Modified lambert beer for bilirubin concentration and blood oxygen saturation prediction

(1) Pek Ek Ong Mail (Universiti Tun Hussein Onn Malaysia, Malaysia)
(2) * Audrey Kah Ching Huong Mail (Universiti Tun Hussein Onn Malaysia, Malaysia)
(3) Xavier Toh Ik Ngu Mail (Universiti Tun Hussein Onn Malaysia, Malaysia)
(4) Farhanahani Mahmud Mail (Universiti Tun Hussein Onn Malaysia, Malaysia)
(5) Sheena Punai Philimon Mail (Universiti Tun Hussein Onn Malaysia, Malaysia)
*corresponding author


Noninvasive measurement of health parameters such as blood oxygen saturation and bilirubin concentration predicted via an appropriate light reflectance model based on the measured optical signals is of eminent interest in biomedical research. This is to replace the use of conventional invasive blood sampling approach. This study aims to investigate the feasibility of using Modified Lambert Beer model (MLB) in the prediction of one’s bilirubin concentration and blood oxygen saturation value, SO2. This quantification technique is based on a priori knowledge of extinction coefficients of bilirubin and hemoglobin derivatives in the wavelength range of 440 – 500 nm. The validity of the prediction was evaluated using light reflectance data from TracePro raytracing software for a single-layered skin model with varying bilirubin concentration. The results revealed some promising trends in the estimated bilirubin concentration with mean ± standard deviation (SD) error of 0.255 ± 0.025 g/l. Meanwhile, a remarkable low mean ± SD error of 9.11 ± 2.48 % was found for the predicted SO2 value. It was concluded that these errors are likely due to the insufficiency of the MLB at describing changes in the light attenuation with the underlying light absorption processes. In addition, this study also suggested the use of a linear regression model deduced from this work for an improved prediction of the required health parameter values.


Bilirubin; Blood oxygen saturation; Modified lambert beer law; Raytracing



Article metrics

Abstract views : 68 | PDF views : 24




Full Text



[1] A. Huong, S. Philimon, and X. Ngu, "Multispectral imaging of acute wound tissue oxygenation," Journal of Innovative Optical Health Sciences, vol. 10, p. 1750004, 2017, doi: 10.1142/S1793545817500043.

[2] J. M. Kirk, "Neonatal jaundice: a critical review of the role and practice of bilirubin analysis," Annals of clinical biochemistry, vol. 45, pp. 452-462, 2008, doi: 10.1258/acb.2008.008076.

[3] S. K. Alla, A. Huddle, J. D. Butler, P. S. Bowman, J. F. Clark, and F. R. Beyette, "Point-of-care device for quantification of bilirubin in skin tissue," IEEE Transactions on Biomedical Engineering, vol. 58, pp. 777-780, 2011, doi: 10.1109/TBME.2010.2093132.

[4] S. A. Kumar, P. R. Bhadri, F. Beyette, J. F. Clark, and W. Wurster, "Non-invasive biomedical system for the quantification of bilirubin in neonates," in 48th Midwest Symposium on Circuits and Systems, 2005., 2005, pp. 1778-1781, doi: 10.1109/MWSCAS.2005.1594466.

[5] N. Polley, S. Saha, S. Singh, A. Adhikari, S. Das, B. R. Choudhury, et al., "Development and optimization of a noncontact optical device for online monitoring of jaundice in human subjects," Journal of biomedical optics, vol. 20, p. 067001, 201, doi: 10.1117/1.JBO.20.6.067001.

[6] Z. Zulkarnay, A. Jurimah, B. Ibrahim, S. Shazwani, E. Cheng, A. Ruzairi, et al., "An overview on jaundice measurement and application in biomedical: The potential of non-invasive method," in 2015 2nd International Conference on Biomedical Engineering (ICoBE), 2015, pp. 1-6, doi: 10.1109/ICoBE.2015.7235896.

[7] P. M. Varughese and L. Krishnan, "Does color really matter? Reliability of transcutaneous bilirubinometry in different skin-colored babies," Indian Journal of Paediatric Dermatology, vol. 19, p. 315, 2018, doi: 10.4103/ijpd.IJPD_3_18.

