氨基糖苷类:Cmax=15 mg/L,t½=8 h,τ=8 h → Cmin = 7.5 mg/L k = ln2/8 = 0.0866 h⁻¹;e^(-k·8) = e^(-ln2) = 0.5;Cmin = 15 × 0.5 = 7.5 mg/L。一个半衰期后剩余一半。{"result":"Cmin = 7.5 mg/L (50% of peak 15 mg/L remaining; drop 7.5 mg/L). Method: Cmin = Cmax · e^(-kτ).","metadata":{"input":{"cmax":15,"halfLife":8,"tau":8},"result":{"cmin":7.5,"cminUnit":"mg/L","k":0.0866,"kUnit":"h⁻¹","fractionRemaining":0.5,"peakToTroughDrop":7.5,"method":"Trough from peak: Cmin = Cmax · e^(-kτ), k = ln2/t½","model":"One-compartment first-order elimination, peak measured post-distribution. Not medical advice."}}}
长间隔:Cmax=15 mg/L,t½=8 h,τ=12 h → Cmin = 5.3033 mg/L k = ln2/8 = 0.0866 h⁻¹;e^(-k·12) = e^(-1.5·ln2) = 0.3536;Cmin = 15 × 0.3536 = 5.3033 mg/L。更长的间隔(1.5 个半衰期)谷浓度更低。{"result":"Cmin = 5.3033 mg/L (35.36% of peak 15 mg/L remaining; drop 9.6967 mg/L). Method: Cmin = Cmax · e^(-kτ).","metadata":{"input":{"cmax":15,"halfLife":8,"tau":12},"result":{"cmin":5.3033,"cminUnit":"mg/L","k":0.0866,"kUnit":"h⁻¹","fractionRemaining":0.3536,"peakToTroughDrop":9.6967,"method":"Trough from peak: Cmin = Cmax · e^(-kτ), k = ln2/t½","model":"One-compartment first-order elimination, peak measured post-distribution. Not medical advice."}}}