M1L2L3L4: Mathematical Fundamentals in Pharmacokinetics; Drug Concentration and Its Significance; Drug concentration and its significance

Rate of Dissolution

The amount of drug (X) dissolving per unit time (t), typically in mg/s

Diffusion Coefficient

Tells how easily the drug molecules move through the liquid. A higher D means the drug can spread out faster.

Diffusion Layer Thickness

The thickness ofbthe stagnant layer of liquid around the dissolving particle. A thinner layer means the drug can escape faster into the bulk liquid.

Saturation Solubility

The maximum concentration of drug that can dissolve in the solvent - like the drug’s limit

Bulk concentration

The current concentration of the drug in the surrounding solution. If C2 is close to C1, dissolution slows down.

differentiation

breaking process down to look at the instantaneous process

integration

sums up the information from small time intervals to give a total result over a larger time period

Trapezoidal Rule

Numerical method frequently used in pharmacokinetics to calculate the area under the plasma drug concentration versus time curve, called the area under the curve (AUC)

chromatographic and mass spectrometric methods

most frequently employed for drug concentration measurement

Invasive methods

method : sampling blood, spinal fluid, synovial fluid, or any biological material requiring parenteral or surgical intervention in the patient

Non-invasive method

method: sampling of urine, saliva, feces, expired air, or any biological material obtained w/o parenteral or surgical intervention

most direct approach

measurement of drug and metabolite concentration (levels) in the blood, serum, or plasma is the ___ to assessing the pharmacokinetics of the drug in the body

plasma

the liquid supernatant obtained after centrifugation of non-clotted whole blood that contains an anticoagulant

albumin

plasma that binds acidic drug

alpha 1 acid glycoprotein

plasma that bind basic drug

whole blood

generally obtained by venous puncture and contains an anticoagulant such as heparin or EDTA

serum

liquid obtained from whole blood after the blood is allowed to clot and the clot is removed

plasma

the liquid supernatant obtained after centrifugation of non-clotted whole blood that contains an anticoagulant

fibrinogen

serum does not contain the cellular elements, __ or the other clotting factors from the blood

whole blood

contains all the cellular and protein elements of blood

plasma

noncellular liquid fraction of whole blood and contains all the proteins including albumin

plasma proteins

drugs in the plasma are often bound to plasma proteins, so __ are removed first from the plasma before drug concentrations are measured. the concentration obtained represent the unbound drug.

total plasma drug concentration

the one which has been measurd from unfiltered plasma.

plasma drug concentration-time curve

generated by obtaining the drug concentration in plasma samples taken at various time intervals after a drug product is administered

coordinate graph paper (or semilog paper)

plasma drug concentration (Cp) is plotted on rectangular __ versus the time

Maximum plasma drug concentration (Cmax)

measured the rate and extent of PK absorption

most variable

AUC

measure the extent of drug absorption

AUC

Consider the most important BA parameter

Minimum Effective Concentration (MEC)

the concentration of the drug in the blood that must be achieved to exhibit an adequate response

Minimum Toxic Concentration (MTC)

drug serum concentrations above this level would be expected to produce dose-related toxic effects

Therapeutic window

the concentration of the drug should be maintained between the MEC and the MTC to exhibit an adequate response and yet not to produce dose-related toxicities

Onset time

the time of the first observable effect, it can be viewed from the graph by noted the time where the plasma drug concentration reaches the MEC

Duration of action

observed from the onset time until such time that the plasma drug concentration is within the MEC line

