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Agonist
CHA P TE R
2
+
Basic Principles of Pharmacology Pamela Flood
This chapter combines Dr. Stoelting’s elegant description of pharmacology with a mathematical approach first presented by Dr. Shafer1 in 1997, and most recently in Miller’s Anesthesia textbook.2,3 The combination of approaches sets a foundation for the pharmacology presented in the subsequent chapters. It also explains the fundamental principles of drug behavior and drug interaction that govern our daily practice of anesthesia.
Steven Shafer
R
ft
A 80
Bound, inactive receptor
R Unbound, inactive receptor
The simple view of receptor activation also explains the action of antagonist. In this case, the antagonist (red) binds to the receptor, but the binding does not cause activation. However, the binding of the antagonist blocks the agonist from binding, and thus blocks agonist drug effect. If the binding is reversible, this is competitive antagonism. If it is not reversible, then it is noncompetitive antagonism.
C 30
60
20
40
10
EEG Amplitude within 11.5-30Hz (µV/sec)
ff
.
Th
Flumazenil 20
0 0.001
0
0.01
0.1
1
10
B 30
−10 0.001
0.01
0.1
1
10
D 5
25 0 20 15
ff !
−5
10
Bretazenil
RO19-4063
−10
5
ffic
0 0.001
eff
0.01
0.1
1
10
0.0001
0.001
0.01
0.1
1
10
Blood concentration(µg/ml)
Th Th
The concentration versus EEG response relationship for four benzodiazepine ligands: midazolam (full agonist), bretazenil (partial agonist), flumazenil (competitive antagonist), and RO 19-4063 (inverse agonist). (From Shafer S. Principles of pharmacokinetics and pharmacodynamics. In: Longnecker DE, Tinker JH, Morgan GE, eds. Principles and Practice of Anesthesiology. 2nd ed. St. Louis, MO: Mosby-Year Book; 1997:1159, based on Mandema JW, Kuck MT, Danhof M. In vivo modeling of the pharmacodynamic interaction between benzodiazepines which differ in intrinsic efficacy. J Pharmacol Exp Ther. 1992;261[1]:56–61.)
ff
11
Shafer_Ch02.indd 11
R*
Midazolam
ff
fl
+
The interaction of a receptor with an agonist may be portrayed as a binary bound versus unbound receptor. The unbound receptor is portrayed as inactive. When the receptor is bound to the agonist ligand, it becomes the activated, R*, and mediates the drug effect. This view is too simplistic, but it permits understanding of basic agonist behavior.
ft
ff
Bound, activated receptor
Th
ffi
ft
Antagonist
Unbound, inactive receptor
ffi
ff
+ R*
ff
Receptor Theory
ff
Agonist
10/24/14 10:16 PM
12
Shafer_Ch02.indd 12
10/24/14 10:16 PM
Chapter 2
Basic Principles of Pharmacology
13
14
Part I
Basic Principles of Physiology and Pharmacology
e
80%
20%
R
R*
Inactive receptor
Active receptor
fl
Th
ff Th
Receptors have multiple states, and they switch spontaneously between them. In this case, the receptor has just two states. It spends 80% of the time in the inactive state and 20% of the time in the active state in the absence of any ligand.
fl
Th
Th
! Th
.
Th Th
ff
ff
(fl
Pharmacokinetics
Receptor Action
"
Th
ff
fi ff
fi
Th Th
#
Th
#
Th
A
Agonist 0%
B
100%
ff
ifi
Partial agonist 50%
Th
# #
fi
difi
50%
Th R
R*
R
R*
Inactive receptor
Active A tive Acti receptor
Inactive receptor
Active A tive Acti receptor
Receptor Types
Th
Th fi ff #
Antagonist
C 20%
80%
Inverse Agonist
D 100%
0%
ff
R
R*
R
R*
Inactive receptor
Active A tive Acti receptor
Inactive receptor
A tive Acti Active receptor
The action of agonists (A), partial agonists (B), antagonists (C), and inverse agonists (D) can be interpreted as changing the balance between the active and inactive forms of the receptor. In this case, in the absence of agonist, the receptor is in the activated state 20% of the time. This percentage changes based on nature of the ligand bound to the receptor.
Shafer_Ch02.indd 13
Distribution
Th
10/24/14 10:16 PM
Th
Shafer_Ch02.indd 14
ft
Th Th
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Chapter 2
Basic Principles of Pharmacology
15
16
Part I
Basic Principles of Physiology and Pharmacology
Phase I Enzymes Dose or amount
fl
Th
Th
Volume
Concentration =
Th
fl
fl ft
Th
ff ff
Th Th
Amount Volume
Th
The central volume is the volume that intravenously injected drug initially mixes into. (From Shafer S, Flood P, Schwinn D. Basic principles of pharmacology. In: Miller RD, Eriksson LI, Fleisher LA, et al, eds. Miller’s Anesthesia. Vol 1. 7th ed. Philadelphia, PA: Churchill Livingstone; 2010:479–514, with permission.)
ff Th ff
ff fi
ft fi
Metabolism
fl
ft
Protein Binding
fi
fi $ fi
Th
$
Th ff
Pathways of Metabolism
Th
fi
Th Th
Th
eff
fi fi ffi
Th
Th Th
Th Th
%
Shafer_Ch02.indd 15
10/24/14 10:16 PM
Shafer_Ch02.indd 16
10/24/14 10:16 PM
Chapter 2
17
Basic Principles of Pharmacology
18
Part I
Basic Principles of Physiology and Pharmacology Metabolism (R) Clearing organ
Conc = C inflow
Conc =C outflow Flow = Q
e
fl fl
fl
fl fl
fi
Drug removed via metabolism R =Q(C inflow −C outflow)
The relationship between drug rate of metabolism can be computed as the rate of liver blood flow times the difference between the inflowing and outflowing drug concentrations. This is a common approach to analyzing metabolism or tissue uptake across an organ in massbalance pharmacokinetic studies. (From Shafer S, Flood P, Schwinn D. Basic principles of pharmacology. In: Miller RD, Eriksson LI, Fleisher LA, et al, eds. Miller’s Anesthesia. Vol 1. 7th ed. Philadelphia, PA: Churchill Livingstone; 2010: 479–514, with permission.)
Hepatic Clearance Th Th
fl
& (
&
(
Th
fl
ff
diff
fl
fl
fl Th
Th fl
fl Th
fl
&
fl
'
0.8
fl
Equation 2-1
ft
Th
Shafer_Ch02.indd 17
0.4
0 0
&
(
fl
fl
0.1
0.01
0.001 0.001
0.6
0.2
fi Phase II Enzymes
Th
1
d fl &
Th
Th
1
Metabolic rate/Vm
fl
fl
Linear kinetics
Response
fl
m
! (
fl Th
Equation 2-3
fl
fl
Th
fl
&
fl
Th
fi
fl
fl
'
fl
e
Th
fl
Th
&
ffi
& fl
Coutflow = ½ Km
Th
Th
o
Equation 2-2
10/24/14 10:16 PM
1
2 3 Concentration/C50
4
5
The shape of the saturation equation. (From Shafer S, Flood P, Schwinn D. Basic principles of pharmacology. In: Miller RD, Eriksson LI, Fleisher LA, et al, eds. Miller’s Anesthesia. Vol 1. 7th ed. Philadelphia, PA: Churchill Livingstone; 2010:479–514, with permission.)
Shafer_Ch02.indd 18
0.01
0.1
Nonlinear kinetics
1 10 Coutflow /Km
100
1000
The relationship between concentration, here shown as a fraction of the Michaelis constant (Km), and drug metabolism, here shown as a fraction of the maximum rate (Vm). Metabolism increases proportionally with concentration as long as the outflow concentration is less than half Km, which corresponds to a metabolic rate that is roughly one-third of the maximal rate. Metabolism is proportional to concentration, meaning that clearance is constant, for typical doses of all intravenous drugs used in anesthesia. (From Shafer S, Flood P, Schwinn D. Basic principles of pharmacology. In: Miller RD, Eriksson LI, Fleisher LA, et al, eds. Miller’s Anesthesia. Vol 1. 7th ed. Philadelphia, PA: Churchill Livingstone; 2010:479–514, with permission.)
10/24/14 10:16 PM
fl
2.5
Clearance (l/min)
ff
fl
fl
ffl
Th
Th
2
1.5
fl fl
⎛
&
fl
⎜
⎝
'
⎞
fl
⎟
⎠
Equation 2-4
fl
fl
⎛
'
fl
⎜
⎝
⎞
fl
⎟
⎠
fl
&
⎜
⎝
fl
1 1.5 2 Liver blood flow (l/min)
0.00 0
3
fl
⎟
(
0.5 1 1.5 Liver disease/ Vm Enzyme induction enzyme inhibition
fl
⎠
'
&
&
Shafer_Ch02.indd 19
⎝
fl fl
'
ff
Th
Th
fl Th
⎟
⎠
fl
⎝
fi ⎞
⎛
⎜
(
⎟
fl
Equation 2-6
(
fl
⎠
⎞
⎜
⎝ fl
(
⎠
fl
fl (
Shafer_Ch02.indd 20
Th
⎟
fl
fi
fl
fl
10/24/14 10:16 PM
&
⎛
fl fl
⎞
fl
fi
& Th
Th fl
&
fl
&
⎜
fl
Th
Th
⎛
fi Th
Th
& fl
100000
Th
fl
fl
)
2
fl
fl
e &
10000
The extraction ratio as a function of the intrinsic calculated for a liver blood flow of 1,400 mL/min. (From Shafer S, Flood P, Schwinn D. Basic principles of pharmacology. In: Miller RD, Eriksson LI, Fleisher LA, et al, eds. Miller’s Anesthesia. Vol 1. 7th ed. Philadelphia, PA: Churchill Livingstone; 2010:479–514, with permission.)
