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Description  |
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STATE OF THE ART
The detection of estrus in dairy cattle has been a serious problem for the
farmer. Failure to detect estrus at the proper time means delayed breeding
and long calving intervals, which result in a decreased production of milk
and beef. The problem is further complicated by the increase in herd size
where one man must observe more cows. In 1976, the New York Dairy Herd
Improvement's reports indicated that the average number of breedings per
conception for New York State herds was 1.6. These figures underestimate
the actual value because the cows sold for reproductive failure are not
included. A conservative average for the calving interval was 398 days
(not including cows culled because of extended periods of non-pregnancy).
Although milk production has increased because of larger herd sizes, the
above examples show that maximum efficiency has not been achieved. Better
heat detection techniques must be employed in order to reduce the calving
interval nearer to the expected optimum of 365 days.
Many reports have been published indicating that there are changes in the
concentrations of various ions (sodium chloride being a major one) in the
vaginal mucus at the time of estrus, and that these changes should be
detectable by measuring the electrical resistance (ER). Although many of
the reports recommend various devices to measure ER, none of them have
presented a fundamental explanation, either empirically or theoretically,
on how the devices "work". This explanation is important to the proper
design of the instrument. It must be sensitive enough to detect the change
in resistance but also must be designed in accordance with the cow's
physiology so as to give accurate measurements.
A ring probe for detection of estrus in cattle has been described by
Metzger et al, Zuchthyg., 7 56-61 (1972). The probe comprised ring
electrodes in a plane perpendicular to the longitudinal axis of the probe
body.
DESCRIPTION OF THE INVENTION
This invention is drawn to a bovine vaginal probe capable of measuring
electrical resistance in a bovine vaginal tract with sufficient accuracy
to allow detection of changes in electrical resistance indicative of
estrus.
The bovine vaginal probe of the invention comprises a non-conductive,
generally cylindrical support means having at least two electrodes
essentially parallel to each other and generally oriented to the
longitudinal axis of the support means, on the surface thereof near and
end of said support means adapted for insertion into a bovine vagina, said
electrodes being electrically connected to an ohm-meter which supplies an
AC voltage to the electrodes. In operation, the probe is inserted into the
vaginal tract of a bovine, e.g. a diary cow, and the electrical resistance
of the vaginal mucus is measured by the AC ohm-meter. As the resistance of
the bovine vaginal mucus fluctuates during the estrus cycle, the cycle can
be followed by repeated measurement. This provides a quick and easy method
for determining the time of estrus.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a general representation of a probe within the scope of the
invention.
FIG. 1-A is a detailed schematic view of the insertion end of a probe
showing electrode placement and wiring.
FIG. 2 is a representation of a probe in an idealized vaginal tract of a
cow.
FIG. 3 is a graph plotting probe sensitivity vs the angle between the
electrodes.
FIG. 4 is a representation of a probe having a finite electrode surface
area.
FIG. 5 is a representation of the electric field shell.
FIG. 6 is a representation of a ring probe in the vaginal tract of a cow.
FIG. 7 is a representation of a spiral electrode probe.
FIG. 8 is a diagram of the circuit for determining frequency effects.
FIG. 9 is a representation of the apparatus used for varying design
parameters.
FIG. 10 is a graph plotting resistance as a function of frequency for
different NaCl solutions.
FIG. 11 is a graph plotting resistance as a function of electrode length
for different thicknesses of 10.sup.-1 M NaCl.
FIG. 12 is a graph plotting resistance as a function of electrode length
for different thicknesses of 1 M NaCl.
FIG. 13 is a graph plotting resistance as a function of solution thickness
for different probe lengths and NaCl.
FIG. 14 is a graph plotting resistance as a function of electrode spacing
for the same length of electrode and thickness of solution.
FIG. 15 is a graph plotting resistance as a function of
##EQU1##
showing experimental validation of prediction equation.
FIG. 16 is a graph plotting resistance as a function of
##EQU2##
showing experimental validation of prediction equation.
FIG. 17 is a graph plotting resistance as a function of
##EQU3##
showing experimental validation of prediction equation.
FIG. 18 is a graph plotting resistance as a function of
##EQU4##
showing experimental validation of prediction equation.
FIG. 19 is a graph plotting resistance as a function of
##EQU5##
showing experimental validation of prediction equation.