AUC

represents the total amount of drug absorbed into the circulation following the administration of a single dose of the drug

rate

the rate of a chemical reaction is the velocity with which it occurs

order

the __ of a reaction is the way in which the concentration of a drug or reactant in a chemical reaction affects the rate

zero-order reaction

the drug concentration changes with respect to time at a constant rate

zero-order process

amount of drug eliminated for each time interal is constant, regardless of the amount of the drug in the body

zero-order proces

the amount of drug eliminated does not change with the amount or concentration of drug in the body, but the fraction removed varies

saturated

zero order elimination is rare mostly occuring when the elimination system is __

alcohol

example of zero order

first-order reaction

the drug concentration changes with respect to time equal the product of the rate constant and the concentration of drug remaining

first order kinetics

the rate of change of drug concentration by any process is directly proportional to the drug concentraiton remaining to undertake that process

directly proportional

in first-order elimination, the amount of drug eliminated in a set of time is __ to the amount of drug in the body. amount of drug eliminated may change with the amount of drug in the body, but the fraction of a drug in the body eliminated over a given time remains constant

first-order elimination kinetics

a linear process rate of elimination is proportional to the drug concentration

first-order elimination kinetics

the eliminatuin processes are not saturated and can adapt to the needs of the body, to reduce accumulation of the drug

95%

__% of the drugs in use at therapeutic concentrations are eliminated by first order elimination kinetics

multivitamin

example of first-order elimination drug

graphical method and half-life method

in the determination of the order of reaction, there two methods use:

t ½ (half-life)

generally, the dosing interval is the same as __

4-5 half-lives

during multiple dosing or continuous IV infusion it takes approximately __ to reach steady-state levels

96

all drugs are decreased by __% after 5 half lives

first-order half-life

no matter what the initial amount or concentration of the drug is, the time required for the amount to decrease by one half is constant

zero-order half life

non constant for a zero-order process

zero-order half life

is proportional the intiail amound or concentration of the drug is inversely proportional to the zero-order rate constant

Model

a mathematic description of a biologic system and is used to express quantitative relations only

compartment

a group of tissues with similar blood flow and drug affinity, but is not a real physiologic or anatomic region

compartment

used to characterize with reproducibility the behavior and the fate of a drug in biological system when given a certain route of adminsitration and in a particular dosage form

pharmacokinetic model

it is a hypothesis using mathematical terms to describe quantitative relationships

Pharmacokinetic parameter

- it is lonstant parameter or property of drug that is estimated from the experimental data (e.g., k, VD, CI).

Pharmacokinetic function -

mathematical equation that relates an independent variable (time) to a dependent variable (drug concentration), often through the use of parameters.

Emperical models

• Are focused on describing the data with the specification of veryfew assumptions about the data being analyzed

mechanistic models

specify assumptions and attempt to incorporate known factors about the sistems surrounding the data into the model, while describing the available data

1. physiologically based models

mechanistic models

1. catenary model

2. mamillary model

compartmentally model

physiologically based models

(model) there is a necessity to sample tissue and monitor blood flow to the liver in vivo

physiologic pharmacokinetic model (flow model)

are also known as blood flow or perfusion models

physiologic pharmacokinetic model (flow model)

are phrmacokinetic models based on known anatomical and physiologic data

Catenary model

consists of compartments joined to one another like the compartments of a train

Mamillary model

estimate the amount of drug in any compartment of the system after the drug is introduced into given compartment

1.one-compartment

2. two-compartment

mamillary model

one-compartment open model

simplest model

one-compartment open model

assumes that the body can be described as a single, uniform compartment and drugs can enter and leave the body

no

one-compartment by iv route has __ asorption

elimination rate constant

governs the rate at which the drug concentration in the body declines over time

volume of distribution

this describes how a drug distributes in the body compared to the blood

volume of distribution

it’s a theoretical volume that relates the amount of drug in the body to the concentration measured in the blood/plasma

drug clearance

refers to the voume of plasma fluid that is cleared of drug per unit time

slow distribution

model- slow distribution of drug between blood stream and tissue

method of residual

also known as feathering or peelimg

method of residuals

a useful procedures for fitting a curve to the experimental data of a drug when the drug doesnnot clearly follow a one-compartment model

IV infusion

maintains an effective constant plasma concentration of drugs with narrow therapeutic index by eliminating flunctuations between the peak and through

equal

at steady state plasma concentration , the rate of drug leaving the body is _ to the rate of drug (infusion rate) entering the body