Near infrared spectroscopy-based evaluation of patellar tendon and knee ligaments

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Dissertations in Forestry and Natural Sciences

DISSERTATIONS | JARI TORNIAINEN | NEAR INFRARED SPECTROSCOPY-BASED EVALUATION OF PATELLAR TENDON... | No 394

JARI TORNIAINEN

Near Infrared Spectroscopy- Based Evaluation of Patellar Tendon and Knee Ligaments

PUBLICATIONS OF

THE UNIVERSITY OF EASTERN FINLAND

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PUBLICATIONS OF THE UNIVERSITY OF EASTERN FINLAND DISSERTATIONS IN FORESTRY AND NATURAL SCIENCES

N:o 394

Jari Torniainen

NEAR INFRARED

SPECTROSCOPY-BASED EVALUATION OF PATELLAR TENDON AND KNEE

LIGAMENTS

To be presented by the permission of the Faculty of Science and Forestry for public examination in the Auditorium SN200 in Snellmania Building at the University of Eastern Finland, Kuopio, on October 30th, 2020, at 16:00 o’clock.

University of Eastern Finland Department of Applied Physics

Kuopio 2020

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Grano Oy Jyväskylä, 2020

Editors: Pertti Pasanen, Raine Kortet, Jukka Tuomela, and Matti Tedre

Distribution:

University of Eastern Finland Library / Sales of publications julkaisumyynti@uef.fi

http://www.uef.fi/kirjasto

ISBN: 978-952-61-3597-7 (print) ISSNL: 1798-5668

ISSN: 1798-5668 ISBN: 978-952-61-3598-4 (pdf)

ISSNL: 1798-5668 ISSN: 1798-5676

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Author’s address: University of Eastern Finland Department of Applied Physics P.O.Box 1627

70211 Kuopio, FINLAND email: jari.torniainen@uef.fi Supervisors: Professor Juha Töyräs

University of Eastern Finland Department of Applied Physics 70211 Kuopio, FINLAND University of Queensland

School of Information Technology and Electrical Engineering Brisbane, AUSTRALIA email: juha.töyräs@uef.fi

Adjunct Professor Lauri Stenroth University of Eastern Finland Department of Applied Physics 70211 Kuopio, FINLAND email: lauri.stenroth@uef.fi Reviewers: Professor Søren Balling Engelsen

University of Copenhagen Department of Food Science Copenhagen, DENMARK email: se@food.ku.dk Professor Dawn M. Elliot University of Delaware

Department of Biomedical Engineering 19716 Newark, Delaware, USA

email: delliot@udel.edu

Opponent: Professor Dr. Jürgen Popp

Leibniz Institute of Photonic Technology Department of Spectroscopy/Imaging 07745 Jena, GERMANY

email: juergen.popp@leibniz-ipht.de

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Jari Torniainen

Near Infrared Spectroscopy-Based Evaluation of Patellar Tendon and Knee Liga- ments

Kuopio: University of Eastern Finland, 2020 Publications of the University of Eastern Finland Dissertations in Forestry and Natural Sciences N:o 394

ABSTRACT

Near infrared spectroscopy (NIRS) represents an attractive tool for supplementing the arthroscopic evaluation of tissues during orthopedic repair procedures of synovial joints. Arthroscopic NIRS is based on statistical multivariate modeling of the interactions between connective tissues and near infrared (NIR) light. As deterioration of the tissue changes its optical absorption and scattering properties, NIRS can rapidly and non-destructively estimate the integrity and overall health of the tissue.

Compared to the traditional arthroscopic evaluation, NIRS is a less subjective, more repeatable, and most importantly, it is a quantitative technique. While arthroscopic NIRS has been proven to be suitable for investigating articular cartilage, meniscus, and subchondral bone, its capabilities in evaluating properties of knee ligaments have largely been ignored.

Knee ligaments are collagenous viscoelastic bands of connective tissue that restrain and support the knee joint under natural loading conditions. Together with the other connective tissues of the knee, they ensure the correct mechanical function of the joint. Ligament injuries, such as anterior cruciate ligament rupture, are rather common and often occur simultaneously with other joint injuries as a result of sudden trauma, such as a traffic or sporting accident. An NIRS-based evaluation could provide additional diagnostic information regarding the ligament’s condition during any arthroscopically performed repair procedure of the knee, as has previously been demonstrated for articular cartilage and meniscus. The similarities in composition and structure between ligaments, cartilage, and meniscus suggest that NIRS could be sensitive in evaluating the ligament’s mechanical function, chemical composition, and internal structure. The first aim of this thesis was to thoroughly investigate which of these properties of knee ligaments and the patellar tendon could be quantitatively evaluated using NIRS.

The accuracy of the multivariate models describing the relationship between the NIR spectra and tissue properties is highly dependent on the quality of the NIRS measurement. Instrumentation noise, saturation, and scattering effects present in the spectra can substantially distort and lower the accuracy of the models. Various preprocessing operations can be sequentially combined into pipelines in order to reduce or eliminate noise contaminants from the spectra. The selection of the best possible pipeline for a given application is not, however, straightforward and needs to be optimized on a case-by-case basis. Therefore, the secondary aim of this thesis was to provide a more systematic and automated way of generating preprocessing pipelines for multivariate NIRS models by developing an open-source NIRS preprocessing module utilizing Python. The module was tested and validated using a set of arthroscopic NIRS measurements from fully characterized equine fetlock joints collected as a part of an earlier study. This dataset was also documented and published as a part of the thesis to further ameliorate the method development in the

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field of chemometrics.

Studies I and II utilized knee ligament and patellar tendon samples from ten bovine stifle joints and subjected them to NIRS measurements as well as under- taking a comprehensive characterization of the joints’ mechanical, chemical, and structural properties. The suitability of NIRS for predicting different properties of the tissue was investigated with multivariate modeling techniques. The results of studyIindicated that mechanical properties related to yield and failure mechanics of the tissue could be predicted with the highest accuracy. This finding was sup- ported by studyIIwhich reported that the collagen and water contents seemed to be the compositional properties with the highest prediction accuracy. However, no evidence was found that NIRS would be sensitive towards the internal structure or morphology of ligament samples. In studyIII, an open source tool was developed for automatically combining spectral preprocessing operations into preprocessing pipelines. Its applicability to real world problems was demonstrated with two public datasets. In both examples, the automated preprocessing managed to improve the accuracy of the baseline (i.e., no preprocessing) models and provided objective means of producing the preprocessing pipeline. StudyIVcurated, documented, and published an open dataset of arthroscopic NIRS measurements and the associated reference variables. The dataset of studyIVwas used to test the preprocessing tool developed in studyIIIand it may in the future be used in a similar fashion for the development or benchmarking of new methods.

In conclusion, NIRS was found to be sensitive towards certain mechanical and compositional properties of knee ligaments and the patellar tendon. Since these properties are related to the overall mechanical strength of the tissue, NIRS could potentially be a useful diagnostic tool for the quantitative evaluation of ligament tissue integrity during arthroscopic evaluation of the joint. Therefore, arthroscopic NIRS could be suitable for obtaining a quantified analysis of all connective tissues found within the knee and other synovial joints. The automated preprocessing optimization improved the prediction accuracy of multivariate models in the two examples evaluated. The open source spectral preprocessing tool developed as a part of this thesis should enable future NIRS investigators to adopt a more systematic, objective, and reproducible approach for optimizing preprocessing pipelines.