FIG. 20 is a representation of the axially parallel electrode design with
four electrodes at 90 degrees.
FIG. 21 is a graphic representation of the values measured in Example 3,
Experiment I.
FIG. 22 is a graphic representation of the values measured in Example 3,
Experiment II.
FIG. 23 is a graphic representation of the values measured in Example 3,
Experiment III.
FIG. 24 is a representation of the probe employed in Examples 1 and 3.
DETAILED DESCRIPTION OF THE INVENTION
With reference to FIG. 1, the bovine vaginal probe of the invention
comprises a generally cylindrical support means formed from a
physiologically acceptable relatively non-conductive material, i.e. a
material havng a D.C. resistivity greater than 10.sup.10 ohm-cm. Many
common organic polymeric materials, both thermosetting and thermoplastic
are useful as the non-conductive material. Polymethylmethacylate casting
resins are particularly suited for use as a support means. The support
means is generally cylindrical and the preferred cross-section is
circular; however, generally cylindrical shapes such as those having oval
cross-sections can be employed so long as the shape conforms to the
vaginal tract and provides assured contact of the electrodes mounted
thereon with the vaginal walls. Secured to the surface of the support
means are one pair of electrodes 2 essentially parallel to each other, and
generally oriented to the longitudinal axis of the support means. In the
preferred embodiment the electrodes are essentially axially parallel. The
electrodes can be of any sufficiently conductive physiologically
acceptable material, e.g. metal, preferably stainless steel. The electrode
support means 1 has associated therewith an insertion means 4, i.e. an
extension which extends beyond the vaginal tract, after proper insertion,
to allow insertion into and extraction of the electrode support means from
the vaginal tract. As shown in FIG. 1, the extension means has a handle 5
attached thereto for ease of manipulation. While the extension means in
FIG. 1 is merely an elongation of the cylindrical electrode support means,
the support means need merely be of a length sufficient to carry the
electrodes and provide contact of the electrodes with the vaginal walls,
and the extension means associated therewith can be of any physiologically
acceptable configuration, and formed from a relatively non-conductive
material so as not to frustrate the functioning of the electrodes.
As shown in FIGS. 1 and 1A, the electrodes are electrically connected, e.g.
by means of wires, to an Ac ohm-meter which provides an AC current havng a
frequency between about 1 KHZ and about 1 MHZ and preferably between about
5 KHZ and about 100 KHZ at a voltage between about 1 vpp and about 10 vpp
and preferably between about 3 vpp and about 6 vpp (vpp=volts
peak-to-peak).
The electrodes are preferably as narrow as possible consistent with the
need for assured reproducible contact with the vaginal mucus, practically
the electrodes are usually between about 1/16" and about 1/2" wide,
preferably being between about 1/8" and about 1/4" wide. Likewise, the
electrodes are preferably as short as possible consistent with the need
for assured reproducible contact with the vaginal mucus practically the
electrodes are usually between about 1" and 4" long, preferably being
between about 2" and about 31/2" long.
In the essentially axially parallel electrode configuration, in order to
obtain the desired sensitivity where one set of electrodes are employed,
the electrodes should be separated from each other by at least 45.degree.
and preferably at least about 90.degree..
The minimum length of the electrode support means is the length of the
electrodes; generally the length of the support means is longer than the
electrodes to assure, good electrode-mucus contact and consistent
electrical measurements.
The diameter of the support means is at least sufficient to assure
consistent electrode-mucus contact, the maximum diameter being that
physiologically acceptable to the bovine.
Referring again to FIGS. 1 and 1A the insertion end of the probe preferably
has a rounded end 3 for ease of insertion.
While the essentially axially parallel electrode configuration is preferred
because of its sensitivity, the electrodes may be secured to the electrode
support means in a spiral parallel configuration, where as shown in FIG.
7, the angle of incidence to the longitudinal axis .alpha. is 45.degree.
or less. The smaller this angle the greater the sensitivity, keeping in
mind the separation angles required in the axially parallel configuration.
Thus, the terms generally axially aligned and generally aligned with the
longitudinal axis of the support means include the positioning of
electrodes parallel to or at an angle of less than 45.degree. from the
longitudinal axis of the support means.
As shown in FIG. 20, one preferred essentially axially parallel
configuration employes two sets of electrodes, each separated by
approximately 90.degree. so that two sets of resistance figures, ventral
and dorsal, can be obtained.
