Model Mathematics

Qc = Qcc {BW}^{0.74} Ql = Qliv Qc Qf = Qfat Qc Qbr = Qbrain Qc Qs = Qslow Qc Qr = Qc - Ql - Qf - Qbr - Qs

Vfat = 0.01 (20 BW + 1.664) Vrap = 1 - Vblood - Vliver - Vfat - Vslow

Vb = Vblood BW Vart = 0.25 Vb Vven = 0.75 Vb Vl = Vliver BW Vbr = Vbrain BW Vf = Vfat BW Vs = Vslow BW Vr = Vrap BW

D0 = F dose BW

KF = \frac{Kfc}{{BW}^{0.3}}

C_art = \frac{A_art}{Vb} C_brain = \frac{A_brain}{Vbr} \frac{d}{d t} (A_ven) = \frac{\frac{Qf A_fat}{Vf}}{Pfat_bl} + \frac{\frac{Qbr A_brain}{Vbr}}{Pbrain_bl} + \frac{\frac{Qs A_slow}{Vs}}{Pslow_bl} + \frac{\frac{Ql A_liv}{Vl}}{Pliv_bl} + \frac{\frac{Qr A_rapid}{Vr}}{Prapid_bl} \frac{d}{d t} (A_art) = \frac{d}{d t} (A_ven) - (\frac{Qc A_art}{Vb}) \frac{d}{d t} (A_fat) = Qf (\frac{A_art}{Vb} - (\frac{\frac{A_fat}{Vf}}{Pfat_bl})) \frac{d}{d t} (A_slow) = Qs (\frac{A_art}{Vb} - (\frac{\frac{A_slow}{Vs}}{Pslow_bl})) \frac{d}{d t} (A_brain) = Qbr (\frac{A_art}{Vb} - (\frac{\frac{A_brain}{Vbr}}{Pbrain_bl})) \frac{d}{d t} (A_rapid) = Qr (\frac{A_art}{Vb} - (\frac{\frac{A_rapid}{Vr}}{Prapid_bl})) \frac{d}{d t} (A_stomach) = (- Ka) A_stomach \frac{d}{d t} (A_liv) = (Ql (\frac{A_art}{Vb} - (\frac{\frac{A_liv}{Vl}}{Pliv_bl})) - (\frac{\frac{KF Vl A_liv}{Vl}}{Pliv_bl})) + Ka A_stomach \frac{d}{d t} (A_liv_CL) = \frac{\frac{KF Vl A_liv}{Vl}}{Pliv_bl}