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LOGARITHM REVIEW Lecture #4

History of Logs John Napier (1614) and Joost Burgi (1620) Why? Simplify astronomical calculations. Multiplication was a simplification of addition – 3 x 5 = Powers are a simplification of multiplication – 5 3 = 5 x 5 x 5 Division is the opposite of Multiplication Logs are opposite to Powers

What do logs do? Allows you to see the relationship between things? Linear Scale Log Scale Makes curves straight.

Logs log base answer = power base power = answer Powers

Powers to Logs Powers VersionLog Version 10 2 =100log =2 3 2 =9log 3 9=2 e 3 =20.085log e =3 e -kt = Clog e C = -kt What is e? =~2.718 * derived from an infinite series.

Properties of Logs: Positive Logs Implicit assumption log = log 10 ln = log e Log 1 = 0 Log 10 = 1 Log 100 = 2

Property of Logs: Negative Logs Log 0.1 = -1 Log 0.01 = -2 Log = -3

Properties of Logs

KINETIC CONCEPTS Lecture #4

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)

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

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

Half-Life (t1/2) Time in which the [drug] is half the initial [drug]

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

Concentration mg L mg/L C = [Drug] V = Volume Distribution

[Drug] Reservoir

[Drug] Reservoir Blood Flow (Q)

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

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

Extraction Ratio

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

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

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

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

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=5L, which is the average volume of blood A=C*V=500 mg of drug in the blood

Volume Distribution (V) C={Drug] Blood Average Volume of Blood = 5L 5L Dose = 500 mg C(0) = 100 mg/L A=500 mg What is the V? 500 mg 5L A = Amount of Drug in the Blood (mg)

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

Volume Distribution (V) C={Drug] Blood Average Volume of Blood = 5L 5L Dose = 500 mg C(0) = 2 mg/L A=10 mg What is the V? 10 mg Brain 490 mg 250 L A = Amount of Drug in the Blood (mg)

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

CL, V and k Clearance (CL, units=L/hr) = Blood Volume of Drug Remove/hr Volume Distribution (V, units=L) What does k = 0.5 /hr mean?

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

Total CL, AUC and V Dose (mg) = CL (L/hr) * AUC ((mg*hr)/L) – IV bolus

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)