Pharmacokinetic–pharmacodynamic modeling in acute and chronic pain: an overview of the recent literature

Figures & data

Figure 1. Effect of naloxone on opioid-induced respiratory depression.

(A)Mechanism-based pharmacokinetic–pharmacodynamic modeling of the ability of different doses of an opioid antagonist (naloxone, given at t = 55 min, low dose = 0.1 mg, high dose = 0.4 mg) to reverse the opioid-induced respiratory depression from an opioid agonist with relatively low k_off value (opioid agonist injected at t = 0 min). The speed of reversal is independent of the antagonist dose and is determined by the agonist opioid receptor k_off value. (B) Effect of variations in the k_off value of an opioid agonist (injected at t = 0 min over 90 s) on the effect of a fixed dose of an opioid receptor antagonist (naloxone, given at t = 55 min over 90 s) on reversal of opioid-induced respiratory depression.

K_off values are relative with 0.2 min^-1 = 0.2 × typical value, 1 = typical value, 5 = 5 × typical value. Here, the typical value = 0.03 min^-1.

K_off: Receptor dissociation constant.

Data taken from [17].

Figure 2. Population pharmacokinetic–pharmacodynamic modeling of epidural analgesia.

(A) Blockade probabilities after an epidural injection of ropivacaine 125 mg in a 50-year-old patient. The size of the dots is proportional to the probability of blockade with 90% (solid line), 75% (broken line) and 50% (dotted line) isoeffect lines. Time is expressed on the x-axis and the dermatome level on the y-axis. (B) Probability of blockade, P(block), for dermatomes S5 (broken line), Th11 (solid line) and Th7 (dotted line) versus time.

Data taken from [32].

Figure 3. Mixture analyses of the effect of a 1-week ketamine treatment (shaded bar) on pain scored in patients with chronic pain.

The analysis objectively divided the total population response into four categories, with (A) no response to treatment, (B) a response in the treatment week only, (C) a long-term response with a slow return towards pretreatment baseline and (D) full recovery.

Data taken from [33].

Table 1. Population pharmacodynamic model estimates for various analgesic agents and naloxone using pain relief or respiration as the effect parameter: studies performed in healthy volunteers or patients.

Drug	t½ke0	kon (ml/ng/min)	koff^† (min^-1)	Kd (koff/kon)	C50	Effect parameter	Population	Ref.
Morphine (men)	1.6 h				250 nM	Antinociception	V	[13]
Morphine (women)	4.8 h				125 nM	Antinociception	V	[13]
Morphine-6-glucuronide	6–8 h				750 nM	Antinociception	V	[12,16]
Morphine	1.2 h	0.85	0.14	160 nM		Respiration	V	[17]
Morphine-6-glucuronide	2.7 h	0.04	0.03	880 nM		Respiration	V	[17]
Naloxone	5–8 min				0.5–2 nM	Respiration	V	[17]
Morphine	1.7 h				124 nM	Postoperative analgesia	P	[20]
Morphine-6-glucuronide	3 h				13 nM	Postoperative analgesia	P	[20]
Buprenorphine	75 min	0.25	0.01	0.09 nM		Respiration	V	[6]
Fentanyl	16.4 min	>100	>100		1140 ng/ml	Respiration	V	[6]
Buprenorphine	155 min	0.06	0.08	2.66 nM		Antinociception	V	[24]
S-ketamine	^‡				373–2200 ng/ml^§	Antinociception	V	[28]
S-ketamine	11 days^¶				10.5 ng/ml	Chronic CRPS pain relief	P	[34]
Pregabalin	11 h				1.54 µg/ml	Chronic fibromyalgia pain relief	P	[35]
SC-75416					5500 ng/ml	Postoral surgery pain relief	P	[29]
Rofecoxib					284 ng/ml	Postoral surgery pain relief	P	[29]
Valdecoxib					68 ng/ml	Postoral surgery pain relief	P	[29]
Ibuprofen					6840 ng/ml	Postoral surgery pain relief	P	[29]
Ibuprofen	28 min				10,200 ng/ml	Postoral surgery pain relief	P	[30]
Acetaminophen	53 min				10 mg/l	Post-tonsillectomy pain relief	P	[32]

^†t_½k_off is calculated as ln2/k_off.

^‡No hysteresis observed between plasma concentration and effect.

^§C₅₀ varied depending on the nociceptive assay employed (see text).

^¶The value of 11 days represent a rate-constant form disease modulation (t_½k) unrelated to the blood effect-site equilibration t_½.

C₅₀: Steady-state concentration causing 50% of the effect; CRPS: Complex regional pain syndrome; K_d: Equilibrium dissociation constant; k_e0: Effect-site equilibration constant; K_off: Receptor dissociation constant; K_on: Receptor-association constant; P: Patients; t_½: Half-life; V: Volunteers.

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