OUTFLOW
I
The Retinal Circulation
If it is to serve its function as the organ of vision,
the eye must have sufficient rigidity to maintain a clearly
focused image, sufficient strength to survive significant
trauma and a sufficiently low rotational inertia to
facilitate rapid and accurately controlled movements. These
specifications are met with a tough, inelastic fluid filled
sphere. Since the tissues within the eye are metabolically
active, they require nourishment, hence the inflow of fluid.
The fluid that enters the eye must also drain from it, and
into a tissue environment whose pressure is lower than that
of the eye. This circumstance defines an important problem
in ocular biophysics: how fluid may escape from the eye in
so controlled a fashion that the reservoirs essential to the
integrity of the eye should not be emptied in the process.
Glaucoma, both in its genesis as an impairment of aqueous
outflow and in its consequence of optic excavation and
atrophy, is a disease that reflects the imperfect solution
to this problem. A control mechanism for outflow is not
unique to the aqueous circulation. Drainage of blood from
the retina and the choroid is similarly controlled. Perhaps
if we can gain some understanding of these latter, more
readily observable circulations, we will have a better idea
of the nature of outflow obstruction in glaucoma.
The three circulations all have the same origin and the
same destination. They all arise from the arterial blood
stream in the ophthalmic artery, and they all drain into the
venous bed of the ophthalmic vein. The central retinal
artery branches from the ophthalmic artery within the
substance of the optic nerve, but the choroidal and aqueous
circulations share the ciliary arteries as a common pathway
to the capillaries of the ciliary body, at which point the
aqueous is discharged into the vitreous cavity. Since the
similarities between the outflow mechanisms of these three
circulations are inapparent, we shall review them in greater
detail.
FIGURE 1 - When a force F is applied to a solid, such as a
rubber band, of length l and cross-section A, which is
tethered at one end, there is induced in the solid a stress
equal to F/A. As a result of this stress, the solid expands
by some small amount dl. The stress F/A divided by the
fractional increase of deformation dl/l is called Young's
modulus, and the fact that for small amounts of deformation
it is a constant is a rule known as Hooke's law. At the
same time that the solid expands in the direction in which
the force is applied, it contracts laterally. The ratio of
these two deformations is called Poisson's ratio. For
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example, Young's moduli for rubber, aluminum and steel are
.0001, 7 and 22 all as 10e+11 dynes/sq. cm. respectively,
and the corresponding Poisson's ratios are .49, .13 and .28.
(Handbook of Physics, Condon and Odishaw, N.Y. 1958)
It is the retinal circulation which is most easily
studied. One needs only an ophthalmoscope to observe the
pattern of arteries and veins on the disc and in the retina.
Fluorescein angiography provides additional insight, but in
the decade that it has been in use, it has received no
systematic fluid dynamic interpretation, a circumstance
which is not surprising, if one considers that through more
than a century of ophthalmoscopic observations their
implications in terms of fluid mechanics have been largely
ignored.
FIGURE 2 - This cylinder serves as a model for a blood
vessel. IP, the intravascular pressure is equal to the
arterial, capillary or venous pressure as the case might be.
EP is the external pressure and, if the blood vessel is
within the globe, is equal to the intraocular pressure. A
pressure is a force acting in a fluid and is transmitted
equally in all directions. A stress is a force within a
solid and its effect depends upon the shape of the solid.
The pressure differential EP - IP induces stresses in the
cylinder which are conveniently described as radial stress
rs, circumferential cs, and longitudinal ls. If IP is
greater than EP, the radial stress will be compressive and
the wall of the cylinder will become thinner as IP
increases, while the circumferential and longitudinal
stresses will be tensile, tending to expand and to lengthen
the cylinder. __________________________________________
Let us in our imagination accompany a small quantity of
blood as it courses from the ophthalmic artery into the eye.
