Biopharmaceutics. Группа авторов

equation: .

Figure 2.8 Plasma drug concentration–time profile followed by an intravenous (IV) dose exhibiting first‐order kinetics. Figure shows the estimation of drug half‐live at three different time points.

Box 2.4 How long it will take for the drug to eliminate completely from the body?

Number of t½ elapsed	Percentage of drug eliminated	Drug	Half‐life (h)	Time for 90% elimination
1	50	Gentamicin	2–3	7–10 h
2	75
3	87.5	Theophylline	6–8	24 h
3.3	90
4	94
4.3	95
5	97	Lithium	15–30	2–4 days
6	98.4
6.6	99
7	99.2	Digoxin	36–51	5–7 days

      Typically, it takes three to five half‐lives for most of the drug to be eliminated from the body.

For a drug with elimination rate constant, k = 0.1 h⁻¹, the half‐life will be ~7 hours. If 100 mg of the drug was present in the body, it will take about seven hours to reduce this to 50 mg by elimination, i.e., to the half; this is also represented by the amount eliminated every hour using elimination rate constant (Box 2.5).

      2.9.1 Clearance

      In pharmacokinetics, clearance (Cl) is defined as the ‘volume of body fluid cleared of the drug per unit time’ and is expressed in units of volume per time, e.g., L h⁻¹ or mL min⁻¹. Clearance can be determined using elimination rate constant (k) and the volume of distribution (V), i.e., Cl = k × V.

The total body clearance (Cl) is a function of renal (ClR) and non‐renal (ClNR) clearance, and can be expressed as Cl = Cl_R + ClNR. The renal clearance is dependent on kidney function as explained earlier in section 2.7.2. The drug metabolism by the liver, termed as hepatic clearance, represents most of the non‐renal clearance. Total body clearance is, therefore, affected by the renal or the hepatic function or both, as the case may be. For a drug, primarily eliminated unchanged in the urine, any changes in renal function will significantly impact on its clearance. Impaired clearance of the drug may lead to accumulation of the drug in the body and may require adjustment in subsequent dosages to avoid potential toxic effects. The dosage adjustment decisions should not be solely based on renal clearance and must consider total body clearance to ensure the hepatic clearance is taken into consideration (Figure 2.9). Many patients with compromised renal function, such as in chronic kidney disease (CKD) or those with acute kidney injury (AKI) and taking drugs that are primarily eliminated by the kidneys, may require dosage adjustments. The total body clearance of the drug in a patient in association with renal function (as estimated by the creatinine clearance) helps to make personalised dosage adjustments in a patient (section 2.7.2).

Box 2.5 The elimination rate constant, k and the elimination half‐life (t_½)

      If the k = 0.1 h^–l it will mean that ~10% of the drug left in the body will be eliminated in the next hour.

Time	Amount eliminated (mg)	Amount in body (mg)
0	0	100
1	10	90
2	9	81
3	8.1	72.9
4	7.3	65.6
5	6.6	59.0
6	5.9	53.1
7	5.3	47.8

      The amount of the drug left in the body at seven hours is reduced to half of the original amount at time zero, correlating to the drug's half‐life, i.e. t_½ = 7 h.

Figure 2.9 The relationship of total body clearance, renal and non‐renal clearance and kidney function.