Index of Simulations 1-Compartment, IV bolus 1-Compartment, IV infusion: Steady- State1-Compartment, IV infusion: Steady- State 1-Compartment, IV infusion: Non- Steady-State1-Compartment, IV infusion: Non- Steady-State 1-Compartment, IV infusion: No Elimination Phase1-Compartment, IV infusion: No Elimination Phase

1-Compartment, IV Bolus The following data were obtained after 100 mg of Drug X was administered to a healthy volunteer. Blood was collected starting at one- hour post-dose for a total of 12 hours. Calculate Cl, V and t 1/2

Data (X 0 = 100 mg) Time (h)[Drug X] (ug/L)

Step 1) Graph on Semi-log Paper Log scale Linear scale

Step 2) Draw best fit line

Step 3) Find V Use the relationship: Rearranged for V: –We know X 0 (100 mg) and C 0 we can get from the graph

Step 3) Find V C0C0 C 0 = 400 ug/L

Step 3) Find V We know X 0 (100 mg) and C 0 we can get from the graph (C 0 = 400 ug/L) (please watch units) Now we have our volume (250 L)

Step 4) Find t 1/2 (and k) Half-life (t 1/2 ) can be obtained directly from the graph by reading how long it takes for the concentration to be reduced by 50%

Step 4) Find t 1/2 C 0 = 400 ug/L 200 t 1/2 = 3 Start with C 0 which equals 400 ug/L Half of 400 is 200. Draw a line from 200 across until it intersects your best fit line At the intesection, draw a line down to the X-axis (time). Read the value the line intersects the axis…this is t 1/2 Your t 1/2 is ~3 hours

Step 5) Find Cl Clearance (Cl) can be calculated from k (Step 4) and V (Step 4) and using the following equation:

Summary Cl = 57.8 L/h V = 250 L t 1/2 = 3 h Return to Table of Contents Onto Steady-State Infusion

1-Compartment, IV Infusion: Steady-State The following data were obtained after 100 mg of Drug X was infused over 15 hours to a healthy volunteer. Blood was collected starting at one- hour post-dose for a total of 24 hours. Calculate Cl, V and t 1/2

Data (X 0 = 100 mg) Time (h)[Drug X] (ug/L)

Step 1) Graph on Semi-log Paper Log scale Linear scale

Step 2) Find t 1/2 (and k) Half-life (t 1/2 ) can be obtained directly from the graph by reading how long it takes for the concentration to be reduced by 50%. –For infusions, you must use the terminal portion where concentrations are falling!! First however, draw a best fit line through the terminal portion

Step 2) Find t 1/2

C ~ 110 ug/L 55 t 1/2 = Start with C which you know C at 15 h = 110 ug/L Half of 110 is 55. Draw a line from 55 across until it intersects your best fit line At the intesection, draw a line down to the X-axis (time). Read the value the line intersects the axis… Your t 1/2 is the time you just read minus infusion time (18 h – 15 h = 3 hours)

Step 2) Find t 1/2 (and k) Half-life (t 1/2 ) from the graph is 3 hours. We can find k by the following equation:

Step 3) Find Cl Clearance (Cl) can be calculated from the steady-state concentration (C ss ) and the infusion rate (k 0 ) using the equation: Rearranged to:

Step 3) Find Cl We know the dose (100 mg) and infusion time (T=15 h), therefore infusion rate is:

Step 3) Find Cl We can obtain C ss from the graph by looking to see when concentrations stop changing. How do we know for sure this is steady- state? Remember steady-state is 3-5 half- lives. –Half-life from Step 2 = 3h –3 x 5 (or 3 or 4) = 15 h –Infusion was stop at 15 hours therefore we are at steady-state and this approach is valid

Step 3) Find Cl C ss = 110 ug/L

Step 3) Find Cl We have k 0 (6.67 mg/h), we have C SS (110 ug/L), now we can calculate Cl

Step 4) Find V Volume (V) can be calculated from k (Step 3) and Cl (Step 1) and using the following equation: Rearrange and solve for V

Summary Cl = 60.6 L/h V = 262 L t 1/2 = 3 h Return to Table of Contents Onto Non-Steady-State Infusion

1-Compartment, IV Infusion: Non-Steady-State The following data were obtained after 100 mg of Drug X was infused over 6 hours to a healthy volunteer. Blood was collected starting at one- hour post-dose for a total of 24 hours. Calculate Cl, V and t 1/2

Data (X 0 = 100 mg) Time (h)[Drug X] (ug/L)

Step 1) Graph on Semi-log Paper Log scale Linear scale

Step 2) Find t 1/2 (and k) Half-life (t 1/2 ) can be obtained directly from the graph by reading how long it takes for the concentration to be reduced by 50%. –For infusions, you must use the terminal portion where concentrations are falling!! First however, draw a best fit line through the terminal portion

