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COPYRIGHT
Prof. Beyenbach
Mammalian Physiology BIOAP 4580
2011
DIFFUSION
1) Fundamental equations in physiology.
There are two basic concepts that describe physiological processes suitable for quantitative
treatment.
One concept relates one force to another, as for example the Nernst equation
which equates a concentration difference of an ion (a chemical force) with a voltage
(electrical force), akin to exchanging $ for Euro or Yen.
Eq. 1 is the Nernst equation that
states the equivalence of a chemical concentration ration and a voltage.
Force = Force,
(eq. 1)
where V is the voltage, [
] indicates the concentration of the ion of interest in compartments
1 and 2, and where R, T, z, and F have their usual meaning: gas constant, temperature,
valence of ion, and Faraday constant, respectively.
Other examples of conversions abound:
hydrostatic pressure/osmotic pressure, volume/size, specific gravity/osmolarity,
calories/joules, pressure/tension, etc.
The other equation sets flow proportional to a driving force, where the driving force can be a
concentration difference.
In particular, a chemical concentration difference drives diffusion;
a voltage difference drives current.
In both cases, the fundamental equation relates potential
energy (a force) to kinetic energy (a movement).
The equation comes in many variations of
the same theme:
Kinetic Energy =
(k) ∆Potential Energy
Movement = (k) ∆Force
where k is a proportionality constant: a hydraulic conductance, an electrical conductance, or
a permeability, and ∆Force is the difference between two forces.
One well known example
relates flow to pressure proportional to the constant k.
Flow = (k) ∆Pressure, where flow takes place from a high pressure to a low
pressure;
(Poiseuille equation)
(eq. 2)
where BP is the blood pressure.
Note that the constant k includes 1) the radius r and the
length (L) of the blood vessel, and 2) the viscosity (η) of blood.
Together these variables
combine to yield the hydraulic conductance g
h
= k.
In general, conductance is the inverse of
resistance, which is best illustrated in Ohm’s Law.