&
fl
fl
Th
1000
(
& fl
100
fl
fl
fi
10
Changes in maximum metabolic velocity (Vm) have little effect on drugs with a high extraction ratio but cause a nearly proportional decrease in clearance for drugs with a low extraction ratio. (From Shafer S, Flood P, Schwinn D. Basic principles of pharmacology. In: Miller RD, Eriksson LI, Fleisher LA, et al, eds. Miller’s Anesthesia. Vol 1. 7th ed. Philadelphia, PA: Churchill Livingstone; 2010: 479–514, with permission.)
fl ⎞
0
0.2
fi
Th Th
0.3
0.1
The relationship between liver blood flow (Q), clearance, and extraction ratio. For drugs with a high extraction ratio, clearance is nearly identical to liver blood flow. For drugs with a low extraction ratio, changes in liver blood flow have almost no effect on clearance. (From Shafer S, Flood P, Schwinn D. Basic principles of pharmacology. In: Miller RD, Eriksson LI, Fleisher LA, et al, eds. Miller’s Anesthesia. Vol 1. 7th ed. Philadelphia, PA: Churchill Livingstone; 2010:479–514, with permission.)
Equation 2-5
Th
2.5
0.4
Intrinsic clearance (mls/min)
0.3 0.2 0.1 0.5
0.6
0.2
0.4
&
fl
⎛
fl
0.8 Extraction ratio 1.0 0.9 0.8 0.7 0.6 0.5
1.00
0
fl
&
1
0.50
0.5
0.5
fl )
0.7 0.6
0
&
1.50
0.8
Th
fl
e
2.00
0.9
1
Basic Principles of Physiology and Pharmacology
0.4
'
fl
Extraction ratio 1.0
Part I
Extraction ratio
3
20
E.R. calculated at Vm = 1 gm/min
fl
Extraction ratio calculated at Q = 1.4 l/min
e
19
Basic Principles of Pharmacology
Clearance (l/min)
Chapter 2
fl
fl fi
Renal Clearance fi Th
10/24/14 10:16 PM
Chapter 2
21
Basic Principles of Pharmacology
22
Part I
Basic Principles of Physiology and Pharmacology
250
fi
Creatinine clearance (mls/min)
fi
Th fl
d
200 150 0.5
50
1.0 1.5 2.0
fl
Ion Trapping diff
0 20
30
40
50
60
70
80
90
fl
Age
Th
fl
fl
fl
fl
ff
Creatinine 100
Creatinine clearance as a function of age and serum creatinine based on the equation of Cockroft and Gault. (From Cockcroft DW, Gault MH. Prediction of creatinine clearance from serum creatinine. Nephron. 1976;16: 31–41, with permission.)
diff fl
Th
Oral istration ft
Th fl Th
fl
ff
Th ff & ' )
fl
Th
)
Equation 2-7
Th
Determinants of Degree of Ionization Th fl
ffi
Th
e fl
Th
ff
Th
Absorption
Th
Characteristics of Nonionized and Ionized Drug Molecules
diff ff
Route of istration and Systemic Absorption of Drugs
Ionization
Th Th
Shafer_Ch02.indd 21
Th
ft
Th
ff
10/24/14 10:16 PM
Shafer_Ch02.indd 22
fl ff
fi
ff eff
Oral Transmucosal istration Th ff fi ff fi
10/24/14 10:16 PM
effi
fi
eff
fi
Th
24
Part I
Basic Principles of Physiology and Pharmacology
Exponential decay curve, as given by x(t) & x0e'kt, plotted on standard axis (A) and a logarithmic axis (B).
A 10
B 10
x0 = 10 k = 0.5
x0 = 10
8
Pharmacokinetic Models
Th
eff
23
6
x (amount)
eff
Basic Principles of Pharmacology
x (amount)
Chapter 2
k = 0.5
4
1
2 0
0.1 0
2
4 6 t (time)
Transdermal istration
8
10
0
2
4 6 t (time)
ffi Zero- and First-Order Processes Th
ff
Th &
Th
Th
&
+ ff +
(
&
ff
Th
Th
fl &
! Th
Th Th
!
&
e e +
fi
fl
e
Equation 2-11
One-Compartment Model
Physiologic Pharmacokinetic Models
% Th e
Th
7
ff '
&
ifi
& & & &
ff Th
*
fl fi &
Equation 2-8
Rectal istration
diff
fi
&
&
Th
Th
fi
*
ffi
Shafer_Ch02.indd 23
&
&
fi
Th
ff
⎞ ⎟ ⎠
Th
⎤ ⎞⎥ ⎟ ⎠⎦ Equation 2-10
Th
ff
⎛ ⎜ ⎝
! Th
!
(fi
,
Th
Th
Th
&
⎡ ⎢⎛⎜ ⎣⎝
*
ff ff
'
,
& Th
10
fl
'
Th
8
)
fl
'
fl
'
( ' *
'
Equation 2-9
Th
e
10/24/14 10:16 PM
)
Compartmental Pharmacokinetic Models
Shafer_Ch02.indd 24
fl
Th
a fi
)
10/24/14 10:16 PM
Chapter 2
Basic Principles of Pharmacology
25
26 A
Q
Part I
Basic Principles of Physiology and Pharmacology
B
I
I
Cardiac output
Lung
V1 Central compartment
V Volume of distribution
Aortic juncture Brain
Venous
C
Arterial
Pancreas
V3 Slowly equilibrating compartment
Gut Liver
Portal juncture
Input juncture
Spleen
k21
fi &
V2 Peripheral compartment
fi ' * &
I k13
k31
V1 Central compartment
k12
k21
V2 Rapidly equilibrating compartment
∫
'
⎛ ⎜ ⎝
-
&
k10
Standard one- (A), two- (B), and three-compartment (C) mammillary pharmacokinetic models. I represents any input into the system (e.g., bolus or infusion). The volumes are represented by V and the rate constants by k. The subscripts on rate constants indicate the direction of flow, noted as kfrom to.
Clock
Kidney Testes
'
-
&
Hepatic artery
Infusion
&
k10
k
Heart
k12
&
∫
'
⎞ ⎟ ⎠
)
&
Equation 2-14
Time Muscle
&
Fat
& Th
Skin
Carcass
Physiologic model for thiopental in rats. The pharmacokinetics of distribution into each organ has been individually determined. The components of the model are linked by zero-order (flow) and first-order (diffusion) processes. (From Ebling WF, Wada DR, Stanski DR. From piecewise to full physiologic pharmacokinetic modeling: applied to thiopental disposition in the rat. J Pharmacokinetic Biopharm. 1994;22:259–292, with permission.)
fi a fi
Th
Equation 2-13
Th
fi
Arterial branch
Venous juncture
fi
'
Equation 2-15
The relationship between volume and clearance and half-life can be envisioned by considering two settings: a big volume and a small clearance (A) and a small volume with a big clearance (B). Drug will be eliminated faster in the latter case.
)
A
B Plasma
Plasma
Th
Clearing organ
&
)
a fi & fi
&
&
Clearing organ
'
ft &
Shafer_Ch02.indd 25
Equation 2-12
fi
10/24/14 10:16 PM
Shafer_Ch02.indd 26
10/24/14 10:16 PM
Chapter 2
& '
&
&
'
28
Part I
Basic Principles of Physiology and Pharmacology
Th
'
Th
'
Th
&
*
27
Basic Principles of Pharmacology
Multicompartment Models Th
*
Th
fi
2 Th &
*
5
fi
Th
*
&
Th
&
Th
Th ff
Th
fi
* -
fi & Th
Th
ff
ff
ft
fl
&
*
*
'
*
100
&
'
'
* &
fi
*
&
'
'
Th
Th
ff
ff &
→-
'
→
&
'
* Th
&
fl
'
'
*
*
*
& '
0
Equation 2-16
Th
fi &
& &
Shafer_Ch02.indd 27
Th
'
'
'
'
1
0.1
' * & ' *
Rapid
10
Concentration
'
&
100
' Concentration
&
fl Th
. fl
Th
ft
ft
*
Th
Th
&
Equation 2-17
10 Intermediate Slow 1
120 240 360 480 600 Minutes since bolus injection
Typical time course of plasma concentration following bolus injection of an intravenous drug, with a rapid phase (red), an intermediate phase (blue), and a slow log-linear phase (green). The simulation was performed with the pharmacokinetics of fentanyl. (From Scott JC, Stanski DR. Decreased fentanyl and alfentanil dose requirements with age. A simultaneous pharmacokinetic and pharmacodynamics evaluation. J Pharmacol Exp Ther. 1987;240: 159–166, with permission.)
