the liver is perfusion-limited with no diffusion delay and that no active transport systems are involved. The latter possibilities have generally been disregarded in most applications.

A key feature of this model is that it equates whole-blood drug clearance, rather than plasma drug clearance, to liver blood flow, because the organ is potentially capable of extracting the drug from both plasma and blood cells. Most reported clearance values are referenced to plasma rather than blood, since it is more common to measure drug concentration in plasma. If plasma drug clearance (CL_H) is to be estimated, then eq. 1 must be modified to take into account the free fraction in plasma (fu) and the total blood to total plasma drug concentration ratio (C_B/C_P):

(2)

As expected conceptually, eq. 1 indicates that hepatic blood clearance cannot exceed liver blood flow. However, from eq. 2, it is possible that hepatic plasma clearance may exceed hepatic blood flow (and hepatic plasma flow) when fuCLu_int,H >> Q_H,B and C_B/C_P > 1 (Hinderling, 1997). Some confusion over the definition of fu_B and a failure to appreciate the conversion between blood and plasma clearance are evident in some of the recent literature, confounding the ability to extrapolate between in vitro and in vivo drug clearance.

	The Definition of fuB

Top The Definition of fuB Estimation of in Vivo... Estimation of Intrinsic Hepatic... Estimation of Hepatic... References

 
The free fraction of drug in blood is given by eq. 3:

(3)

where Au_B is the amount of unbound drug in whole blood and A_B is the total amount of drug in blood. Thus:

(4)

where Cu_RBC is the unbound drug concentration in cells (essentially red blood cells; RBC); V_RBC is the volume of RBC per milliliter of blood; Cu is unbound drug concentration in plasma water; V_P is the volume of plasma per milliliter of blood; and Hc is the hematocrit.

In the original development of the well-stirred model, the assumption was made that the unbound concentration of drug in blood cells equates to the unbound concentration in plasma (Cu_RBC = Cu). Hence, eq. 4 becomes:

(5)

In contrast, Masimirembwa et al. (2003) defined the free fraction in blood as:

(6)

However, this only applies where no drug associates with the cells (Cu_RBC = 0 in eq. 4) when, to provide a correct value of hepatic blood clearance, eq. 1 would need to be modified to eq. 7:

(7)

In the special case of the drug not associating with blood cells at all, it is preferable to report plasma, rather than blood, clearance, using fu and hepatic plasma flow (Q_H,B(1 – Hc)).

	Estimation of in Vivo Hepatic Clearance from in Vitro Data

Top The Definition of fuB Estimation of in Vivo... Estimation of Intrinsic Hepatic... Estimation of Hepatic... References

 
Values of CLu_int,H derived using human liver microsomes, hepatocytes, or recombinant enzymes are often scaled to in vivo hepatic clearance using the well-stirred model. However, in deriving hepatic plasma clearance, several recent studies have used eq. 8 instead of the correct form (eq. 2) (Blanchard et al., 2004; Foti and Fisher, 2004; Blanchard et al., 2005; de Graaf et al., 2006; Mohutsky et al., 2006; Strelevitz et al., 2006):

(8)

This would only be valid if C_B/C_P were equal to unity. For drugs with low values of fuCLu_int,H, estimates of CL_H would be similar using eqs. 2 and 8. Thus, when fuCLu_int,H << Q_H,B (eq. 2 and 8), CL_H approaches fuCLu_int,H, and the factor C_B/C_P is not important. However, major discrepancies would result for higher clearance drugs when C_B/C_P does not equal unity.

	Estimation of Intrinsic Hepatic Clearance from in Vivo Data

Top The Definition of fuB Estimation of in Vivo... Estimation of Intrinsic Hepatic... Estimation of Hepatic... References

 
To assess predictions of intrinsic hepatic drug clearance from in vitro data, estimates are often compared with values back-calculated from in vivo values of hepatic drug clearance using the well-stirred model. In this context, studies (e.g., Takanaga et al., 2000) have employed eq. 9 by rearranging eq. 8, instead of the correct form (eq. 10 from a rearrangement of eq. 2):

(9)

(10)

View larger version (17K): [in this window] [in a new window]   FIG. 1. Comparison of FH values determined using eqs. 11 through 13 [QH,B = 97 l/h; Hc = 0.48 (Valentin, 2002)] and different values of CB/C (0.7 and 2). When CB/CP = 1, eqs. 11 and 13 give the same result; when CB/CP = 1 – Hc, eqs. 12 and 13 give the same result.

	Estimation of Hepatic Availability from in Vivo Data

Top The Definition of fuB Estimation of in Vivo... Estimation of Intrinsic Hepatic... Estimation of Hepatic... References

(11)

(12)

Eq. 11 is only valid if C_B/C_P is unity, and eq. 12 is not valid unless C_B/C_P is equal to (1 – Hc) (i.e., no drug associates with the cells). A more appropriate equation, based on the original assumptions of the well-stirred model, is given by eq. 13:

(13)

The different implications of eqs. 11 through 13 for the estimation of F_H are explored in Fig. 1.

