Because pharmaco*kinetics and biopharmaceutics have a strong mathematical basis, a solid foundation in mathematical principles in algebra, calculus, exponentials, logarithms, and unit analysis are critical for students in these disciplines. A self-exam is included in this chapter to provide a self-assessment of possible weaknesses in one's basic math skills. Difficulties with questions in the self-exam indicate that a review of mathematical essentials is necessary. Mathematical fundamentals are summarized here for review purposes only. For a more complete discussion of fundamental principles, a suitable textbook in mathematics should be consulted.
What are the units for concentration, mass, and volume?
A drug solution has a concentration of 50 mg/mL. What amount of drug is contained within 20.5 mL of the solution? In 0.4 L? What volume of the solution will contain 30 mg of drug?
Convert the units in the above solution from mg/mL to g/L and μg/uL. If the molecular weight of the drug is 325 Da, what are the units in M?
If 20 mg of drug are added to a container of water and result in a concentration of 0.55 mg/L, what volume of water was in the container?
For the following equation:
Sketch a plot of the equation.
Describe the relevance of each part of this equation.
If x = 0.6, what is y?
If y = 4.1, what is x?
Solve the following equations for x:
log x = 0.95
ex = 0.44
ln x = 1.22
What is the slope of the line that connects the following two points?
- Point 1:? x = 2 y = 5.6
- Point 2:? x = 0.6 y = 2.38
For the following graph, determine C if x = 2, if x = 12.
Plot the following data on rectangular coordiantes and semilog graph paper. Pick two points on each graph and determine the slope of the line. Compare the slopes; are they the same? What is the initial concentration when time equals “0”?
Most of the mathematics needed for pharmaco*kinetics and other calculations presented in this book may be performed with pencil, graph paper, and logical thought processes. A scientific calculator or computer software program with logarithmic and exponential functions will make the calculations less tedious. Special computer software (see Appendix B) is available for disease state calculations in clinical pharmaco*kinetics. Spreadsheet software, such as EXCEL® (Microsoft), can also be used for many pharmaco*kinetic calculations and for graphing data. A small manual scientific calculator can also be used for many pharmaco*kinetic calculations.
Students often ask why they should learn to calculate pharmaco*kinetic problems manually if software is available. Computer software is a tool that allows one to solve more complex pharmaco*kinetic problems rapidly, but efficient use requires a thorough understanding of the subject. Many different pharmaco*kinetic ...
FAQs
Pharmaco*kinetics is the study of the way in which the body handles administered drugs. The use of mathematical models allows us to predict how plasma concentration changes with time when the dose and interval between doses are changed, or when infusions of a drug are used.
What is the formula for Ka in pharmaco*kinetics? ›
The absorption rate constant Ka is a value used in pharmaco*kinetics to describe the rate at which a drug enters into the system. It is expressed in units of time−1. The Ka is related to the absorption half-life (t1/2a) per the following equation: Ka = ln(2) / t1/2a.
What are the fundamental of pharmaco*kinetics? ›
An understanding of 4 fundamental pharmaco*kinetic parameters will give the toxicologic pathologist a strong basis from which to appreciate how pharmaco*kinetics may be useful. These parameters are clearance, volume of distribution, half-life, and bioavailability.
How do you calculate C0 pharmaco*kinetics? ›
If two concentrations have been determined, a line containing the two values and extending through the y-axis can be drawn on semilog paper. The point where that line crosses the y-axis gives an estimate of C0.
How do you calculate t1 2 pharmaco*kinetics? ›
The half-life (t1/2) is the time it takes for the plasma concentration of a drug or the amount of drug in the body to be reduced by 50%. The half-life of a drug can be determined using the following equation: t1/2 = (0.7 x Vd) / Cl, where Vd is volume of distribution and Cl is clearance.
What math skills are used to determine medical dosing? ›
Pharmacology uses the metric system, so most dosage instructions refer to milligrams per kilogram (mg/kg) of body weight. However, most American doctors measure patients' weight in pounds. Doctors must convert mg/kg to milligrams per pound, which requires working knowledge of: Ratios or fractions.
What does F mean in pharmaco*kinetics? ›
F represents the bioavailability of drug (IV administration = 1)
How do you calculate bioavailability? ›
- Equation 1: Vd = total amount of drug in the body ÷ plasma drug concentration. ...
- Equation 2: F = mass of the drug delivered to the plasma ÷ total mass of the drug administered. ...
- Equation 3: F = AUC for X route of administration ÷ AUC for IV administration.
The absorption rate is used in the real estate market to evaluate the rate at which available homes are sold in a specific market during a given period. It is calculated by dividing the number of homes sold in the allotted period by the total number of available homes.
What are the 4 pillars of pharmaco*kinetics? ›
This is closely related to but distinctly different from pharmacodynamics, which examines the drug's effect on the body more closely. This field generally examines these four main parameters: absorption, distribution, metabolism, and excretion (ADME).
There are four main components of pharmaco*kinetics: liberation, absorption, distribution, metabolism and excretion (LADME). These are used to explain the various characteristics of different drugs in the body.
Is pharmaco*kinetics hard? ›
Students, however, experience pharmaco*kinetics as difficult, probably due to its abstract and mathematical nature.
What is k0 in pharmaco*kinetics? ›
k0= the drug infusion rate (in amount per unit time, such as mg/h or μg/min).
What is C min in pharmaco*kinetics? ›
Cmin is a term used in pharmaco*kinetics for the minimum blood plasma concentration reached by a drug during a dosing interval, which is the time interval between administration of two doses. This definition is slightly different from Ctrough, the concentration immediately prior to administration of the next dose.
How do you calculate CSS in pharmaco*kinetics? ›
*If the infusion is allowed to continue until steady state is achieved, the steady-state concentration (Css) can be calculated easily: Css = k0 / Cl = k0/ (keV).
What is the importance of mathematics in pharmaceutical calculations? ›
You must know your measurements and how to arrive at them. Since medicine is about providing patients with the right dose, you MUST know how to get the right dose. An error in math, no matter how small, can lead to serious illness, injury, or even the death of a patient.
Why do pharmacists use math? ›
Yes, pharmacists use math, particularly basic arithmetic and algebra, to accurately measure and weigh drugs. In addition to measuring drugs, many pharmacists also use mathematics in other tasks, such as calculating drug dosages, evaluating the cost of drugs and preparing financial spreadsheets.
Does pharmaceutical scientists use math? ›
To become a pharmaceutical scientist, you must have a strong interest in mathematics, biology, chemistry and the scientific process. You may want to decide early on which aspect of the drug development cycle you want to focus on – discovery, development or manufacturing.
What is the mathematical model of drug abuse? ›
Using numerical simulation the dynamical behavior of the model is explored and the result shows the significant contribution by the rate of adequate contact between the susceptible individual and the drug user, and the rate of recovery of drug user after rehabilitation as the major factors or players that dictate the ...