National Library of Medicine Classification:QT 34, QT 34.5, QT 36, QU 34, QY 90, WE 300, WE 600, WN 180

Medical Subject Headings: Spectroscopy, Near-Infrared; Ligaments, Articular; Patellar Ligament; Knee Joint; Collagen; Proteoglycans; Water; Cartilage, Articular; Biomechanical Phenomena; Biochemical Phenomena; Multivariate Analysis

Yleinen suomalainen ontologia:lähi-infrapunaspektroskopia; spektrianalyysi; polvet; nivel- siteet; nivelrusto; jänteet; fysikaaliset ominaisuudet; kemialliset ominaisuudet; rakenne (ominaisuudet); biomekaniikka; vetokokeet; kollageenit; proteoglykaanit; monimuuttujamenetelmät;

avoin lähdekoodi; Python

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ACKNOWLEDGEMENTS

The research work of this thesis was conducted in the Department of Applied Physics of the University of Eastern Finland between the years 2016-2020.

First, I wish to thank my supervisors Professor Juha Töyräs Ph.D and Lauri Stenroth Ph.D for their continuous guidance, support, and patience in all stages of my Ph.D research. I thank Juha for providing me with the opportunity of pursu- ing a Ph.D degree in such a renowned and stimulating research environment, as well as for the professional supervision, constructive criticism, and insightful ad- vice. I thank Lauri for his constant enthusiasm, encouragement and his near infinite knowledge of all things biomechanical.

I would like to thank all my co-authors, especially Jaakko K. Sarin, Mithilesh Prakash, Aapo Ristaniemi and Isaac O. Afara for their unwavering support and expertise. Without their collective contribution, finishing this thesis would certainly have been very difficult if not nearly impossible. I would also thank my co-workers Petri, Aleksi, Abishek, Iman, Bilour, Juho, Satu, Anni, Kata, Miitu, as well as all members (past and present) of the Biophysics of Bone and Cartilage group.

I wish to express my gratitude to the pre-examiners, Professors Dawn Elliot Ph.D and Søren B. Engelsen Ph.D, for their thorough and meticulous work reviewing the thesis. Their helpful and critical feedback greatly improved the quality of the final version.

I am thankful for all the funding provided for my thesis, namely the Doc- toral Programme in Science, Technology and Computing (SCITECO), State Research Funding of Kuopio University Hospital, and Orion Research Foundation.

I wish to thank my art collective friends Kasperi, Aleksander, Henri, and Jukka for providing a welcomed and enjoyable distraction from the academic work.

Last but not least, I want to thank my parents Tuula and Jorma, my sister Suvi and her family; Jussi and Viivi, my paternal grandparents Terttu and Eki and my maternal grandparents Ulla and Pauli.

Kuopio, October 30th, 2020 Jari Torniainen

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LIST OF PUBLICATIONS

This thesis consists of the present review of the author’s work in the field of optical spectroscopy of connective tissues and the following selection of the author’s publications:

I J. Torniainen, A. Ristaniemi, J. K. Sarin, S. Mikkonen, I. O. Afara, L. Stenroth, R.

K. Korhonen and J. Töyräs "Near infrared spectroscopic evaluation of ligament and tendon biomechanical properties,"Annals of Biomedical Engineering47, 213–

222 (2019).

II J. Torniainen, A. Ristaniemi, J. K. Sarin, M. Prakash, I. O. Afara, M. Finnilä, L.

Stenroth, R. K. Korhonen and J. Töyräs, "Near infrared spectroscopic evaluation of biochemical and crimp properties of knee joint ligaments and patellar tendon,"Submitted for publication(2020).

III J. Torniainen, I. O. Afara, M. Prakash, J. K. Sarin, L. Stenroth, and J. Töyräs,

"Open-source python module for automated preprocessing of near infrared spectroscopic data,"Analytica Chimica Acta1108, 1–9 (2020).

IV J. K. Sarin, J. Torniainen, M. Prakash, L. Rieppo, I. O. Afara and J. Töyräs,

"Dataset on equine cartilage near infrared spectra, composition, and functional properties,"Scientific data6, 1–8 (2019).

Throughout the thesis, these papers will be referred to by Roman numerals.

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AUTHOR’S CONTRIBUTION

The studies selected for this dissertation are original research papers on NIRS-based evaluation of ligament properties and development of general chemometric methods for NIRS modeling.

In studies I–II, the author participated in sample preparation, conducted the NIRS measurements, and performed the data analysis. The mechanical reference properties were measured and analysed by A. Ristaniemi, who also oversaw the sample preparation. The chemical reference properties were measured by T. Paakko- nen and E. Rahunen. Histological analysis and calculation of the structural reference properties were conducted by D. Mondal.

In study III, the author wrote the source code for the module framework and most of the preprocessing functions. I. O. Afara also contributed to the individual preprocessing operations in the module. The focus of studyIV was in the publication of an open access dataset consisting of multiple measurements collected in earlier studies. The author collected, curated and documented all of the individual measurements in collaboration with J. K. Sarin. As J. K. Sarin had performed most of the original measurements, he was listed as the first author in studyIVand J. Tor- niainen as the second author. However, J.K. Sarin and J. Torniainen have designated joint first authorship of studyIV.

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Acronyms

ACL Anterior Cruciate Ligament.

API Application Programming Interface.

CCD Charge-Coupled Device.

CV Cross-validation.

DLSNV Dynamic Localized Standard Normal Variate.

ECM Extracellular Matrix.

EDTA Ethylenediaminetetraacetic Acid.

EISC Extended Inverted Signal Correction.

EMSC Extended Multiplicative Scatter Correction.

FN False Negative.

FP False Positive.

GAG Glycosaminoglycan.

GUI Graphical User Interface.

IR Infrared.

LCL Lateral Collateral Ligament.

LSNV Local Standard Normal Variate.

MCL Medial Collateral Ligament.

MCUVE Monte Carlo Uninformative Variable Elimination.

MEMS Microelectromechanical System.

MIRS Mid Infrared Spectroscopy.

MLR Multiple Linear Regression.

MRI Magnetic Resonance Imaging.

MSC Multiplicative Scatter Correction.

NIPALS Nonlinear Iterative Partial Least Squares.

NIR Near Infrared.

NIRS Near Infrared Spectroscopy.

OA Osteoarthritis.

PBS Phosphate-buffered Saline.

PCA Principal Component Analayis.

PCL Posterior Cruciate Ligament.

PCR Principal Component Regression.

PG Proteoglycan.

PLM Polarized Light Microscopy.

PLSR Partial Least Squares Regression.

PT Patellar Tendon.

RMSE Root Mean Square Error.

RMSEC Root Mean Squared Error of Calibration.

RMSECV Root Mean Square Error of Cross-validation.

RMSEP Root Mean Square Error of Prediction.

RNV Robust Normal Variate.

SD Standard Deviation.

SG Savitzky-Golay.

SNR Signal-to-Noise Ratio.

