Anomalous diffusion with absorption: exact time-dependent solutions

Diffusion is the passive movement of substances down their concentration gradients—requiring no expenditure of cellular energy. Substances, such as molecules or ions, diffuse from an area of high concentration to an area of low concentration in the cytosol or across membranes. Eventually, the concentration will even out, with the substance moving randomly but causing no net change in concentration. Such a state is called dynamic equilibrium, which is essential for maintaining overall...

Diffusion is a type of passive transport. In passive transport, a substance tends to move from an area of high concentration to an area of low concentration until the concentration is equal across the space. For example, take the diffusion of substances through the air. When someone opens a perfume bottle in a room filled with people, the perfume is at its highest concentration in the bottle and is at its lowest at the edges of the room. The perfume vapor will diffuse, or spread away, from the...

Passive diffusion is a critical process that allows small lipophilic drugs to cross the cell membrane along a concentration gradient. This mechanism's efficiency depends on four primary factors: the membrane's surface area, the drug's lipid-water partition coefficient, the concentration gradient, and the membrane's thickness.
When administered orally, drugs establish a substantial concentration gradient between the gastrointestinal (GI) lumen and the bloodstream, expediting their diffusion into...

Various dissolution theories provide insight into the factors that influence the dissolution rate. Danckwerts' Model suggests that turbulence, rather than a stagnant layer, characterizes the dissolution medium at the solid-liquid interface. In this model, the agitated solvent contains macroscopic packets that move to the interface via eddy currents, facilitating the absorption and delivery of the drug to the bulk solution. The regular replenishment of solvent packets maintains the concentration...

The first-order absorption model for extravascular administration describes the rate at which a drug is absorbed and eliminated, following the principles of first-order kinetics. This model is vital as it provides a mathematical representation of drug behavior within the body. It also allows for the prediction and interpretation of drug absorption and elimination based on the rate of change in drug concentration over time. This model can be visualized as a plasma concentration-time profile...

When drugs are administered extravascularly, a comprehensive evaluation through noncompartmental analysis becomes imperative. This analytical approach considers various parameters that play a crucial role in understanding the pharmacokinetics of these drugs.
One of the key parameters is the mean transit time (MTT), which refers to the total duration required for drug molecules to transit through the body. MTT is determined by calculating the ratio of the area under the moment curve to the area...