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## Index of Simulations

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**Index of Simulations**• 1-Compartment, IV bolus • 1-Compartment, IV infusion: Steady-State • 1-Compartment, IV infusion: Non-Steady-State • 1-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 t1/2**Log scale**Linear scale Step 1) Graph on Semi-log Paper**Step 3) Find V**• Use the relationship: • Rearranged for V: • We know X0 (100 mg) and C0 we can get from the graph**Step 3) Find V**C0 C0 = 400 ug/L 400 300 200**Step 3) Find V**• We know X0 (100 mg) and C0 we can get from the graph (C0 = 400 ug/L) (please watch units) • Now we have our volume (250 L)**Step 4) Find t1/2 (and k)**• Half-life (t1/2) can be obtained directly from the graph by reading how long it takes for the concentration to be reduced by 50%**C0 = 400 ug/L**200 t1/2 = 3 Step 4) Find t1/2 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 t1/2 Start with C0 which equals 400 ug/L Your t1/2 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 • t1/2 = 3 h Onto Steady-State Infusion Return to Table of Contents**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 t1/2**Log scale**Linear scale Step 1) Graph on Semi-log Paper**Step 2) Find t1/2 (and k)**• Half-life (t1/2) 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**C ~ 110 ug/L**55 t1/2 = 18 - 15 Step 2) Find t1/2 Your t1/2 is the time you just read minus infusion time (18 h – 15 h = 3 hours) At the intesection, draw a line down to the X-axis (time). Read the value the line intersects the axis… 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**Step 2) Find t1/2 (and k)**• Half-life (t1/2) 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 (Css) and the infusion rate (k0) 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 Css 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**Css= 110 ug/L**Step 3) Find Cl**• We have k0 (6.67 mg/h), we have CSS (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 • t1/2 = 3 h Onto Non-Steady-State Infusion Return to Table of Contents**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 t1/2**Log scale**Linear scale Step 1) Graph on Semi-log Paper**Step 2) Find t1/2 (and k)**• Half-life (t1/2) 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**C ~ 260 ug/L**130 t1/2 = 10 - 6 Step 2) Find t1/2 Your t1/2 is the time you just read minus infusion time (10 h – 6 h = 4 hours) At the intesection, draw a line down to the X-axis (time). Read the value the line intersects the axis… 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**Step 2) Find t1/2 (and k)**• Half-life (t1/2) 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 calculations • Equation 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**C2 For this method, we break the curve into individual trapezoids as shown here… The area of the trapezoid (or this case a triangle) is the average height (C1+C2)/2 multiplied by the base (t2-t1) C1 t1 t2**Step 3: Calculate Cl**• Since we now have AUC, using the dose (100 mg), and the equation: • Solve for Cl: Select another Cl calculation Go to Volume 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) Select another Cl calculation Go to Volume 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 Css 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**Css= 110 ug/L**Step 3) Find Cl**• We have k0 (6.67 mg/h), we have CSS (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 t1/2**Log scale**Linear scale Step 1) Graph on Semi-log Paper**Step 2) Find t1/2 (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 CSS**Step 2) Find CSS**We can estimate CSs either taking the average of the last few concentrations or use a best fit line Just read CSS from the intercept of the Y-axis 106.5 ug/L