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SNV Standard Normal Variate.

SVM Support Vector Machines.

TN True Negative.

TP True Positive.

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Symbols

A Absorbance.

r Distance between atoms.

xm Anharmonicity constant of vibration.

c Speed of light.

De Disassociation energy.

re Equilibrium distance between atoms.

e Error term of regression.

h Planck’s constant.

I Intensity.

I0 Intensity of transmitted light.

λ Wavelength.

a Molecule specific constant.

V Morse’s potential energy.

X⁺ Pseudoinverse ofX.

T Projected principal components ofX.

Tn Firstnprincipal components ofX.

Rdark Dark reference reflectance.

y Reference variable.

b Regression coefficients.

R_sample Reflectance measured from the sample.

R_standard Standard reference reflectance.

µ Mean value of a spectrum.

σ Standard deviation of a spectrum.

X Set of NIR spectra.

xcorr A single scatter corrected NIR spectrum.

x A NIR spectrum.

xre f Reference spectrum.

v Frequency.

Ee Vibrational energy of quantum leveln.

n Vibrational quantum number.

P Weighting matrix.

ˆ

y Estimated/predicted reference variable.

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1 Introduction

Knee ligaments, together with the patellar tendon, are fibrous viscoelastic connective tissue that hold the knee joint together. The four primary knee ligaments, anterior cruciate (ACL), posterior cruciate (PCL), lateral collateral (LCL), and medial collateral ligament (MCL) connect the femur to the tibia and fibula, while the patellar tendon (PT) connects the patella to the tibia. Ligaments and the PT stabilize the knee and, together with other support structures, limit the range of disadvantageous translations and rotations of the joint [1].

An ACL rupture is a relatively common knee injury which results in discomfort, pain, reduced mobility, and instability of the joint. Injuries of the PCL and MCL also occur, although they are more rare. In addition to the above mentioned acute effects of ligament rupture, the resulting instability of the joint can subject articular cartilage and meniscus to abnormal loading conditions. Prolonged abnormal loading can lead to osteoarthritis (OA), a degenerative joint disease characterized by the erosion of articular cartilage and abnormal growth of subchondral bone [2, 3]. Ad- vanced OA is associated with pain, loss of mobility, an overall reduced quality of life, and in severe cases, it requires a total knee replacement.

Depending on the severity of the injury, patient age, and the required level of physical activity, injured ligaments (mainly ACLs) can be treated either conserva- tively (i.e., physiotherapy), operatively (i.e., surgery), or via a combination of the two approaches [4]. The operative treatment of ligaments, where damaged tissue is replaced with a graft, is typically performed as an arthroscopic procedure by an orthopedic surgeon [5]. During these graft surgeries and other intracapsular repair procedures, an evaluation of ligament condition is often performed. These evalua- tions are conducted by using manual palpation with an arthroscopic hook and vi- sual observation through an endoscopic camera. Although this technique has been routine in orthopedics for decades, its reliability for evaluating cartilage lesions in terms of objectivity [6, 7], repeatability [6], and as a source of quantitative information [8] has been questioned. It is plausible that the arthroscopic evaluation of other connective tissues, such as ligaments, suffer from similar drawbacks.

Near infrared spectroscopy (NIRS), a vibrational spectroscopic technique typically used for bulk chemical analysis, has recently shown significant potential for evaluating the condition of connective tissues (e.g., articular cartilage and meniscus) in real-time [9–12]. NIRS measures diffusely reflected (or transmitted) broadband NIR light (750 – 2500 nm) from a given sample and uses a spectrometer to determine the absorbance at each wavelength. In the case of cartilage and meniscus, the resulting absorbance spectrum is mainly defined by the concentrations of water and the various proteins in the tissue. As the increase of water in the tissue (i.e., swelling) and changes in the extracellular matrix (i.e., breakdown of the collagen network) are symptoms of cartilage deterioration [13, 14], NIRS measurements can provide diagnostic information about the tissue’s condition. The instrumentation required for NIRS is comparatively simple and measurements can be performed outside of laboratory environments. Therefore, adapting NIRS for arthroscopic evaluation of connective tissues is a relatively straightforward process, requiring only custom-

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made sterile NIRS probes which can fit into the knee cavities. While this technique has previously been demonstrated for articular cartilage, meniscus, and subchondral bone, it has not yet been tested for knee ligaments or the patellar tendon.

The ability to predict tissue properties from the corresponding NIR spectrum is based on building multivariate predictive models, a procedure which is often referred to as chemometrics [15]. Construction of these models consists of several steps, such as sample selection, preprocessing [16–19], variable selection [20–23], calibration [22], and validation [24, 25]. Optimizing the individual steps in the mod- elling process can have a substantial impact on the overall accuracy and precision of the final outcome [18, 22, 26, 27]. While the concept of arthroscopic NIRS has been proven to be feasible, it has been claimed that the models used in arthroscopic NIRS can be further improved by optimizing the modeling pipeline [22]. The development of better chemometric models for arthroscopic tissue evaluation could, therefore, significantly benefit from openly available spectral datasets and open source analysis tools.

Studies Iand II of this thesis focused on establishing whether an NIRS-based evaluation could be applied to the knee ligaments and the patellar tendon. The instrumentation used in these studies spanned both the wavelength regions of visible and NIR light. For the sake of brevity and clarity, however, throughout the thesis the technique is referred to as NIRS (instead of VIS/NIRS). Both of these studies utilized the same set of samples which were extracted from ten bovine stifle joints. Similar studies regarding articular cartilage and meniscus have revealed that NIRS is capable of detecting both biochemical compositions as well as predicting the mechanical properties of collagen-rich connective tissues. StudyIinvestigated the ability of NIRS to predict the tissue responses to stress-relaxation, sinusoidal, and quasi-static mechanical loading. While the mechanical properties of ligaments are their most important functional attribute, they are not directly measurable with NIRS, as they are defined by both the chemical composition and internal structure of the tissue. Therefore, studyIIexpanded the findings of studyIby aiming to predict the water, collagen, elastin, and proteoglycan contents of the ligament and patellar tendon samples. In addition, two parameters describing the crimp of the collagen fibers were also included in the list of reference variables in order to examine if the tissue’s internal structural organization could be evaluated with NIRS.

StudiesIIIand IVaimed to improve the existing methodology for NIRS-based evaluation of connective tissues by providing new methods and open access data for building better calibration models. In studyIII, an open source Python module for preprocessing NIRS data was published. This module enables the researcher to more efficiently explore different preprocessing combinations in order to optimize the final calibration model. All the included features were examined in detail and two real-world examples on how to utilize the module with open access datasets were provided. In studyIV, a dataset consisting of a large number of NIR spectra collected from the fetlock joints of Shetland ponies were published together with a large number of mechanical, biochemical, and histological reference variables.

Study IV describes the technical details of the used instrumentation, information about the data, as well as providing example source code on how to use the dataset.

This open access dataset is primarily intended for researchers aiming to develop predictive models for arthroscopic applications without the need of collecting their own data.

