Wei Yueying, Lopes Bernardo T, Eliasy Ashkan, Wu Richard, Fathy Arwa, Elsheikh Ahmed, Abass Ahmed
Department of Chemical Engineering and Applied Chemistry, University of Toronto, Toronto, Ontario, Canada.
Department of Mechanical, Materials and Aerospace Engineering, School of Engineering, University of Liverpool, Liverpool, UK.
Heliyon. 2021 Dec 18;7(12):e08623. doi: 10.1016/j.heliyon.2021.e08623. eCollection 2021 Dec.
To investigate the capability of Zernike polynomials fitting to reconstruct corneal surfaces as measured by Pentacam HR tomographer, Medmont E300 Placido-disc and Eye Surface Profiler (ESP).
The study utilised a collection of clinical data of 527 participants. Pentacam HR raw elevation data of 660 eyes (430 healthy and 230 keratoconic) were fitted to Zernike polynomials of order 2 to 20. Same analyses were carried out on 158 eyes scanned by Medmont E300 Placido-disc and 236 eyes were scanned by ESP for comparison purposes. The Zernike polynomial fitting was carried out using a random 80% of each individual eye surface's data up to a corneal radius of 5 mm and the root means squared fitting error (RMS) was calculated for the unused 20% portion of the surface data. The process was carried out for the anterior and posterior surfaces of the corneal measurements of the Pentacam HR and the anterior surfaces only with the ESP and the Medmont E300 measurements.
Statistical significances in reduction of RMS were noticed up to order 14 among healthy participants (p < 0.0001 for right eyes, p = 0.0051 for left eyes) and up to order 12 (p < 0.0001 for right eyes, p = 0.0002 for left eyes) in anterior surfaces measured by the Pentacam. Among keratoconic eyes, statical significance was noticed up to order 12 in both eyes (p < 0.0001 for right eyes, p = 0.0003 for left eyes). The Pentacam posterior corneal data, both right and left, healthy and keratotic eyes recorded significance (p < 0.0001) in reduction of RMS up to order 10 with same RMS values of 0.0003 mm with zero standard deviation. RMS of fitting Zernike polynomials to Medmont data up to order 20 showed a consistent reduction in RMS with the increase of the fitting order with no rise at high fitting orders. Minimum RMS = 0.0047 ± 0.0021 mm, 0.0046 ± 0.0019 mm for right and left eyes respectively were recorded at order 20 and were more than 15 times the minimum RMS of the Pentacam. RMS of fitting Zernike polynomials to ESP data also showed a consistent reduction in RMS with the increase of the fitting order with no sign of any rise at high fitting orders. Similar to the Medmont, minimum RMS of 0.0005 ± 0.0003 mm, 0.0006 ± 0.0003 mm was recorded at order 20 for right and left eyes respectively and was 2 times the minimum RMS of the Pentacam for right eyes and 1.7 times the minimum RMS of the Pentacam for left eyes.
Orders 12 and 10 Zernike polynomials almost perfectly matched the raw-elevation data collected from Pentacam for anterior and posterior surfaces, respectively for either healthy or keratoconic corneas. The Zernike fitting could not perfectly match the data collected from Medmont E300 and ESP.
研究泽尼克多项式拟合用于重建由Pentacam HR眼前节分析仪、Medmont E300角膜地形图仪和眼表轮廓仪（ESP）测量的角膜表面的能力。
本研究使用了527名参与者的临床数据集合。对660只眼睛（430只健康眼和230只圆锥角膜眼）的Pentacam HR原始高度数据进行2到20阶的泽尼克多项式拟合。为作比较，对Medmont E300角膜地形图仪扫描的158只眼睛和ESP扫描的236只眼睛进行了相同分析。使用每只眼睛表面数据的随机80%进行泽尼克多项式拟合，直至角膜半径5mm，并计算表面数据未使用的20%部分的均方根拟合误差（RMS）。对Pentacam HR角膜测量的前表面和后表面以及ESP和Medmont E300测量的仅前表面进行该过程。
在健康参与者中，直至14阶均观察到RMS降低具有统计学意义（右眼p<0.0001，左眼p = 0.0051），在Pentacam测量的前表面中，直至12阶具有统计学意义（右眼p<0.0001，左眼p = 0.0002）。在圆锥角膜眼中，双眼直至12阶均观察到统计学意义（右眼p<0.0001，左眼p = 0.0003）。Pentacam角膜后表面数据，无论右眼还是左眼、健康眼还是圆锥角膜眼，在直至10阶时RMS降低均具有统计学意义（p<0.0001），RMS值均为0.0003mm，标准差为零。对Medmont数据进行20阶以下的泽尼克多项式拟合，RMS随拟合阶数增加而持续降低，在高拟合阶数时无上升。在20阶时分别记录到右眼和左眼的最小RMS = 0.0047±0.0021mm、0.0046±0.0019mm，比Pentacam的最小RMS大15倍以上。对ESP数据进行泽尼克多项式拟合，RMS也随拟合阶数增加而持续降低，在高拟合阶数时无上升迹象。与Medmont类似，在20阶时分别记录到右眼和左眼的最小RMS为0.0005±0.0003mm、0.0006±0.0003mm，分别是Pentacam右眼最小RMS的2倍和Pentacam左眼最小RMS的1.7倍。
12阶和10阶泽尼克多项式分别几乎完美匹配了从Pentacam收集的健康或圆锥角膜前表面和后表面的原始高度数据。泽尼克拟合不能完美匹配从Medmont E300和ESP收集的数据。