A convenient manner for constructing a probe in accordance with the
invention is to temporarily secure the electrodes, with wires attached, to
predetermined positions on the wall of a cylindrical mold. The mold is
then filled with a casting resin, e.g. a polymethylmethacrylate casting
composition and the composition cured to provide probe with the wires
embedded therein and extending from the probe at a predetermined location,
usually the end opposite the insertion end of the probe. The resultant
probe has the electrodes embedded in the probe, flush with the
circumference of the probe, a preferred embodiment.
A number of considerations have been taken into account in the development
of the method and probes of the invention, allowing us to arrive at a
useful mathematical model. One such consideration is frequency response.
Bovine vaginal mucus can be considered an electrolytic solution. Charge is
carried through such a solution by the transportation of ions. If an
electric field is set up in the solution, the ions will tend to move
towards the electrode of the opposite charge. However, there are two major
factors which contribute to resist this movement of ions towards the
electrodes (Davies, "The Conductivity of Solutions", John Wiley and Sons,
Inc., New York (1930) page 30).
First, as an ion rests in solution, an "atmosphere" of the opposite charge
is set up around it. This is due simply to the coulombic attraction
between charged particles. If an electric field is than applied to the
solution, the ions of one charge will move one way but their ionic
atmosphere (IA) will tend to move oppositely. The ion must then move
against this flow of oppositely charged particles. There is a certain
characteristic resistance which the solution will have due to this.
However, if the electric field is permitted to stay in one direction
(i.e., a DC voltage is applied), the concentration of ions of the same
charge, around each electrode, will increase to a certain level. This is
referred to as polarization. A region is developed between the electrodes
in which there is a lower concentration of ions which results in an
increase in resistance.
A second phenomenon which contributes to the resistance of a solution also
has to do with the ionic atmosphere. As the ion rests in solution, the IA
is set up spherically symmetric about it. But as the ion moves through the
solution the IA must increase in strength in the direction of motion and
decrease in strength behind it. This causes an asymmetry of the IA which
retards the motion of the ion. If the ion was to be suddenly removed, the
ionic atmosphere would become random and disappear. The disappearance of
the IA, however, takes a finite amount of time and is referred to as the
time of relaxation. This time is dependent on both the thickness of the IA
and the mobility of the ions. For KCl it is approximately equal to
##EQU6##
sec., where C is the molar concentration of the solution. When an AC
voltage is applied across the electrodes the ion will move back and forth
in solution. If the frequency of the voltage is small compared to the time
of relaxation the symmetry of the charge distribution of the IA will
correspond to the instantaneous velocity of the ion. However, at
frequencies which are comparable to the time of relaxation, little or no
asymmetry will result. Therefore, the resistance of the solution will
decrease with increasing frequency.
Employing these two concepts (polarization and asymmetry of the IA), the
response of a solution's resistivity for a very broad range of frequencies
can be predicted. At a low frequency polarization will occur. As the
frequency is increased, polarization will decrease and the resistivity
will fall and level off at some characteristic value. This value will then
be maintained for quite a wide range of frequencies until the frequency
approaches the time of relaxation where it will then decrease.
In designing a probe which would be the most sensitive in detecting the
changes in the resistivity of the vaginal mucus, information as to how
certain parameters, such as the configuration and size of the electrodes,
affect probe sensitivity is essential. Therefore, the probe, as it would
operate within the vaginal tract of the cow, was mathematically modeled.
By varying the parameters, the most theroetically sensitive probe could
then be determined.
When the probe is placed in the vaginal tract of the cow, it is assumed
that there exists a thin layer of mucus with thickness t which completely
surrounds the electrode end of the probe. As the cow comes in heat, the
amount of mucus in the tract increases and the specific electrical
resistivity (.rho.) of the mucus decreases. Therefore, it is desirable to
maximize the probe's sensitivity with respect to changes in both t and
.rho..
Several configurations of electrodes were considered as possible designs
for the probe. The first is known as the axially parallel configuration.
It consists of thin strips of metal embedded parallel to the axis of the
probe. FIG. 2 shows a cross section of such a probe as it would look in
the idealized vaginal tract of the cow. The electrodes are h inches long,
and assumed to be very narrow (surface area effects will be considered
later). They are embedded .theta. degrees apart in a probe r inches in
radius. Around the probe is the thin layer of mucus in which all of the
electric field lines are assumed to be concentrated, as the conductivity
of the mucus is much greater than that of the tissue surrounding it.