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2 Knee ligaments

2.1 ANATOMY AND FUNCTION

The human knee is a modified hinge joint capable of movement in three translational and three rotational directions. The joint consists of the proximal end of the femur, distal end of the tibia, and the patella. The joint is held together by four ligaments and the patellar tendon (Fig. 2.1 a). Two of the ligaments, the anterior cruciate ligament (ACL) and the posterior cruciate ligament (PCL), are positioned inside the joint capsule and sit in a cruciform arrangement between the femoral condyles. The ACL connects the anterior intercondylar area of the tibia posteriorly and superiorly with the lateral femoral condyle [28]. Likewise, the PCL connects the posterior intercondylar area of the tibia to the medial femoral condyle [29]. The lateral collateral ligament (LCL, also known as the fibular collateral ligament) and the medial collateral ligament (MCL, also known as the tibial collateral ligament) are located outside of the articular capsule on the opposite sides of the joint. The LCL connects the lateral femoral epicondyle to the head of the fibula [30], while the MCL connects the medial femoral epicondyle to the tibia and the meniscus [31]. The patellar tendon (PT) is the continuation of the tendon attached to the quadriceps femoris muscle and it connects the apex of the patella to the tuberosity of the tibia [32]. As PT is a ligamentous extension of the quadriceps tendon (i.e., connecting bone to bone), it is sometimes referred to asthe patellar ligament.

The connective soft tissues of the knee work in tandem to support, stabilize, absorb shocks, and ensure smooth movement of the joint. These components are absolutely vital for maintaining an active physical lifestyle and long term mobility.

The primary role of ligaments in this system is to restrain and stabilize the range of motions of which the knee is capable. The ligaments themselves are collagenous

Figure 2.1: a: The four primary ligaments and the patellar tendon of the knee joint. b: An example of how ligaments restrict motions of the knee. Varus and valgus rotations of the joint are limited by the collateral ligaments.

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viscoelastic bands that have adapted to withstand tensile loading along the longitudinal axis. For example, when the knee is maximally extended, the ACL, LCL, and MCL are pulled tight and start to absorb the excess mechanical energy by under- going non-plastic deformation. The ACL primarily resists the forward translation of tibia in relation to femur but it also resists rotation of the joint [33]. Conversely, the PCL resists the backwards translation of the tibia [29]. The LCL and the MCL stabilize the knee in the coronal plane by resisting the varus [30] and valgus [31, 33]

rotations, respectively (Fig. 2.1 b). Additionally, LCL acts as a secondary restraint against posterior tibial translation [30]. Finally, the PT stabilizes the patella while also transmitting forces from the quadriceps femoris muscles to the tibia [34].

2.2 COMPOSITION AND STRUCTURE

Ligaments and tendons are composed of water, an extracellular matrix (ECM), and cells (fibroblasts) [35]. Water is the major component of the tissue, comprising roughly 55–65% of the total wet weight [36]. Fibroblasts account for a very small proportion of the dry weight (e.g., approximately 1.5% in a flexor tendon [37]) and their role is to maintain the ECM by synthesizing and breaking down matrix components [35, 38]. The main component of the ECM is collagen, a fibrous and inter- woven protein structure built from long chains of amino acids, like proline, glycine, and hydroxyproline. The collagen in ligaments and tendons is primarily of type I, although, small amounts of types III, V, VI, XI, and XIV are present as well [35].

Type I collagen is the main tensile load-bearing component, while the other types modulate fibril organization, fibril diameter size, and blood circulation [37]. Col- lagen accounts for approximately 70–80% of ligament [39] and 75–85% of the tendon’s dry weight [36]. In addition to collagen, the ECM also contains a fibrous protein called elastin which consists of amino acids like, glycine, valine, alanine, and proline. Elastin is arranged into elastic fibers and accounts for approximately 10–15% of the dry weight in ligaments [36] and about 1–3% of the dry weight in tendons [40]. The elastin in ligaments is predominantly located between the collagen fibrils and the fascicles [41]. Proteoglycans (PGs) represent a small but important component of the ECM, accounting for 1–3% of the dry weight in ligaments and 1–2% in tendons [36]. PGs are negatively charged macromolecules consisting of a protein core connected to one or more glycosaminoglycan (GAG) side-chains. PGs are hydrophilic and, therefore, attract water into the ECM and also control the size and formation of the collagen fibrils [42]. Ligaments also contain trace amounts of various other non-collagenous proteins (e.g., fibronectin, tenascin-C, and laminin in tendons of a rat [43]) as well as amyloids [44] and lipids [45]. Small amounts of inorganic compounds, mainly, magnesium, calcium, sodium, potassium, and phos- phorus have been detected in tendons [46].

Collagen in ligaments and tendons is organized into dense parallel fascicles which are hierarchically composed of smaller and smaller fibrous elements [47].

At the base level, these structures consist of tropocollagen, a right-handed triple helical molecule, formed by three polypeptide chains. The collagen molecules are also cross-linked [48] which significantly contributes to the tensile strength of the tissue [49]. Tropocollagens join together to form microfibrils which, in turn, form subfibrils and eventually fibrils. At this level, the fibrils exhibit a wave-like pattern commonly known as crimp, which smoothens out when the tissue is stretched [50].

The fibril diameter distribution is known to vary between ligament types (e.g., cru-

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ciate, collateral, and PT) [51], which most likely results from adaptation to specific type of loading. Fibrils are bundled into several distinct fascicles which finally form the whole ligament.

2.3 MECHANICAL RESPONSE

Ligaments aremechanical tissuesand how they respond to physiologically relevant loading is their defining characteristic. As stated in the previous section, the four ligaments and the PT are positioned in such a way to support and stabilizes the joint in all six degrees of freedom. Due to this configuration, most of the loading experienced by each ligament will be tensile stress along the longitudinal axis (i.e., the direction of the collagen fibers). Although under realistic loading conditions, the ligaments will experience stresses (e.g., shear and transverse) in all three dimensions, this section will focus only on the fundamental material properties of ligaments obtained through uniaxial tensile loading along the fibril orientation [1].

The overall biomechanical response of ligaments is primarily determined by the in- trinsic viscoelastic properties of collagen, collagen cross-links, the interconnectivity of the fibers, the collagen crimp, and the amount of elastin present in the tissue.

Like most biological tissues, ligaments are non-linearly viscoelastic, meaning that they exhibit both elastic and viscous material properties with non-linear relationship between stress and strain [50, 52]. Contrary to purely elastic materials, where the stress-induced deformation immediately returns to its initial state upon removal of the stress, the deformation in viscoelastic materials is time-dependent. Elastic materials also immediately release the stored energy when returning to their initial state, whereas in viscoelastic materials, some of this energy is dissipated through deformation. Thus, ligaments possess the typical properties of viscoelastic materials, specifically hysteresis, creep, stress relaxation, and phase lag under oscillatory loading [1]. The mechanical behaviour of ligaments is governed by their material properties which can be empirically determined through mechanical testing. In mechanical testing, a piece of tissue is attached between two clamps and stretched while measuring force and displacement. Normalization of force and displacement with the dimensions of the tissue converts these quantities to stress and strain, which no longer depend on the size of the tissue sample. Different mechanical testing protocols (i.e., how and how fast the tissue is stretched) reveal different mechanical characteristics of the tissue.