The relative thinness of the arterial wall reflects the
circumstance that it is supported externally by the
intraocular pressure. The stresses that arise in the vessel
wall are induced by the difference between the extravascular
and the intravascular pressures, a fact from which one might
infer that the glaucomatous eye with poorly controlled
intraocular pressure might be less susceptible to the
ravages of arterial hypertension. This surmise from the
armchair, to my knowledge, is still awaiting clinical
investigation. An increase in intraocular pressure has
little if any effect on the pressure gradient across the
walls of capillaries or veins because as intraocular
pressure rises or falls so does the pressure in the veins,
and to a lesser extent in the capillaries, so that the
difference between intravascular and extravascular pressure
of these vessels remains approximately unchanged. Palpation
of the carotid arteries in the neck demonstrates how
pulsatile flow rhythmically distends the elastic media of
the arterial wall. It is easily confirmed with
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ophthalmodynamometry that at least in the large arteries
within the globe this pulsatile flow persists. If pulsation
is not visible, this fact must mean that the elastic modulus
of the arterial wall is sufficiently great that the stresses
which the arterial pulse induces in the arterial wall lead
to no visible displacement of tissue.
__________________________________________ FIGURE 3 - The
deformation sustained by an elastic cylinder under increased
internal pressure IP will depend not only on Young's modulus
and Poisson's ratio but also on whether it is isotropic or
anisotropic. Isotropia and anisotropia are terms used to
designate respectively equality and inequality of
coefficients of elasticity in the three spatial dimensions.
An elastic cylinder A) which is tethered at both ends and
subjected to increased internal pressure may, depending on
the relative values of its elastic moduli in the radial,
circumferential and longitudinal dimensions sustain B)
dilation only, C) elongation with narrowing of the lumen, or
D) dilation and elongation combined. Because its ends are
tethered, elongation makes the cylinder tortuous.
__________________________________________
An increase in intravascular pressure also brings about
increased stresses in the vessel wall parallel to the
direction of flow. The effect of these stresses depends
upon the relative value of the circumferential and
longitudinal elastic moduli. Whereas the metallic vessels
considered in engineering are isotropic, their
circumferential and longitudinal elastic moduli being equal,
isotropy is hardly to be expected in blood vessels, each of
whose multiple layers is composed of different cells with
different geometric orientations. If the elastic modulus of
the vessel wall parallel to the axis of flow is relatively
low as compared with that at right angles, then with an
increase in intravascular pressure, one might expect not a
dilation but a constriction of the lumen. This physical
fact should be considered as a partial explanation for the
progressive nature of vascular hypertension. Thus when
increased pressure in the retinal arteries is the result of
systemic hypertension, one observes constriction of the
vessel rather than dilation to accompany its tortuous
lengthening. A different set of circumstances obtains,
however, if there is an occlusion of the central retinal
vein or one of its branches. The blockage of flow will
bring about an increase of the intravenous and
intracapillary pressures to approach the value of the
arterial pressure as a limit. The consequence of this fluid
dynamic change is dramatic and is easily observed with the
ophthalmoscope. The increased stress that is perpendicular
to the axis of flow leads to dilation of the vessels. The
veins become engorged, while the capillaries assume an
irregularly contoured dilatation to which the adjective
telangiectatic is sometimes applied. There is often
lengthening of retinal veins upstream from the site of
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partial occlusion. Such veins, being tethered at intervals
and therefore unable to expand longitudinally, become
tortuous. The veins thus elongated do not become narrow
because the circumferential stresses induced by lengthening,
which tend to constrict the vessel lumen, are more than
offset by opposing stresses that tend to cause dilation of
the vessel.
The pressure in the retinal veins, as is well
understood, is transmitted from the arterial tree through
the capillaries. Upstream from the disc, the venous
pressure is slightly higher than intraocular pressure.