[8] S. Samiee-Zafarghandy, J. Feberova, K. Williams, A. Yasseen, S. Perkins, and B. Lemyre, "Influence of skin colour on diagnostic accuracy of the jaundice meter JM 103 in newborns," Archives of Disease in Childhood-Fetal and Neonatal Edition, vol. 99, pp. F480-F484, 2014, doi: 10.1136/archdischild-2013-305699.

[9] N. Verdel, A. Marin, M. Milanič, and B. Majaron, "Physiological and structural characterization of human skin in vivo using combined photothermal radiometry and diffuse reflectance spectroscopy," Biomedical Optics Express, vol. 10, pp. 944-960, 2019, doi: 10.1364/BOE.10.000944.

[10] T. M. Bydlon, R. Nachabé, N. Ramanujam, H. J. Sterenborg, and B. H. Hendriks, "Chromophore based analyses of steady‐state diffuse reflectance spectroscopy: current status and perspectives for clinical adoption," Journal of biophotonics, vol. 8, pp. 9-24, 2015, doi: 10.1002/jbio.201300198.

[11] C. Veenstra, W. Petersen, I. M. Vellekoop, W. Steenbergen, and N. Bosschaart, "Spatially confined quantification of bilirubin concentrations by spectroscopic visible-light optical coherence tomography," Biomedical optics express, vol. 9, pp. 3581-3589, 2018, doi: 10.1364/BOE.9.003581.

[12] P. Ong, A. K. Huong, W. Hafizah, K. Tay, and S. P. Philimon, "Reflectance spectroscopy system for noninvasive prediction of skin bilirubin concentration related parameter," in 2016 IEEE EMBS Conference on Biomedical Engineering and Sciences (IECBES), 2016, pp. 352-355, doi: 10.1109/IECBES.2016.7843472.

[13] R. B. Saager, M. L. Baldado, R. A. Rowland, K. M. Kelly, and A. J. Durkin, "Method using in vivo quantitative spectroscopy to guide design and optimization of low-cost, compact clinical imaging devices: emulation and evaluation of multispectral imaging systems," Journal of biomedical optics, vol. 23, p. 046002, 2018, doi: 10.1117/1.JBO.23.4.046002.

[14] F. Vasefi, N. MacKinnon, R. B. Saager, A. J. Durkin, R. Chave, E. H. Lindsley, et al., "Polarization-sensitive hyperspectral imaging in vivo: a multimode dermoscope for skin analysis," Scientific reports, vol. 4, p. 4924, 2014, doi: 10.1038/srep04924.

[15] A. Huong and X. Ngu, "The application of Extended Modified Lambert Beer model for measurement of blood carboxyhemoglobin and oxyhemoglobin saturation," Journal of Innovative Optical Health Sciences, vol. 7, 2014, doi: 10.1142/S1793545814500266.

[16] R. N. Pittman and B. R. Duling, "A new method for the measurement of percent oxyhemoglobin," Journal of applied physiology, vol. 38, pp. 315-320, 1975, doi: 10.1152/jappl.1975.38.2.315.

[17] A. K. C. Huong, "Spectroscopic analysis of scattering media via different quantification techniques," Thesis, University of Nottingham, 2012, available at: Google Scholar.

[18] S. J. Madsen and B. C. Wilson, "Optical properties of brain tissue," in Optical methods and instrumentation in brain imaging and therapy, ed: Springer, 2013, pp. 1-22, doi: 10.1007/978-1-4614-4978-2_1.

[19] N. Ali and Z. Z. Abidin, "A Review of Non—Invasive Jaundice detection using Optical Technique in Neonates," in Conference in Advances In Computing, Electronics and Electrical Technology-CEET 2014, 2014, pp. I-3, available at: Google Scholar.

[20] A. Bjorgan, M. Milanic, and L. L. Randeberg, "Estimation of skin optical parameters for real-time hyperspectral imaging applications," Journal of biomedical optics, vol. 19, p. 066003, 2014, doi: 10.1117/1.JBO.19.6.066003.

