Podcast
Questions and Answers
A logarithm with base 10 is known as a ______.
A logarithm with base 10 is known as a ______.
log
The base 'e' is used in natural logarithms and is approximately equal to ______.
The base 'e' is used in natural logarithms and is approximately equal to ______.
2.718
The equation used to convert a common logarithm to a natural logarithm is ______ X = log X × 2.303.
The equation used to convert a common logarithm to a natural logarithm is ______ X = log X × 2.303.
ln
The power needed to reach 1000 in the equation 10^3 = 1000 is ______.
The power needed to reach 1000 in the equation 10^3 = 1000 is ______.
Logarithms are the inverse operations of ______.
Logarithms are the inverse operations of ______.
There are typically two types of graphs used in pharmacokinetics: Cartesian or Rectangular coordinates and ______ coordinates.
There are typically two types of graphs used in pharmacokinetics: Cartesian or Rectangular coordinates and ______ coordinates.
Fitting a curve to the points on a graph implies a relationship between the variables x and y, such as dosage of drug versus ______ effect.
Fitting a curve to the points on a graph implies a relationship between the variables x and y, such as dosage of drug versus ______ effect.
When using curve fitting, the relationship is not confined to isolated points but is a ______ function of x and y.
When using curve fitting, the relationship is not confined to isolated points but is a ______ function of x and y.
If the relationship between x and y is ______ related, it can be expressed as a straight line.
If the relationship between x and y is ______ related, it can be expressed as a straight line.
The general equation of a straight line is ______ = mx + b.
The general equation of a straight line is ______ = mx + b.
In the equation Y = mx + b, 'm' represents the ______ of the line.
In the equation Y = mx + b, 'm' represents the ______ of the line.
In the equation Y = mx + b, 'b' represents the ______-intercept.
In the equation Y = mx + b, 'b' represents the ______-intercept.
Curve fitting involves drawing a curve that best represents the relationship between two ______ plotted on a graph.
Curve fitting involves drawing a curve that best represents the relationship between two ______ plotted on a graph.
Mathematics helps to explain relationships among ______.
Mathematics helps to explain relationships among ______.
For an equation to be valid, the ______ must be constant on both sides.
For an equation to be valid, the ______ must be constant on both sides.
Drug concentrations are typically expressed as mass per ______.
Drug concentrations are typically expressed as mass per ______.
The expressions mcg/mL, µg/mL, and mg/L are ______ and commonly reported.
The expressions mcg/mL, µg/mL, and mg/L are ______ and commonly reported.
Drug concentration can be reported as mg% or mg/______, representing milligrams of the drug per 100 mL.
Drug concentration can be reported as mg% or mg/______, representing milligrams of the drug per 100 mL.
The ______ of a number is the power when that number is in exponential form.
The ______ of a number is the power when that number is in exponential form.
If the base 10 is used, the logarithm is known as the ______.
If the base 10 is used, the logarithm is known as the ______.
The relationship between exponential and ______ functions is fundamental in mathematics.
The relationship between exponential and ______ functions is fundamental in mathematics.
In pharmacokinetics, the relationship between plasma drug concentrations versus time can be expressed as a ______ function.
In pharmacokinetics, the relationship between plasma drug concentrations versus time can be expressed as a ______ function.
The correlation coefficient, denoted by ______, assesses the strength of the linear relationship.
The correlation coefficient, denoted by ______, assesses the strength of the linear relationship.
A positive value of r indicates a ______ slope.
A positive value of r indicates a ______ slope.
If the correlation coefficient r takes the value of +1, it indicates a ______ relationship between the variables.
If the correlation coefficient r takes the value of +1, it indicates a ______ relationship between the variables.
A zero value for the slope indicates that there is no ______ relationship existing between y and x.
A zero value for the slope indicates that there is no ______ relationship existing between y and x.
Linear regression is commonly used in ______ pharmacy studies.
Linear regression is commonly used in ______ pharmacy studies.
When r is -1, it means there is a ______ linear relationship between the variables.
When r is -1, it means there is a ______ linear relationship between the variables.
