Clinical Pharmacokinetics Review Keith Christensen, Pharm D, BCPS Assistant Professor of Pharmacy Practice Pulmonary & Critical Care Medicine Creighton University SPAHP

Case Study #1 l FS is a 35 YO WM (70kg) with nosocomial pneumonia l Current treatment includes gentamicin 80mg IV Q8 hours l Serum concentrations ordered for 3 rd dose

Case Study #1 l Labs: (Dose given at 0900) n Trough(0900)0.5 mg/L n Peak(1000)4 mg/L n SCr1 mg/dL

Questions l How do the peak and trough look versus what is desired? Therapeutic Ranges: Peak (gentamicin/tobramycin) UTI/Synergy4-6 mg/L Bacteremia5-7 mg/L Pneumonia/Sepsis7-9 mg/L Osteomylitis8-10 mg/L Cystic Fibrosis10-12 mg/L Trough (gentamicin/tobramycin) All indications0.5-2 mg/L

Questions l Labs: (Dose given at 0900) n Trough(0900)0.5 mg/L(OK) n Peak(1000)4 mg/L(Low) n SCr1 mg/dL l How do you correct the problem? Calculate new dose to achieve: Peak = 7 and trough = 1

Rules of Thumb l Changes in peak concentrations are usually made with changes in dose Dose = C max X VD l Changes in trough concentrations are usually made with changes in interval Trough = 1/Interval

Equation Definitions l  = Interval l T’ = time change between peak & trough

Time Change

Equation Definitions l  = Interval l T’ = time change between peak & trough T’ =  - (t p – t t ) l t = infusion time l T = peak time from end of infusion T = T p - T eof eof = end of infusion

Time Change

Step 1: Calculate K e Equation: K e = Ln (C p / C t ) T’ = Ln (4 / 0.5) 7 T’ =  - (t p – t t ) = hr -1 T’ = 8 – (1) = 7 Trough(0900)0.5 mg/L Dose(0900) Peak(1000)4 mg/L

Step 2: Calculate T 1/2 Equation: T 1/2 = K e = = 2.33 hr Doublecheck: Gent/Tobra  roughly 3 X T 1/2  = 3 x 2.33 = 7 (~ 8 hours) T1/2 Peak Trough

Step 3: Calculate C max Equation: C max = C pk [e (-Ke x T) ] = 4 [e ( x 0.5) ] = 4.64 mg/L

Step 4: Calculate Vd Equation: Vd = (Dose / t) x [1-e (-Ke x t) ] C max x K e x [1-e (-Ke x  ) ] = (80 / 0.5) x [1-e ( x 0.5) ] 4.64 x x [1-e ( x 8) ] = liters

Step 4: Calculate Vd Doublecheck: Population normal Vd for aminoglycosides: 0.25 – 0.35 L/kg (0.15 – 0.45 L/kg) Calculate VD/kg: L / 70 kg = L/kg

Step 5: Calculate New  Equation:  = Ln (C p {desired} / C t {desired} ) K e + t = Ln (7 / 1) hr = 7.05 hours (~ 8 hours) *NOTE: t is now presumed to be infused/drawn correctly, so it will always be 0.5 for gent/tobra

Doublecheck: Gent/Tobra  roughly 3 X T 1/2  = 3 x 2.33 = 7 (~ 8 hours) T1/2 Peak Trough Step 5: Calculate New  Calculated: T 1/2 = 7.05 hours (~ 8 hours)

Step 6: Calculate New Dose Equation: Dose = C pk {desired} x Vd x K e x [1-e (-Ke x  new ) ] [1-e (-Ke x t*) ] x t = 7 x x x [1-e ( x 8) ] [1-e ( x 0.5) ] x 0.5 = 120mg *NOTE: t is now presumed to be infused/drawn correctly, so it will always be 0.5 for gent/tobra

Rules of Thumb l Changes in peak concentrations are usually made with changes in dose Dose = C max X VD l Changes in trough concentrations are usually made with changes in interval Trough = 1/Interval

New Dose 120mg IV Q8h (  dose for  peak) Estimated Peak / Trough ~ 7 / 1 Satisfies goals - Write the note

Pharmacokinetics Note 9/26/01Clinical Pharmacy re: Gentamicin Kinetics 1300 S:35 YO WM diagnosed with nosocomial pneumonia. O:Wt 70kg SCr 1.0 mg/L Other lab:Peak 4 mg/L (0900) Trough 0.5 mg/L (1000) Current Gentamicin dose 80mg IV Q8h

Pharmacokinetics Note 9/26/01Clinical Pharmacy re: Gentamicin Kinetics 1300 A/P:Calculated kinetic parameters: Ke = hr -1 T 1/2 = 2.33 hours C max = 4.64 mg/L Vd = L (0.25 L/kg) Peak concentration falls short of desired goal of 7 mg/L. Would recommend changing the dose to 120mg IV Q8h for an estimated Peak/Trough of 7 and 1. Would also recommend re-checking serum concentrations with the 3rd new dose. Monitor I/O and SCr. Keith Christensen, Pharm D

Case Study #2 l CJ is a 29 YO WF (90kg) with intra- abdominal infection (Gm – Bacilli) l Current treatment includes gentamicin 80mg IV Q8 hours l Serum concentrations ordered for 3 rd dose

Case Study #2 l Labs: (Dose given at 0900) n Trough(0900)4 mg/L n Peak(1000)6 mg/L n SCr4.8 mg/dL l Clinical Exam n Patient appears to be fluid overloaded

Questions l Labs: (Dose given at 0900) n Trough(0900)4 mg/L(High) n Peak(1000)6 mg/L(Ok?) n SCr4.8 mg/dL (High) l How do you correct the problem? Calculate new dose to achieve: Peak = 7 and trough = 1

Case Study #3 l DC is a 24 YO WF (48kg) with CF and pulmonary exacerbation with Pseudomonas l Current treatment includes gentamicin 160mg IV Q8 hours l Serum concentrations ordered for 3 rd dose

Case Study #3 l Labs: (Dose given at 0900) n Trough(0900)0.75 mg/L n Peak(1015)9.33 mg/L n SCr0.4 mg/dL l Clinical Exam n Unremarkable

Questions l Labs: (Dose given at 0900) n Trough(0900)0.75 mg/L n Peak(1015)9.33 mg/L n SCr0.4 mg/dL l How do you correct the problem? Calculate new dose to achieve: Peak = 11 and trough = 1

1)K e = Ln (C p / C t ) T’ K e = Ln (9.33/ 0.75) 6.75 = hr -1 2)T 1/2 = = 1.86 hours 3)Vd = (Dose / t) x [1-e (-Ke x t) ] C max x K e x [1-e (-Ke x  ) ] = (160/0.5) x [1-e ( x 0.5) ] x x [1-e ( x 8) ] = L(0.26 L/kg) 4)  = Ln (C p {desired} / C t {desired} ) K e + t + T = Ln (11 / 1) = 6.9 hours(~8 hours) Kinetics Review Case Answers 5)Dose = C pk {desired} x Vd x K e x [1-e (-Ke x  new) ] [1-e (-Ke x t) ] x 0.5 Dose = 11 x x x [1-e ( x 8) ] [1-e ( x 0.5) ] = 142.5mg(~150mg) x 0.5 Answer: 150mg IV Q8h 2b)C max = C p e (-Ke x T) C max = 12.35