The most common mechanical test for viscoelastic materials is the measurement of the stress-strain curve by slowly straining the sample to its ultimate breaking point (Fig. 2.2). Different parts of the curve correspond to different quasi-static tensile responses of the sample [36]. For instance, the initial non-linear region (more commonly known as the toe-region) corresponds to the straightening of the collagen fibril crimp [53] and is modulated by elastin [54]. The toe-region is followed by the linear region which results from the tensile properties of collagen [55], PGs [55], and the multi-level interconnected structure of the fibrils and fascicles. The linear region terminates at the yield point which marks the strain at which plastic (i.e., non-recoverable) deformation starts. At this point, the ligament begins to break down and the relationship between strain and stress becomes highly non-linear.

The stress-strain curve ends at the ultimate failure point (defined as the strain with maximum stress value) which represents the complete breakdown of the ligament sample. Several biomechanical properties can be deduced from the resulting curve,

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Stress

Strain

NORMAL LOADING RISK INJURY

Linear region

Quasi-static mechanical properties of ligaments and tendons

Figure 2.2: Quasi-static properties of ligaments can be determined from a tensile mechanical test with a low strain-rate. The non-linear mechanical response of the toe-region corresponds to the unfolding of the collagen crimp while the linear region results from the elongation of the collagen fibers. The yield point marks the begin- ning of irreversible deformation within the tissue as collagen fibers begin to break down. The mechanical breakdown of the tissue culminates at the ultimate failure point which is followed by a sharp decline in tensile stress. Typical physiological loading of the ligaments occurs much below the yield point.

such as the non-linear response to low strains, Young’s modulus of the linear region, as well as maximal strain and stress the tissue can withstand. For instance, the slope of the linear region is indicative of the overall collagen concentration or collagen fibril diameter in the sample [1]. Furthermore, area-under-the-curve metrics can be used to determine the amount of energy required to induce plastic deformation or total failure of the tissue [1].

Another common mechanical test is the stress relaxation test, where the sample is elongated to a predefined level of strain and then (under constant strain) allowed to relax for a long period of time (Fig. 2.3). Consecutive stress relaxation steps can be conducted to cumulatively increase the total strain. It has been speculated that elastin has an important role in the structural reformation of the ligament during relaxation [41]. Stress relaxation describes the ligaments’ non-linear viscoelastic response to constant strain and can be utilized to better understand and how the ligament adapts to sudden strains of varying magnitudes [56, 57]. A similar mechanical test can be performed by applying constant stress instead of a constant

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Single-step

stress-relaxation Multi-step stress-relaxation

Equili

brium modulus

Figure 2.3: Stress-relaxation protocol consists of elongating the sample to a preset level of strain and monitoring the changes in stress over a relaxation period. The relationship between stress and strain describes how well ligaments and tendons adapt to constant loading with a sudden onset. A similar protocol can be used to investigate the creep phenomena by alternating stress in discreet steps while measuring the changes in strain.

strain to measure the creep property of the tissue.

The ability of ligaments to dissipate mechanical energy can be determined through cyclic loading and unloading of the tissue. The total energy loss can be calculated from the resulting stress-strain curve by calculating the integral between the loading and unloading parts of the curve (i.e., the hysteresis loop); the larger the area between the curves, the larger the energy loss due to deformation. The presence of water in the tissue increases the cyclic relaxation [58]. Cyclic sinusoidal loading can also be used to determine the viscoelastic properties of the tissue [59]. In practice this means alternating the strain of the tissue according to a sinusoidal function and measuring the corresponding stress (Fig. 2.4). The phase difference between the measured strain and stress is a measure of viscoelasticity in the tissue under vibrational conditions, which again, is representative of the energy dissipation capacity of the tissue. The results of sinusoidal loading can be formalised as the dynamic modulus, loss modulus, and storage modulus [60]. In the case of ligaments, sinusoidal loading is typically applied at frequencies around 1 Hz, as this is close to the normal walking cadence.

2.4 INJURY AND TREATMENT

Ligament injuries (i.e., sprains) typically occur as a result of a sudden twisting mo- tion or a blow that subjects the tissue to high tensile stresses. Injuries like these are very common in sports, making athletes one of the main group of people affected.

The ACL is the most commonly injured ligament [61], although injuries to MCL [62]

and LCL are also rather prevalent [63]. An injury to the PCL is more rare [63] and usually attributed to vehicular accidents (especially dashboard injuries) or sports injuries [64]. The symptoms associated with a sprained ligament include physical pain, swelling and loss of stability within the joint. The diagnosis of the ligament sprain is based on a physical examination [65] which, in some cases, is followed by an MRI [65, 66]. Sprains are graded from 1 to 3 based on their severity. Grade 1

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Figure 2.4: Cyclic loading at physiologically relevant frequencies (e.g., 1 Hz) can be used as a tensile testing protocol for determining viscoelastic properties of ligaments and tendons under vibrational conditions.

sprains display no macroscopic tears and usually heal on their own. Grade 2 sprains exhibit macroscopic tears and hypermobility of the joint. In grade 2 sprains, loading of the joint should be controlled and physiotherapy might be prescribed. In grade 3 injuries, the ligament is completely or nearly completely torn and requires extensive physiotherapy or possibly graft surgery. It should also be noted that ligament injuries can also affect the well-being and integrity of other support structures within the knee. Since the knee is a complex mechanical system adapted for multiaxial loading, the instability caused by a damaged ligament can subject meniscus and cartilage to excessive loading [1] and even lead to osteoarthritis [2, 3].

In the more severe cases of a ruptured ACL and PCL, the damaged tissue can be replaced with a graft in a procedure called reconstructive knee surgery. The decision regarding the surgery is done by an orthopedic surgeon based on a consideration of several factors, such as the effectiveness of prior physical therapy, the risk of further meniscal or cartilage damage, and the desired level of future physical activity [65].

For example, professional athletes may choose to undergo surgery in order to return to their sport, while other individuals might be content with physiotherapy and a less stable knee joint. In graft surgeries, the damaged ligament is replaced with a graft material and fixed into the bone. The selection of the graft material (e.g., allograft, autograft, or synthetic graft), the donor site, and the repair procedure have been an active field of research [67]. Most ACL grafts today are obtained as autografts from the patellar tendon.

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3 Near infrared spectroscopy

3.1 SPECTROSCOPY

Spectroscopy is an analytical technique for investigating the different properties of matter by observing its interaction with electromagnetic radiation. These interaction mechanisms vary throughout the electromagnetic spectrum (from radio waves to gamma radiation) as do the techniques, instrumentation, and applications. The spectroscopy of ultraviolet, visible, and infrared light falls into the category of optical spectroscopy, where the infrared region is further subdivided into bands of near, mid, and far infrared (Fig. 3.1). In the infrared region, the interaction between matter and light is primarily based on absorption and scattering resulting from the vibrational and rotational transitions of inter-atom bonds within the molecules.

Near infrared spectroscopy (NIRS) measures the intensity of the reflected or transmitted near infrared (NIR) light (750 – 2500 nm) from the sample as a function of the wavelength (Fig. 3.1). The changes observed in the intensity of the light are caused by excitation of molecular vibrations, more specifically the overtone and combination band transitions between atoms in the measured medium.

