Estimating articular cartilage cellularity and cell count using Raman spectroscopy

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Estimating articular cartilage cellularity and cell count using Raman spectroscopy

Ikegbu Godswill Ogbu 309042 Master’s thesis Master’s degree in Medical Physics University of Eastern Finland Department of Applied Physics 31.05.2021

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The University of Eastern Finland, Faculty of Science and Forestry Master’s degree in Medical Physics program

Ikegbu Godswill Ogbu, B.Sc. Estimating articular cartilage cellularity and cell count using Raman Spectroscopy

Master’s thesis, 53 Pages

Supervisors: Academy Research Fellow, Docent Isaac Afara, PhD Rubina Shaikh, PhD

May 2021.

Keywords: Cellularity, Cell count, Articular cartilage, Raman spectroscopy, Mankin score, Osteoarthritis

Abstract:

Articular cartilage is a smooth connective tissue covering the ends of bones in synovial joints, e.g. femur and tibia in the knee joint. This supportive connective tissue reduces friction during movement and ensures the safe transmission of physiological loads in the joint to the underlying subchondral bone. Articular cartilage consists mainly of water (80%), articular cartilage cells (chondrocytes, 2%), and extra-cellular matrix, which mainly includes proteoglycans (40% dry weight) and collagen (60% dry weight). Chondrocytes are the key players in regulating the synthesis and degradation of articular cartilage matrix. More so, it is thought that most idiopathic cartilage pathologies are due to inadequate response from the chondrocyte population. Hence, monitoring alterations in the chondrocyte population is pertinent for early diagnosis of articular cartilage diseases, such as osteoarthritis (OA). OA is a degenerative joint disorder which is characterized by erosion of articular cartilage covering the ends of bones in articulating joints. This results in severe pain, decrease in mobility, and decline in general quality of life. Among the promising optical diagnostic modalities proposed for characterizing biological tissues pathologies, Raman spectroscopy has proven to be a powerful method for providing key information on tissue, structure, composition, and integrity.

This study investigates the capacity of Raman spectroscopy to subjectively estimate the cellularity (from Mankin score) and objectively estimate the cell count of articular cartilage using chemometric approaches. Bovine samples (n = 49) obtained from a local abattoir was used for this study. Mankin score of these samples was performed by four independent observers, twice with a week internal between scoring to minimize the chances of memorizing the samples. The measurement of the samples was done pointwise with a Raman spectrometer (10X objective). Each measurement was repeated three times to enhance reproducibility and reduce operator’s error. For the multivariate data analysis, chemometrics was deployed while classification and regression predictive models were developed. The following pre-processing steps were applied to improve the overall performance of the model; scatter correction, smoothing and spectral derivatives. Matlab was used for Partial Least Square Discriminant Analysis (PLS-DA). Furthermore, Image J was used to manually count the cells across the superficial, middle, deep zones with a three-square box Region of Interest (ROI) and Matlab was used for Partial Least Square Regression (PLSR) analysis. Our results demonstrate that Raman spectra can optimally classify the cellularity of cartilage with first derivative having the best classification accuracy of 100%, 67%, and 90% for calibration, cross validation, and prediction, respectively. Furthermore, there was a strong relationship between the Raman spectra and cell count (70% < 𝑅² < 88%). Thus, we conclude that Raman spectroscopy as an optical spectroscopic technique is a good predictor of the cellularity and cell count of articular cartilage which proves useful for early diagnosis of osteoarthritis.

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Abbreviations

CCD Charged Coupled Device

ECM Extracellular Matrix

EDTA Ethylenediamine tetraacetic acid FTIR Fourier Transform Infrared

GAG Glycosaminoglycan

GIGO garbage in, garbage out

ICRS International Cartilage Repair Society InGaAs Indium-Gallium-Arsenide

MCUVE Monte Carlo Uninformative Variable Elimination

MRI Magnetic Resonance Imaging

MSC Multiplicative Scatter/Signal Correction

NIR Near Infrared

OA Osteoarthritis

OCT Optical Coherence Tomography

PBS Phosphate-Buffered Saline

PG Proteoglycans

PLS Partial Least Square

PLS-DA Partial Least Square Discriminant Analysis PLSR Partial Least Square Regression

RMSE Root Mean Squared Error

RMSEC RMSE of calibration

RMSECV RMSE of cross-validation

RMSEP RMSE of prediction

ROI Region of Interest

SNR Signal to Noise Ratio

SNV Standard Normal Variate

SOFG Safranin O/Fast Green

WHO World Health Organization

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Symbols

𝑚₁ Mass of first object

𝑚₂ Mass of second object

(𝑚₁𝑚₂⁄𝑚₁+ 𝑚₂) Reduced mass

𝑥₁ Displacement of first object

𝑥₂ Displacement of second object

(𝑥₁+ 𝑥₂) Total displacement

𝑡 Time

𝐾 Spring constant

𝑣_𝑚 Molecular vibration

𝛼 Molecule’s polarizability

𝑞 Displacement

𝑃 Dipole moment

𝐸_𝑜 Electric field for incident light source

𝑣₀ Frequency of electric field

𝑃_𝑠 Power of scattered light

𝐼_𝑜 Intensity of incident photons

𝜎_𝑅 Raman cross-section

𝜆 Wavelength of incident photon

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Acknowledgments

This master’s thesis was conducted in the department of Applied Physics, University of Eastern Finland during the years 2020 – 2021.