From FIG. 2 it is seen that the circumferential distance between the
electrodes on one side of the probe (L.sub.1) would be equal to .theta.r
where .theta. is measured in radians. L.sub.2, the distance around the
other side, would then equal (2.pi.-.theta.)r. Consider the "slab of mucus
L.sub.1 inches wide, h long and t thick." Since t is small and all the
electric field lines are assumed to be enclosed within the slab, the
electric field is considered approximately uniform. Thus, the slab
approximates a parallel plate capacitor where the equation
R=.rho.(L/A) (1)
applied (Maron and Putton, "Principles of Physical Chemistry" (4th
Edition), The MacMillan Company, London, (1965) Page 414). R is the total
resistance between the plates, .rho. is the specific resistivity of the
solution, L is the distance between the plates, and A is the area of the
plates. Applying this equation to the upper slab of mucus, R.sub.1, the
resistance of the slab is given by:
R.perspectiveto..rho.(L.sub.1 /th) (2)
Likewise, applying it to the lower slab:
R.sub.2 .perspectiveto..rho.(L.sub.2 /th) (3)
Since these two slabs are connected in a parallel circuit, the total
resistivity of the mucus as read by the probe will be
##EQU7##
Substituting in r.theta. for L.sub.1 and (2.pi.-.theta.)r for L.sub.2 :
##EQU8##
This equation shows the effects that t, h, r, .rho. and .theta. have on the
resistance which the meter would register for this particular
configuration of electrodes. The sensitivity of the probe to changes in
.rho. and t in the cow is given by .differential.R/.differential..rho. and
.differential.R/.differential.t :
##EQU9##
From Equation (6) it is seen that the sensitivity of the probe to changes
in the conductivity of the mucus is directly proportional to r and
inversely proportional to t and h. This would mean, therefore, that the
probe should be designed with the maximum radius (as would comfortably fit
the vaginal tract), the shortest electrodes possible (the electrodes will
need to have some length in order to insure good contact with the mucus).
The thickness of the mucus (t) depends on the radius of the probe and the
physiological make up of the cow. An increased probe radius will probably
decrease t since the mucus will accomodate the larger probe rather than
the vaginal wall. Due to the nature of the axially parallel configuration
both of these effects are desirable (larger r and small t).
If the sensitivity of the probe .differential.R/.differential..rho. is
plotted against .theta. it can be seen that the relationship is parabolic
with the maximum sensitivity obtained at .theta.=.pi. (see FIG. 3).
Therefore, in order to design a probe which would be the most sensitive to
changes in the specific resistivity of the mucus the electrodes should be
180.degree. apart.
However, in a probe where the electrodes are 90.degree. apart (four
electrodes per probe), one can obtain dorsal and ventral readings from the
vaginal tract. Tests show that these two readings may be somewhat
different and that an average of the two may be desired in order to detect
heat more accurately. The probe, then, can be adapted to give both dorsal
and ventral readings and still maintain sensitivity. If the electrodes are
set 135.degree. apart, the probe is still within 90% of its maximum
sensitivity. This allows room on the probe for two more electrodes. The
upper two electrodes can be used for dorsal readings and the lower two for
ventral readings.
By comparing Equation 7 with Equation 6 it is seen that .theta., r and h
all have the same effects on changes in the thickness of the mucus as they
did on changes in the specific resistivity. In this case, however, their
effects decrease rapidly with increasing thickness (i.e., the design of
the probe becomes less crucial with increasing thickness of the
surrounding mucus). Therefore, the same design would serve to maximize the
sensitivity to both changes in .rho. and t.
In the above analysis of the probe the electrodes are assumed to be very
thin. However, this may or may not be the optimum design for the probe.
For example, one might wish to design the probe with two semicircular
plates for electrodes which are separated by only a small distance.
Therefore, the effects of the surface area of the electrodes on the
probe's sensitivity were considered.
For this particular analysis the thickness of the mucus around the probe is
assumed to be very small. To simplify the problem, the effect t has on the
total resistivity will not be considered. Instead it will be assumed that
all the electric field lines are closely "packed together" along the outer
surface of the probe.
