02_one compartment iv bolus
DESCRIPTION
One Compartment IV BolusTRANSCRIPT
![Page 1: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/1.jpg)
1
One Compartment Open ModelIV bolus
Dr Mohammad Issa
![Page 2: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/2.jpg)
2
One compartment
![Page 3: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/3.jpg)
3
More than one compartment
![Page 4: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/4.jpg)
4
One compartment open model
The one-compartment open model offers the simplest way to describe the process of drug distribution and elimination in the body.
This model assumes that the drug can enter or leave the body (ie, the model is "open"), and the body acts like a single, uniform compartment.
The simplest route of drug administration from a modeling perspective is a rapid intravenous injection (IV bolus).
![Page 5: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/5.jpg)
5
One compartment open model
The simplest kinetic model that describes drug disposition in the body is to consider that the drug is injected all at once into a box, or compartment, and that the drug distributes instantaneously and homogenously throughout the compartment.
Drug elimination also occurs from the compartment immediately after injection.
![Page 6: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/6.jpg)
6
One compartment:
![Page 7: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/7.jpg)
7
Properties of a Pharmacokinetic Compartment1. Kinetic homogeneity. A compartment contains tissues that can
be grouped according to similar kinetic properties to the drug allowing for rapid distribution between tissues
2. Although tissues within a compartment are kinetically homogeneous, drug concentrations within a compartment may have different concentrations of drug depending on the partitioning and binding properties of the drug.
3. Within each compartment, distribution is immediate and rapidly reversible.
4. Compartments are interconnected by first-order rate constants. Input rate constants may be zero order
![Page 8: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/8.jpg)
8
One compartment:
Drug amount in the Body (X)
IV bolus administration
(dose = X0)
Elimination process
Elimination rate constant (K)
Based on the assumption of first order elimination process:
XK raten eliminatio
![Page 9: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/9.jpg)
9
C= concentration
D= dose
Vd: Volume of distribution
K: elimination rate constant
t: time
One compartment open modelD
rug
Co
nc
(C)
Time
tKeVd
DC
![Page 10: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/10.jpg)
10
How to distinguish one comp?lo
g (
C)
Time
Plotting log(C) vs. time yields a straight line
![Page 11: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/11.jpg)
11
Fundamental parameters in one compartment Apparent Volume of Distribution (Vd) Elimination rate constant (K) Elimination half life (t1/2) Clearance (Cl)
![Page 12: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/12.jpg)
12
Apparent Volume of Distribution (Vd)
100 mg
C= 10 mg/L C= 1 mg/L
Vd= 10 L Vd= 100 L
![Page 13: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/13.jpg)
13
Apparent Volume of Distribution (Vd) In general, drug equilibrates rapidly in the body. When plasma
or any other biologic compartment is sampled and analyzed for drug content, the results are usually reported in units of concentration instead of amount
Each individual tissue in the body may contain a different concentration of drug due to differences in drug affinity for that tissue. Therefore, the amount of drug in a given location can be related to its concentration by a proportionality constant that reflects the volume of fluid the drug is dissolved in
The volume of distribution represents a volume that must be considered in estimating the amount of drug in the body from the concentration of drug found in the sampling compartment
![Page 14: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/14.jpg)
14
The real Volume of Distribution has physiological meaning and is related to body water
Plasma
Interstitial fluid
Total body water 42 L
Intracellular fluid
Plasma volume 4 L
Interstitial fluid volume 10 L
Intracellular fluid volume 28 L
![Page 15: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/15.jpg)
15
Apparent Volume of Distribution
Drugs which binds selectively to plasma proteins, e.g. Warfarin have apparent volume of distribution smaller than their real volume of distribution
Drugs which binds selectively to extravascular tissues, e.g. Chloroquines have apparent volume of distribution larger than their real volume of distribution. The Vd of such drugs is always greater than 42 L (Total body water)
![Page 16: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/16.jpg)
16
Apparent Volume of Distribution
Lipid solubility of drug Degree of plasma protein binding Affinity for different tissue proteins Fat : lean body mass Disease like Congestive Heart Failure
(CHF), uremia, cirrhosis
![Page 17: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/17.jpg)
17
Apparent Volume of Distribution
