Time Plasma Conc (hr) (mg/L) Below limit of detection 1 Compartment IV Analysis & Renal Elimination 500 mg of tobramycin is administered by iv bolus to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that tobramycin is excreted primarily unchanged in the urine. The following plasma concentrations were observed. 1.What model best describes this profile? 2.Calculate AUC, K, Vd, T½ and Cl. 3. Write an equation that will calculate concentrations at anytime after the 1st dose. 4.How much is in the body at time zero? 5.How much is in the body at 12 hours? 6.Where did the tobramycin go? 7.How much is in the urine at 12 hrs? 8.What is the renal clearance of tobramycin? 9.Is tobra a high or low extraction drug?
Time Plasma Conc (hr) (mg/L) Below limit of detection 1 Compartment IV Analysis 500 mg of tobramycin is administered by iv bolus to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that tobramycin is excreted primarily unchanged in the urine. The following plasma concentrations were observed. 1.What model best describes this profile? 2.Calculate AUC, K, Vd, T½ and Cl. 3. Write an equation that will calculate concentrations at anytime after the 1st dose. 4.How much is in the body at time zero? 5.How much is in the body at 12 hours? 6.Where did the tobramycin go? 7.How much is in the urine at 12 hrs? 8.What is the renal clearance of tobramycin? 9.Is tobra a high or low extraction drug?
Graph Patient Data Using semi-log paper, graph the data following Iv bolus of 500 mg of tobramycin Time Plasma Conc (hr) (mg/L) Below limit of detection
Graph Patient Data in Excel® Using semi-log paper, graph the data following IV bolus of 500 mg of tobramycin. Time Plasma Conc (hr) (mg/L) Below limit of detection What model best describes this profile?
Graph Patient Data What model best describes this profile? … a 1 compartment model with iv bolus input
Time Plasma Conc (hr) (mg/L) Below limit of detection 1 Compartment IV Analysis 500 mg of tobramycin is administered by iv bolus to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that tobramycin is excreted primarily unchanged in the urine. The following plasma concentrations were observed. 1.What model best describes this profile? 2.Calculate AUC, K, Vd, T½ and Cl. 3. Write an equation the will calculate concentrations at anytime after the 1st dose. 4.How much is in the body at time zero? 5.How much is in the body at 12 hours? 6.Where did the tobramycin go? 7.How much is in the urine at 12 hrs? 8.What is the renal clearance of tobramycin? 9.Is tobra a high or low extraction drug? What do you calculate first? Cl T½ AUC Vd K
Time Plasma Conc (hr) (mg/L) Below limit of detection 1 Compartment IV Analysis 500 mg of tobramycin is administered by iv bolus to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that tobramycin is excreted primarily unchanged in the urine. The following plasma concentrations were observed. 1.What model best describes this profile? 2.Calculate AUC, K, Vd, T½ and Cl. 3. Write an equation that will calculate concentrations at anytime after the 1st dose. 4.How much is in the body at time zero? 5.How much is in the body at 12 hours? 6.Where did the tobramycin go? 7.How much is in the urine at 12 hrs? 8.What is the renal clearance of tobramycin? 9.Is tobra a high or low extraction drug? What do you calculate first? Cl Dose/AUC or K x Vd T½ K AUC –/ K Vd - [ ] 0 by back extrapolation of K K …?
Graph Patient Data Slope = -K/2.303 Slope based on log of the concentrations Time ConcLog (hr) (mg/L)Conc BLOQ Slope = (y 2 – y 1 ) / (x 2 – x 1 ) =
Graph Patient Data Slope = -K/2.303 Slope based on log of the concentrations Time ConcLog (hr) (mg/L)Conc BLOQ Slope = (y 2 – y 1 ) / (x 2 – x 1 ) = (-0.15 – 1.29)/(12-1) = (- 1.44) / (11) = K= slope x 2.303
Graph Patient Data Slope = -K/2.303 Slope based on log of the concentrations Time ConcLog (hr) (mg/L)Conc BLOQ Slope = (y 2 – y 1 ) / (x 2 – x 1 ) = (-0.15 – 1.29)/(12-1) = (- 1.44) / (11) = K= slope x = x K= hr -1
Graph Patient Data Slope = -K/2.303 Slope based on log of the concentrations Time ConcLog (hr) (mg/L)Conc BLOQ K= hr -1 T½= / K = / = hr
1 Compartment IV Analysis K T½T½
Time Plasma Conc (hr) (mg/L) Below limit of detection 1 Compartment IV Analysis 500 mg of tobramycin is administered by iv bolus to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that tobramycin is excreted primarily unchanged in the urine. The following plasma concentrations were observed. 1.What model best describes this profile? 2.Calculate AUC, K, Vd, T½ and Cl. 3. Write an equation the will calculate concentrations at anytime after the 1st dose. 4.How much is in the body at time zero? 5.How much is in the body at 12 hours? 6.Where did the tobramycin go? 7.How much is in the urine at 12 hrs? 8.What is the renal clearance of tobramycin? 9.Is tobra a high or low extraction drug? Now calculate Volume. Since it was an IV dose, and appears to be a 1 compartment model, we will assume instantaneous distribution and so we will back-extrapolate to t=0 to determine the initial concentration.
