Introduction
Glaucoma is currently the most common cause of irreversible blindness
worldwide . It comprises malfunctions in the eye that lead
to a subsequent loss of neuronal retinal cells
. There is no curative therapy
available to date which makes early detection and avoiding further damage
the most effective medical intervention . Besides the
subjective method of visual field testing, the correct measurement of the
patient's intraocular pressure (IOP) constitutes a key factor for the
diagnosis and follow-up treatment of glaucoma. Lowering the IOP is the main
therapeutic approach, either through medication or surgery. Thus, a reliable
measurement of the IOP represents the current key aspect to stop progression
of glaucoma .
The Goldmann Applanation Tonometer (GAT), initially described in 1955
, is still the clinical gold standard for
IOP measurements and has an uncertainty of 1–2 mmHg
, which can increase to 3.8 mmHg in interindividual
comparison . It detects the static force that is
needed to indent the cornea with a glass stamp to a predefined flattened area
with a diameter of 3.06 mm. The IOP can then be calculated according
to the Imbert–Fick law . Aside from the
medical experience of the user , the uncertainty of
the result also depends on the thickness and age-related material parameter
changes in the cornea . In addition, the measurement
requires a local anesthetic, and the procedure is unpleasant, carries
infection risks, and can only be performed by physicians and optometrists.
Noncontact tonometers, such as air-puff tonometers, reduce these negative
factors to a certain extent . By using an air impulse, the
elapsed time to flatten the cornea is measured, which defines the pressure
that had to be applied. Despite its dynamic appearance, the method is based on
the same static physical principle as the GAT . The
results correlate well with GAT measurements in the physiologically desired
IOP range from 10 to 20 mmHg . However, the
measurement uncertainty of air-puff tonometers of 5 mmHg is larger
than that of the GAT . Besides the dominant
use for out-patient screening tests, air-puff tonometers do not meet clinical
requirements of an uncertainty of <3 mmHg and cannot be used in
the home environment .
Several concepts exist that try to provide the potential of home measurements
to yield diurnal IOP trends. The Ocuton S, which is based on the measurement
principle of the GAT following the concept of , leads to
a deviation of 6 mmHg from the mean of GAT reference measurements
. Yet the contact-related disadvantages of the GAT exist for
the Ocuton S as well. With the pressure phosphene tonometer, an unpowered
spring applanation tonometer that indents the eye through the eyelid, no
anesthetic is required, but measurements reach an absolute mean difference
from the GAT reference of 6.6 mmHg . The Tiolat iCare
measurement device evaluates the bounce-back of a small plastic stick that is
shot onto the cornea, and is therefore considered to use a dynamic principle.
The iCare reaches a deviation of ±3 mmHg from the GAT
measurements . Although it is not considered
a self-tonometer and generates higher deviations when it is not pointed
directly on the vertex , it helps with the IOP
measurement for children . conclude
that there is no approved technology for measuring diurnal IOP trends in
a home environment to date.
Instead of the static pressure estimation based on the Imbert–Fick law,
dynamic approaches to noncontact tonometry try to analyze changes in
mechanical eigenvalues due to different IOP levels of the eye. It was shown
through finite-element analysis and optical measurements of the corneal
vibration response of an acoustic excitation that the resonant frequencies
of the eyeball change with the IOP .
estimated a sensitivity of 3 HzmmHg-1 for one
tested subject. Although the results seemed promising, there are no medical
devices available based on this principle so far. Considering the measurement
uncertainty of air-puff tonometers, no noncontact tonometers exist which
meet the clinical requirements.
(a) Cross section of the measurement setup (CAD illustration) with the inside of the pressure chamber, a 30 mm
loudspeaker, and a model of a porcine eye connected by a cannula. (b) Laboratory experiments with a freshly enucleated
porcine eye and a liquid column for pressure application. The diaphragm movement of the loudspeaker is detected by an infrared
reflection sensor represented by CNY70 in front of it.
