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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 References: 1. 2. 3. 4. 5. 6. 7. 8. 9. Fox RI, Stern M, Michelson P. Update in Sjogren syndrome. Curr Opin Rheumatol. Sep 2000;12(5):391-398. Kottaiyan R, Yoon G, Wang Q, Yadav R, Zavislan JM, Aquavella JV. Integrated multimodal metrology for objective and noninvasive tear evaluation. Ocul Surf. Jan 2012;10(1):43-50. Kawali A. Thermography in ocular inflammation. Vol 232013. Arora N, Martins D, Ruggerio D, et al. Effectiveness of a noninvasive digital infrared thermal imaging system in the detection of breast cancer. American Journal of Surgery. Oct 2008;196(4):523-526. Gowen AA, O'Donnell CP, Esquerre C, Downey G. Influence of polymer packaging films on hyperspectral imaging data in the visiblenear-infrared (450-950 nm) wavelength range. Applied Spectroscopy. Mar 2010;64(3):304-312. Azharuddin M, Bera SK, Datta H, Dasgupta AK. 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