In general, drug equilibrates rapidly in the body. When plasma or any other biologic compartment is sampled and analyzed for drug content, the results are usually reported in units of concentration instead of amount
Each individual tissue in the body may contain a different concentration of drug due to differences in drug affinity for that tissue. Therefore, the amount of drug in a given location can be related to its concentration by a proportionality constant that reflects the volume of fluid the drug is dissolved in
The volume of distribution represents a volume that must be considered in estimating the amount of drug in the body from the concentration of drug found in the sampling compartment
![Page 18: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/18.jpg)
18
Apparent Volume of Distribution: Mathematics In order to determine the apparent volume of distribution
of a drug, it is necessary to have plasma/serum concentration versus time data
0
0
C
X
conc. initial
doseVd
![Page 19: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/19.jpg)
19
Apparent volume of distribution estimation1. Plot log(C) vs. time
2. Plot the best-fit line
3. Extrapolate to the Y-axis intercept (to estimate initial concentration, C0)
4. Estimate Vd:
0
0
C
X
conc. initial
doseVd
![Page 20: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/20.jpg)
20
1- Plot log(C) vs. time
5.8
6
6.2
6.4
6.6
6.8
7
0 1 2 3 4 5 6
Lo
g (
Co
nc)
Time
![Page 21: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/21.jpg)
21
2- Plot the best-fit line
5.8
6
6.2
6.4
6.6
6.8
7
0 1 2 3 4 5 6
Lo
g (
Co
nc)
Time
![Page 22: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/22.jpg)
22
3-Extrapolate to the Y-axis intercept (to estimate C0)
5.8
6
6.2
6.4
6.6
6.8
7
0 1 2 3 4 5 6
Lo
g (
Co
nc)
Time
C0
![Page 23: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/23.jpg)
23
4-Estimate Vd
5.8
6
6.2
6.4
6.6
6.8
7
0 1 2 3 4 5 6
Lo
g (
Co
nc)
Time
Log(C0)
0
0
C
X
conc. initial
doseVd
![Page 24: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/24.jpg)
24
The Extent of Distribution and Vd in a 70 kg Normal Man
Vd, L% Body Weight
Extent of Distribution
5 7 Only in plasma
5-20 7-28 In extracellular fluids
20-40 28-56 In total body fluids.
>40 >56In deep tissues; bound to peripheral tissues
![Page 25: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/25.jpg)
25
Elimination rate constant (K)
Elimination rate constant represents the fraction of drug removed per unit of time
K has a unit of reciprocal of time (e.g. minute-1, hour-1, and day-1)
With first-order elimination, the rate of elimination is directly proportional to the serum drug concentration
![Page 26: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/26.jpg)
26
Elimination rate constant estimation
1. Plot log(C) vs. time
2. Plot the best-fit line
3. Calculate the slope using two points on the best-fit line
4. Estimate K: 303.2 SlopeK
![Page 27: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/27.jpg)
27
1- Plot log(C) vs. time
6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
0 1 2 3 4 5 6
Lo
g (
Co
nc)
Time
![Page 28: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/28.jpg)
28
2- Plot the best-fit line
6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
0 1 2 3 4 5 6
Lo
g (
Co
nc)
Time
![Page 29: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/29.jpg)
29
3- Calculate the slope using two points on the best-fit lin
6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
0 1 2 3 4 5 6
Lo
g (
Co
nc)
Time
(Log(C1), t1)
(Log(C2), t2)
21
21 )log()log(
tt
CCSlope
![Page 30: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/30.jpg)
30
4- Estimate K
6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
0 1 2 3 4 5 6
Lo
g (
Co
nc)
Time
303.2 SlopeK
![Page 31: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/31.jpg)
31
Elimination half life (t1/2)
The elimination half life is sometimes called ‘‘biological half-life’’ of a drug
The elimination half life is defined as the time (h, min, day, etc.) at which the mass (or amount) of unchanged drug becomes half (or 50%) of the initial mass of drug
![Page 32: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/32.jpg)
32
Elimination half life (t1/2) estimation
Two methods:From the value of K:
Directly from Conc vs. time plot Select a concentration on the best fit line (C1) Look for the time that is needed to get to 50% of
C1 half-life
Kt
693.02/1
![Page 33: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/33.jpg)
33
Clearance (Cl)
Clearance is a measure of the removal of drug from the body
Plasma drug concentrations are affected by the rate at which drug is administered, the volume in which it distributes, and its clearance
A drug’s clearance and the volume of distribution determine its half life
![Page 34: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/34.jpg)
34
Clearance (Cl) Clearance (expressed as volume/time) describes the removal of
drug from a volume of plasma in a given unit of time (drug loss from the body)
Clearance does not indicate the amount of drug being removed. It indicates the volume of plasma (or blood) from which the drug is completely removed, or cleared, in a given time period.