Downstream from the disc, it is low, approximating the
negligible venous pressure of the other cephalic veins. It
is on the disc itself that there occurs, visible to the
ophthalmoscope as a collapse in the vessel wall, a
precipitous drop in the venous pressure. This biologic
pressure-reducing valve is able to compensate not only for
fluctuations in the intraocular pressure, but also to a
large extent for variations in the flow rate. If, however,
as a result of partial arterial or arteriolar obstruction,
the flow rate diminishes beneath a critical point, then the
discharge from the capillaries will no longer be able to
distend the veins, the large veins of the entire fundus
collapse, and as they do so, their cross-section changes.
They become more and more elliptical until, just before flow
ceases entirely, they take the shape of a broad thin ribbon.
The orientation of this ribbon determines how the collapsed
vein appears through the ophthalmoscope. If the edge of the
ribbon faces the observer, it looks like a narrow thread.
If its breadth faces him, it appears as a broad band, which
is often misinterpreted as congestion whereas just the
opposite is the case.
FIGURE 4 - The vein at A is normally distended with blood
forced into it from the capillary bed. The vein at B is
partially collapsed because the rate of flow is insufficient
to keep it distended. Such partial collapse occurs when
there is arteriosclerotic narrowing of the carotid,
ophthalmic or retinal arteries and in hypertensive small
vessel disease. As the vein collapses the area of its
cross-section decreases but the circumference remains
unchanged. If as is usually the case, the long axis of the
collapsed vein is parallel to the surface of the globe, the
vein, although it in fact contains less blood, will appear
wider. A totally collapsed vein is 1.57 times as wide as a
fully distended vein. An increased ratio of the width of
the vein to that of the accompanying artery has long been
recognized as a sign of arteriosclerotic disease but the
explanation that such widened veins are not distended but
flattened, and that the widening reflects a decrease in the
flow rate, has not, to my knowledge, appeared in the
literature. Infrequently the vein collapses with its long
axis radial to the globe. It then appears narrow to the
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point of being thread-like.
__________________________________________
In general, when the vein collapses from intraocular
pressure in the face of insufficient filling, it forms a
ribbon whose breadth is tangential to the globe. This
circumstance is the primary cause of the increased V/A ratio
long recognized as a stigma of arteriosclerotic and
hypertensive vascular disease. In that condition, not
enough blood is transmitted through the capillary bed to
keep the cross-section of the vein circular. Instead, it
becomes elliptical, and the major axis of the ellipse is
seen as a broadening of the vein. It represents not, as one
might assume, an increase, but a decrease in volume.
At A-V crossings, however, the vein is bound to the
artery by a common sheath of adventitia. A collapse of the
vein in a plane tangential to the globe would entail a sharp
outward deflection of the overlying artery. Perhaps the
artery is too stiff to permit such a deflection. In any
event, it is the failure of the vein to flatten in the
tangential plane that creates the appearance of relative
constriction at the A-V crossing. Sometimes radially
oriented collapse occurs at the A-V crossing. Then the
narrow side of the band only is visible to the observer,
giving the vein the appearance of having been choked off by
the artery. Paradoxically, flattening of the vein is not
likely to be associated with permanent occlusion. So long
as only a small fraction of the total flow resistance is
attributable to the collapsed vein, the velocity of flow
will be approximately inversely proportional to its cross-
section. The smaller the vessel lumen, the greater the
velocity of flow at any given point. Thus, so long as flow
is not entirely stopped, one would not expect vein collapse
to predispose to thrombus formation. On the contrary, if
the vein were held open by a rigid frame that
prevented it from collapsing, as is probably the case at
some A-V crossings, then with decreasing flow, there would
develop in the vein just under the artery a pool of stagnant
blood to serve as a nidus for thrombus formation. And it
seems indeed to be the case that the occlusive thrombus of
branch vein occlusion often propagates from just this point.
__________________________________________ FIGURE 5 - At
points 1 and 2 the vein A is collapsed from lack of flow.
As it passes under the artery at 3, the vein seems to be
constricted, a phenomenon referred to as A-V nicking.
* * * * *
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Copyright 2006, Ernst Jochen Meyer