Continuing with the basic model, the theoretical probe will be a rod with
electrodes running along it 180.degree. apart but with variable surface
area (see FIG. 4). An angle .theta. is measured from the vertical running
between the two electrode plates. An expression for the resitivity, as the
probe would record it, taking into account the effects of the electrode's
surface area, will now be developed.
Consider a small shell volume with thickness rd.theta. and depth h which
starts at one electrode and follows the path of the electric field to the
other (see FIG. 5). Its circumferential length is approximately 2.theta.r
since its shape approximates that of an arc of a circle (the electric
field lines to the right and left of it are enclosed within the small
thickness of mucus surrounding the probe).
Because this volume is thin and follows the path of the electric field, it
can be assumed that there is a uniform electric field within it. Its
resistivity is expressed as:
##EQU10##
To simplify the following steps, the solution's conductivity for each shell
volume (C.sub.s) rather than its resistivity will be calculated:
##EQU11##
Since there exist many of these shell volumes laying on top of one another,
all connected in a parallel circuit, the conducitivity of every small
shell volume along the surface of the probe can be summed up to obtain an
expression for the total conductivity of the solution as the probe would
record it. It is true that since the electric field lines lay on top of
one another, the length of each small volume would change according to the
thickness of the mucus (the longer shell volumes would be on the outer
layer of the mucus). However, since, for the analysis of the surface area,
it is assumed that the thickness is small, approximately no changes in
lengths will result due to t. Thus, it can be assumed that the length of
the shall volume is independent of t.
When .theta.=90.degree., the electric field lines bend around the other
side of the probe. Therefore, only the top half of the probe is considered
in the equation and then the conductivity is doubled to get:
##EQU12##
where .theta..sub.1 is the angle at which the electrode begins.
Converting back to R:
##EQU13##
Defining the sensitivity of the probe as
.differential.R/.differential..rho., its relationship to h and
.theta..sub.1 is:
##EQU14##
According to this equation, to maximize the sensitivity of the probe, h
should be minimized. Also .pi./2.theta..sub.1 should be minimized which
can be done by making .theta..sub.1 very close to .pi. (i.e., make the
electrode a very thin wire). Of course, if one makes the electrode too
thin, its contact with the mucus may be hindered and invalid readings
would be obtained. Therefore, a moderately thin (approximately 1/8")
electrode might be used.
While the above discussion has been directed to the axially parallel
configuration of electrodes, other designs have been suggested and even
tried. In light of our ability to theoretically predict the relationship
between th solutions resistance and the probe's design parameters, two
other configurations were considered.
The first was the prior art ring electrode. As the name suggests, the
electrodes are made of two metal rings separated a distance d apart on the
shaft of the probe r inches in radius (FIG. 6).
Consider the volume of mucus around the probe where the electric field
passes through. It is d inches long and t inches thick. Again the
electrodes are assumed to be very thin so d may be an exact distance. If d
is fairly large with respect to t, the electric field can be said to be
fairly uniform through this volume (neglecting end effects). Thus:
R=.rho.(L/A) (13)
where L=d and A=the cross sectional area of the mucus (which is equal to
2.pi.rt+.pi.t.sup.2).
Substituting in for L and A:
##EQU15##
and the probe's sensitivity with respect to .rho. and t would be:
##EQU16##
According to Equations 15 and 16, d should clearly be maximized in order to
maximize the overall sensitivity of the probe. This might appear to be an
improvement over the key configuration since there is essentially no limit
as to how large one could make d (except for the length of the vagina). Of
course, if d becomes too large, the mucus in the vaginal tract of the cow
may not extend between the electrodes and loss of continuity might result.
Equation 15 indicates that r should be minimized. If t is assumed to be
very small (powers of t greater than t.sup.2 become insignificant),
Equation 16 reduces to:
##EQU17##
which would also indicate that r should be minimized. This is where the
problem with the ring configuration arises. In trying to minimize r,
either contact with the mucus of the vaginal tract would be lost
(resulting in random resistance readings) or t would effectively be
increased (which would also lower the probe's sensitivity). In the axially
parallel configuration, however, r was to be maximized (along with t being
maximized). This situation is more desirable in relation to the cow's
physiology and therefore the axially parallel configuration becomes a
better overall design.