Figures in the following two slides represent two ways of thinking about drug clearance: In the first Figure, the amount of drug (the number of dots)
decreases but fills the same volume, resulting in a lower concentration
Another way of viewing the same decrease would be to calculate the volume that would be drug-free if the concentration were held constant as resented in the second Figure
![Page 35: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/35.jpg)
35
Clearance (Cl)
the amount of drug (the number of dots) decreases but fills the same volume, resulting in a lower concentration
![Page 36: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/36.jpg)
36
Clearance (Cl)
![Page 37: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/37.jpg)
37
Clearance (Cl)
The most general definition of clearance is that it is ‘‘a proportionality constant describing the relationship between a substance’s rate of elimination (amount per unit time) at a given time and its corresponding concentration in an appropriate fluid at that time.’’
Clearance can also be defined as ‘‘the hypothetical volume of blood (plasma or serum) or other biological fluids from which the drug is totally and irreversibly removed per unit time.’’
![Page 38: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/38.jpg)
38
Clearance (Cl) estimation
For ALL LINEAR pharmacokinetics (including one compartment) , clearance is calculated using:
where AUC is the area under the concentration curve (it will be discussed later)
AUC
doseCl
![Page 39: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/39.jpg)
39
Clearance (Cl) estimation
For One compartment pharmacokinetics , clearance is calculated using:
VdKCl
![Page 40: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/40.jpg)
40
Clearance (Cl)
Drugs can be cleared from the body by different pathways, or organs, including hepatic biotransformation and renal and biliary excretion. Total body clearance of a drug is the sum of all the clearances by various mechanisms.
Cl) hepatic and renal,total,Cl and Cl,(Cl
ClClClCl
hrt
otherhrt
![Page 41: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/41.jpg)
41
Elimination rate
The elimination rate at any time can be calculated using: Elimination rate = K*X(t)OR Elimination rate = Cl*C(t)
where X(t) is the amount of drug in the body at time t, C(t) is the concntration of drug at time t
![Page 42: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/42.jpg)
42
Area Under the Conc. Time Curve(AUC) calculation Two methods:
Model dependent: can be used only for one compartment IV bolus
Model independent: Can be used for any drug with any route of administration
![Page 43: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/43.jpg)
43
AUC calculation: Model dependent
With one compartment model, first-order elimination, and intravenous drug administration, the AUC can be calculated using:
K
C
VdK
DoseAUC 0
![Page 44: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/44.jpg)
44
0
200
400
600
800
1000
1200
0 2 4 6 8 10 12
AUC calculation: Model independent
![Page 45: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/45.jpg)
45
0
200
400
600
800
1000
1200
0 2 4 6 8 10 12
AUC calculation: Model independent
1
23
4 5
1- Divide the area into different parts based on the observed concentration points (parts 1-5)
![Page 46: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/46.jpg)
46
0
200
400
600
800
1000
1200
0 2 4 6 8 10 12
AUC calculation: Model independent
1
23
4 5
2- Calculate the area for each part of the parts 1,2,3 and 4 (until the last observed concentration) using trapezoidal rule
![Page 47: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/47.jpg)
47
Trapezoidal rule(Trapezoid = المنحرف (شبه
C1
C2
t1 t2
)(2
C area 12
12 ttC
where C = concentration
t = time
![Page 48: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/48.jpg)
48
AUC calculation: Model independent
3- For part 5 (area between the last observed concentration and infinity) use the following equation:
C*K
C area
*
![Page 49: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/49.jpg)
49
0
200
400
600
800
1000
1200
0 2 4 6 8 10 12
AUC calculation: Model independent
1
23
4 5
4- The total AUC (from zero to infinity) is the sum of the areas of parts: 1,2,3,4, and 5
543210 AUCAUCAUCAUCAUC AUC
![Page 50: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/50.jpg)
50
Fraction of the dose remaining
Fraction of dose remainig (F = X(t)/X0) is given by the following equation:
since t1/2= 0.693/k, the equation can be represented as:
tKtK
ee
0
0
X
X
dose
tat timeAmount F
2/12/1
2
1F
693.0 t
t
t
t
e
![Page 51: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/51.jpg)
51
Time to get to certain conc.