NIRS is especially sensitive to bonds involving hydrogen (e.g., C-H, O-H, N-H, and S-H bonds) and is therefore well suited for analysing materials with organic compounds. In contrast to mid-IR spectroscopy (MIRS), where absorption is caused by fundamental transitions, the NIR spectrum is less clearly defined with broader overlapping peaks and lower intensity [68] (Fig. 3.1). These limitations are offset by the benefits of NIRS, which include deeper penetration depth and less stringent requirements for sample preparation [15]. NIRS is suitable for determining the chemical, physical, and bulk properties of various materials and due to its robustness, it is not restricted to laboratory use but can be utilized in the field or for automated monitoring of a chemical process [69].

The phenomenon of NIR radiation was originally discovered by Herschel in the early 1800s but remained largely ignored until the 1980s [70]. During this time, NIRS was largely overshadowed by mid-infrared spectroscopy due to the fact that it is easier to interpret, thanks to the higher molecular absorption and clearer spectral peaks. The development of computer-based multivariate analysis methods and improved instrumentation in the following decades demonstrated the potential of the technique and dramatically increased the research interests around NIRS [71].

NIRS initially found its use in agriculture [72] but the technique soon propagated to other fields of industry and is today a key analytical tool in many fields like petro- chemistry [73], pharmaceutics [74], polymer chemistry [75], and biomedical tissue analysis [76].

3.2 THEORY

Molecules store part of their energy in quantized states of rotation and vibration of their constituent atoms. Since these energy levels are discrete, a transition from one level to another can only occur if an exact amount of energy is introduced into the

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Figure 3.1: The wavelength region of infrared light is located between visible light and microwaves. The absorption occurring in the near infrared wavelengths is caused by the overtone and combination band transitions between atoms. In contrast to the fundamental transitions of the mid infrared region, the overtone absorptions are broader and substantially weaker in amplitude. The relationship between the bond-length and stored energy in terms of the anharmonic oscillator model is also visualized.

system via electromagnetic radiation (i.e., a photon). In other words, a photon is only absorbed by the molecule if the energy of the said photon is high enough to excite a transition. The energy of a photon is defined by the equation

E=hv= ^hc

λ, (3.1)

where h is the Planck’s constant, v the frequency, c the speed of light, and λ is the wavelength. Since the energy of a photon is wavelength-dependent and certain wavelengths are only absorbed as a result of specific transitions, the resulting spectrum can be used for identification of materials or to quantify the composition of the material.

The wavelength range of NIR light is approximately 750 – 2500 nm, corresponding to photon energies of 0.50 – 1.65 eV. In this range, only vibrational stretching and bending transitions occur. The vibration frequency of a chemical bond is determined by the mass of the participating atoms as well as the strength of the bond.

Vibrations of the molecular bonds can be modeled mechanically as a diatomic anharmonic oscillator (Fig. 3.1) [68], which extends the simple harmonic oscillator by accounting for repulsive forces when the atoms are close and dissociation when the atoms are far apart. In this model, the bond is represented by two spherical masses connected with a spring and its potential energy can be approximated using Morse’s potential energy function

V(r) =De(1−ê⁻â(r⁻^rê⁾)², (3.2) where De is the dissociation energy, ais a molecule-specific constant, re the equilibrium distance, and r the distance between the two atoms [69]. By applying

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constraints of the quantum mechanical stationary states according to Schrödinger’s equation, the energy of vibrational levels can be described by the equation

En =hv(n+¹

2)−^xmhv(n+¹

2)², (3.3)

where,nis the vibrational quantum number andxmis the anharmonicity constant of the vibration. The energy required for a transition can be calculated as the difference between the potential energies of the two levels [69]:

∆E=En1−^En2. (3.4)

Excitation from quantum number 0 (i.e., ground state) to 1 is known as a fundamental transition while higher transitions (e.g., 0→2, 0→3, etc.) are known as overtones. Due to the anharmonic nature of the oscillation, the order of the overtone is inversely proportional to the additional energy required for the transition.

It is also possible for two fundamental transitions to occur simultaneously, these phenomena are known as combination bands. Fundamental transitions occur in the MIR range, while the NIR range contains overtones and combination bands.

3.3 INSTRUMENTATION

NIRS instruments (also known as spectrophotometers) consist of three key elements:

a light source, a detector, and a dispersive element (Fig. 3.2 a). The light source pro- vides broadband illumination of the target sample and the returning light (either transmitted or reflected) is measured by the detector. The dispersive element acts as a wavelength selector enabling the measurement of specific wavelengths. Each component has multiple options and the best possible combination for a given application depends on various design criteria (e.g., cost, size, spectral range, resolution, and sensitivity) [77].

An ideal NIRS light source has a stable broadband spectral output over the wavelength range of interest and a long operating life cycle [78]. The most commonly used light sources for visible and NIR range are tungsten halogen lamps [69].

The tungsten halogen lamp produces a relatively flat spectral output of 320 – 2500 nm [78]. The added active halogen inside the bulb reduces the build-up of evap- orated tungsten inside the bulb, thus increasing the lifespan of the source while reducing the fluctuation of the output [79]. Light emitting diodes (LEDs) are another viable option as a NIR light source. The main benefits of LEDs are low cost, low power consumption, and robustness [15, 78]. Since LEDs emit light in a very narrow wavelength range around their center point, combining them to cover a large wavelength range can be technically challenging [78]. The light source can also be implemented using a tunable laser, where the output wavelength can be controlled with high precision [80]. Since the output wavelength of the laser source can be adjusted, instruments with tunable lasers do not require a separate dispersive element.

The incoming light is detected, quantized, and converted to an electrical signal by a detector. Similar to the light source, the characteristics of an ideal detector include stable broadband spectral sensitivity throughout the wavelength region of interest, a high dynamic range, and a high signal-to-noise ratio (SNR) [78]. In the NIR range, the most common detector types are photo-sensitive semiconductors made from silicon, lead sulfide (PbS), indium gallium arsenide (InGaAs) or a combination of the three [15, 69]. Most semiconductor detectors require some level of active cooling

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Dispersive element Detector

(linear array)

Light source

Solid sample

Sample holder

m max

i.) Specular re ection ii.) Di use re ection iii.) Absorption iv.) Transmittance v.) Scattering

v.

ii.

i. iii. iv.

Absorbance Incoming light

Reected light

b

a

Spectrum

Figure 3.2: a: A schematic of an NIRS instrument operating in reflectance mode.

Broadband light from the source is reflected from the sample and directed to the dispersive element. The dispersive element fans out the incoming light to a specific wavelength regions of interest before it arrives at the detector. The detector consists of photo-sensitive semiconductors arranged in a linear array which registers the intensity of individual wavelengths which can be used to compute the corresponding absorbances.b:The interaction mechanisms between NIR light and solid matter.

in order to maintain acceptable SNR [79]. The randomly distributed instrumentation noise of the detectors can be further reduced by collecting and averaging multiple spectra.

