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

A patient with diabetes is sweaty and shaky. Blood glucose is 3.0 mmol/L (54 mg/dL). The patient is awake and can swallow. What should the nurse do first?

  1. AGive intramuscular glucagon at once
  2. BGive 15–20 g of fast-acting carbohydrate, such as juice
  3. CGive the next scheduled dose of insulin
  4. DGive a large meal high in fat and protein to keep glucose up for longer
2.药理学困难

A patient taking a GLP-1 receptor agonist such as semaglutide has severe, constant upper abdominal pain spreading to the back, with vomiting. What should the nurse suspect?

  1. AHypoglycaemia; the patient should eat sweets and continue as usual
  2. BAcute pancreatitis; the drug is stopped and urgent assessment arranged
  3. CExpected nausea; the patient should take the next dose with food
  4. DConstipation; a laxative will solve the problem
3.剂量计算中等
2 g+ 9.2 mLV = ? mL

一个药瓶中含有 2 g 的粉末。标签上写着：加入 9.2 mL 注射用水，得到总容量 10 mL。医嘱为 400 mg。你应给予复溶后溶液的多少容量 V？

2 g+ 9.2 mL → 10 mL400 mg
V = mL
4.剂量计算困难
50%储备液V₁ = ? mL

你需要用 50%（w/v）储备液配制 250 mL 1%（w/v）溶液。 你需要多少容量的储备液 V₁？

C₁ = 50%C₂ = 1%V₂ = 250 mL
V₁ = mL
5.临床药代动力学中等
110100t (h)C (mg/L)C₀ = 9 mg/Lt½ = 2.5 hC₀/2

练习题（虚构数值，不作为临床指导）。 一位患者静脉推注 250 mg tobramycin。外推回时间零点的浓度为 9 mg/L，半衰期为 2.5 h。 求清除率CL（L/h）。

D = 250 mgC₀ = 9 mg/Lt½ = 2.5 h
CL = L/h
6.临床药代动力学困难
0.1110t (h)C (mg/L)Cpeak​ = 6τ = ?Ctrough​ = 0.5

练习题（虚构数值，不作为临床指导）。 一位患者的gentamicin半衰期为 3 h。目标是峰浓度 6 mg/L、谷浓度 0.5 mg/L。假设为快速静脉给药和一级消除，多长的给药间隔τ可使浓度从峰值降到谷值？ 保留一位小数。

t½ = 3 hCpeak = 6 mg/LCtrough = 0.5 mg/L
τ = h

3溶液

1.药理学

答案: B · Give 15–20 g of fast-acting carbohydrate, such as juice

为什么是这个答案

Conscious hypoglycaemia is treated with 15–20 g of fast-acting carbohydrate, with glucose rechecked after about 15 minutes. Fat slows absorption, and glucagon is kept for patients who cannot swallow.

答案

B · Give 15–20 g of fast-acting carbohydrate, such as juice
2.药理学

答案: B · Acute pancreatitis; the drug is stopped and urgent assessment arranged

为什么是这个答案

Mild nausea is common with GLP-1 agonists, but severe persistent abdominal pain radiating to the back suggests pancreatitis. The drug is stopped and the patient needs urgent assessment, including serum lipase or amylase.

答案

B · Acute pancreatitis; the drug is stopped and urgent assessment arranged
3.剂量计算

答案: V = 2 mL

Dose calculation: the amount to give equals what is prescribed divided by what you have, times the quantity it comes in: amount = (desired dose/stock strength) × stock volume. Always keep the units the same (convert g to mg, mg to mcg first) and check that the answer is sensible.

混合后的浓度

2000 mg/10 mL = 200 mg/mL

体积

V = 400/200 = 2 mL

答案

V = 2 mL
4.剂量计算

答案: V₁ = 5 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.

储备液的容量

V₁ = 1·250/50 = 5 mL

答案

V₁ = 5 mL
5.临床药代动力学

答案: CL = 7.702 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 = 250/9 = 27.78 L

速率常数

k = 0.693/2.5 = 0.2773 h⁻¹

清除率

CL = 0.2773·27.78 = 7.702 L/h

答案

CL = 7.702 L/h
6.临床药代动力学

答案: τ = 10.8 h

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。

速率常数

k = 0.693/3 = 0.231 h⁻¹

给药间隔

τ = ln(6/0.5)/0.231 = 2.485/0.231 = 10.75 ≈ 10.8 h

答案

τ = 10.8 h

实际中，间隔会取整到 8、12、24 或 36 h 等方便的数值，并再次检测浓度。

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