A study by presented a noncontact measurement approach that is
based on the acoustic stimulation of the eye to be measured. The general
distinction of IOP variations in a porcine eye regarding observed changes in
the pressure attenuation in an enclosed chamber was demonstrated. However,
a detailed characterization or a plausible physical model of the measurement
concept was not provided. Therefore the potential of this measurement approach
remains an open question.
For these reasons a dynamic IOP measurement system based on the approach
described in is presented and characterized with respect
to the achievable measurement uncertainty. Note that the results derived from
the experiments are necessary for the definition of the requirements for
a discrete, handheld self-tonometer, which is the long-term aim of our
research. The measurement system, which is formed by a loudspeaker,
a pressure chamber, and the patient's eye, can be treated as a coupled
spring–mass–damper system. The response of the mechanical system is measured
by an optical displacement sensor in front of the loudspeaker's diaphragm,
and a microphone in the pressure chamber. The presented work now provides
a clear physical model of the measurement principle that explains the
relation between IOP values and the damping ratio of the coupled mechanical
system. Allocating the adjusted IOP values to the oscillation parameters of
the system's response allows the calculation of the expected uncertainty for
the IOP determination for the first time. The measurement principle and the
experimental setup is described in Sect. . The IOP measurement
system is characterized with experiments on porcine eyes, which is presented
in Sect. . The discussion of measurement errors and a respective
comparison with other measurement devices follows in Sect. . The
article closes with a summary in Sect. .
Methods
Measurement principle
The principle of the IOP measurement approach can be illustrated with the
behavior of a pressurized ball that is dropped from a specified height. The
height of the ball bouncing back depends on its inner pressure as well as the
material elasticity. The lower the pressure level is, the lower the
bouncing height is, since more energy is consumed by deformation processes of
the ball . This phenomenon is linked to the behavior of
a damped harmonic oscillator where the amount of damping defines the ratio
between consecutive peaks in a harmonic signal. It is postulated by the
authors that the eyeball behaves accordingly. At low IOP levels the
deformation of the cornea is assumed to be larger, since more work is
expended on the eye. Work is defined as
w=F⋅s
and is the product of a constant magnitude force F that is multiplied by
a distance s in the direction of the force. The amount of work that is
performed on the eye converts a measurable share of the inner energy of the
system into heat. With a variation of the IOP the energy conversion in the
pressure chamber changes, which is measurable as the damping of the
characteristic oscillation of the system. This can be measured with
a microphone that records the sound pressure level (SPL) within the pressure
chamber and by a displacement sensor that detects the movement of the
loudspeaker's diaphragm.
A general spring–mass–damper system is described by
mx¨+dx˙+kx=0,
where m is the mass, d is the damping constant, and k is the spring rate
. If the system is excited by an external force, the time
it takes for the oscillation to settle down is defined by d. The fade-out
of a technical harmonic oscillation against the time reads
x(t)=x0⋅cos2πft+ϕ⋅e(-δt),
where x0 is the amplitude of the signal at t0, f is the frequency,
ϕ is the phase, and δ is the damping coefficient. The damping
coefficient is calculated by two consecutive extremal values xi and
x(i+1) of the curve, with a distance of one period T using the
relation
xix(i+1)=eδT.
In order to evaluate the damping characteristics of the observed system, the
damping ratio
D=Λ(2π)2+Λ2withΛ=δT=lnxix(i+1)
is calculated . While every constant of the observed
system remains unchanged, the variation in damping results solely from the
energy dissipation due to the work performed on the eye. It is going to be
demonstrated by means of laboratory tests on porcine eyes that the damping
ratio of a coupled spring–mass–damper system changes with the IOP of the
connected eye.
Experimental setup
The experimental setup consists of a pressure chamber with an inner volume of
70 cm3. In order to avoid resonances, the chamber has no parallel
walls. Connected to the chamber are a 6.35 mm electret microphone for
high SPL up to 150 dB, with a signal-to-noise ratio of 33 dB,
and a full-range loudspeaker with 30 mm diameter, 8 Ω, and
2 W (see Fig. a). Additionally, the oscillation of the
loudspeaker's diaphragm is measured by evaluating the current of an intensity-based distance sensor represented by an analog infrared reflection sensor
CNY70 (Vishay). The loudspeaker, the gas volume, and the eye are considered
a coupled mechanical system.