0.1 0
120
240
360
480
600
Minutes since bolus injection
Hydraulic equivalent of the model in Figure 2-18. (Adapted from Youngs EJ, Shafer SL. Basic pharmacokinetic and pharmacodynamic principles. In: White PF, ed. Textbook of Intravenous Anesthesia. Baltimore, MD: Lippincott Williams & Wilkins; 1997:10, with permission.)
fi
10/24/14 10:16 PM
Shafer_Ch02.indd 28
10/24/14 10:16 PM
Chapter 2
29
Basic Principles of Pharmacology
fi
fi
30
Part I
Basic Principles of Physiology and Pharmacology
B
A 0
30
0
1500
Fentanyl
'#
'"
$% #% " &
&
(
(
ffi (
(
5 EEG
20
10
10
15
&
fi
15 20
5
10
15
20
0
25
ffi
Th ft
& &
'$
(
'#
(
'"
ffic $
$ #
(
fi
ff
#
"
Th Th
C(t ) = Ae−αt
'
& (
C(t ) = Ae−αt + Be−βt + Ce−γt
Th
Th
'
60
120
The polyexponential equation that describes the decline in plasma concentration for most intravenous anesthetics, is the algebraic sum of the exponential that represent rapid phase shown in red, intermediate phase shown in blue and slow phase shown in green.
&
'
&
'
Equation 2-21
ff I
Th
V3 Slowly equilibrating compartment
ff
e Th
ff Th
k13 k31
V1 Central compartment
k10
V2 Rapidly equilibrating compartment
k12 k21
k1e
Effect compartment
ff (
& (
*
ff
240
Minutes since bolus injection
'
ff
Th
180
*
ff
Equation 2-19
ff
1
25
ff Th
The Time Course of Drug Effect
ff
'
&
C(t ) = Ce−γt
0
a fi
Th
ft
20
ff
Th
ffi
Th
C(t ) = Be−βt
ff
fi
"
10
10 15 Time (min)
&
#
100
Concentration
n
Th
Th
Shafer_Ch02.indd 29
Th
'"
Equation 2-18
$ "
(
5
Fentanyl and alfentanil arterial concentrations (circles) and electroencephalographic (EEG) response (irregular line) to an intravenous infusion. Alfentanil shows a less time lag between the rise and fall of arterial concentration and the rise and fall of EEG response than fentanyl because it equilibrates with the brain more quickly. (Modified from Scott JC, Ponganis KV, Stanski DR. EEG quantitation of narcotic effect: the comparative pharmacodynamics of fentanyl and alfentanil. Anesthesiology. 1985;62:234–241, with permission.)
Th
'#
25
Infusion 0
0
'$
10
EEG
0
fi
5
1000
20
Infusion
ff
Alfentanil (ng/ml)
ff
Arterial level
'"
(
Spectral edge (Hz)
'$
Th
'#
(
Fentanyl (ng/ml)
'$
&
Spectral edge (Hz)
fl
ft
Alfentanil Arterial level
'
'
ke0
'
ff
Equation 2-20
10/24/14 10:16 PM
Shafer_Ch02.indd 30
ff
The three-compartment model from Figure 2-16 with an added effect site to for the equilibration delay between the plasma concentration and the observed drug effect. The effect site has a negligible volume. As a result, the only parameter that affects the delay is ke0.
10/24/14 10:16 PM
Chapter 2
A
B
80 60 40 17%
20
32
0
Part I
Basic Principles of Physiology and Pharmacology
Th
100
Alfentanil concentration (percent of peak plasma)
Fentanyl concentration (percent of peak plasma)
100
31
Basic Principles of Pharmacology
ft
ff
60
2 4 6 8 Minutes since bolus injection
ff
ff
ff
40 37%
ff
20
ff
0 0
The Time to Peak Effect and t ½ ke0 following a Bolus Dose
80
10
0
2 4 6 8 Minutes since bolus injection
Th
Th
10
ff ff
Plasma (black line) and effect site (red line) concentrations following a bolus dose of fentanyl (A) or alfentanil (B). (Adapted from Shafer SL, Varvel JR. Pharmacokinetics, pharmacodynamics, and rational opioid selection. Anesthesiology. 1991;74:53–63, with permission.)
&
Equation 2-22 &
.
ff diff
Th
ff &
ff
)
!
Th
ff
ff
ff
eff
ff
ff !
ff
ff
Th
! Th Th ff
ff
ff
fl
ff
fi ff
ff
Maintenance Infusion Rate ff
ff diff
ff
eff
ff
Th
Fentanyl concentration (ng/ml)
)
Dose = 720 µg = Target x Vdss
10
Volume of Distribution at the Time of Peak Effect.
Dose = 150 µg = Target x Vdss
&
)
)
Th Th !
Th
ff
ff
ff Dose = 26 µg = Target x Vdss
uffi 0
Shafer_Ch02.indd 31
ft
ft
1
0.1
!
)
100
fi
fi
!
Th
Th
fi
Bolus Dosing
Th
ff
ff
Dose Calculations
&
!
Th
5
10 15 Minutes since bolus
20
10/24/14 10:16 PM
ffi
ff
The volume of the central compartment of fentanyl is 13 L. The volume of distribution at steady state is 360 L. For a target concentration of 2 !g/L (dotted line), the dose calculated on V1, 26 !g, results in a substantial undershoot. The dose calculated using Vdss, 720 !g, produces a profound overshoot. Only a dose based on Vdpeak effect, 150 !g, produces the desired concentration in the effect site. The black lines show plasma concentration over time. Red lines show effect site concentration over time.
Th ff
fl
Shafer_Ch02.indd 32
10/24/14 10:16 PM
Chapter 2
e
400
33
34
Part I
Basic Principles of Physiology and Pharmacology 6.0
5.0
Th
4.5
4.0 Fentanyl (ng/ml)
300
200
Th
100
3.0 2.0 1.0
60 120 180 240 300 Minutes since bolus injection
360
0.0
ff
'
(
'
(
Equation 2-23
Context Sensitive Half-time fi
Th
ft
fi
& ) Th ft Th Th
Th
Th Th
Th
1.5
Alfentanil (ng/ml)
1.25
400
1.0 300
0.75
200
0.5
100
0.25
0 2.0
1.0
1.5 1.2
0.8
1.0 0.9 0.8 0.7 0.6 0.5
0.6 0.4
0.3 0.15
0.2 0.0 300
8.0
250 200 180 160 140 120 100 75
6.0
4.0
2.0
(µg/kg/min)
Th
Th
1.75
500
Propofol (µg/ml)
Th
2.0
(µg/kg/hr)
Infusion rates to maintain stable plasma concentrations
& )
2.5 2.25
(µg/kg/min)
Th
)
3.0
600
Fentanyl infusion rate to maintain a plasma concentration of 1 !g/hr. The rate starts off quite high because fentanyl is avidly taken up by body fat. The necessary infusion rate decreases as the fat equilibrates with the plasma.
Sufentanil (ng/ml)
0
Suggested Initial Target
Th
0
3.6 3.0 2.7 2.4 2.1 1.8 1.5 1.2 0.9
(µg/kg/hr)
Fentanyl infusion rate (µg/hr)
Basic Principles of Pharmacology
50 25
0.0 0
60
120
180
240
300
Minutes since beginning of infusion
Dosing nomogram, showing the infusion rates (numbers on the perimeter) required to maintain stable concentrations of fentanyl (1.0 !g/mL), alfentanil (75 !g/mL), sufentanil (0.1 !g/mL), and propofol (3.5 ng/mL).
ft
2.4 !
! ! !
! ff
Shafer_Ch02.indd 33
ff
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Shafer_Ch02.indd 34
10/24/14 10:17 PM
Chapter 2 Body weight (kg)
Basic Principles of Pharmacology
35
36
Part I 60
100
90
80
70
60
50
40
30
20
Basic Principles of Physiology and Pharmacology
20% decrement
50
10
40 240 120 45 180 60 30
Propofol-target-concentration (µg/ml) 1
15
2
10
3
20
4
30
5
40
50
60
70
80
90
100 110 120 130140150
Infusion rate propofol 1% (ml/h)
Propofol slide ruler to calculate maintenance infusion rate, based on the patient’s weight and the time since the start of the infusion, as proposed by Bruhn and colleagues (Adapted from Bruhn J, Bouillon TW, Ropcke H, et al. A manual slide rule for target-controlled infusion of propofol: development and evaluation. Anesth Analg. 2003;96:142–147.). To make use of the calculator, make a photocopy and cut in to top (body weight), middle (time since start of infusion/propofol target concentration), and bottom (infusion rate propofol 1%) sections—calculation requires sliding the middle piece in relationship to the top and bottom segments, which are fixed.
e
e
Th
ff ff
"
Eff
30
0
Minutes for a given decrement in effect site concentration
Time since start of infusion (min)
(
&
'
"
20
Equation 2-24
"
eff
10 0
(
0
360
120
240
360
480
ff
600
50% decrement
300 Fentanyl Alfentanil Sufentanil Remifentanil
240 180 120
"
Th
"
fi
60
(
"
(
0 0
120
720
240
360
480
600
ffic
"
80% decrement
Th
600
"
480 360
"
240
ff
120
Th
ff
fi ffi
0
Pharmacodynamics Concentration versus Response Relationships ff
Th
Th
ff
600
Potency and Efficacy Th
ft Th
ff ff
ff
Context-sensitive half-times as a function of the duration of intravenous drug infusion for each fentanyl, alfentanil, sufentanil, propofol, midazolam, and thiopental. (From Hughes MA, Glass PSA, Jacobs JR. Context-sensitive half-time in multicompartment pharmacokinetic models for intravenous anesthetic drugs. Anesthesiology. 1992;76:334–341, with permission.)