Another possible configuration of electrodes is the "spiral" configuration
where the two electrodes are wound around the probe shaft in a double
helix fashion (FIG. 7). This design tends to average out the differences
between dorsal and ventral readings as well as between anterior and
posterior readings.
To develop the equation for the resistance of this configuration, consider
two slabs of mucus wrapped continuously down the probe between the
electrodes (FIG. 7). The first has width k and goes from the (+) to the
(-) electrode. Its resistance is R.sub.1. The second slab has width m and
goes from the (-) to the (+) electrode. Its resistance is R.sub.2. The sum
of the two widths is equal to d, the perpendicular distance from the (+)
electrode to the (+) electrode after one revolution around the rod. Both
slabs have thickness t and length s (the arc length of the spiral).
Thus:
R.sub.1 =.rho.(k/st) (18)
R=.rho.(m/st) (19)
Thus, the total resistance, R, would be:
##EQU18##
Thus:
##EQU19##
Plotting .differential.R/.differential..rho. against m, the probe's
sensitivity is found to be greatest when m=1/2d (i.e., the (-) electrode
should be exactly between the (+) electrode). Setting m equal to 1/2d our
equation becomes:
(.differential.R/.differential..rho.)=(d/4st) (23)
From this equation it is clear that in order to maximize the sensitivity d
must be maximized and s minimized. In order to do this the path of the
spiral would have to be a maximum; the limiting case being two straight
electrodes running along the length of the rod, 180.degree. apart (i.e.,
the axially parallel configuration). Another way to minimize s would be to
decrease the radius of the probe. Therefore, the spiral configuration
would also seem to be inferior to the axially parallel configuration as
far as sensitivity is concerned.
To test whether or not the theories developed above were correct, a number
of experiments were conducted. The experiments were divided into two
categories: frequency response of the solution, and configuration and size
of the electrodes.
EXAMPLE 1
To test the hypothesis of the frequency response of the solution, a circuit
like that shown in FIG. 8 was used. The probe used in this Example, as
well as Example 3, is shown in FIG. 24 and was made from a cast acrylic
(Plexiglass) tube (0.75" O.D.; 0.50" I.D.). The electrodes were made from
stainless steel (3" long.times.3/16" wide and 1/16" thick) flush mounted
by means of epoxy resin into milled grooves in the tube at the insertion
end. Insulated copper wires were soldered to the electrodes and passed
through the interior of the tube through the end opposite the insertion
end and connected to a switch permitting connection of either electrode
pair to the readout instrument. The probe was placed in a salt solution
(NaCl) of known concentration. It was then connected in series with a
resistor of known resistance (R) and a sinusoidal voltage was applied by a
signal generator (V.sub.s). By measuring the voltage across the voltage
source (V.sub.s) and the voltage across the known resistor (V.sub.r), the
voltage across the electrodes of the probe (V.sub.p) was calculated. Then
by knowing R and V.sub.r, the current (I) through the circuit was
calculated. Finally, by dividing V.sub.p by I, the resistance of the
solution (R.sub.p) between the electrodes was found. The dependence of
R.sub.p on frequency could be observed by varying the frequency of the
signal generator.
FIG. 10 shows the results for various concentrations of solutions. There
is, in fact, a plateau region for the probe where the resistance of the
solution is independent of the frequency. At a frequency lower than this,
the resistance did rise significantly due to polarization as was expected.
However, at the highest frequency which the solutions were tested for
(10.sup.6 Hz) the only solution which showed a significant change in
resistance (outside of the error bars of the experiment) was the 10.sup.31
2 M NaCl. This could be expected since the time of relaxation is very
small and is dependent on the concentration of the ions. Therefore, if
10.sup.6 Hz was a high enough frequency to effect the resistance of the
solutions, the effects would first be seen in the most dilute solution,
10.sup.-2 M. Its resistance did decrease as was expected. For the other
two solutions, a higher frequency would have to be used. The frequency of
the probe should therefore be set between 5 KHz and 100 KHz in order to
minimize the polarization and ionic atmosphere effects, although a
frequency as low as about 2.5 KHz is useful. (Of course, as just
mentioned, the upper bound to the frequency is still uncertain).
EXAMPLE 2
All of the suggested parameters for the axially parallel probe mentioned
above rest on the validity of Equation 5. If this expression for the
relationship between resistance and the probe's design parameters is not a
correct one, neither is the expression for its sensitivity to changes in
.rho. and t. Therefore, verification of Equation 5 was sought.
