Download Aniridia and Keratoprosthesis

Exponential Decay Modeling to Study Ocular
Surface Temperature Changes Measured by
Thermography
Ranjini Kottaiyan1,
Holly Hindman1, Geunyoung Yoon1,2,3, James Zavislan2,3, James Aquavella1
1Flaum Eye Institute, 2Center for Visual Science, 3Institute of Optics
University of Rochester
Background
• Sjögren’s Syndrome (SS) is a chronic autoimmune disorder causing
dryness of the mouth and the eyes 1.
• These severe forms of dry eye can lead to vision-threatening
complications and therefore, early differential diagnosis is important.
• Of the several new multimodal metrology systems available to
clinicians, thermal imaging is a promising approach to the study of
pre-corneal tear film noninvasively 2-6.
• The goal was to establish the use of thermal imaging as a practical,
reliable method of detecting dry eye through ocular surface
temperature measurements in patients with Sjögren’s syndrome.
Purpose
Corneal temperature after every blink (imaginary figure)7
A. Corneal temperature decreases with every blink in normal subjects
B. Has smaller change in patients with dry eye
Dry eye
Normal eye
As seen from the above figures, ocular surface temperature (OST) does not
decrease linearly over time, so we utilized exponential decay modelling to
study ocular surface cooling.
The purpose of the study was to fit an exponential decay model of ocular
surface cooling and evaluate the OST decay rates in patients with severe dry
eyes secondary to Sjögren’s syndrome (SS) and compare these results with
those of healthy normal eyes.
Methods: Subjects
• Forty eyes of subjects with SS and forty normal eyes were measured with an
infrared thermal camera in a controlled chamber under standardized
conditions of 24 °C and 40% relative humidity.
• Custom-developed Matlab software was used to quantify OST at three circular
regions of interest (ROI) on a fully opened eye:
– Central cornea (ROI 1),
– Nasal conjunctiva (ROI 2)
– Temporal conjunctiva (ROI 3)
• Average and standard deviation of OST was computed for the blink interval
Figure 1. Region of interest (ROI) spot selection on a static ocular thermograph, ROI 1-central cornea, ROI 2-nasal
conjunctiva, ROI 3-temporal conjunctiva.
Methods: Data Analysis
• A separate exponential decay model was fit to the data for each region of the
eye to assess the difference in exponential rate of cooling for the dry versus
normal eyes groups.
• To test for differences in the slopes of the cooling rates between dry and
normal eyes, the model is fit using PROC NLMIXED within SAS v9.3 and
ESTIMATE statements produce approximate t-tests using the delta method
(Cox 1998) to approximate the appropriate standard errors.
Results : Fitting an Exponential Decay Model
• Normal eye: yij = exp {ß1D + b1i}* exp {- (ß2D + b2i) tj} + εij
Dry eye:
yij = exp {ß1N + b1i}* exp {- (ß2N + b2i) tj} + εij
–
–
–
–
temperature for the ith subject at the jth time point,
tj represents the time points ranging from 1 to 5 seconds,
30 frames measured in each second,
total of 150 time points for each subject.
• β2N : exponential decay model rate of cooling for normal eyes
β2D : exponential decay model rate of cooling for dry eyes
• β1N : initial ocular surface temperature immediately after a blink for normal eyes
β1D : initial ocular surface temperature immediately after a blink for dry eyes
• ϵij :random error representing deviation from the fitted line and the true
measurements.
Results
• Model suggests OST decreases at a rate proportional to its current value, thus
the rate of OST decrease at the very beginning is bigger than later frames.
• Fitting the exponential model to each region of the eye—ROI 1, ROI 2, and ROI
3—we conclude the following:
estimated mean
(standard error)
ROI 1
ROI 2
ROI 3
Normal eye
0.0002265
(0.000241)
0.001312
(0.000143)
0.0001698
(0.000188)
Dry eye
0.002945
(0.000286)
0.001188
(0.000122)
0.002430
(0.000245)
P value
(*p<0.05)
0.0356*
0.4135 (NS)
0.0064*
Exponential Decay Rate of Cooling in
Different Regions of the Ocular Surface
It is apparent from the figures that the temperature does not decrease linearly over
time.
It is also evident that the general slope decreases more quickly in the first second or
two and then evens out thereafter, which means that the cooling is more rapid right
after the lid opens and gradually evens out subsequently.
Conclusion
Thermal imaging shows a non-linear pattern of cooling in both groups.
However, an increased rate of cooling occurs in the central corneal and
temporal conjunctival regions in Sjogren’s dry eyes than in normal subjects.
Infrared thermal imaging shows clear differences in decay rates of cooling
between normal and dry eyes.
Discussion
• The two groups showed significant differences in decay rates of cooling in the
central corneal and temporal conjunctival regions, where most of the cooling
happens, attributed to the ellipsoidal isotherms observed with horizontal
central axis8.
• The difference in cooling rates between the different regions of the ocular
surface can be due to the differing neural anatomy of the cornea and
conjunctiva.
• Owing to the physiological flow of tears to the meniscus and medial canthus 9,
the nasal conjunctiva has lesser cooling effect than the temporal conjunctival
and corneal regions.
Acknowledgements: Research support provided by an Unlimited challenge
grant by Reseach to Prevent Blindness (RPB)
No financial disclosures
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