Fentanyl 200 Thiopental
ft ft
ft
Th
250
fi
diff
Th
Emax
100
Effect
Context-sensitive half-time (minutes)
Th
fi
300
ft
Efficacy
50
Sufentanil 0
1
2
3
Midazolam
ft
5
ft C50
Drug exposure (dose, concentration, etc.) versus drug effect relationship. Potency refers to the position of the curve along the x-axis. Efficacy refers to the position of the maximum effect on the y-axis.
Propofol 4
6
7
8
9
Infusion duration (hours)
10/24/14 10:17 PM
Shafer_Ch02.indd 36
ft
Potency
fi
Dose, concentration, or other measure of exposure
Alfentanil
ff
fi
50
0
Fentanyl
100
ft
ff
150
0
Shafer_Ch02.indd 35
120 240 360 480 Infusion duration (minutes)
Effect site decrement times. The 20%, 50%, and 80% decrement times for fentanyl (black), alfentanil (green), sufentanil (red), and remifentanil (blue). When there is substantial plasma-effect site disequilibrium, the effect site decrement time will provide a better estimate of the time required for recover than the context-sensitive halftime. (Adapted from Youngs EJ, Shafer SL. Pharmacokinetic parameters relevant to recovery from opioids. Anesthesiology. 1994;81:833–842, with permission.)
Th Th
"
0
Th eff
ffi .
ff
Th
fi
ff ffi
ff
ffi ff
10/24/14 10:17 PM
Chapter 2
C
Potency more less
Dose, concentration, or other measure of exposure
Dose versus response relationship for three drugs with potency. Drug A is the most potent, and drug C is the least potent.
fl
Th diff
Death
80
60 Therapeutic index LD50 400 = =4 ED50 100
40
ED50
LD1 ED99 LD50
100
200
400
Th
ff
ffi
ff fi
1600
Analysis to determine the LD50, the LD99, and the therapeutic index of a drug.
diff
fi
800
Dose (mg)
ff
5
diff
4 3
Desflurane
2
Isoflurane
1 2
4 6 8 Fentanyl (ng/ml)
Th
Th
fi
Th
Interaction between fentanyl and isoflurane or desflurane on the minimum alveolar concentration required to suppress movement to noxious stimulation. (Adapted from Sebel PS, Glass PS, Fletcher JE, et al. Reduction of the MAC of desflurane with fentanyl. Anesthesiology. 1992;76:52–59; McEwan AI, Smith C, Dyar O, et al. Isoflurane minimum alveolar concentration reduction by fentanyl. Anesthesiology. 1993;78:864–869.)
Stereochemistry Th
ffi ff
10
ft
Th Th
6
0
50
ffi
Basic Principles of Physiology and Pharmacology
0
20
0
ffi ff
Inspired desflurane or isoflurane
B
Percent of animals responding
Effect
A
0
ff
Part I 7
Hypnosis
ffi
38
100
100
eff
37
Basic Principles of Pharmacology
Th
ff
Th
ff
efl
e
Effective Dose and Lethal Dose 400
fi
ff
100
Full agonist
Alfentanil concentration (ng/ml)
Th
Drug Interactions Actions at Different Receptors
Effect
80 60
Partial agonist
40 20 0
Neutral Antagonist
1.5
ft
' Th ft
(
Emergence
(
100
'
Th 0
Th
2 4 6 8 10 Propofol concentration (µg/ml)
Interaction of propofol with alfentanil on the concentration required to suppress response to intubation, maintain nonresponsiveness during surgery, and then awaken from anesthesia. (Adapted from Vuyk J, Lim T, Engbers FH, et al. The pharmacodynamics interaction of propofol and alfentanil during lower abdominal surgery in women. Anesthesiology. 1995;83:8–22, with permission.)
Th
Concentration versus response curves for drugs with differing efficacies. Although the C50 of each curve is the same, the partial agonist is less potent than the full agonist because of the decreased efficacy.
Shafer_Ch02.indd 37
Maintenance 200
0
efi
Inverse agonist Dose, concentration, or other measure of exposure
Intubation 300
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Shafer_Ch02.indd 38
A Th fi
fi
fi
10/24/14 10:17 PM
Basic Principles of Pharmacology
39
40
Part I
Basic Principles of Physiology and Pharmacology
8+1a** 1
10 + 4a
1¶
1a
Na+ channel
2a
1a
1
3
1a
4a
1a
3
3 Ad 2 ag ditiv 1 on e ist
2 t gonis
1
1 + 3a 1
4 +8a 2+ 1a
7a
2
1 1a
1a
3 Pa 2 ag rtia on l ist
A
0
B
1
1 0
3
2 nist Ago
1a
3 pra 2 ag -add 1 on itiv ist e
1
1a
1a
1a
1+1a
2
0.5 0.0
Su
1a
E
1.0
0.5 0.0
1a
3
1a
3a
2a
0.5 0.0
1.0 5+3a
Halothane
2 t gonis
1
3 Co 2 an mpe tag titi 1 on ve ist
3
A
0
3
2 t gonis
1 A
0
2a
Enflurane
1
Isoflurane
1
3a
1a
1aI
2 Sevoflurane
Effect
Xe
N 2O
Desflurance
Sevoflurane
Isoflurane
1a
12 Dopamine
Enflurane
0.0
2a 2a
1¶¶ 3a
Halothane
Na+ channel
Dopamine
Opioid
α2 5
0.5
Effect
2 1
Opioid
2*
D
1.0
1
1
1 +1a§
Desflurance 1
2
1
Xe
1
Additivity
0.5 0.0 −0.5
Inf
Hypnosis Synergy
3 ra- 2 ag add 1 on itiv ist e
F
1.0
0.5 0.0
N 2O
C
1.0
2 +2a 1+1aI
1
Effect
α2
3
Effect
NMDA
1
A
1.0
Effect
GABABDZ
1
2
NMDA
GABA GABA
GABABDZ
Immobility
Effect
Chapter 2
1
2 t gonis
0
A
3
3
Inv 2 ag erse on ist
1
1
0
3
2
t
nis Ago
Interaction surfaces, showing simple additivity (A), synergy (B), and infra-additivity (C). More complex relationships exist between agonists and partial agonists (D), agonists and competitive antagonists (E), and agonists and inverse agonists (F). (From Minto CF, Schnider TW, Short TG, et al. Response surface model for anesthetic drug interactions. Anesthesiology. 2000;92:1603–1616, with permission.)
Infra-additivity
Survey of interactions between hypnotics and analgesics by Hendrickx et al. (From Hendrickx JF, Eger EI II, Sonner JM, et al. Is synergy the rule? A review of anesthetic interactions producing hypnosis and immobility. Anesth Analg. 2008;107:494–550, with permission.)
Th ifi
Th
Th
diff
Th ff
ifi Th fi
fi
ff
fi diff
fi
ffin
fi
Th
fl fi Th
( ' ff
ifi
diff
fi
diff
fl
Clinical Aspects of Chirality
diff
ff
Shafer_Ch02.indd 39
10/24/14 10:17 PM
Shafer_Ch02.indd 40
10/24/14 10:17 PM
Chapter 2
Basic Principles of Pharmacology
Part I
Th
ffi
Th ff
fi
Individual Variability Th
ff
Enzyme Activity
fi
diffi
ff
ffi
fl
Th
Genetic Disorders
fl
References
diff
diff
Th
fl
% 200
fl
fi
ff
fi
ff
Th eff
diff
ff
fi
ft diff
fi
fl
ff
Th
diff
diff
ff
nfl
ft
efl
Basic Principles of Physiology and Pharmacology
Th
fl fl
42
diff
fi
41
ff
) e a fi
.
ff
fi Th ft efi Events Responsible for Variations in Drug Responses between Individuals
ff
Drug Interactions Elderly Patients
ff
fl fl diff
Shafer_Ch02.indd 41
fi
efl
Th
Th
ff
10/24/14 10:17 PM
Shafer_Ch02.indd 42
ff
ff
fl
10/24/14 10:17 PM
Chapter 2
Basic Principles of Pharmacology
43
ff Th
Th
fl
Shafer_Ch02.indd 43
fl
Th
10/24/14 10:17 PM
CHA P TE R
2
+
Basic Principles of Pharmacology Pamela Flood
This chapter combines Dr. Stoelting’s elegant description of pharmacology with a mathematical approach first presented by Dr. Shafer1 in 1997, and most recently in Miller’s Anesthesia textbook.2,3 The combination of approaches sets a foundation for the pharmacology presented in the subsequent chapters. It also explains the fundamental principles of drug behavior and drug interaction that govern our daily practice of anesthesia.