[21] M. Hirose, M. Kuroshima, and N. Tsumura, "Nonlinear estimation of chromophore concentrations, shading and surface reflectance from five band images," in Color and Imaging Conference, 2015, pp. 161-166, available at: Google Scholar.

[22] G. Einstein, P. Aruna, and S. Ganesan, "Monte Carlo based model for diffuse reflectance from turbid media for the diagnosis of epithelial dysplasia," Optik, vol. 181, pp. 828-835, 2019, doi: 10.1016/j.ijleo.2018.12.158.

[23] A. Moy and J. Tunnell, "Diffuse Reflectance Spectroscopy and Imaging," in Imaging in Dermatology, ed: Elsevier, 2016, pp. 203-215, doi: 10.1016/B978-0-12-802838-4.00017-0.

[24] L. Hou, Y. Liu, L. Qian, Y. Zheng, J. Gao, W. Cao, et al., "Portable Near-Infrared Technologies and Devices for Noninvasive Assessment of Tissue Hemodynamics," Journal of Healthcare Engineering, vol. 2019, 2019, doi: 10.1155/2019/3750495.

[25] Y. Karamavuş and M. Özkan, "Newborn jaundice determination by reflectance spectroscopy using multiple polynomial regression, neural network, and support vector regression," Biomedical Signal Processing and Control, vol. 51, pp. 253-263, 2019, doi: 10.1016/j.bspc.2019.01.019.

[26] E. E. Tripoliti, T. G. Papadopoulos, G. S. Karanasiou, K. K. Naka, and D. I. Fotiadis, "Heart failure: diagnosis, severity estimation and prediction of adverse events through machine learning techniques," Computational and structural biotechnology journal, vol. 15, pp. 26-47, 2017, doi: 10.1016/j.csbj.2016.11.001.

[27] P. Ong and A. K. Huong, "Point Spectroscopy System for Noncontact and Noninvasive Prediction of Transcutaneous Bilirubin Concentration," in IOP Conference Series: Materials Science and Engineering, 2017, p. 012130, doi: 10.1088/1757-899X/226/1/012130.

[28] K. Grohmann, M. Roser, B. Rolinski, I. Kadow, C. Müller, A. Goerlach-Graw, et al., "Bilirubin measurement for neonates: comparison of 9 frequently used methods," Pediatrics, vol. 117, pp. 1174-1183, 2006, doi: 10.1542/peds.2005-0590.

[29] N. Danaei, R. Ghorbani, A. Emadi, and S. Nooripour, "Evaluating the diagnostic value of skin bilirubin in comparison with plasma bilirubin to identify hyperbilirubinemia in healthy babies," Middle East Journal of Rehabilitation and Health, vol. 3, 2016, doi: 10.17795/mejrh-33493.

[30] T. M. Slusher, I. A. Angyo, F. Bode-Thomas, F. Akor, S. D. Pam, A. A. Adetunji, et al., "Transcutaneous bilirubin measurements and serum total bilirubin levels in indigenous African infants," Pediatrics, vol. 113, pp. 1636-1641, 2004, doi: 10.1542/peds.113.6.1636.

[31] S. J. Jo and O. S. Kwon, "Structure and Function of Skin: The Application of THz Radiation in Dermatology," in Convergence of Terahertz Sciences in Biomedical Systems, ed: Springer, 2012, pp. 281-299, doi: 10.1007/978-94-007-3965-9_16.

[32] A. Bhandari, B. Hamre, Ø. Frette, K. Stamnes, and J. Stamnes, "Modeling optical properties of human skin using Mie theory for particles with different size distributions and refractive indices," Optics express, vol. 19, pp. 14549-14567, 2011, doi: 10.1364/OE.19.014549.

[33] S. L. Jacques, "Optical assessment of tissue heterogeneity in biomaterials and implants," in Laser-Tissue Interaction XI: Photochemical, Photothermal, and Photomechanical, 2000, pp. 576-581, doi: 10.1117/12.388080.

[34] J. A. Iglesias‐Guitian, C. Aliaga, A. Jarabo, and D. Gutierrez, "A biophysically‐based model of the optical properties of skin aging," in Computer Graphics Forum, 2015, pp. 45-55, doi: 10.1111/cgf.12540.

