PHA6120: UNIT 1: MATH CONCEPTS, RATES, HALF-LIFE

x

In the expression: 𝑁 = 𝑏^x

is the exponent

b

In the expression: 𝑁 = 𝑏^x

is the base

N

In the expression: 𝑁 = 𝑏^x

is the number when b is raised to the xth power (b^x)

logarithm

The _ of a positive number N to a given base b is the exponent x to which the base must be raised to equal the number N.

pH

_ of biological fluids can affect LADME

logarithmic

pH scale is is a _ scale

Time

independent variable, plotted on the abscissa (x axis)

Drug concentration

dependent variable, plotted on the ordinate (y axis)

RECTANGULAR COORDINATES

SEMILOG COORDINATES

CURVE FITTING

Implies that there is some sort of relationship between variables x and y (ie. drug vs. pharmacologic effect).

CURVE FITTING

Continuous function of x and y

x

y=mx+b

• Where

  • _ = independent variable

y

y=mx+b

• Where

  • _ = dependent variable

b

y=mx+b

• Where

  • _ = the y-intercept 

m

y=mx+b

• Where

  • _ = the slope of the straight line

EQUATION OF A STRAIGHT LINE

y=mx+b

POSITIVE

ZERO

NEGATIVE

LINEAR REGRESSION

• This method is often encountered and used in clinical pharmacy studies to construct a linear relationship between an independent variable and a dependent variable

Coefficient of determination (r²)

expresses how much variability in the outcome is explained by the input factor

RATE PROCESSES

The rate of chemical reaction is the velocity with which the reaction occurs

RATE PROCESSES

is used to describe processes such as drug absorption or drug elimination

ORDER OF REACTION

The way in which the concentration of the drug or reactant in a chemical reaction affects the rate of chemical reaction or process

ZERO-ORDER KINETICS

Proceeds over time (t) independent from the concentration of the drug (C)

ZERO-ORDER KINETICS

Fixed amount of drug is removed per unit time

FIRST-ORDER KINETICS

The rate of a first-order process is dependent upon the concentration of the drug (C)

FIRST-ORDER KINETICS

Fixed percentage of drug is removed per unit time

HALF-LIFE

The time required for one-half of the drug concentration to disappear (t½ )

ZERO-ORDER KINETICS

Dependent on: 

Concentration at time zero Rate constant

ZERO-ORDER KINETICS

Independent of:

Concentration at time zero

ZERO-ORDER KINETICS

FIRST-ORDER KINETICS

FIRST-ORDER KINETICS

• Plot the data on a semi-log graph

• If the data appear to form a straight line with good correlation using linear regression, then the data likely follow _

non-zero order

• Plot the data on a rectangular graph

• If the data appear to be a curve rather than a straight line, the reaction rate for the data is _

ZERO-ORDER KINETICS

Fixed amount of drug is removed per unit time

ZERO-ORDER KINETICS

Concentration independent

ZERO-ORDER KINETICS

ZERO-ORDER KINETICS

(mg/L)/h

ZERO-ORDER KINETICS

A plot of C vs time on a rectangular graphing paper yields a straight line.

ZERO-ORDER KINETICS

FIRST-ORDER KINETICS

Fixed percentage of drug is removed per unit time

FIRST-ORDER KINETICS

Concentration dependent

FIRST-ORDER KINETICS

FIRST-ORDER KINETICS

1/h

FIRST-ORDER KINETICS

A plot of C vs time on semi-log graphing paper yields a straight line.

FIRST-ORDER KINETICS