Steven Shafer
R
ft
A 80
Bound, inactive receptor
R Unbound, inactive receptor
The simple view of receptor activation also explains the action of antagonist. In this case, the antagonist (red) binds to the receptor, but the binding does not cause activation. However, the binding of the antagonist blocks the agonist from binding, and thus blocks agonist drug effect. If the binding is reversible, this is competitive antagonism. If it is not reversible, then it is noncompetitive antagonism.
C 30
60
20
40
10
EEG Amplitude within 11.5-30Hz (µV/sec)
ff
.
Th
Flumazenil 20
0 0.001
0
0.01
0.1
1
10
B 30
−10 0.001
0.01
0.1
1
10
D 5
25 0 20 15
ff !
−5
10
Bretazenil
RO19-4063
−10
5
ffic
0 0.001
eff
0.01
0.1
1
10
0.0001
0.001
0.01
0.1
1
10
Blood concentration(µg/ml)
Th Th
The concentration versus EEG response relationship for four benzodiazepine ligands: midazolam (full agonist), bretazenil (partial agonist), flumazenil (competitive antagonist), and RO 19-4063 (inverse agonist). (From Shafer S. Principles of pharmacokinetics and pharmacodynamics. In: Longnecker DE, Tinker JH, Morgan GE, eds. Principles and Practice of Anesthesiology. 2nd ed. St. Louis, MO: Mosby-Year Book; 1997:1159, based on Mandema JW, Kuck MT, Danhof M. In vivo modeling of the pharmacodynamic interaction between benzodiazepines which differ in intrinsic efficacy. J Pharmacol Exp Ther. 1992;261[1]:56–61.)
ff
11
Shafer_Ch02.indd 11
R*
Midazolam
ff
fl
+
The interaction of a receptor with an agonist may be portrayed as a binary bound versus unbound receptor. The unbound receptor is portrayed as inactive. When the receptor is bound to the agonist ligand, it becomes the activated, R*, and mediates the drug effect. This view is too simplistic, but it permits understanding of basic agonist behavior.
ft
ff
Bound, activated receptor
Th
ffi
ft
Antagonist
Unbound, inactive receptor
ffi
ff
+ R*
ff
Receptor Theory
ff
Agonist
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12
Shafer_Ch02.indd 12
10/24/14 10:16 PM
Chapter 2
Basic Principles of Pharmacology
13
14
Part I
Basic Principles of Physiology and Pharmacology
e
80%
20%
R
R*
Inactive receptor
Active receptor
fl
Th
ff Th
Receptors have multiple states, and they switch spontaneously between them. In this case, the receptor has just two states. It spends 80% of the time in the inactive state and 20% of the time in the active state in the absence of any ligand.
fl
Th
Th
! Th
.
Th Th
ff
ff
(fl
Pharmacokinetics
Receptor Action
"
Th
ff
fi ff
fi
Th Th
#
Th
#
Th
A
Agonist 0%
B
100%
ff
ifi
Partial agonist 50%
Th
# #
fi
difi
50%
Th R
R*
R
R*
Inactive receptor
Active A tive Acti receptor
Inactive receptor
Active A tive Acti receptor
Receptor Types
Th
Th fi ff #
Antagonist
C 20%
80%
Inverse Agonist
D 100%
0%
ff
R
R*
R
R*
Inactive receptor
Active A tive Acti receptor
Inactive receptor
A tive Acti Active receptor
The action of agonists (A), partial agonists (B), antagonists (C), and inverse agonists (D) can be interpreted as changing the balance between the active and inactive forms of the receptor. In this case, in the absence of agonist, the receptor is in the activated state 20% of the time. This percentage changes based on nature of the ligand bound to the receptor.
Shafer_Ch02.indd 13
Distribution
Th
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Th
Shafer_Ch02.indd 14
ft
Th Th
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Chapter 2
Basic Principles of Pharmacology
15
16
Part I
Basic Principles of Physiology and Pharmacology
Phase I Enzymes Dose or amount
fl
Th
Th
Volume
Concentration =
Th
fl
fl ft
Th
ff ff
Th Th
Amount Volume
Th
The central volume is the volume that intravenously injected drug initially mixes into. (From Shafer S, Flood P, Schwinn D. Basic principles of pharmacology. In: Miller RD, Eriksson LI, Fleisher LA, et al, eds. Miller’s Anesthesia. Vol 1. 7th ed. Philadelphia, PA: Churchill Livingstone; 2010:479–514, with permission.)
ff Th ff
ff fi
ft fi
Metabolism
fl
ft
Protein Binding
fi
fi $ fi
Th
$
Th ff
Pathways of Metabolism
Th
fi
Th Th
Th
eff
fi fi ffi
Th
Th Th
Th Th
%
Shafer_Ch02.indd 15
10/24/14 10:16 PM
Shafer_Ch02.indd 16
10/24/14 10:16 PM
Chapter 2
17
Basic Principles of Pharmacology
18
Part I
Basic Principles of Physiology and Pharmacology Metabolism (R) Clearing organ
Conc = C inflow
Conc =C outflow Flow = Q
e
fl fl
fl
fl fl
fi
Drug removed via metabolism R =Q(C inflow −C outflow)
The relationship between drug rate of metabolism can be computed as the rate of liver blood flow times the difference between the inflowing and outflowing drug concentrations. This is a common approach to analyzing metabolism or tissue uptake across an organ in massbalance pharmacokinetic studies. (From Shafer S, Flood P, Schwinn D. Basic principles of pharmacology. In: Miller RD, Eriksson LI, Fleisher LA, et al, eds. Miller’s Anesthesia. Vol 1. 7th ed. Philadelphia, PA: Churchill Livingstone; 2010: 479–514, with permission.)
Hepatic Clearance Th Th
fl
& (
&
(
Th
fl
ff
diff
fl
fl
fl Th
Th fl
fl Th
fl
&
fl
'
0.8
fl
Equation 2-1
ft
Th
Shafer_Ch02.indd 17
0.4
0 0
&
(
fl
fl
0.1
0.01
0.001 0.001
0.6
0.2
fi Phase II Enzymes
Th
1
d fl &
Th
Th
1
Metabolic rate/Vm
fl
fl
Linear kinetics
Response
fl
m
! (
fl Th
Equation 2-3
fl
fl
Th
fl
&
fl
Th
fi
fl
fl
'
fl
e
Th
fl
Th
&
ffi
& fl
Coutflow = ½ Km
Th
Th
o
Equation 2-2
10/24/14 10:16 PM
1
2 3 Concentration/C50
4
5
The shape of the saturation equation. (From Shafer S, Flood P, Schwinn D. Basic principles of pharmacology. In: Miller RD, Eriksson LI, Fleisher LA, et al, eds. Miller’s Anesthesia. Vol 1. 7th ed. Philadelphia, PA: Churchill Livingstone; 2010:479–514, with permission.)
Shafer_Ch02.indd 18
0.01
0.1
Nonlinear kinetics
1 10 Coutflow /Km
100
1000
The relationship between concentration, here shown as a fraction of the Michaelis constant (Km), and drug metabolism, here shown as a fraction of the maximum rate (Vm). Metabolism increases proportionally with concentration as long as the outflow concentration is less than half Km, which corresponds to a metabolic rate that is roughly one-third of the maximal rate. Metabolism is proportional to concentration, meaning that clearance is constant, for typical doses of all intravenous drugs used in anesthesia. (From Shafer S, Flood P, Schwinn D. Basic principles of pharmacology. In: Miller RD, Eriksson LI, Fleisher LA, et al, eds. Miller’s Anesthesia. Vol 1. 7th ed. Philadelphia, PA: Churchill Livingstone; 2010:479–514, with permission.)
10/24/14 10:16 PM
fl
2.5
Clearance (l/min)
ff
fl
fl
ffl
Th
Th
2
1.5
fl fl
⎛
&
fl
⎜
⎝
'
⎞
fl
⎟
⎠
Equation 2-4
fl
fl
⎛
'
fl
⎜
⎝
⎞
fl
⎟
⎠
fl
&
⎜
⎝
fl
1 1.5 2 Liver blood flow (l/min)
0.00 0
3
fl
⎟
(
0.5 1 1.5 Liver disease/ Vm Enzyme induction enzyme inhibition
fl
⎠
'
&
&
Shafer_Ch02.indd 19
⎝
fl fl
'
ff
Th
Th
fl Th
⎟
⎠
fl
⎝
fi ⎞
⎛
⎜
(
⎟
fl
Equation 2-6
(
fl
⎠
⎞
⎜
⎝ fl
(
⎠
fl
fl (
Shafer_Ch02.indd 20
Th
⎟
fl
fi
fl
fl
10/24/14 10:16 PM
&
⎛
fl fl
⎞
fl
fi
& Th
Th fl
&
fl
&
⎜
fl
Th
Th
⎛
fi Th
Th
& fl
100000
Th
fl
fl
)
2
fl
fl
e &
10000
The extraction ratio as a function of the intrinsic calculated for a liver blood flow of 1,400 mL/min. (From Shafer S, Flood P, Schwinn D. Basic principles of pharmacology. In: Miller RD, Eriksson LI, Fleisher LA, et al, eds. Miller’s Anesthesia. Vol 1. 7th ed. Philadelphia, PA: Churchill Livingstone; 2010:479–514, with permission.)