Time to get to certain concentration (C*) is given by:
tKeC 0C **
C 0
Ce tK
*
Cln 0
CtK
KCt
*C
ln
0
![Page 52: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/52.jpg)
52
Applications of one compartment model Case 1: Predicting Plasma Concentrations
Case 2: Duration of Action
Case 3:Value of a Dose to Give a Desired Initial Plasma Concentration
![Page 53: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/53.jpg)
53
Case 1: Predicting Plasma Concentrations A 20-mg dose of a drug was
administered as an intravenous bolus injection. The drug has the following pharmacokinetic parameters: k = 0.1 h−1 and Vd = 20 L
1. Calculate the initial concentration (C0 )
2. Calculate the plasma concentration at 3 h
![Page 54: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/54.jpg)
54
1. Calculate the initial concentration (C0 )
2. Calculate the plasma conc. at 3 h
Case 1: Predicting Plasma Concentrations
mg/L 1L 20
mg 20
Vd
dose C0
mg/L 0.74e1 eC C (3)-(0.1)tK0
![Page 55: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/55.jpg)
55
Case 2: Duration of Action
The duration of action of a drug may be considered to be the length of time the plasma concentration spends above the MEC. Its determination is best illustrated by example 2.
![Page 56: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/56.jpg)
56
Case 2: Duration of Action
Continuing with the drug used in Example 1, if the therapeutic range is between 5 and 0.3 mg/L, how long are the plasma concentrations in the therapeutic range?
![Page 57: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/57.jpg)
57
Case 2: Duration of Action
As indicated in the diagram (previous slide) C0 =1 mg/L. Thus, at time zero the plasma concentration is in the therapeutic range. The plasma concentration will remain therapeutic until it falls to the MEC (0.3 mg/L). At what time does this occur?
hr 0.121.0/3.0
1ln*
Cln
0
KCt
![Page 58: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/58.jpg)
58
Case 3: Value of a Dose to Give a Desired Initial Plasma Concentration
Continuing with the drug used in Examples 1 and 2, If the initial Cp of 1 mg/L is unsatisfactory, Calculate a dose to provide an initial plasma concentration of 5 mg/L.
Vd
dose C0 Vd 0C dose
mg 100 L 20L
mg 5 dose
![Page 59: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/59.jpg)
59
Examples
![Page 60: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/60.jpg)
60
Example 1
Ten mg metoclopramide was administered intravenously to a 72 kg patient. The minimum plasma concentration required to cause significant enhancement of gastric emptying is 50 ng/mL. The following plasma concentrations were observed after analysis of the specimen.
![Page 61: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/61.jpg)
61
Example 1
Time (hr) Conc. (ng/ml)
1 90.0
2 68.0
4 40.0
6 21.5
8 12.0
10 7.0
![Page 62: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/62.jpg)
62
Example 1
Calculate the biological half-life of the drug elimination (t½), the overall elimination rate constant (K), the volume (Vd), the coefficient of distribution and the duration of action (td)
![Page 63: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/63.jpg)
63
Example 1
y = -0.1243x + 2.0832
R2 = 0.9995
0
0.5
1
1.5
2
2.5
0 2 4 6 8 10 12
time (hr)
log
(C
on
c)
![Page 64: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/64.jpg)
64
Example 1
The elimination rate constant can be obtained from the slope:
Another way to calculate the slope is using:
1hr 0.286(2.303)(0.1243)
2.303SlopeK
t2-t1
log(C2)-log(C1) Slope
![Page 65: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/65.jpg)
65
Example 1
Another way to calculate the slope (if you do not have the ability to do regression) is using:
where (C1,t1) and (C2,t2) are two different conc. time points
It is important to note that the first method for calculating the slope is more accurate
t2-t1
log(C2)-log(C1) Slope
![Page 66: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/66.jpg)
66
Example 1
Calculating the slope using the second method:
Note that the value of the slope is similar to the
value estimated using the first method (-0.1243)
-0.134816-4
log(21.5)-log(40) Slope
![Page 67: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/67.jpg)
67
Example 1
the biological half-life of the drug elimination (t½):
