Pharmacokinetic Models One Compartment Model IV Bolus Absorption
One Compartment Model v Simplest compartmental model Body is assumed to behave as if it were a single, well stirred fluid. v CL I.V. Bolus Dose -dX/dt = CL•Cp -d(X/V)/dt = (CL/V)•Cp = -dCp/dt Cp = Cp,oe-(CL/V)t
Example: Dose = 300 mg, as iv bolus V = 35 L and CL = 2 L/h Cp,o = Dose/V = 300 mg ÷ 35 L = 8.57 mg/L
One Compartment Model Cp = Cp,oe-(CL/V)t log Cp = log Cp,o – (CL/V)t/2.3 Slope = -(CL/V)/2.3 -2.3Slope = CL/V = KE V = Dose ÷ Cp,o V = 300 mg ÷ 8.56 mg/L = 35 L CL = KEV
One Compartment Model -2.303 x Slope = KE Slope = (y2 – y1)/(x2 – x1) = (log Cp2 – log Cp1)/ ( t2 – t1) = log (Cp2/Cp1)/(t2 – t1) = log (7.65/1.10)/(2 – 36) = -0.0248 KE = (-2.303)(-0.0248) = 0.0571 h-1
One Compartment Model CL = KEV = (0.0571 h-1)(35 L) = 2 L/h Half Life: t1/2 = ln 2/KE = 0.693/0.0571 h-1 = 12 h t1/2 = 0.693 V/CL = 0.693•35L/2L h-1 = 12 h
One Compartment Model KEY CONCEPT! Half Life and KE depend on both CL and V; a change in either CL or V will cause a change in t1/2 and KE. KE t1/2 CL V
Area Under the Curve AUC = the area under the Cp,t profile, from time = 0 to time = , usually for a single dose. AUCt1-t2 = the area under the curve from time = t1 to time = t2.
Summary of Wednesday v I.V. Bolus Dose Cp = Cp,oe-(CL/V)t CL - 2.3 x Slope = CL/V = KE V = Dose ÷ Cp,o CL = KEV KE t1/2 CL V
Calculation of AUC Trapezoidal Method, R&T, p.469 2 3 2.4 1.8 Cp mg/L 1 2 4 8 Time [h] AUC = 1+2.5+5.4+8.4+6 = 23.3 mg•h/L
CL for individual pathways MB Murine CL = CLH + CLR + CLP CLH CLR DB Durine CLP Expired air
One Compartment Model A two-fold change in CL:
One Compartment Model A two-fold change in V:
One Compartment Model Absorption Input Drug enters body by a first-order, monoexponential process. ka dX/dt = kaXg - CL•Cp v CL
Absorption The slope of the log-linear phase reflects the smaller of ka and KE.
Absorption Shape parameters Cmax Tmax AUC t1/2 Use shape parameters to deduce changes in PK parameters: ka, CL, V, F
v CL ka Tmax At the peak Cp, dCp/dt = 0
v CL ka Cmax
AUC
ka ka ___Cmax ___Tmax ___t1/2 ___AUC
CL CL ___Cmax ___Tmax ___t1/2 ___AUC
F•Dose F•Dose ___Cmax ___Tmax ___t1/2 ___AUC
V V ___Cmax ___Tmax ___t1/2 ___AUC
Shape parameters as functions of PK parameters
Peak Shape Analysis
Peak Shape Analysis
PK Parameters from single-dose plasma concentration profile Uncertainty in ‘F’ is transmitted to CL. The ratio Dose/AUC gives the true value of CL only when F=1. If F1, then the calculation gives a CL value that is larger than the true value.
PK Parameters from single-dose plasma concentration profile -2.3 x slope = KE (usually)
Pharmacokinetic Models One Compartment Model Absorption Rate Bioavailability
Absorption Rate v XG = Dose•e-kat CL ka XG = Dose•e-kat How can the value of ka be determined from the Cp,t profile?
Determination of ka v XGI XB XE X = amount CL ka Determination of ka XGI XB XE X = amount XGI cannot be measured; ka must come from Cp,t profile
v CL ka Determination of ka 1. Computer fit of equation using software such as WinNonlin. 2. Graphical analysis; aka “method of residuals”, “feathering”, “peeling”
Method of Residuals When ka > 4KE, e-kat goes to 0 before e-KEt does. After e-kat goes to 0:
Method of Residuals Subtract the Cp,t profile from the line:
Method of Residuals What if KE > 4ka?
Bioavailability - F
Bioavailability - F When AUCstd is from an i.v. dose, Fstd = 1.00 and the “absolute bioavailability” of the test is determined. When AUCstd is somethingelse such as the innovator’s product or a solution, “relative bioavailability” is determined.