Biomedical Engineering Reference
In-Depth Information
loading frequencies, 1.5 and 15 Hz, are illustrated by plotting the transcortical
interstitial pore fluid pressure differences at these frequencies. This panel also
illustrates the effect of frequency on the interstitial pore fluid pressure gradients.
The PLC is the porosity associated with the osteocytes that are the prime candidates
for the mechanosensory cell in bones because of the fluid movement induced by
the interstitial pore fluid pressure gradients [1-4]. The bone fluid in the smallest
porosity, the collagen-hydroxyapatite porosity, is considered to be immovable
under normal conditions, because it is bound to the collagen-hydroxyapatite
structure.
Over the last 40 years, many researchers have used tracers to document bone fluid
transport [37, 45, 61, 63, 68, 70, 79, 80] (S.D. Doty, 1997, Private communication);
see [70] for a summary of the tracers employed. An excellent recent summary of
these efforts is given by Fritton and Weinbaum [4]. These tracers show that the
normal bone fluid flow is from the marrow cavity to the periosteal lymphatic vessels
through the Volkmann and Haversian canals. The flow passes from the Haversian
canal into the PLC to the cement line of the osteon.
9.8.3
Electrokinetic Effects in Bone
Electrodes placed on two different bone surfaces will measure a difference in
voltage when wet bones are deformed. These voltages are called strain-generated
potentials (SGPs). SGPs in wet bone are now recognized as dominantly
electrokinetic phenomena explained by an extension of poroelasticity. From an
experimental viewpoint, SGPs are a significant technique for the investigation of
the poroelastic behavior of the bone. The source of SGPs stems from the fact that
the extracellular bone matrix is negatively charged due to negative fixed charges on
carbohydrates and proteins; thus, a fluid electrolyte bounded by the extracellular
matrix will have a diffuse double layer of positive charges. When the fluid moves,
the excess positive charge is convected, thereby developing streaming currents
and streaming potentials. The fluid motion is caused by the pore fluid pressure
gradients induced by the deformation of the extracellular matrix due to whole bone
mechanical loading. Pollack and coworkers [81-83] have laid an important foun-
dation for explaining the origin of SGPs. The foundation is based on poroelasticity
and begins with the fluid movement in the bone channels convecting the charge
accumulated in the diffuse double layer of positive charges. The charge distribution
in the channel is determined from the linear Poisson-Boltzmann equation.
The electrical potential attenuates exponentially with distance into the fluid,
perpendicular to the charged surface, divided by
λ
,where
λ
is the Debye length
characterizing the diffuse double layer. The typical Debye length
for normal
physiological saline is 1 nm or less; hence, the decay of the potential with respect to
distance from the surface is very rapid. The total streaming current vector per unit
area
λ
passing through all the channels of a material because of the pressure-driven
axial flow can be obtained by multiplying the charge density by the local velocity
field in the channel and integrating this result over the cross section of the channel.
j