First, I thank the almighty God for His infinite mercies and strength He made available to me throughout my studies.

My gratitude goes to my parents (Mr./Mrs. Richness Ikegbu Diogu) for providing me with the prerequisite education and giving me the opportunity to travel away from home to get advanced quality education.

A special appreciation to my siblings; Emmanuel, Princeyoko and Chizaram for providing me with the emotional support needed throughout my programme.

My principal supervisors, Drs. Isaac Afara and Rubina Shaikh were very instrumental to the success of this work. Their indefatigable guidance, supervision, belief, and tutoring helped me pull through and I am very grateful to them.

How can I forget Ervin Nippolainen, Iman Kafian Attari, Awuniji Linus and Jari Torniainen for those meetings we held to point me to the right direction when I was stuck? I am sincerely grateful.

My hearty appreciation also goes to my Uncles; Uncles Victor Egbebu (blessed memory), Chris Egbebu and John Egbebu for their consistent words of encouragement and financial support prior to the start and during my programme. God bless you richly, amen.

I want to thank my friends; Faith, George, Uju, Opemipo, D Lion, Richard, Kemi, Omolade, Akuroma, Glory and Adeola Adeyemo, Pracheta, Lejish, Mehvash, Raju, Precious, Jennifer, Happiness, Vera, Lebechi, Ubah Ada, Sophie, Uwaoma, Yousri, Aya, Eslam, Sajeda for providing me with the mental support I needed to complete my studies.

Finally, I want to thank Mr./Mrs. Promise Mpamah for showing me so much love and care and giving me a family away from home. You made my studies in Kuopio, Finland smooth, God bless you.

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Chapter 1

1 Introduction

1.1 Motivation

Musculoskeletal disorders, such as osteoarthritis (OA), are degenerative conditions that affect fundamental joint function. OA is a degenerative joint disorder which is characterized by erosion of articular cartilage covering the ends of bones in articulating joints. This results in severe pain, decrease in mobility, and decline in general quality of life, among other impacts of the disease [1]. Thus, OA and related pathologies of articular cartilage are associated with significant socio-economic impact and places significant burden on healthcare systems of societies. So far, the etiology and pathological process of OA is not fully understood, although some risk factors associated with the condition have been identified and include injury, age, obesity, and unhealthy lifestyle [2][3][4][5][6]. However, studies reveal that constant moderate exercises play a vital role in the prevention of the development of OA [7]. During OA, the deteriorative alterations occur in articular cartilage where the initial changes take place in the superficial layer of the tissue. The results are decrease in the quantity of proteoglycans and the occurrence of fibrillation of the collagen network [3][8][9]. In developed countries, for instance, OA is the most prevalent cause of disability in older adults. Globally, OA has increased the number of sick leave and untimely retirement among working population.

According to the World Health Organization (WHO), about 15% of adults over 60 years of age possess a level of OA worldwide and estimates that 80% of those adults with OA will experience difficulties in mobility [10]. United Nations postulates that adults over the age of 60 will make up more than 20% of the global population by 2050. A traditional approximation of 15% of those 20% will develop symptomatic OA, with one-third of these persons being seriously disabled. This indicates that by 2050, 130 million individuals globally will be affected by OA, with 40 million of them seriously incapacitated.

Articular cartilage, bone, ligaments, tendons, and muscles form the musculoskeletal system of vertebrates. Articular cartilage is a smooth connective tissue covering the ends of bones in synovial joints, e.g., femur and tibia in the knee joint [11]. This supportive connective tissue reduces friction during movement and ensures the safe transmission of physiological loads in the joint to the underlying subchondral bone. The main constituents of articular cartilage include water and extracellular matrix (ECM). The ECM of articular cartilage consists primarily of collagen, proteoglycans (PG) and chondrocytes (articular cartilage cells) [12].

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While the collagen and proteoglycans are responsible for the biomechanical function of cartilage, the chondrocytes are responsible for synthesis and support of the matrix of cartilage [13][14]. Cartilage gets degenerated because the destructive process happens at a faster rate than the chondrocytes can synthesis extra cellular matrix, resulting in an overall degeneration and erosion of articular cartilage matrix [15].

Since articular cartilage is aneural and avascular (i.e., having no nervous tissue, so no pain and lacking blood vessels), its regenerative capacity is limited. Therefore, without intervention, cartilage often undergoes progressive degeneration post-injury. Nevertheless, surgical procedures can be adopted to treat little injuries [3][16]. Presently, it is impossible to find pharmaceutical therapies for the severe degeneration of articular cartilage especially at its late stages. During these stages, the tissue may wear out completely, but arthroscopy provides diagnostic and therapeutic possibilities [3][17].

