(Key to Case Study1)Case study 1.(PHA5127)Fall 2003Question 1. A 80 year old, 70-Kg patient with pneumonia, was being treated by an iv. bolus ofgentamicin ( 0.5 mg / kg ). Serum samples were taken at 0.5 and 6 hours post injection,and the lab reported drug concentrations of 3.41µg/ml, and 0.83 µg/ml, respectively.Assume gentamicin follows one compartment, first-order elimination. 1.) Calculate the half-life of gentamicin in this patient. )(26.065.0)41.3/83.0ln()/ln(12112−=−−=−= hrttCCKe.)(66.226.0693.02/1hrt ==2.) Calculate the volume of distribution of gentamicin in this patient. Dose = 0.5 × 70 = 35 (mg)Recall: tKteeCC−⋅=0 then )/(88.341.35.026.00mlgeeCCtkteµ=⋅=⋅=⋅Then: )(0.988.3350lCDoseVd ===3.) Can you predict what is the drug concentration two half-lives after iv. bolus injection..)(32.566.22hrt =⋅=)/(97.088.332.526.00mlgeeCCtKteµ=⋅=⋅=⋅−−Or :Recall the definition of half-life. In one half-life, ttCC *5.02/1= . Then two half-lives,)/(97.088.325.05.05.05.02/12/12mlgCCCtttµ=⋅=⋅⋅=⋅=Question 2. A 25-year-old, 60-kg female patient was given an iv. bolus of a aminophyllline, ( 200 mg). Theophylline concentration-time profiles after the first dose was given as following(table). Given the fact that 1mg of aminophylline is equivalent to 0.8mg theophylline andelimination occurs by first-order kinetics, please answer the following questions. Table1. Theophylline concentration-time profiles after iv. bolus of aminophylline. t(hr) Con (ug/ml) AUC(t1-t2)09.641 7.898.763 5.2913.185 3.558.847 2.385.9212 0.878.13AUC 0-1244.831.) Calculate the AUC0-12 of theophylline by using trapezoidal rule.)(2.0)121()89.7/87.0ln()()/ln(12112−=−=−= hrttCCKeAgain: tKteeCC⋅−⋅=0 Then, )/(64.987.0122.00mlgeeCCtKteµ=⋅=⋅=⋅⋅Then, using trapezoidal rule: )(2)(122121ttCCAUC −⋅+=−The final answer is: 44.83 mg*h/L.2.) Calculate the AUC0-∞.)/(35.42.087.012LhrmgKCAUCet⋅===∞−Then, )/(18.4935.483.44121200LhrmgAUCAUCAUC
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