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A New In Situ Brain Perfusion Flow Correction Method for Lipophilic Drugs Based on the pH-Dependent Crone-Renkin Equation

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ABSTRACT

Purpose

To determine the flow-corrected luminal permeability, Pc, of lipophilic drugs measured by the in situ brain perfusion method under circumstances where the traditional Crone-Renkin equation (CRE) method, using diazepam as a flow marker, often fails.

Methods

The pH-dependent rate of brain penetration of five lipophilic drugs (amitriptyline, atomoxetine, imipramine, indomethacin, maprotiline, sertraline), as well as of atenolol and antipyrine, were measured in Sprague-Dawley rats. A new pH-dependent CRE was derived and applied to remove the hydrodynamic component of effective permeability, Pe, to produce Pc values.

Results

It was shown by the analysis of the in situ data in the pH 6.5–8.5 interval for the lipophilic bases that the average vascular flow Fpf = 0.036 mL∙g−1∙s−1, centered in a “flow-limit window” (FLW) bounded by P mine  = 170 and P maxe  = 776 (10−6 cm∙s−1 units). It was shown that the traditional CRE is expected not to work for half of the molecules in the FLW and is expected to underestimate (up to 64-fold) the other half of the molecules.

Conclusion

The new pH-CRE flow correction method applied to lipophilic ionizable drugs, based on the pH partition hypothesis, can overcome the limitations of the traditional CRE.

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Abbreviations

DRW:

dynamic range window for flow-limited drugs, \( {\hbox{DRW }} = { \log }\left( {{{\hbox{F}}_{\rm{pf}}}/{\hbox{S}}} \right){ }--{ \max }\left( {{ \log }{{\hbox{P}}_{\rm{i}}},{ \log }{{\hbox{P}}_{\rm{para}}}} \right) \)

FLW:

flow limit window: \( {\hbox{FLW }} = { \log }\left( {{{\hbox{F}}_{\rm{pf}}}/{\hbox{S}}} \right){ }\pm { 3} \) \( {\hbox{SD }} = { } - {3}.{44 }\pm { }0.{33} \) (SD = standard deviation)

Fpf :

cerebrovascular flow velocity of perfusion fluid (mL·g−1·s−1 brain tissue)

Kin :

unidirectional transfer constant (mL·g−1·s−1): \( {{\hbox{K}}_{\rm{in}}} = { }\left( {{ }{{\hbox{Q}}_{\rm{br}}}/{ }{{\hbox{C}}_{\rm{pf}}}} \right){ }/{\hbox{ T}} \), where Qbr = test compound parenchymal brain concentration (nmol·g−1 brain tissue) (corrected for the vascular volume), Cpf = perfusion fluid concentration (nmol·mL−1), T = perfusion time (s).

PABL :

aqueous boundary layer permeability coefficient (cm·s−1), in vitro or PAMPA model

Papp :

apparent in vitro transcellular permeability coefficient (cm·s−1)

Pc :

corrected-for-flow luminal permeability coefficient (cm·s−1) depends on pH for ionizable permeants (hyperbolic function); basis of the pH partition hypothesis

Pc S:

permeability-surface area product (mL·g−1·s−1), traditionally determined from Kin using Crone-Renkin equation (CRE): \( {{\hbox{P}}_{\rm{c}}}{\hbox{S }} = { } - { }{{\hbox{F}}_{\rm{pf}}}{ \ln }\left( {{1 }--{ }{{\hbox{K}}_{\rm{in}}}/{{\hbox{F}}_{\rm{pf}}}} \right) \)

Pe :

effective permeability coefficient (cm·s−1), not corrected for flow: \( {{\hbox{P}}_{\rm{e}}} = { }{{\hbox{K}}_{\rm{in}}}/{\hbox{ S}} \) depends on pH for ionizable permeants (sigmoidal function)

pH-CRE:

new pH-dependent Crone-Renkin equation (CRE) flow correction method

Pi :

luminal permeability coefficient (cm·s−1) of the ionized form of permeant

pK fluxa :

pH where 50% of the permeation is due to luminal permeability and 50% due to the effective permeability at the hydrodynamic limit

Pm :

PAMPA transmembrane permeability coefficient (cm·s−1), at pH 7.4, corrected for ABL

Po :

intrinsic luminal permeability coefficient (cm·s−1) of the neutral form of permeant for ionizable drugs, \( {{\hbox{P}}_{\rm{o}}} = {{\hbox{P}}_{\rm{c}}}\left( {{1}{0^{\pm ({\rm{pH }} - {\rm{ pKa}})}} + {1}} \right) \), with ‘+’ for acids, ‘-’ for bases

Ppara :

paracellular permeability coefficient (cm·s−1), indicating aqueous diffusion of permeant through the tight junctions formed by the blood-brain barrier

S:

endothelial surface area in a gram of brain tissue (assumed to be 100 cm2∙g−1)

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ACKNOWLEDGMENTS

We thank Drs. Feng Zhou and Ismael J. Hidalgo of Absorption Systems for their effort in the in situ brain perfusion measurements and for the valuable background discussions. The technical assistance of Oksana Tsinman (pION) is gratefully acknowledged. Part of this work was supported by Grant Number R44MH75211 from the National Institutes of Health (to pION). The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institute of Mental Health or the National Institutes of Health.

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  1. pION INC, 5 Constitution Way, Woburn, Massachusetts, 01801, USA

    Alex Avdeef & Na Sun

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  1. Alex Avdeef
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Correspondence to Alex Avdeef.

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The current article is contribution number 32 in the Drug Absorption In Vitro Model series from pION. Ref. 16 is part 31 in the series.

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Avdeef, A., Sun, N. A New In Situ Brain Perfusion Flow Correction Method for Lipophilic Drugs Based on the pH-Dependent Crone-Renkin Equation. Pharm Res 28, 517–530 (2011). https://doi.org/10.1007/s11095-010-0298-0

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