Calculation of Volume Back extrapolation can be completed a number of ways 1.Graphically Intercept
Time Plasma Conc (hr) (mg/L) Back extrapolation can be completed a number of ways 1.Graphically 2.By equation [ ] t = C 0 e -Kt or [ ] 0 = C 1 e +Kt = Intercept Calculation of Volume
Time Plasma Conc (hr) (mg/L) Back extrapolation can be completed a number of ways 1.Graphically 2.By equation [ ] t = C 0 e -Kt or [ ] 0 = C 1 e +Kt [ ] 0 = 19.5 e ( x 1) = mg/L Volume = Dose / [ ] 0 = Intercept Calculation of Volume
Time Plasma Conc (hr) (mg/L) Back extrapolation can be completed a number of ways 1.Graphically 2.By equation [ ] t = C 0 e -Kt or [ ] 0 = C 1 e +Kt [ ] 0 = 19.5 e ( x 1) = mg/L Volume = Dose / [ ] 0 = 500 / = L Intercept Calculation of Volume
Back extrapolation can be completed a number of ways 1.Graphically 2.By equation 3.By Excel Using Intercept function =10^(INTERCEPT(C5:C9,A5:A9))
Time Plasma Conc (hr) (mg/L) Below limit of detection 1 Compartment IV Analysis 500 mg of tobramycin is administered by iv bolus to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that tobramycin is excreted primarily unchanged in the urine. The following plasma concentrations were observed. 1.What model best describes this profile? 2.Calculate AUC, K, Vd, T½ and Cl. 3. Write an equation the will calculate concentrations at anytime after the 1st dose. 4.How much is in the body at time zero? 5.How much is in the body at 12 hours? 6.Where did the tobramycin go? 7.How much is in the urine at 12 hrs? 8.What is the renal clearance of tobramycin? 9.Is tobra a high or low extraction drug? Now calculate AUC. Since it was an IV dose, we must realise that the data set starting at 1 hour is missing concentration data from 0 to 1 hour. Therefore, AUC by trapezoidal rule must use a time zero concentration of mg/L.
Calculation of AUC Trapezoidal Rule AUC =((C 0 +C 1 )/2)*(t 1 -t 0 ) The value of 9.75 for the AUC is based on a no concentration or a concentration of 0.00 at time zero. Was the Concentration zero? Or should we determine the time zero concentration Trapezoidal Rule (Excel) AUC = ((B4+B5)/2)*(A5-A4) The value of 9.75 in this cell is based on a no concentration or a concentration of 0.00 at time zero in cell B4.
Calculation of AUC Trapezoidal Rule If the initial concentration of is used in the calculation of AUC from time 0 to 1 hr, a more appropriate AUC of mg*hr/L is estimated. AUC 0-12h is mg*hr/L. = You must also calculate AUC from 12 hr to . This can only be done using the PCK method: [ ] LP /K.
Calculation of AUC AUC from 12hr to Recall that K was calculated as hr-1 using concentrations at 1 hr and 12 hrs. Using this K value, AUC 12- is: [ ] LP /K. = 0.7/ = 2.32 mg*hr/L. = The sum of the AUC (0-12hr) and AUC (12hr- ). is: AUC (0- ) = = mg*hr/L.
Calculation of AUC Other Estimates of AUC (0- ) Several AUC (0- ) estimates are possible based on the estimate of K and the method used. 1.Kinetic method Using the determined back-extrapolated t=0 concentration of mg/L AUC 0- can also be estimated as: [ ] t=0 /K. = 26.38/ = mg*hr/L.