Errors in the estimation of F_H may be further propagated into estimates of the fraction avoiding first-pass loss across the gut wall (F_G) from the relationship F/(faF_H), where F is net oral bioavailability and fa is the fraction of the dose entering the intestinal wall (Takanaga et al., 2000; Kharasch et al., 2004a,b).

In summary, we emphasize that the mixing of plasma free fraction and hepatic blood flow is inadvisable and illogical when using the well stirred liver, or indeed any model of hepatic drug clearance, for in vitro/in vivo extrapolation.

	Footnotes

 
Article, publication date, and citation information can be found at http://dmd.aspetjournals.org.

doi:10.1124/dmd.106.013359.

ABBREVIATION: RBC, red blood cells.

Address correspondence to: Dr. Jiansong Yang, Simcyp Limited, Blades Enterprise Centre, John Street, Sheffield S2 4SU, UK. E-mail: j.yang{at}simcyp.com

	References

Top The Definition of fuB Estimation of in Vivo... Estimation of Intrinsic Hepatic... Estimation of Hepatic... References

 


Blanchard N, Alexandre E, Abadie C, Lave T, Heyd B, Mantion G, Jaeck D, Richert L, and Coassolo P (2005) Comparison of clearance predictions using primary cultures and suspensions of human hepatocytes. Xenobiotica 35: 1–15.[CrossRef][Medline]

Blanchard N, Richert L, Notter B, Delobel F, David P, Coassolo P, and Lave T (2004) Impact of serum on clearance predictions obtained from suspensions and primary cultures of rat hepatocytes. Eur J Pharm Sci 23: 189–199.[CrossRef][Medline]

de Graaf IA, de Kanter R, de Jager MH, Camacho R, Langenkamp E, van de Kerkhof EG, and Groothuis GM (2006) Empirical validation of a rat in vitro organ slice model as a tool for in vivo clearance prediction. Drug Metab Dispos 34: 591–599.[Abstract/Free Full Text]

Foti RS and Fisher MB (2004) Impact of incubation conditions on bufuralol human clearance predictions: enzyme lability and nonspecific binding. Drug Metab Dispos 32: 295–304.[Abstract/Free Full Text]

Gillette JR (1971) Factors affecting drug metabolism. Ann NY Acad Sci 179: 43–66.[CrossRef][Medline]

Hinderling PH (1997) Red blood cells: a neglected compartment in pharmacokinetics and pharmacodynamics. Pharmacol Rev 49: 279–295.[Abstract/Free Full Text]

Kharasch ED, Hoffer C, Whittington D, and Sheffels P (2004a) Role of hepatic and intestinal cytochrome P450 3A and 2B6 in the metabolism, disposition, and miotic effects of methadone. Clin Pharmacol Ther 76: 250–269.[CrossRef][Medline]

Kharasch ED, Walker A, Hoffer C, and Sheffels P (2004b) Intravenous and oral alfentanil as in vivo probes for hepatic and first-pass cytochrome P450 3A activity: noninvasive assessment by use of pupillary miosis. Clin Pharmacol Ther 76: 452–466.[CrossRef][Medline]

Lau YY, Okochi H, Huang Y, and Benet LZ (2006) Pharmacokinetics of atorvastatin and its hydroxy metabolites in rats and the effects of concomitant rifampicin single doses: relevance of first-pass effect from hepatic uptake transporters, and intestinal and hepatic metabolism. Drug Metab Dispos 34: 1175–1181.[Abstract/Free Full Text]

Mohutsky MA, Chien JY, Ring BJ, and Wrighton SA (2006) Predictions of the in vivo clearance of drugs from rate of loss using human liver microsomes for phase I and phase II biotransformations. Pharm Res (NY) 23: 654–662.

Rowland M, Benet LZ, and Graham GG (1973) Clearance concepts in pharmacokinetics. J Pharmacokinet Biopharm 1: 123–136.[CrossRef][Medline]

Strelevitz TJ, Foti RS, and Fisher MB (2006) In vivo use of the P450 inactivator 1-aminobenzotriazole in the rat: varied dosing route to elucidate gut and liver contributions to first-pass and systemic clearance. J Pharm Sci 95: 1334–1341.[CrossRef][Medline]

Takanaga H, Ohnishi A, Matsuo H, Murakami H, Sata H, Kuroda K, Urae A, Higuchi S, and Sawada Y (2000) Pharmacokinetic analysis of felodipine-grapefruit juice interaction based on an irreversible enzyme inhibition model. Br J Clin Pharmacol 49: 49–58.[Medline]

Valentin J (2002) Basic Anatomical and Physiological Data for Use in Radiological Protection: Reference Values. Pergamon, Oxford, UK.

Wilkinson GR and Shand DG (1975) A physiological approach to hepatic drug clearance. Clin Pharmacol Ther 18: 377–390.[Medline]

This Article Full Text (PDF) Submit a response Alert me when this article is cited Alert me when eLetters are posted Alert me if a correction is posted Services Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Yang, J. Articles by Tucker, G. T. Search for Related Content PubMed PubMed Citation Articles by Yang, J. Articles by Tucker, G. T.