Case Study 6 2008 1. B.F. is 30 year old, 65 kg, 5’6” female patient to be started on gentamicin to treat a gram-negative infection. The target true maximum concentration is 8mg/L and the target true minimum concentration is 1mg/L. The clearance of the drug is equal to creatinine clearance and the Vd=0.25L/kg. This drug is typically given as a 30 minute IV infusion. Serum creatinine is 1.2mg/dL. This drug displays a two-compartment body model. A. Calculate the ke and half-life IBW=45.5+2.3*6=59.3kg TWB/IBW*100=65kg/59.3kg*100<120 this patient is not obese Clcr=(140-30)*65/(85*1.2)=70.10 mL/min=4.206L/hr Vd=0.25*65kg=16.25L Ke=4.206L/hr/16.25L=0.259hr-1 Half-life=0.693/ke=0.693/0.259hr-1=2.68 hr B. Calculate the dosing interval. (Hint on your equation sheet tau (τ) is the dosing interval.) Tau=Ln(Cmax/Cmin)/ke+infusion time=Ln(8/1)/0.259+0.5hr=8.53~8hr. We can’t use and 8.5 hr dosing interval because it’s not practical. We round to 8 hours so it’s given three times a day. C. Calculate the dose (mg). Dose=8mg/L*0.259 hr-1*16.25L*0.5hr*(1-e^-0.259hr-1*8hr)/(1-e^-0.259hr-1*0.5hr) =121.145mg~120mg D. Once steady state was reached blood is drawn at 1 hr after the start of the infusion and 0.5 hr before the next infusion is started. The levels come back as 12mg/L and 4mg/L, respectively. Calculate the true Cmax and Cmin (these concentrations should be used to see if we are in the therapeutic window). Ke=ln(C2/C1)/(∆t)=Ln(12/4)/(6.5)=0.169hr-1 C=C0*e^(-ke*t) We are infusing the drug over 0.5 hr than the maximum concentration will be reached at the end of infusion. Cmax=C/e^(-ke*t)=12mg/L/e^(-0.169*0.5)=13.1mg/L Cmin=C0*e^(-ke*t)=4*e^(-0.169*0.5)=3.7mg/LE. If trough concentration is not below at least 2mg/L there is a chance of toxicity. Please recommend a new dose using the information obtained and assuming that Vd is correct. (Meaning that the estimate of CL is incorrect). Dose=8mg/L*0.169 hr-1*16.25L*0.5hr*(1-e^-0.169hr-1*8hr)/(1-e^-0.169hr-1*0.5hr) =100.5~100mg 2. The next table shows the resulting pharmacokinetic parameters in this Patient 1. Let's assume a second patient will receive the same dose of this drug given orally as well. Both patients differ in the tissue and plasma protein binding to this drug. 100% of the drug in plasma and tissue is free for Patient 1. Contrary to this, in Patient 2, 50% of the drug present in tissue is free (fuT = 0.5) and 50% of the drug in plasma is free (fu=0.5). Ka is equal in both patients. In the following table indicate whether the PK parameter will be higher, lower, or the same in patient 2 compared to patient 1. PK parameter Patient 1 Patient 2 Vd (L) 40 Same CL (L/hr) 80 Same Peak (mg/L) 5 Same F 0.001 Increased 3. You wish to begin a patient on an oral formulation of Drug X and maintain an average plasma concentration of 15mg/L. You take the population average for Vd and Ke to be 10 L and 0.4hr-1. A. If the bioavailability is 70% and the normal dosing interval is 8 hours, what dose should we give? CL=ke*Vd=0.4hr-1*10L=4.0L/hr Caverage=Dose*F/(CL*tau) Dose=Caverage*CL*tau/F=15mg/L*4.0L/hr*8hr/(0.7)=685.71mg~700mg B. After steady-state is reached the patient’s blood is drawn and this patient has a supratherapeutic Cpaverage of 25mg/L. What is the patient’s clearance? Cl=Dose*F/(tau*Cpaverage)=700mg*0.7/(8hr*25mg/L)=2.45L/hr C. At this concentration toxicity is a concern, calculate a new dose based on this
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