The method used to construct a linear relationship is known as the Least Squares ______.
The method used to construct a linear relationship is known as the Least Squares ______.
In pharmacokinetics, two orders are of importance: zero order and ______ order.
In pharmacokinetics, two orders are of importance: zero order and ______ order.
A zero-order process has a rate that is ______ and does not change with the concentration of the drug.
A zero-order process has a rate that is ______ and does not change with the concentration of the drug.
In a zero-order example, a transdermal patch consistently releases ______ mg of drug per hour.
In a zero-order example, a transdermal patch consistently releases ______ mg of drug per hour.
In a first-order process, the rate of drug absorption or elimination is ______ to its current concentration.
In a first-order process, the rate of drug absorption or elimination is ______ to its current concentration.
A drug with a half-life of 4 hours means that its concentration decreases by half every ______ hours.
A drug with a half-life of 4 hours means that its concentration decreases by half every ______ hours.
If the initial drug concentration is 100 mg/L, after 4 hours it would drop to ______ mg/L.
If the initial drug concentration is 100 mg/L, after 4 hours it would drop to ______ mg/L.
In zero-order kinetics, the rate of drug release remains constant at ______ mg per hour, regardless of concentration.
In zero-order kinetics, the rate of drug release remains constant at ______ mg per hour, regardless of concentration.
The rate of decrease in drug concentration in a first-order process is influenced by the ______ of the drug.
The rate of decrease in drug concentration in a first-order process is influenced by the ______ of the drug.
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Study Notes
Pharmacokinetics Graphs
- Two main types of graphs are used to analyze drug concentration over time: Cartesian (rectangular) coordinates and semilog coordinates.
Curve Fitting
- Curve fitting establishes a continuous relationship between two variables, such as drug dosage and pharmacologic effect.
- A hypothesis is formed to represent the relationship, and an empirical equation is applied to fit observed data, typically expressed as (Y = mx + b) where (m) is the slope and (b) is the y-intercept.
- Curve fitting provides a clear depiction of how one variable changes in relation to another, rather than connecting isolated data points.
Linear Regression/Least Squares Method
- This method constructs a linear relationship between an independent variable (input) and a dependent variable (output), commonly used in clinical pharmacy.
- In pharmacokinetics, it illustrates the plasma drug concentration over time.
- The correlation coefficient ((r)) assesses the strength of this linear relationship, ranging from -1 to +1. A value of 1 or -1 indicates a perfect linear relationship, while a value of 0 indicates no relationship.
Mathematical Expressions and Units
- Mathematics is essential for explaining relationships among variables in pharmacokinetics.
- For valid equations, units must be consistent on both sides, ensuring meaningful relationships.
Units for Expressing Blood Concentrations
- Drug concentrations are expressed as mass per volume, common units include:
- mcg/mL (micrograms/milliliter)
- µg/mL (micrograms/milliliter)
- mg/L (milligrams/liter)
- Additional expressions include mg% or mg/dL, indicating milligrams of drug per 100 mL of solution.
Exponential and Logarithmic Functions
- Logarithms and exponentials are inversely related; logarithms determine the exponent for a given base.
- Logarithms with base 10 are common ((\log)), while base (e) (approximately 2.718) defines natural logarithms ((\ln)).
- Conversion from common logarithms to natural logarithms involves the factor 2.303, expressed as (\ln X = \log X \times 2.303).
Rates and Orders of Processes
- The rate of processes like drug absorption or elimination can define their "order," specifically zero-order and first-order kinetics.
Zero-Order Kinetics
- Drug release occurs at a constant rate regardless of concentration. An example includes a transdermal patch releasing a steady 10 mg of drug per hour.
- Concentration decreases predictably (e.g., from 100 mg/L to 90 mg/L after one hour), but the rate remains unchanged at 10 mg/hour.
First-Order Kinetics
- The rate of drug elimination or absorption varies proportionally with the drug concentration.
- For instance, a drug with a half-life of 4 hours sees its concentration halve every 4 hours (e.g., from 100 mg/L to 50 mg/L, then 25 mg/L).
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