&
fl
fl
Th
1000
(
& fl
100
fl
fl
fi
10
Changes in maximum metabolic velocity (Vm) have little effect on drugs with a high extraction ratio but cause a nearly proportional decrease in clearance for drugs with a low extraction ratio. (From Shafer S, Flood P, Schwinn D. Basic principles of pharmacology. In: Miller RD, Eriksson LI, Fleisher LA, et al, eds. Miller’s Anesthesia. Vol 1. 7th ed. Philadelphia, PA: Churchill Livingstone; 2010: 479–514, with permission.)
fl ⎞
0
0.2
fi
Th Th
0.3
0.1
The relationship between liver blood flow (Q), clearance, and extraction ratio. For drugs with a high extraction ratio, clearance is nearly identical to liver blood flow. For drugs with a low extraction ratio, changes in liver blood flow have almost no effect on clearance. (From Shafer S, Flood P, Schwinn D. Basic principles of pharmacology. In: Miller RD, Eriksson LI, Fleisher LA, et al, eds. Miller’s Anesthesia. Vol 1. 7th ed. Philadelphia, PA: Churchill Livingstone; 2010:479–514, with permission.)
Equation 2-5
Th
2.5
0.4
Intrinsic clearance (mls/min)
0.3 0.2 0.1 0.5
0.6
0.2
0.4
&
fl
⎛
fl
0.8 Extraction ratio 1.0 0.9 0.8 0.7 0.6 0.5
1.00
0
fl
&
1
0.50
0.5
0.5
fl )
0.7 0.6
0
&
1.50
0.8
Th
fl
e
2.00
0.9
1
Basic Principles of Physiology and Pharmacology
0.4
'
fl
Extraction ratio 1.0
Part I
Extraction ratio
3
20
E.R. calculated at Vm = 1 gm/min
fl
Extraction ratio calculated at Q = 1.4 l/min
e
19
Basic Principles of Pharmacology
Clearance (l/min)
Chapter 2
fl
fl fi
Renal Clearance fi Th
10/24/14 10:16 PM
Chapter 2
21
Basic Principles of Pharmacology
22
Part I
Basic Principles of Physiology and Pharmacology
250
fi
Creatinine clearance (mls/min)
fi
Th fl
d
200 150 0.5
50
1.0 1.5 2.0
fl
Ion Trapping diff
0 20
30
40
50
60
70
80
90
fl
Age
Th
fl
fl
fl
fl
ff
Creatinine 100
Creatinine clearance as a function of age and serum creatinine based on the equation of Cockroft and Gault. (From Cockcroft DW, Gault MH. Prediction of creatinine clearance from serum creatinine. Nephron. 1976;16: 31–41, with permission.)
diff fl
Th
Oral istration ft
Th fl Th
fl
ff
Th ff & ' )
fl
Th
)
Equation 2-7
Th
Determinants of Degree of Ionization Th fl
ffi
Th
e fl
Th
ff
Th
Absorption
Th
Characteristics of Nonionized and Ionized Drug Molecules
diff ff
Route of istration and Systemic Absorption of Drugs
Ionization
Th Th
Shafer_Ch02.indd 21
Th
ft
Th
ff
10/24/14 10:16 PM
Shafer_Ch02.indd 22
fl ff
fi
ff eff
Oral Transmucosal istration Th ff fi ff fi
10/24/14 10:16 PM
effi
fi
eff
fi
Th
24
Part I
Basic Principles of Physiology and Pharmacology
Exponential decay curve, as given by x(t) & x0e'kt, plotted on standard axis (A) and a logarithmic axis (B).
A 10
B 10
x0 = 10 k = 0.5
x0 = 10
8
Pharmacokinetic Models
Th
eff
23
6
x (amount)
eff
Basic Principles of Pharmacology
x (amount)
Chapter 2
k = 0.5
4
1
2 0
0.1 0
2
4 6 t (time)
Transdermal istration
8
10
0
2
4 6 t (time)
ffi Zero- and First-Order Processes Th
ff
Th &
Th
Th
&
+ ff +
(
&
ff
Th
Th
fl &
! Th
Th Th
!
&
e e +
fi
fl
e
Equation 2-11
One-Compartment Model
Physiologic Pharmacokinetic Models
% Th e
Th
7
ff '
&
ifi
& & & &
ff Th
*
fl fi &
Equation 2-8
Rectal istration
diff
fi
&
&
Th
Th
fi
*
ffi
Shafer_Ch02.indd 23
&
&
fi
Th
ff
⎞ ⎟ ⎠
Th
⎤ ⎞⎥ ⎟ ⎠⎦ Equation 2-10
Th
ff
⎛ ⎜ ⎝
! Th
!
(fi
,
Th
Th
Th
&
⎡ ⎢⎛⎜ ⎣⎝
*
ff ff
'
,
& Th
10
fl
'
Th
8
)
fl
'
fl
'
( ' *
'
Equation 2-9
Th
e
10/24/14 10:16 PM
)
Compartmental Pharmacokinetic Models
Shafer_Ch02.indd 24
fl
Th
a fi
)
10/24/14 10:16 PM
Chapter 2
Basic Principles of Pharmacology
25
26 A
Q
Part I
Basic Principles of Physiology and Pharmacology
B
I
I
Cardiac output
Lung
V1 Central compartment
V Volume of distribution
Aortic juncture Brain
Venous
C
Arterial
Pancreas
V3 Slowly equilibrating compartment
Gut Liver
Portal juncture
Input juncture
Spleen
k21
fi &
V2 Peripheral compartment
fi ' * &
I k13
k31
V1 Central compartment
k12
k21
V2 Rapidly equilibrating compartment
∫
'
⎛ ⎜ ⎝
-
&
k10
Standard one- (A), two- (B), and three-compartment (C) mammillary pharmacokinetic models. I represents any input into the system (e.g., bolus or infusion). The volumes are represented by V and the rate constants by k. The subscripts on rate constants indicate the direction of flow, noted as kfrom to.
Clock
Kidney Testes
'
-
&
Hepatic artery
Infusion
&
k10
k
Heart
k12
&
∫
'
⎞ ⎟ ⎠
)
&
Equation 2-14
Time Muscle
&
Fat
& Th
Skin
Carcass
Physiologic model for thiopental in rats. The pharmacokinetics of distribution into each organ has been individually determined. The components of the model are linked by zero-order (flow) and first-order (diffusion) processes. (From Ebling WF, Wada DR, Stanski DR. From piecewise to full physiologic pharmacokinetic modeling: applied to thiopental disposition in the rat. J Pharmacokinetic Biopharm. 1994;22:259–292, with permission.)
fi a fi
Th
Equation 2-13
Th
fi
Arterial branch
Venous juncture
fi
'
Equation 2-15
The relationship between volume and clearance and half-life can be envisioned by considering two settings: a big volume and a small clearance (A) and a small volume with a big clearance (B). Drug will be eliminated faster in the latter case.
)
A
B Plasma
Plasma
Th
Clearing organ
&
)
a fi & fi
&
&
Clearing organ
'
ft &
Shafer_Ch02.indd 25
Equation 2-12
fi
10/24/14 10:16 PM
Shafer_Ch02.indd 26
10/24/14 10:16 PM
Chapter 2
& '
&
&
'
28
Part I
Basic Principles of Physiology and Pharmacology
Th
'
Th
'
Th
&
*
27
Basic Principles of Pharmacology
Multicompartment Models Th
*
Th
fi
2 Th &
*
5
fi
Th
*
&
Th
&
Th
Th ff
Th
fi
* -
fi & Th
Th
ff
ff
ft
fl
&
*
*
'
*
100
&
'
'
* &
fi
*
&
'
'
Th
Th
ff
ff &
→-
'
→
&
'
* Th
&
fl
'
'
*
*
*
& '
0
Equation 2-16
Th
fi &
& &
Shafer_Ch02.indd 27
Th
'
'
'
'
1
0.1
' * & ' *
Rapid
10
Concentration
'
&
100
' Concentration
&
fl Th
. fl
Th
ft
ft
*
Th
Th
&
Equation 2-17
10 Intermediate Slow 1
120 240 360 480 600 Minutes since bolus injection
Typical time course of plasma concentration following bolus injection of an intravenous drug, with a rapid phase (red), an intermediate phase (blue), and a slow log-linear phase (green). The simulation was performed with the pharmacokinetics of fentanyl. (From Scott JC, Stanski DR. Decreased fentanyl and alfentanil dose requirements with age. A simultaneous pharmacokinetic and pharmacodynamics evaluation. J Pharmacol Exp Ther. 1987;240: 159–166, with permission.)
