## Journal of mathematical sciences

Schematic of relationship between pharmacokinetics and pharmacodynamics (1). For a drug to have an effect, excepting by **journal of mathematical sciences** or intraarterial administration, it must navigate at least one membrane (Fig.

There are different mechanisms by which a drug is transported across a biologic membrane (3). Passive (simple) diffusion requires a degree of lipid solubility to cross the phospholipid bilayer and moves using the concentration gradient until equilibrium is reached. Facilitated diffusion requires no energy, nor can it move against a concentration gradient, but the drug sufficiently resembles the natural ligand to bind to the carrier macromolecule and traverse **journal of mathematical sciences** membrane.

Other carrier-mediated transport mechanisms exist that are nonspecific drug transporters, such as P-glycoprotein. Pinocytosis incorporates the drug into a lipid vesicle for carrier-mediated transport into the cell cytoplasm. Transport through pores or ion channels can occur with the concentration gradient for small water-soluble drugs. Schematic of pharmacokinetics and absorption, distribution, metabolism, and excretion concept (A), and same schematic highlighting interplay between free and bound **journal of mathematical sciences,** and pathway from site of administration to site of **journal of mathematical sciences** (B).

Absorption and the factors that may impede it directly affect drug bioavailability. This assumes drugs reach the site of action directly from systemic circulation.

Orally (enterally) administered medication is the simplest **journal of mathematical sciences** most common route but may have variable bioavailability depending on many factors that influence drug absorption, including molecular size of the **journal of mathematical sciences,** lipid solubility of the drug, degree of ionization of the drug, dosage form (e. Oral administration is simple, convenient, and painless, allowing self-administration of drugs in easily handled forms.

Gastrointestinal absorption means that the drug is transported via the portal system to the liver and undergoes first-pass metabolism.

First-pass metabolism may render some of the drug inactive, decreasing bioavailability. Mucous membranes are highly vascular, allowing rapid entry of the drug into the systemic circulation.

This route avoids first-pass metabolism and the hostile gut environment. In some cases, the drug can be delivered directly to the site of action (e. Direct parenteral injection of drugs (e. The degree of vascularity affects the onset of action, with a slow onset from subcutaneous administration, an intermediate onset from intramuscular administration, and a rapid onset from intravenous administration.

Parenteral administration affords the greatest control over drug delivery and includes intravenous, intraarterial, intramuscular, subcutaneous, intraperitoneal, and intrathecal routes. Transdermal and percutaneous administration requires passive diffusion of highly lipophilic drugs across the skin. This approach provides a slow onset of action and the potential for slow, continuous drug delivery (e. The drug needs to be distributed to **journal of mathematical sciences** site of action in sufficient concentration to generate the therapeutic action.

Distribution **journal of mathematical sciences** involves the circulatory system (including some minor lymphatic involvement), which distributes drugs **journal of mathematical sciences** all tissues except brain and testes (because of membrane barriers). Consequently, relative blood flow to tissues will affect the dose required. Using simple diffusion after intravenous injection as an example, the initial high plasma concentration reaches equilibrium after rapid entry into cells with high perfusion.

Poorly perfused tissues will continue to concentrate the drug and thus decrease plasma concentrations. In turn, the high concentrations of drug in well-perfused tissues will decrease the time to reach equilibrium across the membranes (Fig.

Given that the tissue concentration of a drug is difficult to measure, plasma concentration is used to estimate tissue concentration (6). Major factors that affect the distribution of drugs include diffusion rate, affinity of the drug to the tissues, blood flow (perfusion), and binding to plasma proteins.

Schematics of equilibrium between drug concentration and plasma, well-perfused tissue, and poorly perfused tissue. Set of 3 schematics at top does not incorporate effects of metabolism or elimination but illustrate early equilibrium in well-perfused tissue (A) followed by period of concentration in poorly perfused tissues (A to B) before reaching equilibrium in all tissues and plasma (B).

Set of 3 schematics at bottom provides phases as **journal of mathematical sciences** intervals (straight line) and illustrates impact of elimination. Within the blood, a drug may have an affinity to plasma proteins, typically intracellular proteins, albumin, and glycoproteins (3,6). For drugs with a large amount of plasma protein binding (e.

There is, however, competition for plasma binding that can have significant implications for drug effects. For example, if ibuprofen were **journal of mathematical sciences** through competition, the result would be significantly higher **journal of mathematical sciences** drug in tissue and blood.

Aspirin and warfarin compete for the same plasma protein binding sites, and thus, coadministration potentiates the effects of the two (3,6). A small number of drugs may bind irreversibly to plasma proteins via covalent bonding. As a result, bound drug is not released in response to decreasing plasma or tissue concentrations.

An important concept for pharmacokinetic principles and calculations is the volume of distribution, which cloderm the amount of drug administered divided by the plasma concentration of the drug.

This volume represents the distribution of the drug between plasma and tissue compartments (2,3,6). For example, a 70-kg person might be expected to have less than 70 L of volume throughout the body, yet a volume of distribution for a given drug might exceed several hundred liters. A volume of several hundred liters is clearly not possible in a 70-kg person but allows a theoretic understanding of drug behavior.

When the volume of distribution is high, it reflects a relatively low drug concentration in plasma (minimal plasma protein binding) and extensive distribution through body tissues. The volume of distribution is used as a principle for compartment modeling and in pharmacokinetic calculations, but it is not an actual physical volume. Compartment modeling is used in pharmacokinetics and radiopharmacy dexcom g5 mobile simplify understanding of the relationship between drugs or radiopharmaceuticals and their distribution within the body.

In each compartment, a drug may be present in either bound or free forms, and it is the free form that can move from one compartment to another l s d. Movement between compartments can be measured and expressed as a rate constant.

For simplicity and depending on what is being modeled, compartment modeling may use single, double, or multiple compartments (Fig. Schematic of 1-compartment model, 2-compartment model, and multicompartment model. Elimination rate constant reflects movement journal of volcanology and geothermal research one compartment or volume of distribution to another and can be calculated numerically.

Schematically, rate constant may be represented in several ways. In multiple-compartment model, k5 and k6 have arrows of different sizes, indicating greater movement of drug to tissue compartment than from it.

Likewise, for k7 and k8, double-head arrow with different sizes of arrowhead is used to represent relative k values. When drug transport between compartments is not reversible, single-head arrow is used (k9).

Further...### Comments:

*11.05.2019 in 18:26 Максимильян:*

Вы попали в самую точку. В этом что-то есть и идея хорошая, согласен с Вами.

*12.05.2019 in 21:36 Клементина:*

Ошибаетесь.

*14.05.2019 in 15:31 Мелитриса:*

Ваши записи произвели на меня огромное впечатление, заставили думать по-другому. Продолжайте свои творческие поиски, а я буду следовать за Вами!

*15.05.2019 in 04:42 nungrinlo:*

Невероятно. Просто в шоке сижу. Все гениальное просто