Step 2) Find t 1/2

C ~ 260 ug/L 130 t 1/2 = Start with C which you know. C at 6 h = 260 ug/L Half of 260 is 130. Draw a line from 130 across until it intersects your best fit line At the intesection, draw a line down to the X-axis (time). Read the value the line intersects the axis… Your t 1/2 is the time you just read minus infusion time (10 h – 6 h = 4 hours)

Step 2) Find t 1/2 (and k) Half-life (t 1/2 ) from the graph is 3 hours. We can find k by the following equation:

Step 3) Find Cl Clearance (Cl) can be calculated two- ways. Please select a method to calculate clearance AUC Method – More exact but more calculationsAUC Method – More exact but more calculations Equation Method – Quicker but less exactEquation Method – Quicker but less exact

Clearance Via AUC To calculate clearance via the AUC, you must first calculate the AUC via the trapezoidal rule

Trapezoidal Rule For this method, we break the curve into individual trapezoids as shown here… C1C1 C2C2 t1t1 t2t2 The area of the trapezoid (or this case a triangle) is the average height (C 1 +C 2 )/2 multiplied by the base (t 2 -t 1 )

Step 2) Setup the table ABA*B Time[Drug X](C 2 +C 1 )/2 (t 2 -t 1 )AUC Tail SUM2622.7

Step 3: Calculate Cl Since we now have AUC, using the dose (100 mg), and the equation: Solve for Cl: Go to Volume calculation Select another Cl calculation

Clearance via Infusion Equation We can use the equation that describes an infusion and solve for Cl. –During Infusion (t = time during infusion) –Solving for Cl

Clearance via Equation Now plug in the values we know (infusion rate, C, t, k) Go to Volume calculation Select another Cl calculation

Step 3) Find Cl We know the dose (100 mg) and infusion time (T=15 h), therefore infusion rate is:

Step 3) Find Cl We can obtain C ss from the graph by looking to see when concentrations stop changing. How do we know for sure this is steady- state? Remember steady-state is 3-5 half- lives. –Half-life from Step 2 = 3h –3 x 5 (or 3 or 4) = 15 h –Infusion was stop at 15 hours therefore we are at steady-state and this approach is valid

Step 3) Find Cl C ss = 110 ug/L

Step 3) Find Cl We have k 0 (6.67 mg/h), we have C SS (110 ug/L), now we can calculate Cl

Step 4) Find V Volume (V) can be calculated from k (Step 2) and Cl (Step 3) and using the following equation: Rearrange and solve for V

1-Compartment, IV infusion: No elimination phase The following data were obtained after 100 mg of Drug X was infused over 15 hours to a healthy volunteer. Blood was collected starting at one- hour post-dose for a total of 15 hours. Calculate Cl, V and t 1/2

Data (X 0 = 100 mg) Time (h)[Drug X] (ug/L)

Step 1) Graph on Semi-log Paper Log scale Linear scale

Step 2) Find t 1/2 (and k) Since we do not have an elimination phase, we must find another way to estimate half-life. We will use the approach to steady-state method. So first we need to estimate C SS

Step 2) Find C SS We can estimate C Ss either taking the average of the last few concentrations or use a best fit line ug/L Just read C SS from the intercept of the Y-axis

Step 2) Find C SS Our C SS = ug/L We can find K by plotting –C SS -C t versus time on semi-log paper…but first lets find C Ss -C t

Data (X 0 = 100 mg) Time (h)[Drug X] (ug/L)(C Ss -C t )/C SS 00( )/106.5 = ( )/106.5 = ( )/106.5 = ( )/106.5 = ( )/106.5 = ~ ~ ~ 0

Step 2) Find t 1/2 Start with (Css- 0)/Css which you know 1 Half of 1 is 0.5. Draw a line from 0.5 across until it intersects your best fit line At the intersection, draw a line down to the X-axis (time). Read the value the line intersects the axis… Your t 1/2 is the time you just read (2.5 hours) ~ 1 t 1/2 =

Step 2) Find t 1/2 (and k) Half-life (t 1/2 ) from the graph is 2.5 hours. We can find k by the following equation:

Step 3) Find Cl Clearance (Cl) can be calculated from the steady-state concentration (C ss ) and the infusion rate (k 0 ) using the equation: Rearranged to:

Step 3) Find Cl We know the dose (100 mg) and infusion time (T=15 h), therefore infusion rate is:

Step 3) Find Cl We can obtain C ss from the graph as we just did and had a value of ug/L

Step 3) Find Cl We have k 0 (6.67 mg/h), we have C SS (110 ug/L), now we can calculate Cl

Step 4) Find V Volume (V) can be calculated from k (Step 3) and Cl (Step 1) and using the following equation: Rearrange and solve for V

Summary Cl = 62.6 L/h V = 226 L t 1/2 = 2.5 h Return to Table of Contents

Lesson Done!