For the measurements, an enucleated porcine eye is placed on top of the
pressure chamber, sealing it fully. The eye lies on a circular vent, with the
cornea facing the inside of the chamber, and is fixed with two instant
adhesive spots. It is penetrated by a cannula (1.1 mm outer diameter,
flow-rate 61 mLmin-1) connected to a liquid column of 0.9 %
saline solution. The cannula was inserted into the eye from the side; about
7 mm behind the limbus, reaching into the vitreous body; see
Fig. b. The pressure level can be adjusted between 5 and
60 mmHg, in order to determine the influence of IOP changes on the
damping characteristic of the system. The measurements start at a low level
of 5 mmHg, and begin 60 s after altering the column to allow
for pressure equalization. In order to preclude a negative effect of prior
measurements on the same specimen, hysteresis tests are done directly after
initial measurements. During hysteresis tests, the IOP is successively
lowered from the maximum value of 60 mmHg and the measurements at
intermediate IOP levels are repeated. For hysteresis tests the vitreous body
was replaced by 0.9 % saline solution; otherwise no decrease in pressure
could be measured because of the vitreous body blocking the entrance of the
cannula.
The porcine eyes used for the experiment have been enucleated about 90 min
prior to the measurements. To avoid changes in material behavior due to dry-out effects of sclera and cornea, the eyes have been kept in a 0.9 %
saline solution, and can be considered freshly enucleated. In order to
achieve best comparability, the eyes have been carefully cleansed from fat
and muscular tissue prior to the examination. The weight was recorded before
and after regular measurements with the vitreous body in place. It was found
that the eyes weigh on average 7.54±0.79 g before and
7.85±0.74 g after the measurement, gaining a weight of
0.31±0.09 g on average.
In order to achieve an optimal rectangular signal, the excitation signal for
the loudspeaker is generated by two voltage sources. They are switched
successively between -2.5 V (duration 1 ms) and 3.5 V
(duration 2 ms) via external electronics. Hereby the speaker generates
a pressure pulse of 1000 Pa within the chamber. After excitation, the
speaker's oscillation can settle freely. The pulse response of the coupled
mechanical system is analyzed using the information provided by the
microphone and the measured oscillation of the speaker's diaphragm (see
Fig. ). For this purpose, the analog output signals of the
microphone and the infrared reflection sensor are sampled with a frequency of
51.2 kHz and digitized with 24 bit A / D converters. Changes between
successive measurements exclusively concern the adjustment of the IOP level.
Accordingly, any systematic change in the system's response can be attributed
to the IOP level. Considering formulae (1) and (5), it is expected that the
damping of the coupled mechanical system changes according to the IOP
adjustments. In order to test the reproducibility of the measurements, at
least 18 pressure pulses are recorded for each IOP level and specimen.
Results
The speaker's voltage and current, the output signal of the microphone and
the movement of the speaker's diaphragm have been recorded for 9 eyes at 10
IOP levels and 18 impulses each. It was found that the microphone signal and
the oscillation of the speaker's diaphragm provide information about the IOP
in the specimen.
Each of the curves represents the mean of 18 individual impulses that were recorded at one example IOP level. Confidence
bounds with the expanded standard uncertainty of the mean (coverage factor k=2) are drawn by two adjacent lines that surround the
mean values (only visible in close-up view). The voltage input causes the speaker to oscillate, i.e., a movement of the diaphragm of the
speaker results. The pressure in the closed chamber is monitored with a microphone.
Allocation of curves measured from eyes with vitreous body and measurements after vitrectomy with 0.9 % saline solution as
replacement for the vitreous body. A similar ascending order of the individual IOP response proves that the principle works on eyes
with the vitreous body in place. Except for 15 mmHg amplitude, heights only change by 0.3 % with respect to the excitation
pulse. The frequency changes by 1.5 to 3 %.