[35] V. V. Tuchin, I. L. Maksimova, D. A. Zimnyakov, I. L. Kon, A. H. Mavlyutov, and A. A. Mishin, "Light propagation in tissues with controlled optical properties," Journal of biomedical optics, vol. 2, pp. 401-418, 1997, doi: 10.1117/1.429841.

[36] H. Ding, J. Q. Lu, W. A. Wooden, P. J. Kragel, and X.-H. Hu, "Refractive indices of human skin tissues at eight wavelengths and estimated dispersion relations between 300 and 1600 nm," Physics in Medicine & Biology, vol. 51, p. 1479, 2006, doi: 10.1088/0031-9155/51/6/008.

[37] J.-C. Lai, Y.-Y. Zhang, Z.-H. Li, H.-J. Jiang, and A.-Z. He, "Complex refractive index measurement of biological tissues by attenuated total reflection ellipsometry," Applied optics, vol. 49, pp. 3235-3238, 2010, doi: 10.1364/AO.49.003235.

[38] S. Chatterjee, J. Phillips, and P. Kyriacou, "Monte Carlo investigation of the effect of blood volume and oxygen saturation on optical path in reflectance pulse oximetry," Biomedical Physics & Engineering Express, vol. 2, p. 065018, 2016, doi: 10.1088/2057-1976/2/6/065018.

[39] I. Krasnikov, C. Suhr, A. Seteikin, B. Roth, and M. Meinhardt-Wollweber, "Two efficient approaches for modeling of Raman scattering in homogeneous turbid media," JOSA A, vol. 33, pp. 426-433, 2016, doi: 10.1364/JOSAA.33.000426.

[40] V. Barun and A. Ivanov, "Role of epidermis in the optics and thermal physics of human skin," Optics and Spectroscopy, vol. 107, p. 909, 2009, doi: 10.1134/S0030400X09120121.

[41] S. Prahl, "Optical absorption of hemoglobin," 1999, available at:

[42] L. G. Henyey and J. L. Greenstein, "Diffuse radiation in the galaxy," The Astrophysical Journal, vol. 93, pp. 70-83, 1941, doi: 10.1086/144246.

[43] R. Anderson and E. Ross, "Laser-tissue interactions," Cutaneous Laser Surgery: The Art and Science of Selective Photo-thermolysis. Mosby-Year Book: St Louis, pp. 1-18, 1994, available at: Google Scholar.

[44] G. Agati and F. Fusi, "New trends in photobiology recent advances in bilirubin photophysics," Journal of Photochemistry and Photobiology B: Biology, vol. 7, pp. 1-14, 1990, doi: 10.1016/1011-1344(90)85138-M.

[45] I. V. Meglinski and S. J. Matcher, "Quantitative assessment of skin layers absorption and skin reflectance spectra simulation in the visible and near-infrared spectral regions," Physiological Measurement, vol. 23, p. 741, 2002, doi: 10.1088/0967-3334/23/4/312.

[46] T. Kitai, A. Tanaka, A. Tokuka, K. Tanaka, Y. Yamaoka, K. Ozawa, et al., "Quantitative detection of hemoglobin saturation in the liver with near‐infrared spectroscopy," Hepatology, vol. 18, pp. 926-936, 1993, doi: 10.1002/hep.1840180426.

[47] D. Rimini, F. Molinari, W. Liboni, M. Balbo, R. Darò, E. Viotti, et al., "Effect of ocular movements during eye movement desensitization and reprocessing (EMDR) therapy: a near-infrared spectroscopy study," PloS one, vol. 11, p. e0164379, 2016, doi: 10.1371/journal.pone.0164379.

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

International Journal of Advances in Intelligent Informatics
ISSN 2442-6571  (print) | 2548-3161 (online)
Organized by Informatics Department - Universitas Ahmad Dahlan , and UTM Big Data Centre - Universiti Teknologi Malaysia
Published by Universitas Ahmad Dahlan
W :
E :, (paper handling issues), (publication issues)

View IJAIN Stats

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0