The Erythromycin Breath Test For the Prediction of Drug Clearance

Abstract

The erythromycin breath test (EBT) is a putative probe of cytochrome P450 (CYP) 3A4 activity in vivo. Therefore, the EBT might prove useful for the individualisation of doses of drugs that have a low therapeutic window (for example the immunosuppressants or cytotoxics) and are metabolised by CYP3A4. However, there is a lack of consensus as to how the EBT should be used to predict total body clearance (CL), and the results so far have been largely disappointing.

We argue that the required assumption that individuals produce 5 mmol of CO₂/min per m² at rest is one of the problems with the existing EBT, as the literature suggests significant variability and possible gender differences in this parameter. An examination of the EBT with a simple compartment model suggests that alternative parameters could be more useful in the prediction of CL. In particular, there is theoretical support for the use of the time-point at which breath radioactivity is maximal (t_max) as a correlate for CL. This is in agreement with our recent study of the pharmacokinetics of erythromycin in patients with cancer.

Appendix

Consider the 1-compartment model illustrated in appendix figure 1 The concentrations of [¹⁴C]erythromycin (C) and formaldehyde product (M) are described by the differential equations:

$${\rm{Vd}}{{{\rm{dC}}} \over {{\rm{dt}}}} = - ({{\rm{f}}_{\rm{u}}}\; \cdot \;{\rm{C}}{{\rm{L}}_{{\rm{in\;t}}}} + {\rm{C}}{{\rm{L}}_{{\rm{other}}}})\; \cdot \;{\rm{C}}$$

((eq. 1))

$${\rm{Vd}}{{{\rm{dM}}} \over {{\rm{dt}}}} = {{\rm{f}}_{\rm{u}}}\; \cdot\; {\rm{C}}\;{{\rm{L}}_{{\rm{in\;t}}}}\; \cdot \;{\rm{C}} - {\rm{C}}\;{{\rm{L}}_{\rm{M}}}\; \cdot \;{\rm{M}}$$

((eq. 2))

Appendix fig. 1

A 1-compartment model to describe the concentrations of erythromycin (C), the formaldehyde intermediate (M) and the flux of CO₂ following the administration of the erythromycin breath test (EBT). The cytochrome P450 (CYP) 3A4-mediated clearance of erythromycin is represented by the product of unbound fraction (f_u) and intrinsic hepatic clearance (CL_int), the balance of the total body clearance is indicated as CL_other, and CL_M is the total body clearance of the metabolite.

in which CL_other is the balance of the total clearance (CL) not due to CYP3A4-mediated metabolism (i.e. CL = CL_int · f_u + CL_other). The flux of CO₂ at time t, CER(t), is usually expressed as a percentage of the dose. It follows that:

$${\rm{CER}}({\rm{t}}) = {{{\rm{M}}\; \cdot \;{\rm{C}}{{\rm{L}}_{\rm{M}}}} \over {{\rm{dose}}}}\; \cdot\; 100$$

((eq. 3))

Substituting the solution for M from the differential equations yields:

$${\rm{CER}}({\rm{t}}) = {{{{\rm{f}}_{\rm{u}}}\;\cdot\;{\rm{C}}{{\rm{L}}_{{\mathop{\rm int}} }}\;\cdot\;{\rm{C}}{{\rm{L}}_{\rm{M}}}} \over {{\rm{Vd}}\;\cdot\;({\rm{CL}} - {\rm{C}}{{\rm{L}}_{\rm{M}}})}}\;\cdot\;\left( {{\rm{e}}{{{\rm{C}}{{\rm{L}}_{\rm{M}}}} \over {{\rm{Vd}}}}{\rm{t}} - {\rm{e}}{{{\rm{CL}}} \over {{\rm{Vd}}}}{\rm{t}}} \right)\;\cdot\;100$$

((eq. 4))

This equation is similar to those proposed by Lown et al.[15] and Lane and Parashos.[7]

Integration of the area under the flux curve to infinity yields:

$${\rm{AUCE}}{{\rm{R}}_\infty } = {{{{\rm{f}}_{\rm{u}}}\; \cdot\; {\rm{C}}{{\rm{L}}_{{\rm{int}}}}} \over {{\rm{CL}}}}$$

((eq. 5))

At the t_max of the breath flux versus time profile (equation 4), dCER/dt = 0 and, therefore:

$${1 \over {{{\rm{t}}_{\max }}}} = {{{\rm{C}}{{\rm{L}}_{\rm{M}}} - {\rm{CL}}} \over {{\rm{Vd}}\; \cdot\; \ln \left( {{{{\rm{C}}{{\rm{L}}_{\rm{M}}}} \over {{\rm{CL}}}}} \right)}}$$

((eq. 6))

Note the loss of the CL_int term from this relationship. This underscores the fact that this novel parameter is unlikely to correlate with CYP3A4 activity per se unless, of course, this activity is the principal factor in determining CL.