PHARMACOKINETICS Allie punke apunke@uthsc.edu INTRAVASCULAR DOSING PHARMACOKINETICS Allie punke apunke@uthsc.edu

CONTINUOUS IV INFUSION Continuous IV infusion (CIVI) releases the drug at a constant rate. In contrast to IV Bolus, where the maximum concentration occurs immediately/initial concentration, the maximum concentration for continuous IV infusion occurs at the end of infusion. Basic equation: IV Bolus equation: Ct=Co*e^-kt CIVI equation: Ro/CL*(1-e^-ktinf)(e^-ktpi)

Continuous IV infusion A drug is being given by continuous IV infusion at a rate of 10 µg/hour to reach the steady state concentration of 46 mg/L. What should the infusion rate be increased to in order to reach a steady state concentration of 120 mg/L? 26 10 ug/hour x ------------- ---------- 46 mg/L 120 mg/L

Concentration Time Profiles Infusion is stopped Ln concentration During infusion, at steady state During infusion, before steady state Post infusion Time General Expression for plasma concentration: Ct= R0 * (1-e-k * Tinf) (e-k * ( t - Tinf)) CL Only important before steady state has been achieved Only important after the infusion is ended

During infusion, before steady state Infusion is stopped Reasoning: Since time and time of infusion are equal, t = Tinf, this term becomes e0 = 1. Ln concentration During infusion, before steady state Time General Expression for plasma concentration: Ct= R0 * (1-e-k * Tinf) (e-k * ( t - Tinf)) CL Only important before steady state has been achieved Only important after the infusion is ended

During infusion, at steady state Reasoning: Since time and time of infusion are equal, t = Tinf, this term becomes e0 = 1. When Tinf > Tss = 5*T1/2, then we assume e→∞ = 0. [1 ─ 0 = 1] making this term 1. Infusion is stopped Ln concentration During infusion, at steady state Time General Expression for plasma concentration: Ct= R0 * (1-e-k * Tinf) (e-k * ( t - Tinf)) CL Only important before steady state has been achieved Only important after the infusion is ended

After infusion, before steady state Infusion is stopped Reasoning: Both terms are necessary for finding Ct. Ln concentration After infusion, before steady state Time General Expression for plasma concentration: Ct= R0 * (1-e-k * Tinf) (e-k * ( t - Tinf)) CL Only important before steady state has been achieved Only important after the infusion is ended

After infusion that ended at steady state Infusion is stopped Reasoning: When Tinf > Tss = 5*T1/2, then we assume e→∞ = 0. [1 ─ 0 = 1] making this term 1. Ln concentration Post infusion, after steady state was reached Time General Expression for plasma concentration: Ct= R0 * (1-e-k * Tinf) (e-k * ( t - Tinf)) CL Only important before steady state has been achieved Only important after the infusion is ended

Continuous IV infusion A patient is receiving a drug by CIVI at a rate of 800 mg/h to reach a steady state concentration level of 60 mg/L. A blood level drawn at 7 hours results in a concentration of 40 mg/L. What is the half-life? Ct=Css (1-e^-ktinf) 40 mg/L=60 mg/L (1-e^-k*7) K=0.158, Half-life: 4.4 hours What is the CL? Css=Ro/CL 60 mg/L=800 mg/h/CL CL=13.3 L/h How long to reach steady state? 22 hours

Continuous IV Infusion Maximum concentration after 40 hours? Cmax=60 mg/L(1-e^-0.158*40) Cmax=59.89 Suppose the team decides that a level of 47 mg/L is desired. What should the new rate be? 627 mg/h

Continuous IV Infusion A patient is started on a CIVI at a rate of 150 mg/h to reach Css of 6 mg/L. A blood level of 4 mg/L is drawn at 16 hours. What is the half-life of the drug? 10 hours, k=0.068 4 mg/L=6 mg/L (1-e^-k*16) What is the CL? Css=Ro/CL CL=25L/h When is steady state reached? 50 hours What is the maximum concentration achieved if the infusion runs for 36 hours? Ct=6 mg/L(1-e^-0.068*36 hours)=5.5 mg/L

