Absorption Model Pk Concordia Cayetano C0029 Oct 2017 Pedro Zavala In Class Posting

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ABSORPTION MODEL PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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SOURCES

Some portions of lecture notes extracted from SHARGEL & DIPIRO

PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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OBJECTIVES 1. Explain the absorption model

2. Recognize pchem and clinical PK terms in the absorption model 3. Calculate pchem and clinical PK parameters using the absorption model

PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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SECTIONS A. ABSORPTION MODEL B. EQUATION RECOGNITION EXAMPLE C.

TERMS

D. IN CLASS EXERCISES PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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A.

ABSORPTION MODEL

1 compartment model ; V = volume of distribution (L) ka = Absorption rate constant (first order, h-1) k = Elimination rate constant (first order, h-1) PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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ABSORPTION MODEL

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ABSORPTION MODEL ❖ Previous diagram shows absorption phase, elimination phase, Cmax , tmax ❖ More exact name: 1st Order Absorption, 1st Order Elimination, 1 Compartment Model ❖ Absorption Model Characteristics ❖ One compartment ❖ First order absorption ❖ First order elimination PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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ABSORPTION MODEL ❖ dC/dt = Rate In – Rate Out ❖ dC/dt = Change in system [drug] per time ❖ Rate In = Drug absorption rate (from GI into system) ❖ Rate Out = Drug elimination rate (from system) Comment: Model typically used for oral absorption but applies to other EV routes, e.g., skin patches, suppositories, IM PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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ABSORPTION MODEL

C = V= F = ka = k =

Drug plasma level (mg/L) Volume of distribution (L) Bioavailability ; D = Administered dose (mg) absorption rate constant (h-1) elimination rate constant (h-1) PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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ABSORPTION MODEL

Resembles Where A’ is a constant

Note: A’ is used as a constant, do not confuse with A used for amounts PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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ABSORPTION MODEL Model equation can be written in different ways

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B.

EQUATION RECOGNITION ABSORPTION MODEL EXAMPLE

ABSORPTION MODEL EXAMPLE PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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EQUATION RECOGNITION ABSORPTION MODEL EXAMPLE Following oral intake of three 500 mg tablets of a cardiac drug (bioavailability 45%), patient plasma drug levels (mg/L) vs. time (h) were given by

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EQUATION RECOGNITION ABSORPTION MODEL EXAMPLE 1)

What is k ?

2)

What is ka ?

3)

What is the elimination t1/2 ?

4)

What is the absorption t1/2 ?

5)

What is C0 ?

6)

What is V ? PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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EQUATION RECOGNITION ABSORPTION MODEL EXAMPLE Compare general & patient specific equations:

1) k = 0.1 h-1 2) ka = 0.9 h-1 PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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EQUATION RECOGNITION ABSORPTION MODEL EXAMPLE 3) Elimination t1/2 = ln 2 / k = 0.693/k = 0.693/0.1 = 6.93 h 4) Absorption t1/2 = ln 2 / ka = 0.693/ka = 0.693/0.9 = 0.77 h 5) C0 = 0 (initial concentration at t = 0)

MATH: If t = 0 is substituted in the absorption model equation C = 0 GRAPH: Looking at absorption model plot C vs. t it can be seen that initial concentration is zero PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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EQUATION RECOGNITION ABSORPTION MODEL EXAMPLE 6) Comparing general & patient specific equations

ANSWER :

V = 13.6 L

Comment: Only one volume of distribution for one compartment model PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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EQUATION RECOGNITION ABSORPTION MODEL EXAMPLE COMMENTS (a)

can be written as

(b) A’ = 56 mg/L (units !!) (c) ka >> k

In example:

0.9 h-1 >> 0.1 h-1

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C.

ABSORPTION MODEL TERMS

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ABSORPTION MODEL TERMS

 Cmax & tmax 

LAG TIME



FLIP FLOP KINETICS

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ABSORPTION MODEL TERMS

Cmax tmax PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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Cmax

and tmax

 Cmax is highest [drug] (peak level) which occurs at time tmax (peak time)

PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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Cmax

and tmax

QUESTIONS For previous cardiac drug example

1.

What is tmax ?

2.

What is Cmax ? PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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Cmax

and tmax

1.

PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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Cmax

and tmax

2.

PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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Cmax

and tmax

Comments:

➢ See Cmax , tmax , and C0 in C vs. t plot ➢ Do estimated results for above parameters make sense? ➢ Shouldn’t Cmax be 56 mg/L ? PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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ABSORPTION MODEL TERMS

LAG TIME FLIP FLOP KINETICS PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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LAG TIME 

Delay in time for absorption , e.g., for an orally ingested drug



Causes for delay include stomach emptying time, intestinal motility, others



See graph with lag time



For this course lag time calculations are not considered PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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FLIP FLOP KINETICS  Not common in marketed products, can be seen in some drugs with very fast elimination ( k >> ka )  For this course flip flop calculation cases are not considered PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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D.

ABSORPTION MODEL IN CLASS EXERCISES

IN CLASS EXERCISES

PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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DATA I

DATA I PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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DATA I Patient levels vs. time after oral administration of four 250 mg antibiotic capsules (F 0.65) Time (h) 0.2 0.5 1.0 2.0 3.0 4.0 6.0 8.0 12.0 PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

C (mg/L) 6.10 12.46 18.11 20.29 18.25 15.44 10.52 7.06 3.18 DR.

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DATA I 1. 2. 3. 4. 5.

Estimate k , ka and A’ What are the general & patient specific equations ? What is tmax and Cmax? Looking at C vs. t plot do calculated Cmax and tmax make sense? Estimate V PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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DATA I 1.

From feathering analysis:

k = 0.19789 h-1 ka = 1.2239 h-1 A’ = 34.2797 mg/L Comment: Explain feathering qualitatively PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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DATA I 2.

GENERAL

SPECIFIC

PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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DATA I 3.

tmax

Cmax

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DATA I 4. DATA I highest [ ] is 20.29 mg/L at 2 h. It is close to calculated Cmax 20.2 mg/L at tmax ~1.8 h using fitted curve, so calculated parameters make sense Comments: 1) Also look at C vs. t plot to check if calculated values make sense 2) Highest observed [ ] is not necessarily the real Cmax PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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DATA I 5. Volume of distribution

V = 22.6 L PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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DATA II

DATA II PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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DATA II Patient levels vs. time after oral intake of four 500 mg cancer drug tablets (F 0.3 , AU∞ 250 mg) Time (h) 0.2 0.5 1.0 2.0 3.0 4.0 6.0 8.0 12.0

C (mg/L) 2.42 5.17 8.05 10.25 10.37 9.78 8.19 6.73 4.52

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DATA II

Estimate

1. 2. 3.

CL AUC CLR PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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DATA II From feathering analysis:

k = 0.09697

h-1

ka = 1.031626 h-1 A’ = 14.5394

mg/L

PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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DATA II GENERAL

SPECIFIC

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DATA II 1.

CLEARANCE CL = kV (k 0.0970 h-1, find V)

V = 45.55 L CL = kV = 0.0970 * 45.55 = 4.42 L/h PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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DATA II 2. AUC = FD/CL = 0.3 * 2000 mg / 4.42 L/h = 136 mg-h/L 3.

CLR = fR CL

fR = AU∞/FD = 250 mg /(0.3*2000) = 0.42 CLR = 0.42*4.42 = 1.84 L/h PHARMACOKINETICS/CONCORDIA/CAYETANO C0029 PEDRO ZAVALA/ABSORPTION-MODEL/OCT 2017

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