To do this, an apparatus was built in which t, h and .rho. could be varied
and the resistance as read by the probe recorded. The results could then
be compared with the theoretical predictions.
Basically the apparatus consisted of a series of interchangeable plexiglass
tubes which could be held down vertically by springs to a plexiglass base
(See FIG. 9). The probe was inserted inside one of the tubes; its tip
centered by a centering cone and its shaft held parallel to the sides of
the tube by three centering screws. A saline solution of NaCl was poured
in the space around the probe, .rho. was varied by changing the
concentration of the saline solution and t was varied by interchanging
various diameter tubes. h was varied by filling up the tubes to a certain
depth and leaving part of the electrodes exposed. Thus, the only part
which would measure resistance would be the part of the electrodes which
were submerged. To vary .theta., separate probes were constructed in which
the electrodes were 45.degree., 90.degree., 135.degree. and 180.degree.
apart. The radius of the probe was not varied due to limitations on time,
but instead held constant.
One test was made using vaginal mucus in the plexiglass test apparatus.
Here h was varied and plotted against R for a given t and .theta.. By
doing this, the ER characteristics of the mucus could be compared to those
of the saline solution. There was very close agreement between vaginal
mucus and the 10.sup.-1 M NaCl with mucus slightly lower in resistance but
similar in curve shape.
The experimental results fit very closely to what was expected
theoretically for the axially parallel probe. FIGS. 11 and 12 show that
the resistance of the solution around the electrodes is in fact inversely
proportional to h for both the 10.sup.-1 M and the 1 M NaCl solution.
Thus, an expression can be written R=k.sub.1 /h, where k.sub.1 is some
constant. By varying t, the value of k.sub.1 would be expected to change
(since k.sub.1 contains t) however, the shape of the curve (1/h) would
remain the same. This can also be seen in FIGS. 11 and 12.
The resistance also seems to be inversely proportional to t. This is seen
in FIG. 13. After t gets thinner than 0.1 inches, problems arise in the
support and centering of the probe in the plexiglass tubes. Thus, data
could not be obtained for less than 0.1 inches and the full shape of the
curve seen. For a more dilute solution t has an effect over a larger range
whereas for a more concentrated solution (1 M) the effect of t is rather
small beyond 0.15 inches.
When .theta. was tested against the resistance, the data fit very closely
to the expected curve R=k.sub.2 .theta.(2.pi.-.theta.) where k.sub.2 is
some constant. This is seen in FIG. 14. An appropriate value of k.sub.2
was selected and the theoretical expression was plotted along with the
data to show the high degree of correlation.
From the above individual results, an expression can be written:
##EQU20##
where k.sub.3 is another constant containing k.sub.1 and k.sub.2.
This expression which has been experimentally verified is very close to the
form of Equation 5. If the two expressions were equal, k.sub.3 would equal
.rho.r/2.pi..
The form of Equation 5 can be further checked by graphing R vs.
##EQU21##
If this is done a straight line with slope of .rho. (units being ohm-in)
and an intercept of 0 would be obtained. FIGS. 15 and 19 show that there
is in fact a linear relationship to a very high degree of correlation (as
fitted by the least square method). Each graph shows a fixed value of t,
.theta., and r as h was varied. If one considers all the points together
(where t and h are varied together) a straight line with a correlation
coefficient of 0.926 can be fit to the points. The slope of the lines tend
to increase as t increases. It is thought that this is due to a spreading
of the electric field lines as the thickness of the solution around the
probe increases. This would result in an apparent increase in .rho. which
would in turn lead to a larger slope.
Thus, the effects due to changes in t, h and .theta. have been
experimentally verified.
When actual bovine mucus was tested in the plexiglass apparatus, curves
similar to the expression R=k.sub.1 /h were obtained for given .theta.'s
and a given t. This suggests that the mucus behaves similar to an
electrolytic solution and thus the equations developed apply.
The above correlations suggest very strongly that Equation 5 is in fact
valid if t is small compared to r. Therefore, the design parameters
suggested above for the axially parallel probe should, in fact, maximize
its sensitivity to the physiological changes in the cow's vaginal tract.
The prior art ring probe was tested in vivo instead of varying its
parameters in vitro (Gartland et al, Journal of Dairy Science, 59, pp.