Loading Dose What LD would we give this pt initially to reach a Css of 6mg/L? LD=V*Ctarget=6 mg/L*367L=2200 mg CL=k*V 25L/h=0.068h^-1*V What LD would we give if the patient has a concentration of 6 mg/L, and we want to achieve a concentration of 14 mg/L? LD=(Ctarget-Ccurrent)*Vd LD=(14-6)*367L=2,936 mg

Maintenance Dose What would the MD be to achieve 10 mg/L? MD=CL*Ctarget MD=25L/h*10 mg/L=250 mg/h

Loading and Maintenance Dosing If CL is increased, this affects: A. Loading dose B. Maintenance dose C. Both D. Neither loading or maintenance dose

CIVI is Stopped After CIVI is stopped, at hours 2 and 12, the concentrations were 12.9 mg/L and 6 mg/L. What is the concentration at the end of the infusion? K=ln(12.9/6)/(12-2)=0.077 Ct=Co*e^-0.077t C0=15 mg/L What will the concentration be 24 hours after the infusion was stopped? Ct=15 mg/L(e^-0.077*24 hours) Ct= 2.4 mg/L

Short term infusion HP is given a 1000mg dose of vancomycin over a 30 min infusion. Levels are taken at 1 hour and 3 hours and found to be 20mg/L and 14mg/L respectively. The population Vd for vancomycin is 44L. What is the concentration at 5 hours? K=0.178 CL=7.85 L/h DR=2000 mg/h Ct=255 mg/L (1-e^-0.178*0.5)(e^-0.0178*4.5)=9.8mg/L

Short term infusion When will the concentration be below 7mg/L? 7mg/L=255 mg/L(1-e^-0.178*0.5)(e^-0.178*tpi) 6.36 hours +0.5 hours=6.88 hours

Cumulative Drug in Urine If Drug X has an fe=1 and a pt is given a dose of 2 grams IVB what will the ΣDu be at t=∞? 2 grams What if fe=0.75? Fe*dose=0.75*2 grams=1.5 grams

Calculate kr Calculate kr using the following time points (specifically using Time 4 and 6): kr=ln(139/115.5)/(5-3)=0.092 Time Du (mg) Du/t Rate t* 400 1 356 2 301 4 278 278/2 hours 139 3 6 231 115.5 5 8 199

Calculate FE What is FE if kr is the value found in the previous problem and you have the following information: A patient is given 400 mg IVB. At 4 hours, the concentration was 16 mg/L and at 10 hours, the concentration was 5 mg/L. Fe=kr/k Fe=0.092/0.193=0.47

Extravascular Dosing You have to take into account bioavailability now! Calculate the bioavailability (F): 72% is not absorbed, 23% does not get first-pass metabolized by the liver, and 80% is metabolized by the gut F=0.28*0.23*0.2=0.0128

Extravascular Dosing A patient is taking a new drug (500 mg) that has the population values of: Half-life: 8 hours, Vd: 50 L, kr: 0.021 h-1, Ka: 1.45-1, 90% reaches the bloodstream Solve for: K: 0.087 h-1 FE:kr/k=0.242 CL (total):4.35L/h

Extravascular Dosing (Continued) CL (renal): kr*Vd, Cltotal*fe=1.05L/h Cmax: 7.266 Tmax: ln(1.45/0.087)/(1.45-0.087)=2 hours AUC: FD/CL (A/k-A/ka)=0.9*500 mg/(4.35)=103.9

Extravascular Dosing What is it called when the absorption phase is the rate limiting step? If you were given time points with concentrations and told to assume the drug followed flip-flop kinetics, how could you calculate ka? Ka=ln(C2/C1)/(Change in time)

Summary Things to think about when making calculations for the exam: 1. Is it IVB, CIVI, or oral medications? 2. If it is CIVI, has it been stopped or is it still running? Double check your work! Think about if your answers actually make sense based on the information given. Good luck!