药理学：速成包

公式表、每个专题的关键方法步骤和 6 道练习题，完整解答附在最后。

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1公式与方法

剂量计算

由浓度计算剂量
体积 = 剂量 / 浓度
按体重给药
剂量 = mg/kg × 体重
片剂
片数 = 剂量 / 每片规格
单位
1 g = 1000 mg, 1 mg = 1000 mcg

方法

  1. 把医嘱剂量和药品规格换算为同一单位。
  2. 用“需要量除以现有量再乘以数量”：(D/H) × Q。
  3. 按体重给药时，先乘以以 kg 计的体重，再用日剂量除以给药次数。
  4. 先估算，再检查答案是否合理。

临床药代动力学

速率常数和半衰期
k = ln 2/t½ = 0.693/t½
一级衰减
C = C₀·e−kt = C₀·(1/2)t/t½
两个浓度
k = ln(C₁/C₂)/Δt
容积和清除率
Vd = dose/C₀, CL = k·Vd
负荷剂量
LD = Vd·C/(S·F)
维持速率
R = CL·Css/(S·F)
平均稳态
Css,avg = S·F·D/(CL·τ)
稳态
n 个半衰期后为 1 − (1/2)ⁿ； 5 个半衰期后 ≈ 97%
输注
C = (R/CL)(1 − e−kt)
由峰浓度和谷浓度确定间隔与剂量
τ = ln(Cpeak/Ctrough)/k, D = Vd·(Cpeak − Ctrough)
Cockcroft–Gault
CrCl = (140 − 年龄) × kg/(72 × SCr mg/dL)，女性 × 0.85
肾功能调整
剂量 × CrCl/正常值； Dettli Q = 1 − fe·(1 − CrCl/正常值)

方法

  1. 把半衰期换算为速率常数：k = 0.693/t½。
  2. 把按每 kg 的数值换算为总量：Vd（L）= L/kg × 体重，CL（L/h）= L/kg/h × 体重。
  3. 选定关系式：C = C₀·e−kt，LD = Vd·C/(S·F)，维持速率 = CL·Css/(S·F)，τ = ln(Cpeak/Ctrough)/k。
  4. 对于肾功能，先用 Cockcroft–Gault 估算 CrCl，再调整剂量或间隔。
  5. 核对结果：浓度每个半衰期减半，达到稳态约需五个半衰期。

2练习题

1.药理学中等

Why are many drugs started at lower doses in older adults?

  1. AKidney and liver clearance often decline, and sensitivity to drugs increases
  2. BOlder adults absorb no drugs from the stomach
  3. COlder adults always weigh more than younger adults, so drugs last longer
  4. DLower doses are cheaper for older patients
2.药理学困难

A patient with angina is taught to use sublingual glyceryl trinitrate (nitroglycerin). Which statement shows a need for further teaching?

  1. A"I will replace my tablets before the expiry date."
  2. B"If the pain is no better after one tablet, I will wait an hour before calling for help."
  3. C"I will sit down before I take the tablet, because it can make me feel faint or dizzy."
  4. D"I may get a headache after taking it."
3.剂量计算中等
1:10 000安瓿V = ? mL

一支肾上腺素预充式注射器标示为 1:10 000（0.1 mg/mL）。医嘱为心脏骤停时 1 mg 静脉注射（IV）。你应给多少体积 V？

1:10 0001 mg
V = mL
4.剂量计算困难
55 kg177 cmBSA = √(h·w/3600)25 mg/m²D = ? mg

一名患者身高 177 cm，体重 55 kg。医嘱为 25 mg/m²。用 Mosteller 公式 BSA = √(身高 (cm) × 体重 (kg)/3600) 求剂量 D，以 mg 表示。

177 cm55 kg25 mg/m²
D = mg
5.临床药代动力学中等
110t (h)C (mg/L)C₀ = 6 mg/Lt½ = 3.5 hC₀/2

练习题（虚构数值，不作为临床指导）。 一位患者静脉推注 170 mg gentamicin。外推回时间零点的浓度为 6 mg/L，半衰期为 3.5 h。 求清除率CL（L/h）。

D = 170 mgC₀ = 6 mg/Lt½ = 3.5 h
CL = L/h
6.临床药代动力学困难
Vd = 0.7 L/kg6 → 15 mg/LLD = ? mg72 kg · S = 0.92 · F = 1