Diaphragm displacement detected with a Vishay CNY70 reflection sensor for porcine eye no. 3 for IOP values between 5 and
60 mmHg. The dashed-line curves are recorded when the pressure was consecutively lowered, for the hysteresis test. The close-up view
of the first extremal value after excitation demonstrates the IOP dependent damping behavior. The higher the adjusted IOP is, the
higher the amplitude is, the lower the damping ratio is. For hysteresis tests the vitreous body was replaced by 0.9 % saline
solution, to avoid blocking effects of the cannula.
(a) The damping ratio calculated with formulae (4) and (5) is plotted against the IOP level. The sensitivity is
represented by the slope of the curve which has the largest absolute value between 10 and 35 mmHg. For higher IOP levels the
absolute value of the slope decreases, which shows a lower sensitivity. The curve is fitted by a third-order polynomial (R2=0.992)
for the error propagation calculation. (b) The derived standard uncertainty of the IOP determination with a coverage factor
k=2 is plotted against the IOP. In the range from 5 to 35 mmHg, the estimated standard uncertainty of the mean is below
1 mmHg. This confirms the feasibility of the measurement principle for clinical application.
Damping ratio calculated according to formulae (4) and (5) for nine different porcine eyes. For all eyes the damping ratio
decreases with the IOP level. The highest sensitivity is available in the range of 10 to 30 mmHg. Two outlying data points have been
excluded for the eyes 7 and 8 due to artifacts. Note that error bars are drawn but too small for visualization.
Characteristics of porcine eye measurements
Figure shows one sample impulse alongside the excitation
signal. Each curve represents the mean of 18 individual impulses that were
recorded at one sample IOP level. The voltage input causes the diaphragm of
the speaker to oscillate back and forth, which can be followed via the
reflection sensor. The pressure in the closed chamber is monitored with
a microphone. The narrow confidence bounds display the standard uncertainty
of the mean with coverage factor (k=2) and demonstrate the good
reproducibility of the 18 single measurements from the microphone and the
diaphragm movement. A perfect reproducibility of the input signal is crucial
for the analysis of the system's behavior concerning IOP changes in the eye.
In order to verify that the change in vibration characteristic of the coupled
system is free from temporal effects concerning the measurement object and
procedure, hysteresis tests have been performed. When lowering the liquid
column for the hysteresis test, the vitreous body blocks the entrance of the
cannula, since the pressure level within the eye is higher than outside.
Thus, no hysteresis test can be performed with the vitreous body in place.
The influence of vitreous replacement is shown in Fig. . The
oscillation frequency changes by 1.5 to 3 %, equal to 1–2 sample points,
which is close to the resolution limit of the A / D converter. The first
extremum after excitation changes between 0.3 and 1 % when the vitreous
body is replaced by saline solution. As a result, it was possible to
demonstrate that the response of the system remains constant and equivalent
IOP levels, with and without vitreous body, can be allocated.
Damping of the coupled system
The response of the coupled spring–mass–damper system, as detected by the
movement of the speaker's diaphragm, is shown in Fig. for the
tested IOP levels. The effect of different IOP values on the system can be
clearly distinguished in the close-up view of the first minimum after
excitation. As a noticeable result, higher IOP values lead to higher
amplitudes after excitation. Thus the order of the amplitudes represents the
ascending IOP level.
On average, the standard uncertainty is 0.03 % at the extremal values
successive to the excitation pulse. Figure also shows the
results of the hysteresis test in the dashed lines. They correspond closely
to the results of the initial measurements. At the IOP levels of 20 and
25 mmHg the difference between related extrema of the hysteresis test
to the initial measurement is less than 0.2 % of the excitation impulse.
For the other IOP levels the differences lie within the range of 0.2 to
0.5 %. Thus, results of the hysteresis tests show the same
distinguishable effect of the IOP level on the ascending order of amplitudes.
This implies that the principle works irrespective of the eye's IOP history.
Furthermore, it shows that material changes due to possible dry-out effects
on the test bench do not influence the measurement to a significant extent.
A significant change in the oscillation frequency is not observed.
The findings support the physical analogy with the pressurized ball and the
assumption from formulae (1) and (5) that the major influence of the IOP can
be observed in the damping of the system.