Calculation of AUC Other Estimates of AUC (0- ) Several AUC (0- ) estimates are possible based on the estimate of K and the method used. 2.Estimates of K In the Excel sheet using the last 2 … or last 3 …or last 4… K values can be estimated ranging from of hr hr hr -1 and hr -1 (these are effectively the same ~ differ by less than hr -1 ) These variations will produce small differences in AUC
Calculation of AUC Other Estimates of AUC Excel sheet shows some of the possible estimates of K and using hr-1 and calculates AUC 12h- As 2.32 mg*hr/L. Also shown are
Calculation of AUC Other Estimates of AUC Excel sheet shows some of the possible estimates of K and using hr-1 and calculates AUC 12h- As 2.32 mg*hr/L. Also shown are two estimates of AUC 0- : 1. Based on kinetic method from the t=0 determined concentration and 2. Based on sum of Trap Rule AUC & kinetic method from LP
Calculation of AUC Other Estimates of AUC AUC 0- is mg*hr/L calculated by trapezoidal rule. But if we use the PCK method from time zero (26.38 mg/L) we would calculate AUC 0- as mg*hr/L. Which is more correct?
Time Plasma Conc (hr) (mg/L) Below limit of detection 1 Compartment IV Analysis 500 mg of tobramycin is administered by iv bolus to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that tobramycin is excreted primarily unchanged in the urine. The following plasma concentrations were observed. 1.What model best describes this profile? 2.Calculate AUC, K, Vd, T½ and Cl. 3. Write an equation the will calculate concentrations at anytime after the 1st dose. 4.How much is in the body at time zero? 5.How much is in the body at 12 hours? 6.Where did the tobramycin go? 7.How much is in the urine at 12 hrs? 8.What is the renal clearance of tobramycin? 9.Is tobra a high or low extraction drug? Now calculate Clearance. This can be completed by at least 2 methods: 1.Dose / AUC 2.K x Vd
Calculation of Clearance Estimates of Clearance Although a variety of estimates of K have been calculated all are very close (~ hr -1 ) Using the volume calculated from the t=0 concentration determined by back-extrap using this K value (Excel Sheet) Cl = K x Vd = x L = L/hr
Calculation of Clearance Estimates of Clearance Although a variety of estimates of K have been calculated all are very close (~ hr -1 ) Cl = L/hr (K x V) When we use AUC calculated by the PCK method, clearance estimate is identical to estimate determined by K*Vd. Clearance is 5.72 L/hr and AUC 0- of mg*hr/L. is the more correct estimate.
Time Plasma Conc (hr) (mg/L) Below limit of detection 1 Compartment IV Analysis 500 mg of tobramycin is administered by iv bolus to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that tobramycin is excreted primarily unchanged in the urine. The following plasma concentrations were observed. 1.What model best describes this profile? 2.Calculate AUC, K, Vd, T½ and Cl. 3. Write an equation that will calculate concentrations at anytime after the 1st dose. 4.How much is in the body at time zero? 5.How much is in the body at 12 hours? 6.Where did the tobramycin go? 7.How much is in the urine at 12 hrs? 8.What is the renal clearance of tobramycin? 9.Is tobra a high or low extraction drug?
[ ] t = C 0 e -Kt Where K = hr -1 and C 0 can always be calculated from Dose/V C t = (Dose / V) e -Kt and for our patient K = hr -1 V = L Equation describing profile Profile is a 1 compartment model with bolus input.
[ ] t = C 0 e -Kt Where K = hr -1 and C 0 can always be calculated from Dose/V C t = (Dose / V) e -Kt and for our patient K = hr -1 V = L Equation describing profile Profile is a 1 compartment model with bolus input.
Time Plasma Conc (hr) (mg/L) Below limit of detection 1 Compartment IV Analysis 500 mg of tobramycin is administered by iv bolus to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that tobramycin is excreted primarily unchanged in the urine. The following plasma concentrations were observed. 1.What model best describes this profile? 2.Calculate AUC, K, Vd, T½ and Cl. 3. Write an equation that will calculate concentrations at anytime after the 1st dose. 4.How much is in the body at time zero? 5.How much is in the body at 12 hours? 6.Where did the tobramycin go? 7.How much is in the urine at 12 hrs? 8.What is the renal clearance of tobramycin? 9.Is tobra a high or low extraction drug?