In order to produce meaningful spectra, the detector must be able to scan over the full wavelength range in small increments. This feature is implemented with a dispersive element, i.e., a wavelength selector [78]. Wavelength selection can be implemented in multiple ways, for example by using, optical filters, acousto-optic tunable filters (AOTFs), gratings, or microelectromechanical systems (MEMS). Filter- based solutions utilize mechanical switching of narrow band-pass filters. In AOTFs, the wavelength pass-band is modulated by changing the refractive indices of aTeO2

crystal with sound waves [81]. Grating and prism based monochromators use diffraction and dispersion to divide the incoming light into different wavelengths before hitting the detector sensor array. Finally, MEMS use electronically controlled

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micromechanical mirrors which can be tuned to pass only a specific wavelength of the light [82]. The dispersive elements differ in terms of scanning speed, spectral resolution, and cost [78]. As stated earlier, instruments with a tunable light source do not need a separate dispersive element. Tunable light sources, however, intro- duce their own set of engineering challenges, such as spectral resolution, complexity of the setup, cost, and acquisition time.

3.4 BASICS OF NIRS MEASUREMENTS

NIRS measurements can be performed in different modes. The two main modes are transmittance and reflectance. In the transmittance mode, the source and detector are situated on opposite sides of the measured sample and the NIR light penetrates the sample. Conversely, in the reflectance mode, both the light source and the detector are on the same side of the sample and the detected light results from diffuse reflection within the sample (Fig. 3.2 a). Of these two modes, reflectance has been more widely used, although, most NIRS devices support both modes.

The main benefit of the reflectance mode is the lack of requirements for sample thickness, which makes it more appealing for conducting bulk chemical analysis of various solids. In the reflectance mode, however, the penetration depth of the NIR light must be estimated separately for each material as it depends on the optical properties of the sample and it is also wavelength dependent [83] (Fig. 3.2 b).

In the transmittance mode, the absorbance can be derived from the Beer-Lambert law, which describes the light attenuation in a given medium as a function of material properties, concentrations, and path length. Absorbance is defined as the negative logarithm of the ratio between transmitted intensity (I₀) and measured intensity (I) according to the following equation:

A=−^log10(^I⁰

I). (3.5)

Absorbance for reflectance mode is calculated as the logarithmic ratio of reflectance of the sample (Rsample) and a standard reflectance (Rstandard):

A=−log10(Rrelative) =−log10( ^R^sample

R_standard). (3.6)

Standard reflectance represents the maximum reflectance that the instrument is capable of registering and is measured from a highly reflective material (>95%), such as Spectralon. The background spectrum (i.e., the spectrum the device registers in the absence of any light, also known as the dark spectrum), caused by instrumentation noise, is subtracted from both the sample and standard reflectance.

The absorbance for reflectance mode can, therefore, be written as AR=−^log10( ^R^sample−^Rdark

R_standard−^Rdark

), (3.7)

whereRdark is the dark spectrum. NIRS device is calibrated by measuring the standard and dark reflectance spectrum before every measurement.

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4 Chemometrics

4.1 IN GENERAL

NIRS is used to rapidly evaluate some property of a given material through a non- destructive optical measurement. The evaluation is based on a calibration model which establishes the relationship between the NIR spectra (X) and the properties of interest (y), also known as reference variables (Fig. 4.1). As an example, the protein content of meat products could be determined through NIRS measurement [84]. The calibration model requires the collection of both spectra and reference variables from a sufficiently large pool of samples. An accurate measurement of the reference variables is crucial for the construction of the model, as it represents the ground truth of the property that NIRS is trying to predict. Furthermore, the samples used for the calibration model should encompass the entire expected variation of the reference variable or the model will not generalize to new samples. Once the performance of the calibration model is validated, it can be used for the intended application to predict values for new samples. The field of science focusing on development of NIRS analysis and creation of calibration models is known aschemometrics.

As established in the previous chapter, the NIR spectrum consists of several overtone and combination bands meaning that the absorbance of a given chemical bond in the measured material can manifest itself in multiple parts of the spectrum.

In addition, the spectral peaks are relatively broad and overlapping. The resulting NIR spectrum is considerably more difficult to interpret than the distinct peaks

NIR spectra (X)

Reference variable (y) Training set (70%)

Testing set (30%) Sample selection

Accept model?

No

Yes No

Yes

Figure 4.1: Calibration models are constructed sequentially from preprocessing, variable selection, and modeling stages. Since each stage can be implemented in various ways and each method contains a number of tunable parameters, selecting the optimal combination is often an iterative process. Candidate models are evaluated using cross-validation after which the real world performance is assured with a validation step. Sample selection (i.e., splitting the data to training and test sets) can be performed randomly or according to a predefined criterion.

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of the MIR spectrum, a fact which initially held back the wider adoption of the technique. The analysis of NIRS data requires specialized multivariate statistical models that simultaneously utilize multiple parts of the spectrum.

The accuracy of the calibration model depends heavily on the quality of the data and the used modeling technique. The performance of the model, however, can be further improved by preprocessing and variable selection. Preprocessing consists of a number of sequential operations aimed at removing uninformative variance from the measured spectra. The variable selection, on the other hand, aims to reduce the full set of predictors (i.e., individual wavelengths of the spectrum) to a subset of the most relevant predictors. Combining preprocessing, variable selection, and modeling into an optimized pipeline is one of the key concepts of chemometrics (Fig. 4.1). The following sections will cover the pertinent methods in each of the pipeline steps.

4.2 PREPROCESSING

Chemometric models, like many other computational analysis techniques, adhere to thegarbage in, garbage outprinciple, which states that flawed inputs into the model often produce erroneous outputs. Preprocessing, therefore, aims to improve the overall performance of the model by cleaning up the input spectra of all external noise. Preprocessing of spectral data consists of sequential steps that aim to reduce noise, scattering effects, and other similar uninformative sources of variance from the measured spectra (Fig. 4.2 a). Most preprocessing methods are unsupervised operations that do not depend on the values of the reference variable although ex- ceptions to the rule do exist. The development and evaluation of various NIRS preprocessing techniques have been active fields of chemometric research [19].

The simplest preprocessing operations are based on a priori knowledge of the spectrum. These include removing especially noisy or saturated wavelength regions.

For example, in certain applications, the strong absorbance of water might not be of any importance and therefore should be ignored. Likewise, an existing knowledge of the chemical composition of the measured material might enable the exclusion of certain overtone regions.

Scatter correction is a family of preprocessing methods that aim to counter the particle size effect in the measured spectrum. The particle size effect refers to the presence of scattering particles in the measured material which can affect the path length of the diffusely reflected NIR light. Since the size and distribution of these scatterers in heterogeneous materials (such as biological tissue) are random, the resulting inter-sample variation between the spectra can be substantial. Scatter correction is essentially a spectrum-specific normalization that eliminates inter-sample dif- ferences arising from scattering particles. Scatter correction can be as simple as subtracting the baseline (i.e., mean) spectrum, however, the two most commonly used methods are standard normal variate (SNV) [85] and multiplicative scatter/signal correction (MSC) [86]. In SNV, the correction is performed according to the equation

xcorr= ^x−^µ

σ , (4.1)

where xcorr is the corrected spectrum, x the original spectrum, µthe mean of the spectrum, andσthe standard deviation of the spectrum. In MSC, each spectrum is

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represented as scaled and offset versions of a reference spectrum according to the equation

x=a+x_{re f}b+e, (4.2)

where x is the measured spectrum, x_{re f} the reference spectrum, a offset factor, b scaling factor, and e residual error. The terms a and b can be estimated through ordinary least-squares regression and the correction performed by subtracting these from the measured spectrum according to the equation

xcorr = ^x−a

b . (4.3)

The reference spectrum in MSC can be any estimate of a clean spectrum but the most common approximation is the mean spectrum over all samples. Although the two methods differ in the form of computation, they produce very similar results [17]. Both methods also have numerous variations, such as the extended multiplicative scatter correction (EMSC) [87], extended inverted signal correction (EISC) [88], robust normal variate (RNV) [89], and dynamic localized standard normal variate (DLSNV) [90].

