Lecture 4 LOGARITHM REVIEW 1 History of Logarithms

Lecture #4 LOGARITHM REVIEW 1

History of Logarithms (Logs) • John Napier (1614) and Joost Bürgi (1600) • Why? Simplify astronomical calculations • Multiplication was a simplification of addition 3 x 5=5+5+5 • Powers are a simplification of multiplication 53 = 5 x 5 • Division is the opposite of multiplication • Logs are the opposite to powers 2

Logs logbase answer = power Powers basepower = answer 3

Powers to Logs Powers Version Log Version 102=100 log 10100=2 32=9 log 39=2 e 3=20. 085 loge 20. 085=3 e-kt = C loge. C = -kt What is e? =~2. 718 * derived from an infinite series. 4

Properties of Logs Implicit assumption log = log 10 ln = loge • Log 0. 001 = -3 • Log 0. 01 = -2 • Log 0. 1 = -1 • • Log 1 = 0 Log 10 = 1 Log 100 = 2 Log 1000 =3 5

Properties of Logs

What do logs do? Allows you to see the relationship between things? 3. 5 1200 3 800 Log Scale Linear Scale 1000 600 400 2. 5 2 1. 5 0 Item 1 Item 2 Item 3 Category Item 4 0 Makes curves straight. Item 1 Item 2 Item 3 Category Item 4 Log Scale Linear Scale 120 5 log([Drug]plasma) 100 [Drug]plasma Series 1 1 80 60 40 20 0 0 5 10 time (hours) 15 4 3 2 1 0 -1 0 5 10 15 time (hours) 7

Lecture #4 KINETIC CONCEPTS 8

Linear vs. Log Linear/Cartesian Plot Semilogarithmic plot Fractional Elimination Rate (k) = - slope 9

Linear vs. Log Linear/Cartesian Plot Which one has the higher rate? Semilogarithmic Plot Fractional Elimination rate (k) = - slope

Things you will learn • • Fractional elimination rate constant (k) Half-time (t 1/2) Mean residence time (MRT) Extraction ratio (E) Amount of Drug (A) Volume distribution (V) Clearance (CL) 11

Half-Life (t 1/2) Time in which the [drug] is half the initial [drug] 12

Mean Residence Time (MRT) MRT = Average time that a molecule stays in the body 13

Concentration mg mg/L L 14

Reservoir [Drug] 15

Reservoir Blood Flow (Q) [Drug] 16

Reservoir Blood Flow (Q) [Drug] Cout Extractor C [Drug] Extracted 17

Reservoir Blood Flow (Q) [Drug] Cout Extractor C [Drug] Extracted = C-Cout Initial [Drug] = C 18

Reservoir Extraction Ratio [Drug] Cout Blood Flow (Q) Extractor C [Drug] Extracted 19

How fast are drugs presented to the extractor (mg/hr)? Reservoir Blood Flow (Q) [Drug] Cout Extractor C [Drug] Extracted 20

How fast are drugs eliminated by the extractor (mg/hr)? Reservoir Blood Flow (Q) [Drug] Cout Extractor C [Drug] Extracted 21

What is the volume of blood with drug extracted per hour? Reservoir Blood Flow (Q) [Drug] Cout Extractor C [Drug] Extracted 22

Clearance Reservoir Blood Flow (Q) [Drug] Cout Extractor C [Drug] Extracted 23

Volume Distribution (V) Case #1 Not distributed C=100 mg/L Dose=500 mg Case #2 Distributed Volume Distribution Systemic Circulation Dose = 500 mg C(0) = 100 mg/L A=500 mg What is the V? 5 L Systemic Circulation C=0. 1 mg/L Dose=500 mg A = Amount of Drug in the Blood (mg) Average Volume of Blood = 5 L Dose = 500 mg C(0) = 0. 1 mg/L A=500 mg What is the V? 5, 000 L 24

Amount of Drug (A) in the Blood • • C = [Drug] (mg/L) V = Volume Distribution (L) A (mg) = C (mg/L) * V (L) Example C=100 mg/L V=5 L, which is the average volume of blood A=C*V=500 mg of drug in the blood 25

Volume Distribution (V) Brain Blood C=[Drug] 250 mg 5 L Dose = 500 mg C(0) = 50 mg/L A=250 mg What is the V? 10 L A = Amount of Drug in the Blood (mg) Average Volume of Blood = 5 L 26

What does Volume Distribution (V) Tell Us? • If V=~5 L, tells us that the drug is primarily in the blood. • If V>5 L, that is typical. • If V>>5 L, tells us that the drug is distributed away from the blood. • Can V<5 L? . No. 27

CL, V and k • Clearance (CL, units=L/hr) – Volume of blood with drug removed per hour • Volume Distribution (V, units=L) What does k = 0. 5 /hr mean? 28

CL, V and t 1/2: Time in which the [drug] is half the initial [drug] 29

Total CL, AUC and V • Dose (mg) = CL (L/hr) * AUC ((mg*hr)/L) – IV bolus 1) 3) 2) 30

Things you learned • • Fractional elimination rate constant (k) Half-time (t 1/2) Mean residence time (MRT) Extraction ratio (E) Amount of Drug (A) Volume distribution (V) Clearance (CL) **Equations can be rearranged!! If you are given only a few variables, look at equation possibilities then plug and chug!**31