Time Plasma Conc (hr) (mg/L) Below limit of detection 1 Compartment IV Analysis 500 mg of tobramycin is administered by iv bolus to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that tobramycin is excreted primarily unchanged in the urine. The following plasma concentrations were observed. 1.What model best describes this profile? 2.Calculate AUC, K, Vd, T½ and Cl. 3. Write an equation that will calculate concentrations at anytime after the 1st dose. 4.How much is in the body at time zero? 5.How much is in the body at 12 hours? 6.Where did the tobramycin go? 7.How much is in the urine at 12 hrs? 8.What is the renal clearance of tobramycin? 9.Is tobra a high or low extraction drug? At time zero, immediately following the dose, there should be 500 mg in the body. The entire dose is delivered into the body.
Time Plasma Conc (hr) (mg/L) Below limit of detection 1 Compartment IV Analysis 500 mg of tobramycin is administered by iv bolus to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that tobramycin is excreted primarily unchanged in the urine. The following plasma concentrations were observed. 1.What model best describes this profile? 2.Calculate AUC, K, Vd, T½ and Cl. 3. Write an equation that will calculate concentrations at anytime after the 1st dose. 4.How much is in the body at time zero? 5.How much is in the body at 12 hours? 6.Where did the tobramycin go? 7.How much is in the urine at 12 hrs? 8.What is the renal clearance of tobramycin? 9.Is tobra a high or low extraction drug?
C t = (Dose / V) e -Kt and for our patient K = hr -1 Dose = 500 mg V = L So the concentration at 12 hr would be: Amount in the body at 12 hours C 12hr =
C t = (Dose / V) e -Kt and for our patient K = hr -1 Dose = 500 mg V = L So the concentration at 12 hr would be: Amount in the body at 12 hours C 12hr = (500 / 18.95) e ( x 12) = e ( ) = mg/L and the concentration reported at 12 hours was 0.7 mg/L
Amount in the body at 12 hours C 12hr = (500 / 18.95) e ( x 12) = e ( ) = mg/L and the concentration reported at 12 hours was 0.7 mg/L Since the volume is L, the amount in the body at 12 hours is: Amount = [ ] x V = 0.7 mg/L x L = mg Only mg of the initial 500 mg dose remains.
We could have also calculated the amount in the body directly from the equation: Instead of C t = (Dose / V) e -Kt We would have Amt t = Amount in the body at 12 hours
We could have also calculated the amount in the body directly from the equation: Instead of C t = (Dose / V) e -Kt We would have Amt t = Dose e -Kt and for our patient K = hr -1 Dose = 500 mg So the amount in the body at 12 hr would be: Amount in the body at 12 hours Amt 12hr = (500) e ( x 12) = 500 e ( ) = mg
Time Plasma Conc (hr) (mg/L) Below limit of detection 1 Compartment IV Analysis & Renal Elimination 500 mg of tobramycin is administered by iv bolus to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that tobramycin is excreted primarily unchanged in the urine. The following plasma concentrations were observed. 1.What model best describes this profile? 2.Calculate AUC, K, Vd, T½ and Cl. 3. Write an equation that will calculate concentrations at anytime after the 1st dose. 4.How much is in the body at time zero? 5.How much is in the body at 12 hours? 6.Where did the tobramycin go? 7.How much is in the urine at 12 hrs? 8.What is the renal clearance of tobramycin? 9.Is tobra a high or low extraction drug?
Where did the tobramycin go? 500 mg of tobramycin is administered by iv bolus to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that tobramycin is excreted primarily unchanged in the urine. The following plasma concentrations were observed.
Time Plasma Conc (hr) (mg/L) Below limit of detection 1 Compartment IV Analysis & Renal Elimination 500 mg of tobramycin is administered by iv bolus to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that tobramycin is excreted primarily unchanged in the urine. The following plasma concentrations were observed. 1.What model best describes this profile? 2.Calculate AUC, K, Vd, T½ and Cl. 3. Write an equation that will calculate concentrations at anytime after the 1st dose. 4.How much is in the body at time zero? 5.How much is in the body at 12 hours? 6.Where did the tobramycin go? 7.How much is in the urine at 12 hrs? 8.What is the renal clearance of tobramycin? 9.Is tobra a high or low extraction drug?
Where did the tobramycin go? Amount = [ ] x V = 0.7 mg/L x L = mg Only 13.3 mg of the initial 500 mg dose remains. 500 mg of tobramycin is administered by iv bolus to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that tobramycin is excreted primarily unchanged in the urine. The following plasma concentrations were observed. Amt 12hr = (500) e ( x 12) = 500 e ( ) = mg Does this mean that mg is in the urine in the first 12 hours following the dose?