0.1 0
120
240
360
480
600
Minutes since bolus injection
Hydraulic equivalent of the model in Figure 2-18. (Adapted from Youngs EJ, Shafer SL. Basic pharmacokinetic and pharmacodynamic principles. In: White PF, ed. Textbook of Intravenous Anesthesia. Baltimore, MD: Lippincott Williams & Wilkins; 1997:10, with permission.)
fi
10/24/14 10:16 PM
Shafer_Ch02.indd 28
10/24/14 10:16 PM
Chapter 2
29
Basic Principles of Pharmacology
fi
fi
30
Part I
Basic Principles of Physiology and Pharmacology
B
A 0
30
0
1500
Fentanyl
'#
'"
$% #% " &
&
(
(
ffi (
(
5 EEG
20
10
10
15
&
fi
15 20
5
10
15
20
0
25
ffi
Th ft
& &
'$
(
'#
(
'"
ffic $
$ #
(
fi
ff
#
"
Th Th
C(t ) = Ae−αt
'
& (
C(t ) = Ae−αt + Be−βt + Ce−γt
Th
Th
'
60
120
The polyexponential equation that describes the decline in plasma concentration for most intravenous anesthetics, is the algebraic sum of the exponential that represent rapid phase shown in red, intermediate phase shown in blue and slow phase shown in green.
&
'
&
'
Equation 2-21
ff I
Th
V3 Slowly equilibrating compartment
ff
e Th
ff Th
k13 k31
V1 Central compartment
k10
V2 Rapidly equilibrating compartment
k12 k21
k1e
Effect compartment
ff (
& (
*
ff
240
Minutes since bolus injection
'
ff
Th
180
*
ff
Equation 2-19
ff
1
25
ff Th
The Time Course of Drug Effect
ff
'
&
C(t ) = Ce−γt
0
a fi
Th
ft
20
ff
Th
ffi
Th
C(t ) = Be−βt
ff
fi
"
10
10 15 Time (min)
&
#
100
Concentration
n
Th
Th
Shafer_Ch02.indd 29
Th
'"
Equation 2-18
$ "
(
5
Fentanyl and alfentanil arterial concentrations (circles) and electroencephalographic (EEG) response (irregular line) to an intravenous infusion. Alfentanil shows a less time lag between the rise and fall of arterial concentration and the rise and fall of EEG response than fentanyl because it equilibrates with the brain more quickly. (Modified from Scott JC, Ponganis KV, Stanski DR. EEG quantitation of narcotic effect: the comparative pharmacodynamics of fentanyl and alfentanil. Anesthesiology. 1985;62:234–241, with permission.)
Th
'#
25
Infusion 0
0
'$
10
EEG
0
fi
5
1000
20
Infusion
ff
Alfentanil (ng/ml)
ff
Arterial level
'"
(
Spectral edge (Hz)
'$
Th
'#
(
Fentanyl (ng/ml)
'$
&
Spectral edge (Hz)
fl
ft
Alfentanil Arterial level
'
'
ke0
'
ff
Equation 2-20
10/24/14 10:16 PM
Shafer_Ch02.indd 30
ff
The three-compartment model from Figure 2-16 with an added effect site to for the equilibration delay between the plasma concentration and the observed drug effect. The effect site has a negligible volume. As a result, the only parameter that affects the delay is ke0.
10/24/14 10:16 PM
Chapter 2
A
B
80 60 40 17%
20
32
0
Part I
Basic Principles of Physiology and Pharmacology
Th
100
Alfentanil concentration (percent of peak plasma)
Fentanyl concentration (percent of peak plasma)
100
31
Basic Principles of Pharmacology
ft
ff
60
2 4 6 8 Minutes since bolus injection
ff
ff
ff
40 37%
ff
20
ff
0 0
The Time to Peak Effect and t ½ ke0 following a Bolus Dose
80
10
0
2 4 6 8 Minutes since bolus injection
Th
Th
10
ff ff
Plasma (black line) and effect site (red line) concentrations following a bolus dose of fentanyl (A) or alfentanil (B). (Adapted from Shafer SL, Varvel JR. Pharmacokinetics, pharmacodynamics, and rational opioid selection. Anesthesiology. 1991;74:53–63, with permission.)
&
Equation 2-22 &
.
ff diff
Th
ff &
ff
)
!
Th
ff
ff
ff
eff
ff
ff !
ff
ff
Th
! Th Th ff
ff
ff
fl
ff
fi ff
ff
Maintenance Infusion Rate ff
ff diff
ff
eff
ff
Th
Fentanyl concentration (ng/ml)
)
Dose = 720 µg = Target x Vdss
10
Volume of Distribution at the Time of Peak Effect.
Dose = 150 µg = Target x Vdss
&
)
)
Th Th !
Th
ff
ff
ff Dose = 26 µg = Target x Vdss
uffi 0
Shafer_Ch02.indd 31
ft
ft
1
0.1
!
)
100
fi
fi
!
Th
Th
fi
Bolus Dosing
Th
ff
ff
Dose Calculations
&
!
Th
5
10 15 Minutes since bolus
20
10/24/14 10:16 PM
ffi
ff
The volume of the central compartment of fentanyl is 13 L. The volume of distribution at steady state is 360 L. For a target concentration of 2 !g/L (dotted line), the dose calculated on V1, 26 !g, results in a substantial undershoot. The dose calculated using Vdss, 720 !g, produces a profound overshoot. Only a dose based on Vdpeak effect, 150 !g, produces the desired concentration in the effect site. The black lines show plasma concentration over time. Red lines show effect site concentration over time.
Th ff
fl
Shafer_Ch02.indd 32
10/24/14 10:16 PM
Chapter 2
e
400
33
34
Part I
Basic Principles of Physiology and Pharmacology 6.0
5.0
Th
4.5
4.0 Fentanyl (ng/ml)
300
200
Th
100
3.0 2.0 1.0
60 120 180 240 300 Minutes since bolus injection
360
0.0
ff
'
(
'
(
Equation 2-23
Context Sensitive Half-time fi
Th
ft
fi
& ) Th ft Th Th
Th
Th Th
Th
1.5
Alfentanil (ng/ml)
1.25
400
1.0 300
0.75
200
0.5
100
0.25
0 2.0
1.0
1.5 1.2
0.8
1.0 0.9 0.8 0.7 0.6 0.5
0.6 0.4
0.3 0.15
0.2 0.0 300
8.0
250 200 180 160 140 120 100 75
6.0
4.0
2.0
(µg/kg/min)
Th
Th
1.75
500
Propofol (µg/ml)
Th
2.0
(µg/kg/hr)
Infusion rates to maintain stable plasma concentrations
& )
2.5 2.25
(µg/kg/min)
Th
)
3.0
600
Fentanyl infusion rate to maintain a plasma concentration of 1 !g/hr. The rate starts off quite high because fentanyl is avidly taken up by body fat. The necessary infusion rate decreases as the fat equilibrates with the plasma.
Sufentanil (ng/ml)
0
Suggested Initial Target
Th
0
3.6 3.0 2.7 2.4 2.1 1.8 1.5 1.2 0.9
(µg/kg/hr)
Fentanyl infusion rate (µg/hr)
Basic Principles of Pharmacology
50 25
0.0 0
60
120
180
240
300
Minutes since beginning of infusion
Dosing nomogram, showing the infusion rates (numbers on the perimeter) required to maintain stable concentrations of fentanyl (1.0 !g/mL), alfentanil (75 !g/mL), sufentanil (0.1 !g/mL), and propofol (3.5 ng/mL).
ft
2.4 !
! ! !
! ff
Shafer_Ch02.indd 33
ff
10/24/14 10:16 PM
Shafer_Ch02.indd 34
10/24/14 10:17 PM
Chapter 2 Body weight (kg)
Basic Principles of Pharmacology
35
36
Part I 60
100
90
80
70
60
50
40
30
20
Basic Principles of Physiology and Pharmacology
20% decrement
50
10
40 240 120 45 180 60 30
Propofol-target-concentration (µg/ml) 1
15
2
10
3
20
4
30
5
40
50
60
70
80
90
100 110 120 130140150
Infusion rate propofol 1% (ml/h)
Propofol slide ruler to calculate maintenance infusion rate, based on the patient’s weight and the time since the start of the infusion, as proposed by Bruhn and colleagues (Adapted from Bruhn J, Bouillon TW, Ropcke H, et al. A manual slide rule for target-controlled infusion of propofol: development and evaluation. Anesth Analg. 2003;96:142–147.). To make use of the calculator, make a photocopy and cut in to top (body weight), middle (time since start of infusion/propofol target concentration), and bottom (infusion rate propofol 1%) sections—calculation requires sliding the middle piece in relationship to the top and bottom segments, which are fixed.
e
e
Th
ff ff
"
Eff
30
0
Minutes for a given decrement in effect site concentration
Time since start of infusion (min)
(
&
'
"
20
Equation 2-24
"
eff
10 0
(
0
360
120
240
360
480
ff
600
50% decrement
300 Fentanyl Alfentanil Sufentanil Remifentanil
240 180 120
"
Th
"
fi
60
(
"
(
0 0
120
720
240
360
480
600
ffic
"
80% decrement
Th
600
"
480 360
"
240
ff
120
Th
ff
fi ffi
0
Pharmacodynamics Concentration versus Response Relationships ff
Th
Th
ff
600
Potency and Efficacy Th
ft Th
ff ff
ff
Context-sensitive half-times as a function of the duration of intravenous drug infusion for each fentanyl, alfentanil, sufentanil, propofol, midazolam, and thiopental. (From Hughes MA, Glass PSA, Jacobs JR. Context-sensitive half-time in multicompartment pharmacokinetic models for intravenous anesthetic drugs. Anesthesiology. 1992;76:334–341, with permission.)
