An empirical investigation of deviations from the Beer-Lambert law in near-infrared spectroscopy: A case study of lactate in aqueous solutions, serum, blood and tissue

An empirical investigation of deviations from the Beer-Lambert law in near-infrared spectroscopy: A case study of lactate in aqueous solutions, serum, blood and tissue | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article An empirical investigation of deviations from the Beer-Lambert law in near-infrared spectroscopy: A case study of lactate in aqueous solutions, serum, blood and tissue Mohammad Mamouei, Karthik Budidha, Nystha Baishya, Meha Qassem, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-192224/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 8 You are reading this latest preprint version Abstract The linear relationship between optical absorbance and the concentration of analytes -as postulated by the Beer-Lambert law- is one of the fundamental assumptions that much of the optical spectroscopy literature is explicitly or implicitly based upon. The common use of linear regression models such as principal component regression and partial least squares exemplifies how the linearity assumption is upheld in practical applications. However, the literature also establishes that deviations from the Beer-Lambert law can be expected when a) the light source is far from monochromatic, b) the concentrations of analytes are very high and c) the medium is highly scattering. The lack of a quantitative understanding of when such nonlinearities can become predominant, along with the mainstream use of nonlinear machine learning models in different fields, have given rise to the use of methods such as random forests, support vector regression, and neural networks in spectroscopic applications. This raises the question that, given the small number of samples and the high number of variables in many spectroscopic datasets, are nonlinear effects significant enough to justify the additional model complexity? In the present study, we empirically investigate this question in relation to lactate, an important biomarker. Particularly, to analyze the effects of scattering matrices, three datasets were generated by varying the concentration of lactate in phosphate buffer solution, human serum, and sheep blood. Additionally, the fourth dataset pertained to invivo, transcutaneous spectra obtained from healthy volunteers in an exercise study. Linear and nonlinear models were fitted to each dataset and measures of model performance were compared to attest the assumption of linearity. To isolate the effects of high concentrations, the phosphate buffer solution dataset was augmented with six samples with very high concentrations of lactate between (100-600 mmol/L). Subsequently, three partly overlapping datasets were extracted with lactate concentrations varying between 0-11 mmol/L, 0-20 mmol/L and 0-600 mmol/L. Similarly, the performance of linear and nonlinear models were compared in each dataset. This analysis did not provide any evidence of substantial nonlinearities due high concentrations. However, the results suggest that nonlinearities in scattering media may be substantial, justifying the use of complex, nonlinear models. Photonics/optics Optics/Lasers Optical Materials and Devices Computational Physics Beer-Lambert law optics near-infrared spectroscopy Figures Figure 1 Figure 2 Figure 3 Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Major revision 30 Mar, 2021 Reviews received at journal 27 Feb, 2021 Reviewers agreed at journal 24 Feb, 2021 Reviewers invited by journal 24 Feb, 2021 Editor assigned by journal 16 Feb, 2021 Editor invited by journal 10 Feb, 2021 Submission checks completed at journal 10 Feb, 2021 First submitted to journal 30 Jan, 2021 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-192224","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":11214533,"identity":"a0f4e47a-a7f1-4523-9134-92976f6ea03b","order_by":0,"name":"Mohammad Mamouei","email":"data:image/png;base64,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","orcid":"","institution":"University of Oxford","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Mohammad","middleName":"","lastName":"Mamouei","suffix":""},{"id":11214535,"identity":"e0b28358-5f43-4fcb-a2a5-ff5d844fcd9e","order_by":1,"name":"Karthik Budidha","email":"","orcid":"","institution":"City, University of London","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Karthik","middleName":"","lastName":"Budidha","suffix":""},{"id":11214536,"identity":"8c5d63fe-b405-41b7-967a-15d9c8e668f9","order_by":2,"name":"Nystha Baishya","email":"","orcid":"","institution":"City, University of London","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Nystha","middleName":"","lastName":"Baishya","suffix":""},{"id":11214538,"identity":"9cdc8d01-90c6-469d-9cd4-348327d09c0b","order_by":3,"name":"Meha Qassem","email":"","orcid":"","institution":"City, University of London","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Meha","middleName":"","lastName":"Qassem","suffix":""},{"id":11214539,"identity":"bf4da1b0-4485-4b46-a2aa-3cd215dc05b5","order_by":4,"name":"Panayiotis Kyriacou","email":"","orcid":"","institution":"City, University of London","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Panayiotis","middleName":"","lastName":"Kyriacou","suffix":""}],"badges":[],"createdAt":"2021-01-30 22:29:01","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-192224/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-192224/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":5992013,"identity":"3f1dd5fb-bc05-4e29-84ae-cfe7c01ce668","added_by":"auto","created_at":"2021-02-15 23:32:16","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":103191,"visible":true,"origin":"","legend":"The comparison of the performance of linear and nonlinear models is datasets with low, medium, and high ranges of lactate concentrations. 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