Time Plasma Conc (hr) (mg/L) Below limit of detection 1 Compartment IV Analysis & Renal Elimination 500 mg of tobramycin is administered by iv bolus to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that tobramycin is excreted primarily unchanged in the urine. The following plasma concentrations were observed. 1.What model best describes this profile? 2.Calculate AUC, K, Vd, T½ and Cl. 3. Write an equation that will calculate concentrations at anytime after the 1st dose. 4.How much is in the body at time zero? 5.How much is in the body at 12 hours? 6.Where did the tobramycin go? 7.How much is in the urine at 12 hrs? 8.What is the renal clearance of tobramycin? 9.Is tobra a high or low extraction drug?
Calculation of Clearance Since renal elimination appears to be the only way tobramycin is cleared from the body, Total Body Clearance should equal renal clearance…? Clearance is 5.7 L/hr
At constant concentration, clearance can be estimated from blood flow and the difference between arterial and venous concentrations. Cl H = Q [ (Ca – Cv) / Ca ] But in our situation the concentration changing. In the first hour concentration started at mg/L and declined to mg/L and we collected mg of tobramycin in the urine. In the second hour concentration started at mg/L and declined to mg/L and we collected mg of tobramycin in the urine. Equations Conc = Dose / V V = Dose/Conc Cl = Q x ER ER = Cl / Q Renal Clearance of tobramycin
As the concentration declines we recover less in the urine and because urinary excretion is the only method of elimination, drug excretion into the urine is tied to elimination from the body. Rate of appearance of drug in the urine is proportional to the amount in the body Therefore: Where X is the amount of drug in the body at time t and X u is the amount of drug eliminated in the urine to time t. Equations Conc = Dose / V V = Dose/Conc Cl = Q x ER ER = Cl / Q Renal Clearance of tobramycin dX u dt --- = k e X
Since X, the amount drug in the body at time t changes according to X = X 0 e (-Kt) or as we have previous written Amt t = Dose e (-Kt) Then … and a semi-log plot of excretion rate of drug in the urine vs. time should be linear and have a slope of –K/ This is the same slope as for a plasma concentration curve. Equations Conc = Dose / V V = Dose/Conc Cl = Q x ER ER = Cl / Q Renal Clearance of tobramycin dX u dt --- = k e X 0 e (-Kt)
Evaluation of excretion rate vs. time. Note: Time scale expanded Conc. & Amount/time Difference produces “Amount Lost” both total and during each 1 hour interval. An excretion rate per hour (mg/hr) is then calculated. Renal Clearance of tobramycin
Plots of excretion rate (mg/hr) vs. time and concentration vs. time are parallel. Slope of the log of excretion rate vs. time is a function of the overall elimination rate (K), NOT the urinary excretion rate constant – k e. Renal Clearance of tobramycin
The urinary excretion rates that were calculated are not instantaneous rates, Rather, they are average rates determined over an interval. The average excretion rate closely approximates the instantaneous rate seen at the mid-point of the urine collection interval. Therefore, urinary excretion rates should be plotted at the midpoints of the urine collection period. Equations Conc = Dose / V V = Dose/Conc Cl = Q x ER ER = Cl / Q Renal Clearance of tobramycin dX u dt --- = k e X 0 e (-Kt) Xu tXu t
Just as the plasma concentration-time profile can be characterized by both an elimination rate constant (K) and a clearance term (Cl T or TBC), so can urinary excretion data: renal excretion rate constant (k e ) and a renal clearance term (Cl R ). We have seen that the rate at which drug is cleared into the urine is proportional to the plasma concentration at the mid point of the urine collection interval. Equations Conc = Dose / V V = Dose/Conc Cl = Q x ER ER = Cl / Q Renal Clearance of tobramycin (dX u / dt ) C MID Cl R =
We have seen that the rate at which drug is cleared into the urine is proportional to the plasma concentration at the mid point of the urine collection interval. In practice renal clearance is estimated by dividing the urinary excretion rate by the plasma concentration at the mid point of the urinary collection interval. where X U is the amount of drug appearing in the urine Equations Conc = Dose / V V = Dose/Conc Cl = Q x ER ER = Cl / Q Renal Clearance of tobramycin (dX u / dt ) C MID Cl R = ( X u / t ) C MID Cl R =
In practice renal clearance is estimated by dividing the urinary excretion rate by the plasma concentration at the mid point of the urinary collection interval. where X U is the amount of drug appearing in the urine. Equations Conc = Dose / V V = Dose/Conc Cl = Q x ER ER = Cl / Q Renal Clearance of tobramycin ( X u / t ) C MID Cl R = Rearrangement yields: ( X u / t ) = Cl R x C MID which indicates that Cl R will be the slope of a straight-line relationship between the amount recovered in the urine during an interval and the midpoint plasma concentration.