Fentanyl 200 Thiopental
ft ft
ft
Th
250
fi
diff
Th
Emax
100
Effect
Context-sensitive half-time (minutes)
Th
fi
300
ft
Efficacy
50
Sufentanil 0
1
2
3
Midazolam
ft
5
ft C50
Drug exposure (dose, concentration, etc.) versus drug effect relationship. Potency refers to the position of the curve along the x-axis. Efficacy refers to the position of the maximum effect on the y-axis.
Propofol 4
6
7
8
9
Infusion duration (hours)
10/24/14 10:17 PM
Shafer_Ch02.indd 36
ft
Potency
fi
Dose, concentration, or other measure of exposure
Alfentanil
ff
fi
50
0
Fentanyl
100
ft
ff
150
0
Shafer_Ch02.indd 35
120 240 360 480 Infusion duration (minutes)
Effect site decrement times. The 20%, 50%, and 80% decrement times for fentanyl (black), alfentanil (green), sufentanil (red), and remifentanil (blue). When there is substantial plasma-effect site disequilibrium, the effect site decrement time will provide a better estimate of the time required for recover than the context-sensitive halftime. (Adapted from Youngs EJ, Shafer SL. Pharmacokinetic parameters relevant to recovery from opioids. Anesthesiology. 1994;81:833–842, with permission.)
Th Th
"
0
Th eff
ffi .
ff
Th
fi
ff ffi
ff
ffi ff
10/24/14 10:17 PM
Chapter 2
C
Potency more less
Dose, concentration, or other measure of exposure
Dose versus response relationship for three drugs with potency. Drug A is the most potent, and drug C is the least potent.
fl
Th diff
Death
80
60 Therapeutic index LD50 400 = =4 ED50 100
40
ED50
LD1 ED99 LD50
100
200
400
Th
ff
ffi
ff fi
1600
Analysis to determine the LD50, the LD99, and the therapeutic index of a drug.
diff
fi
800
Dose (mg)
ff
5
diff
4 3
Desflurane
2
Isoflurane
1 2
4 6 8 Fentanyl (ng/ml)
Th
Th
fi
Th
Interaction between fentanyl and isoflurane or desflurane on the minimum alveolar concentration required to suppress movement to noxious stimulation. (Adapted from Sebel PS, Glass PS, Fletcher JE, et al. Reduction of the MAC of desflurane with fentanyl. Anesthesiology. 1992;76:52–59; McEwan AI, Smith C, Dyar O, et al. Isoflurane minimum alveolar concentration reduction by fentanyl. Anesthesiology. 1993;78:864–869.)
Stereochemistry Th
ffi ff
10
ft
Th Th
6
0
50
ffi
Basic Principles of Physiology and Pharmacology
0
20
0
ffi ff
Inspired desflurane or isoflurane
B
Percent of animals responding
Effect
A
0
ff
Part I 7
Hypnosis
ffi
38
100
100
eff
37
Basic Principles of Pharmacology
Th
ff
Th
ff
efl
e
Effective Dose and Lethal Dose 400
fi
ff
100
Full agonist
Alfentanil concentration (ng/ml)
Th
Drug Interactions Actions at Different Receptors
Effect
80 60
Partial agonist
40 20 0
Neutral Antagonist
1.5
ft
' Th ft
(
Emergence
(
100
'
Th 0
Th
2 4 6 8 10 Propofol concentration (µg/ml)
Interaction of propofol with alfentanil on the concentration required to suppress response to intubation, maintain nonresponsiveness during surgery, and then awaken from anesthesia. (Adapted from Vuyk J, Lim T, Engbers FH, et al. The pharmacodynamics interaction of propofol and alfentanil during lower abdominal surgery in women. Anesthesiology. 1995;83:8–22, with permission.)
Th
Concentration versus response curves for drugs with differing efficacies. Although the C50 of each curve is the same, the partial agonist is less potent than the full agonist because of the decreased efficacy.
Shafer_Ch02.indd 37
Maintenance 200
0
efi
Inverse agonist Dose, concentration, or other measure of exposure
Intubation 300
10/24/14 10:17 PM
Shafer_Ch02.indd 38
A Th fi
fi
fi
10/24/14 10:17 PM
Basic Principles of Pharmacology
39
40
Part I
Basic Principles of Physiology and Pharmacology
8+1a** 1
10 + 4a
1¶
1a
Na+ channel
2a
1a
1
3
1a
4a
1a
3
3 Ad 2 ag ditiv 1 on e ist
2 t gonis
1
1 + 3a 1
4 +8a 2+ 1a
7a
2
1 1a
1a
3 Pa 2 ag rtia on l ist
A
0
B
1
1 0
3
2 nist Ago
1a
3 pra 2 ag -add 1 on itiv ist e
1
1a
1a
1a
1+1a
2
0.5 0.0
Su
1a
E
1.0
0.5 0.0
1a
3
1a
3a
2a
0.5 0.0
1.0 5+3a
Halothane
2 t gonis
1
3 Co 2 an mpe tag titi 1 on ve ist
3
A
0
3
2 t gonis
1 A
0
2a
Enflurane
1
Isoflurane
1
3a
1a
1aI
2 Sevoflurane
Effect
Xe
N 2O
Desflurance
Sevoflurane
Isoflurane
1a
12 Dopamine
Enflurane
0.0
2a 2a
1¶¶ 3a
Halothane
Na+ channel
Dopamine
Opioid
α2 5
0.5
Effect
2 1
Opioid
2*
D
1.0
1
1
1 +1a§
Desflurance 1
2
1
Xe
1
Additivity
0.5 0.0 −0.5
Inf
Hypnosis Synergy
3 ra- 2 ag add 1 on itiv ist e
F
1.0
0.5 0.0
N 2O
C
1.0
2 +2a 1+1aI
1
Effect
α2
3
Effect
NMDA
1
A
1.0
Effect
GABABDZ
1
2
NMDA
GABA GABA
GABABDZ
Immobility
Effect
Chapter 2
1
2 t gonis
0
A
3
3
Inv 2 ag erse on ist
1
1
0
3
2
t
nis Ago
Interaction surfaces, showing simple additivity (A), synergy (B), and infra-additivity (C). More complex relationships exist between agonists and partial agonists (D), agonists and competitive antagonists (E), and agonists and inverse agonists (F). (From Minto CF, Schnider TW, Short TG, et al. Response surface model for anesthetic drug interactions. Anesthesiology. 2000;92:1603–1616, with permission.)
Infra-additivity
Survey of interactions between hypnotics and analgesics by Hendrickx et al. (From Hendrickx JF, Eger EI II, Sonner JM, et al. Is synergy the rule? A review of anesthetic interactions producing hypnosis and immobility. Anesth Analg. 2008;107:494–550, with permission.)
Th ifi
Th
Th
diff
Th ff
ifi Th fi
fi
ff
fi diff
fi
ffin
fi
Th
fl fi Th
( ' ff
ifi
diff
fi
diff
fl
Clinical Aspects of Chirality
diff
ff
Shafer_Ch02.indd 39
10/24/14 10:17 PM
Shafer_Ch02.indd 40
10/24/14 10:17 PM
Chapter 2
Basic Principles of Pharmacology
Part I
Th
ffi
Th ff
fi
Individual Variability Th
ff
Enzyme Activity
fi
diffi
ff
ffi
fl
Th
Genetic Disorders
fl
References
diff
diff
Th
fl
% 200
fl
fi
ff
fi
ff
Th eff
diff
ff
fi
ft diff
fi
fl
ff
Th
diff
diff
ff
nfl
ft
efl
Basic Principles of Physiology and Pharmacology
Th
fl fl
42
diff
fi
41
ff
) e a fi
.
ff
fi Th ft efi Events Responsible for Variations in Drug Responses between Individuals
ff
Drug Interactions Elderly Patients
ff
fl fl diff
Shafer_Ch02.indd 41
fi
efl
Th
Th
ff
10/24/14 10:17 PM
Shafer_Ch02.indd 42
ff
ff
fl
10/24/14 10:17 PM
Chapter 2
Basic Principles of Pharmacology
43
ff Th
Th
fl
Shafer_Ch02.indd 43
fl
Th
10/24/14 10:17 PM
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