The volume of distribution (Vd):
hr 2.420.286
0.693
K
0.693t0.5
L 83ml10
L
mg
ng10
ng/ml
mg 0.083
121.12
10
10
10
C
doseVd
3
6
2.08320
![Page 68: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/68.jpg)
68
Example 1
y = -0.1243x + 2.0832
R2 = 0.9995
y = -0.1243x + 2.0832
R2 = 0.9995
0
0.5
1
1.5
2
2.5
0 2 4 6 8 10 12
time (hr)
log
(C
on
c)
Intercept = log (C0)
C0= 10intecept
![Page 69: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/69.jpg)
69
Example 1
the coefficient of distribution = Vd/wt=83 L/ 72 kg= 1.15 L/kg
the duration of action (td). td is the time needed for the conc. To get to 50 ng/ml :
hrKCt 1.3286.0
50121.12
ln *
Cln
0
![Page 70: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/70.jpg)
70
Example 2
An adult male patient was given the first dose of an antibiotic at 6:00 AM. At 12:00 noon the plasma level of the drug was measured and reported as 5 µg/ml. The drug is known to follow the one compartment model with a half-life of 6 hours. The recommended dosage regimen of this drug is 250 mg q.i.d. the minimum inhibitory concentration is 3 µg/ml. Calculate the following: Apparent volume of distribution Expected plasma concentration at 10 AM. Duration of action of the first dose Total body clearance Fraction of the dose in the body 5 hours after the injection Total amount in the body 5 hours after the injection Cumulative amount eliminated 5 hours after the injection Total amount in the body immediately after injection of a second dose at 12:00 noon Duration of action of first dose only if dose administered at 6:00 AM was 500 mg.
![Page 71: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/71.jpg)
71
Example 2
Elimination rate constant:
Initial concentration: The conc. at 12:00 noon (6 hrs after the
first dose) is 5 µg/ml:
1
0.5hr 0.1166
0.693t
0.693K
ug/ml 105)5(
)5(
6116.00
0
ee
tCC
eCtC
tk
tk
![Page 72: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/72.jpg)
72
Example 2
Apparent volume of distribution: C(t=6hrs)= 5 ug/ml. Since the half life is 6 hrs, C0
= 10 ug/ml.
Expected plasma concentration at 10 AM
L 25ml 25000
μg
mg10
ml
μg 10
mg 250
C
XV
3-0
0D
150 11550669306930 -. hr././t.K
μg/ml 6.3 eC4)C(t tK0
![Page 73: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/73.jpg)
73
Example 2
Duration of action of the first dose
Total body clearance
Fraction of the dose in the body 5 hours after the injection
hr 42.101155.03
10ln *
Cln
0
KCt
L/hr 89.2 DVKCl
56.02
1F
6
5
![Page 74: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/74.jpg)
74
Example 2
Total amount in the body 5 hours after the injection = (0.56)(250 mg) = 140 mg
Cumulative amount eliminated 5 hours after the injection = dose – amount in the body = 250 – 140 = 110 mg
Total amount in the body immediately after injection of a second dose at 12:00 noon
Total amount = amount from the first dose + amount from the second dose = 125 + 250 = 375 mg
![Page 75: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/75.jpg)
75
Example 2
Duration of action of first dose only if dose administered at 6:00 AM was 500 mg
Note that 6 hrs (one t0.5) is needed for the amount in the body to decline from 500 mg to 250 mg
hrs 16.42 hr 6 hr 42.10 dt
![Page 76: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/76.jpg)
76
Example 3
The therapeutic range of a drug is 20-200 mg/L. After an intravenous bolus injection of 1.0 gm followed by regression analysis of the concentration of the drug in plasma (in units of mg/L) versus time (in hours), the following linear equation was obtained
Calculate the following Duration of action Total body clearance Rate of elimination at 2 hours
tCp 1.02log
![Page 77: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/77.jpg)
77
Example 3
From the equation:
The following were estimated:
tslopeCtCp )log(1.02log 0
mg/L 1001020 C
1hr 0.23(2.303)(0.1) 2.303SlopeK
L 10mg/L 100
mg 1000
C
XV
0
0D
![Page 78: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/78.jpg)
78
Example 3
Duration of action:
Total body clearance= K∙Vd=(0.23)(10) =2.3 L/hr Rate of elimination at 2 hours: Elimination rate = Cl*C(t=2) = 2.3*63 =145 mg/hr
hr 723.020
100ln *
Cln
0
KCtd
mg/L 63102)Cp(t
1.8(0.1)(2)22))log(Cp(t1.8
![Page 79: 02_One Compartment IV Bolus](https://reader035.vdocuments.net/reader035/viewer/2022062314/563db77f550346aa9a8b9dc5/html5/thumbnails/79.jpg)
79