Renal Clearance of tobramycin The excretion rate (mg/hr) has been plotted against the plasma concentration at the midpoint of the interval.
Renal Clearance of tobramycin The slope is renal clearance (Cl R ) and you can see that it equivalent to total clearance (Cl T ) calculated previously.
Renal Clearance of tobramycin The slope is renal clearance (Cl R ) and you can see that it equivalent to total clearance (Cl T ) calculated previously.
Renal Clearance of tobramycin Example: Blood Urine Urine Urine AmountExcretion Sample CollectionVolume Conc. Excreted Rate Time Interval (hr)Start-Stop (mL)(mg/mL)(mg)(mg/hr) – 2 hr – 6 hr – 12 hr In practice, renal clearance is calculated from a series of urine collections with blood samples taken at the mid-point of the interval. Urinary Excretion Rate is calculated from the urine volume, the drug concentration in the urine and period over which the urine is collected.
Renal Clearance of tobramycin Example: Blood Urine Urine Urine AmountExcretion Sample CollectionVolume Conc. Excreted Rate Time Interval (hr)Start-Stop (mL)(mg/mL)(mg)(mg/hr) – 2 hr – 6 hr – 12 hr In practice, renal clearance is calculated from a series of urine collections with blood samples taken at the mid-point of the interval. Urinary Excretion Rate is calculated from the urine volume, the drug concentration in the urine and period over which the urine is collected.
Renal Clearance of tobramycin Calculated Renal Clearance L/hr
Another method for calculating Renal Clearance Since dX u / dt is equivalent to k e X, Substitution in the equation: Results in Where X/C = V, and so… Cl R = k e V Equations Conc = Dose / V V = Dose/Conc Cl = Q x ER ER = Cl / Q Renal Clearance of tobramycin (dX u / dt ) C MID Cl R = (k e X ) C MID Cl R =
Time Plasma Conc (hr) (mg/L) Below limit of detection 1 Compartment IV Analysis & Renal Elimination 500 mg of tobramycin is administered by iv bolus to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that tobramycin is excreted primarily unchanged in the urine. The following plasma concentrations were observed. 1.What model best describes this profile? 2.Calculate AUC, K, Vd, T½ and Cl. 3. Write an equation that will calculate concentrations at anytime after the 1st dose. 4.How much is in the body at time zero? 5.How much is in the body at 12 hours? 6.Where did the tobramycin go? 7.How much is in the urine at 12 hrs? 8.What is the renal clearance of tobramycin? 9.Is tobra a high or low extraction drug?
Equation Summary Conc = Dose / V V = Dose/Conc Cl = Q x ER ER = Cl / Q ( X u / t ) = Cl R x C MID Cl R = k e V Renal Clearance of tobramycin Renal blood flow = 25% CO 1.5 L/min. Hct = 0.5 in our patient Therefore, renal plasma flow is Q plasma = 1.5 L/min x 0.5 = 0.75 L/min = 45 L/hr. Using plasma because renal clearance was based on plasma concentrations and the volume of distribution was based on plasma concentrations
Equation Summary Conc = Dose / V V = Dose/Conc Cl = Q x ER ER = Cl / Q ( X u / t ) = Cl R x C MID Cl R = k e V Renal Clearance of tobramycin Renal blood flow = 25% CO 1.5 L/min. Hct = 0.5 in our patient Therefore, renal plasma flow is Q plasma = 1.5 L/min x 0.5 = 0.75 L/min = 45 L/hr. Tobramycin renal clearance in our patient was 5.72 L/hr ER = Cl R / Q plasma =
Equation Summary Conc = Dose / V V = Dose/Conc Cl = Q x ER ER = Cl / Q ( X u / t ) = Cl R x C MID Cl R = k e V Renal Clearance of tobramycin Renal blood flow = 25% CO 1.5 L/min. Hct = 0.5 in our patient Therefore, renal plasma flow is Q plasma = 1.5 L/min x 0.5 = 0.75 L/min = 45 L/hr. Tobramycin renal clearance in our patient was 5.72 L/hr ER = Cl R / Q plasma = 5.72 / 45 = Low Extraction … compare Theophylline (liver) 5% Creatinine (renal) 14.6% Ciprofloxacin (renal) 71%