Figure a shows the damping ratio, plotted with respect to
the IOP. It has been calculated from the excitation pulse and the following
first minimum of the system response, using formulae (4) and (5). For further
evaluation a third-order polynomial fit (R2=0.992) is applied, where the
sensitivity regarding changes in the IOP is represented by the slope of the
curve. For higher IOP levels the absolute value of the slope decreases from
0.2 % at 10 mmHg to 0.015 % at 60 mmHg, which shows
a lower sensitivity.
Using an error propagation calculation, the measurement uncertainty due to
random fluctuations of the damping ratio is determined. It is shown with
a coverage factor of k=2 in Fig. b with respect to the
IOP. The achievable standard uncertainty of the mean is below
0.35 mmHg from 5 to 30 mmHg with a minimum of
0.07 mmHg at 10 mmHg adjusted IOP. For IOP values above
30 mmHg the uncertainty is higher than 1 mmHg. With an
estimated measurement uncertainty of significantly less than
±3 mmHg the clinical relevance of this approach is demonstrated.
For nine different eyes, a similar tendency can be observed in the calculated
damping ratio of the system; see Fig. . Higher IOP values lead
to higher amplitudes, and to a lower damping ratio accordingly. The reason
for the deviant behavior of different specimens will be addressed in the
discussion section.
Discussion
With the objective of designing a handheld self-tonometer a novel measurement
approach was analyzed in a laboratory environment. The physical relation
between the damping ratio of a coupled system that consists of a loudspeaker,
a pressure chamber, and an enucleated porcine eye was validated. In agreement
with the physical analogy it was found that higher IOP values lead to a lower
damping ratio of the coupled speaker–air–eye system, resulting from the
amount of converted energy of the system for deformation processes of the
cornea. Individual IOP values are clearly distinguishable with this
principle. The determined standard uncertainty of less than 0.35 mmHg
in laboratory tests raises expectations for the currently performed in vivo study.
The sensitivity of this measurement principle is highest in the normal IOP
range, between 10 and 20 mmHg , and decreases for
higher IOP values. The effect is known from current tonometry methods such as
the iCare tonometer , Tono-pen , or
air-puff tonometers that the sensitivity decreases at
higher IOP levels . This is explained
by the fact that the possible deformation of the eye with a constant force
decreases, which leads to a lower signal-to-noise ratio. Due to stochastic
deviations, the sensitivity of the measurement principle decreases
proportional to the signal-to-noise ratio, which then leads to a larger
measurement uncertainty. It is a challenging task for static and dynamic
methods to determine elevated IOP values above 30 mmHg with a low
uncertainty. Fortunately the exact determination at raised IOP levels above
30 mmHg is of low clinical relevance, as long as raised IOP levels
can be precisely distinguished from IOP levels in the normal physiological
range.
The hysteresis test was obligatory to confirm that the observed differences
are free from artifacts of IOP adjustment or dry-out effects of the eye on
the test bench. The reproducibility of the system response demonstrated that
the IOP directly affects the damping. Additional examinations confirmed that
the measurement principle is applicable regardless of vitreous body
replacement.
Despite consistent tendencies, deviations in the damping ratio occur when
different eyes are compared. The individual weight of the eyes was recorded
and tested for correlation of the observed differences. In fact, the
variation of the weight does not correlate well (correlation coefficient
-0.3) with the damping ratio of the system. The biometric variations among
the tested eyes could not be measured during the laboratory tests. As a main
potential factor for the deviations, the influence of the central corneal
thickness (CCT) should be analyzed, since it is known to have major impact on
measurement devices based on the Imbert–Fick law
. Although this approach is not
based on that principle, the cornea is still the prominent structure that is
reached by the pressure pulse first, even though it is not indented. It is
assumed that the CCT and the curvature of the cornea influence the performed
work for the deformation process. This will be addressed in the future
in vivo measurements, by recording the participants' biometric parameters
with ophthalmic measurement devices. It is desired to bring a handheld
self-tonometer with the above concept to market within the next 5 years.