练习题（虚构数值，不作为临床指导）。 一位体重 72 kg 的患者的phenytoin浓度为 6 mg/L；目标是 15 mg/L。药物以phenytoin sodium（S = 0.92）静脉给予，分布容积为 0.7 L/kg。 需要追加多少负荷剂量LD才能使浓度升到目标值？

72 kgVd = 0.7 L/kgC = 6 → 15 mg/LS = 0.92
LD = mg

3溶液

1.药理学

答案: A · Kidney and liver clearance often decline, and sensitivity to drugs increases

为什么是这个答案

Ageing reduces kidney function, changes body composition and often slows liver metabolism. Many drugs also have stronger effects on the ageing brain, so doses are started low and increased slowly.

答案

A · Kidney and liver clearance often decline, and sensitivity to drugs increases
2.药理学

答案: B · "If the pain is no better after one tablet, I will wait an hour before calling for help."

为什么是这个答案

Unrelieved chest pain may be a heart attack, so help must not be delayed. In US teaching, emergency services are called if pain is not better 5 minutes after the first dose; UK advice is to repeat the dose after 5 minutes and call 999 if pain persists 5 minutes after the second. Sitting down prevents falls from hypotension, and headache is a common effect.

答案

B · "If the pain is no better after one tablet, I will wait an hour before calling for help."
3.剂量计算

答案: V = 10 mL

Solution strengths: a percentage strength is grams per 100 mL, so 1% = 1 g/100 mL = 10 mg/mL. A ratio strength 1:1000 means 1 g in 1000 mL = 1 mg/mL; 1:10 000 is 0.1 mg/mL. For a dilution the amount of drug stays the same: C₁·V₁ = C₂·V₂.

浓度

1:10 000 = 1 g/10000 mL = 0.1 mg/mL

体积

V = 1/0.1 = 10 mL

答案

V = 10 mL

美国的标签现在标示 mg/mL（1 mg/mL = 1:1000；0.1 mg/mL = 1:10 000）。切勿静脉推注 1 mg/mL 的肾上腺素。

4.剂量计算

答案: D = 41.11 mg

Body-surface-area dosing: many cytotoxic and some paediatric doses are prescribed per square metre of body surface area: dose (mg) = dose per m² × BSA (m²). The Mosteller formula estimates BSA = √(height (cm) × weight (kg)/3600).

体表面积

BSA = √(177·55/3600) = √2.704 = 1.644 m²

剂量

D = 25·1.644 = 41.11 mg

答案

D = 41.11 mg
5.临床药代动力学

答案: CL = 5.611 L/h

清除率和容积：在稳态时，给药速率等于消除速率，所以维持速率 = CL × Css。负荷剂量 LD = Vd × C/(S × F)，其中 S 是盐因子（盐中活性药物所占的比例），F 是生物利用度（静脉给药为 1）。由两个浓度可得 k = ln(C₁/C₂)/Δt；对于静脉推注，Vd = 剂量/C₀，CL = k × Vd。 这些数字仅供练习；在临床工作中务必遵循当地规程，高危剂量须经双人核对。

分布容积

Vd = 170/6 = 28.33 L

速率常数

k = 0.693/3.5 = 0.198 h⁻¹

清除率

CL = 0.198·28.33 = 5.611 L/h

答案

CL = 5.611 L/h
6.临床药代动力学

答案: LD = 493 mg

设计给药方案：快速静脉给药时，血药浓度在间隔期内从峰值降到谷值，所以 τ = ln(Cpeak/Ctrough)/k，使血药浓度恢复到峰值的剂量为 Vd × (Cpeak − Ctrough)。平均稳态浓度为 Css,avg = S·F·剂量/(CL·τ)。输注时浓度按 C = (R/CL)(1 − e−kt) 上升。对于经肾脏清除的药物，剂量要根据肌酐清除率调整。 这些数字仅供练习；在临床工作中务必遵循当地规程，高危剂量须经双人核对。

分布容积

Vd = 0.7·72 = 50.4 L

需要升高的量

15 − 6 = 9 mg/L

负荷剂量

LD = 50.4·9/(0.92·1) = 493 mg

答案

LD = 493 mg

实际中，剂量会取整到方便的数值。

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