Randomly distributed instrumentation noise can be smoothed using a simple moving average filter or convolution with some other windowing function. A more common and effective approach in chemometrics is to use a Savitzky-Golay filter [91]. The Savitzky-Golay filter iterates a moving window through the spectrum and at each window the original spectrum is replaced with a polynomial approximation (typically 2^nd– 4^thorder) obtained through a least-squares regression. The strength of the filtering can be tuned by changing the window size and the complexity of the fit can be adjusted with the order of the polynomial. Polynomials are well-suited for approximating the peaks of the spectrum resulting in stronger smoothing and less blurring of the individual peaks compared to simpler filters.

Spectral derivatives are a fairly standard preprocessing method in analysing spectroscopic data. As the name suggests, spectral derivatives are obtained by dif- ferentiating the spectrum along the wavelengths but typically only up to the first or second degree. The use of derivatives can highlight smaller and less distinct peaks while suppressing absorption from broader peaks. Additionally, derivatives can eliminate particle size effects, much in the same way as scattering correction. The downside of derivatives is that while it enhances some features of the spectrum, it can also drastically increase the noise, thus reducing the SNR of the spectrum.

Derivatives can be computed in multiple different ways. The simplest way to nu- merically compute the derivative is to use the finite difference method. The more noise-tolerant techniques, like the Norris-Williams derivative [19], combine finite difference method with some smoothing in order to counteract the added noise.

The derivatives can also computed be during the Savitzky-Golay filtering, as the derivative can be obtained directly from the convolution coefficients [91].

In typical applications, preprocessing consists of multiple operations, for example, scatter correction combined with filtering (Fig. 4.2 a). Although different preprocessing methods have been extensively reviewed in the past, there is currently no clear consensus on what should be the correct order of these operations. Fur- thermore, the possible combinations of operations and the parameters of individual operations provide a nearly infinite number of possible ways to perform preprocessing. While certain level of preprocessing will improve the model performance, it is

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Detector 1

Detector 2

SNV SNV SG SNV SG D1 SNV SG D2

D2

Standard normal variate Savitzky-Golay ltering Spectral derivative

(1st and 2nd) Preprocessing operations

y = X b + E X_n b_n+ E

Important

features Simpli ed model

Full model Variable selection

a

b

Figure 4.2: a: An example of the effect different preprocessing combinations on the NIR spectra. The data used in the example consists of measurements from two detectors. The effect of preprocessing is highlighted within in a smaller region of interest. Shaded regions represent the total variation between measurements (N=250) while the thick black line represents the mean spectrum.b:The concept of variable selection demonstrated through multiple linear regression. The original full model uses the entire feature set (i.e., full spectrum), resulting in a more complex model and larger number of regression coefficients (b). The reduced set of features after variable selection produces a simpler and more robust model (b_n)

entirely possible to also overdo it by removing crucial information from the spectra.

The preprocessing protocol should, therefore, be individually tuned for each application to ensure optimal outcome. Several chemometric studies have reported strate- gies for systematically selecting the optimal preprocessing protocol [26, 27, 92, 93].

4.3 VARIABLE SELECTION

The different wavelengths of the NIR spectra represent the set of features or predictors that will be fed into the calibration model. While part of this feature space is strongly related to the reference property, some of the features carry no real information. Removal of non-informative wavelengths (i.e., features) is known as variable selection, which depending on the literature, is also called feature extraction or dimensionality reduction. Variable selection produces a smaller subset of features which will result in simpler regression/classification models, increased accuracy, and more robust performance (Fig. 4.2 b). The reduced feature space also improves

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the interpretation of the model by highlighting the contribution of individual wavelengths, thus providing information about the chemical interactions between the NIR light and the measured material.

The development and comparison of different variable selection methods have been the focus of much recent chemometric research [20, 21, 23]. The total number of available methods today is immense, consisting of techniques, such as step-wise regression, genetic algorithms [94], signal decomposition [95], interval partial least squares [96], interval combination optimization [97], Monte Carlo uninformative variable elimination (MCUVE) [98], to name a few. Simpler methods, like the step- wise regression, increase or decrease the number of features according to cross- validated performance of the model. A more sophisticated variable selection, like MCUVE for instance uses Monte Carlo sampling to single out the important features [98].

4.4 CALIBRATION

Calibration model projects the preprocessed and variable selected spectra to the reference variable. If the objective of the application is to quantify some property of the target material (e.g., the protein content in meat [84]), regression-based methods are used. If, however, the objective is to assign a given sample to one of the pre- determined groups (e.g., identification of agricultural products [99]) the model is based on classification. Both types offer a number of different methods from which to choose. The two most common regression methods for creating calibration models are principal component regression (PCR) and partial least squares regression (PLSR) [100], both of which can also be modified for classification.

In multiple linear regression (MLR), the relationship between the dependent and independent variable can be written as

y=Xb+E, (4.4)

where y is the dependent (i.e., reference) variable, X independent variables (i.e., spectra),b regression coefficients, andE the residual error. New values ( ˆy) can be predicted by first solving the regression coefficients through pseudoinverse ofX.

ˆ

y=Xb (4.5)

b=X⁺y (4.6)

X⁺= (X^TX)⁻¹X^T (4.7)

The MLR model, however, assumes that all the predictors inXare independent and that the number of predictors (columns) is less than the number of observations (rows). The NIR spectrum is highly multicollinear, i.e., the absorbance values of adjacent wavelengths are strongly correlated and thus, not independent. Further- more, the number of wavelengths in the spectrum is nearly always greater than the number of samples in the calibration dataset. Without some prior transformation ofX (e.g., variable selection), techniques like MLR are unsuitable for building the calibration model.

This limitation can be bypassed by first projecting the original features to new linearly uncorrelated components (also called latent variables). One method that

Near infrared spectroscopy-based evaluation of patellar tendon and knee ligaments

Dissertations in Forestry and Natural Sciences

JARI TORNIAINEN

Near Infrared Spectroscopy- Based Evaluation of Patellar Tendon and Knee Ligaments

Jari Torniainen

NEAR INFRARED

SPECTROSCOPY-BASED EVALUATION OF PATELLAR TENDON AND KNEE

LIGAMENTS

TABLE OF CONTENTS

Acronyms

Symbols

1 Introduction

2 Knee ligaments

Stress

Strain

Quasi-static mechanical properties of ligaments and tendons

3 Near infrared spectroscopy

b

a

4 Chemometrics

a

b