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Encyclopedia of Physical Science and Technology EN011J-559 July 25, 2001 18:57

808 Pharmacokinetics

separated by the cell membrane, which is typically a lipid
bilayer with low permeability to water or water-soluble
molecules. Lipid-soluble molecules will therefore trans-
port across such barriers more rapidly than substances
which have very poor solubility in lipid. The relative sol-
ubility of a substance is often defined as the partition co-
efficient, which is the ratio of the solute’s concentration in
octanol to its concentration in a water-based buffer. The
stomach mucosa and the epithelium of the colon display
the property of increasing transport rates with increasing
lipid solubility. However, mammalian epithelia such as
the rat intestine demonstrate a maximal rate of transport
at a partition coefficient between 10 and 20 because of an
unstirred fluid layer which is maintained by the microvilli
coating the epithelia. In human skin, the partition coeffi-
cient for optimal rates of transport appears to be between
FIGURE 4 Transport mechanisms across biological barriers. 200 and 250.
Most drugs diffuse down their concentration gradient at a rate
Convection is a process by which a substance is dragged
defined by the product of the diffusion coefficient D, the area A,
along by the flow of fluid; hence the term solvent drag is
and the concentration gradient dC/dx. A second passive mech-
used to describe this type of transport. The flow is powered
anism is convection or solvent drag, which moves a solute at the
effective solvent flow rate Q according to the existing pressure by osmotic or hydrostatic pressure gradients which exist
gradient. Active transport requires energy to move solutes in a across tissue boundaries. The kidney is an example of an
direction opposite to the electrochemical gradient. organ which depends on hydrostatic pressure-driven con-
vection for filtration of substances by the glomerulus and
osmotic-pressure driven convection for solute reabsorp-
barrier; A is the area of barrier exposed to the drug; and
tion in the proximal tubule. Filtration and reabsorption by
dC/dx is the concentration gradient within the barrier.
blood capillaries depends on Starling’s relationship:
Often, it is impossible to define A or the relationship
between C and the distance x within the barrier, and the

transport is described by the expression
fluid flux = L p (P 1 − P 2 ) − σ i (π i,1 − π i,2 ) , (7)
rate or mass transfer = PA(C 1 − C 2 ), (5) i
where PA is the mass transfer–area coefficient, which where L p is the hydraulic conductivity of the barrier; P j
lumps the effective area and apparent permeability of the is the hydrostatic pressure in compartment j; σ i is the
barrier to the solute; C i is the concentration in each com- reflection coefficient of solute i; and π i, j is the osmotic
partment. Often the concentration in the “receiving com- pressure exerted by solute i in compartment j. A solute
partment” or C 2 is unknown, and PA is termed a clearance with σ i = 1 does not cross the barrier and exerts its full
term, defined by the rate of solute loss from the originating osmotic force on the barrier. If σ i = 0, the solute exerts no
compartment to the receiving compartment divided by C 1 . osmotic force across the barrier.
A special form of passive transport is carrier-mediated Molecular size has a significant effect on the rate of
transport, which is important in the handling of urea transport across biological barriers. Smaller substances
by the kidney and in the absorption of certain solutes from such as urea or glucose transport across membranes
the intestine. The general expression for carrier-mediated rapidly via carriers or pores. While substances with molec-
transport is defined by the typical equation for enzyme ular weights greater than 1000 Da transport easily across
kinetics endothelia of most tissues, they are typically absorbed
V max C across epithelia very slowly. In the absorption of drugs,
transport rate or reaction rate = , (6) proteins, or peptides, pinocytosis or phagocytosis may
K M + C
play a role: Pinocytosis is the process by which the cell
where V max is the maximal rate of transport or chemical engulfs material in the fluid external to the cell and trans-
reaction, K M is the concentration at which the rate is one- portsitintothecell,whereitmaycombinewithalysosome
half maximum, and C is the concentration. and be metabolized; phagocytosis is the process by which
Compartmentsinanorganismconsistofvolumesofwa- resident macrophages and leukocytes take up and digest
ter in which substances are in solution. Compartments are solid material or particles.