982-985 (1976). A definite pattern could be seen in the Electrical
Resistance Readings which followed the cycle of the cow, however,
variations were too great to establish any firm results. After analyzing
the electric field of the ring probe as was done with the axially parallel
probe, it seems clear why this is so. There seems to be a conflict between
trying to minimize its radius and also maintain contact with the mucus
lining of the vagina. For this reason, the design seems to be limited and
thus not very hopeful.
The above mathematical model and experiments demonstrate that the frequency
of the current supplied to the electrodes should be between about 5 KHz
and about 100 KHz; the resistivity of the solution as measured by the
axially parallel probe can be expressed as
##EQU22##
the optimal parameter settings of the axially parallel configuration are
as follows: (a) .theta.=180.degree. (may be less than this to accomodate 4
electrodes), (b) h should be relatively small (.about.2-3"), (c) r should
be relatively large (.about.0.3-0.5"), (d) electrodes should be moderately
thin (.about.1/8"); the optimal design of the spiral probe is the axial
parallel probe; and that the ring probe contains problems inherent to its
design, i.e., the minimization of its radius. It has been shown that
bovine mucus appears to have ER characteristics similar to that of a
saline solution.
EXAMPLE 3
Three different groups of animals were probed to measure ER of vaginal
mucus. The probe as described in Example 1 was operated at a frequency of
2.5 KHz, 3 vpp. These groups were considered as three experiments.
Experiment I.
29 nonpregnant but sexually mature Holstein heifers at Cornell University's
Reed Farm.
Experiment II.
24 lactating nonpregnant dairy cows at the New York State College of
Agriculture and Life Sciences, Animal Science Teaching and Research Center
(ASTARC).
Experiment III.
62 lactating, primarily nonpregnant Holstein cows in Lansing, New York.
A. Loose Housing
1. Gordon Cook Farm
2. David Hardie Farm
B. Convention (stanchion) Barn
1. Lawrence Howser Farm
Animals in Experiment I were probed for 28 days, in Experiment II for 28
days, and in Experiment III for 40 days. ER was measured by probing on
alternate days throughout each experiment. The probe was thoroughly washed
with a disinfectant and rinsed at each farm as well as between each
animal. The probe was wet with water as a lubricant to facilitate
insertion and minimize inflammation. The vulva of each animal was cleaned
with a dry paper towel, and the lips of the vulva were widely parted
before introducing the probe to prevent carrying organisms and debris into
the vagina. The probe was inserted into the anterior portion of the vagina
until the os of the cervix was felt. It was then pulled back approximately
one centimeter and positioned against the dorsal surface of the anterior
vagina. After this ER measurement was taken, the switch connecting the
electrodes on the ventral surface of the probe was changed and the ER of
the ventral anterior vagina measured. Both measurements were recorded on
the individual animal's record form, along with the date.
Milk samples were collected each day the cows were being probed in
Experiments II and III. These samples were refrigerated and then frozen in
a metanol-dry ice bath, later to be analyzed for milk progesterone levels
(by the standard procedure used for milk progesterone, Department of
Animal Science, Cornell University).
Visual observations were relied upon for estrus detection in Experiment II.
In Experiments I and III, KaMaR, Heatmount Detectors, or a line of
"Paintstik" (applied from the tailhead along the midline to the anterior
pelvis area), along with visual observations, were used to determine the
time of estrus.
RESULTS
Experiment I 24 Heifers
The mean ventral and dorsal ER values for Experiment I are illustrated in
FIG. 21. The standard errors are not given, but they usually are about
.+-.2.0 ohms. There was individual variations, with 7% of the ventral ER
values minimal at some time other than at estrus. The remaining values
were lowest at estrus (.+-.1 day). This compared with 85% of the heifers
showing a triggered KaMaR or rubbed chalk when visually observed to be in
estrus. Generally there were slightly lower ER readings 3-4 days after
estrus than at other nonestrus times, which may have been caused by
metestrus bleeding. A slight dip at mid-cycle could be due to mid-cycle
follicular development known to be present in cattle (and often
accompanied by a slight estrogen rise), but not studied in the present
experiment.
The dorsal ER readings were not as reliable an indication of estrus, with
only 56% having minimal dorsal ER values at estrus (.+-.1 day).
Experiment II ASTARC Lactatin | | |