The International Cartilage Repair Society (ICRS) sets out a grading system for the characterization of OA and arthroscopy is designed to score the health condition of cartilage tissue [17][18]. Given the subjectivity, lack of accuracy and reproducibility of the current arthroscopic methods, quantitative spectroscopic techniques applied on articular cartilage have potentials to be applied in disease diagnostics and surgeries [3]. Current stage of arthroscopy is augmented with novel spectroscopic techniques to optimize the arthroscopic interventions by providing objective evaluation of cartilage biophysical and biomechanical properties [19].

These spectroscopic techniques may include Near Infrared (NIR), Fourier Transform Infrared (FTIR), Raman spectroscopies and Optical Coherence Tomography (OCT). They provide phenomenal mechanisms for investigating articular cartilage [3][20]. So far, absorption in NIR [19], FTIR [21] and Raman spectral range [22] has been used to estimate biophysical and biomechanical properties of articular cartilage.

Furthermore, the FTIR spectroscopic imaging technique provides a notable specificity within tissue molecules and is utilized alongside NIR and Raman spectroscopies for imaging the biochemical structure of cartilage tissue sections. A method that proves useful and reliable to provide early diagnosis of OA is Raman spectroscopy by providing barely noticeable molecular and biochemical alterations that happen in tissues in OA. This method characterizes the biophysical properties of tissue by means of molecular vibration and in-elastic Raman scattering.

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3 1.2 Aims and hypotheses

The aim of this master’s thesis is to investigate the capacity of Raman spectroscopy in estimating the cellularity and cell count of articular cartilage. Cell count refers to the actual number of cells in a tissue, while cellularity refers to the distribution of cells in the tissue. This is because the degeneration of articular cartilage and the eventual trigger of OA is associated to cell death or lower cellularity [23]. More precisely:

In this thesis, we hypothesize that Raman spectra has the capability of estimating the cellular properties of cartilage. The cellular properties of cartilage are qualitatively obtained using the Mankin score while the cell-count was quantitatively obtained by manually counting the cells across different zones of the tissue.

1.3 Significance

The findings from this research work is clinically relevant because investigating the capacity of Raman spectroscopy to characterize the cellular properties of articular cartilage would aid the development of spectroscopic approach and tools for early detection of osteoarthritis. More so recently, Raman spectroscopy has shown potentials in biomedical applications like diagnosis of cancers [24]. However, adaptation of Raman spectroscopy in biomedical engineering is still at the research and development phase where its potential for clinical translation is still being assessed [25].

- To evaluate cellularity of articular cartilage using Raman spectroscopy and - To evaluate cell count of articular cartilage using Raman spectroscopy

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Chapter 2

2 Background

2.1 Articular cartilage

Articular cartilage envelops the ends of articulating bones bearing the mechanical loads that acts on it. It acts as a surface for reducing friction, load transmission, and resisting wears during movement. Articular cartilage is categorized as hyaline cartilage, and this cartilage is the prevailing cartilage in a human body. Under a microscope observation, healthy adult cartilage appears as a smooth, shiny, white tissue [26] with standard thickness varying between 1 – 6 mm, based on the location of its anatomy [27][28]. Articular cartilage can withstand excessive compressive loads [29] and it has an exceptional lubricating capacity with a coefficient of friction from approximately 0.0005 – 0.04 when moisturized with the synovial fluid [30].

Furthermore, articular cartilage can be termed as viscous and porous, having three unique phases – the solid, liquid, and ionic phase [31].

2.1.1 Structure and function

Articular cartilage is composed of a dense extracellular matrix (ECM) and a specialized cellular component known as chondrocytes, which is surrounded by the ECM. The ECM of articular cartilage is considered as a material with multiple phases. First, a two-unique liquid and solid phases; the liquid phase containing water and ions while the solid phase contains proteoglycans (PGs), collagen fibrils. The remaining constituents are chondrocytes and some less in abundance minor proteins and minerals. Formatively, a matured articular cartilage can be categorized into four distinct zones: the superficial, middle, deep, and calcified cartilage zones.

Inside each zone, cartilage is further divided into regions based on the nearness of a region to the specialized cells [12]. The functional properties of articular cartilage is defined by its organized compound design and changes to this design often results to failure of the tissue [12].

The biggest component of articular cartilage matrix is water [32]. Based on the health and location of cartilage, it makes up about 60% of the tissue’s wet weight. Within cartilage tissue, water content is lowest at the deep zone and increases significantly to the superficial layer.

More so, water plays the role of bearing the mechanical loads applied to cartilage tissue.

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Fig. 2.1: Illustration of the structure of articular cartilage (from M. S. Venäläinen dissertation with permission)

Articular cartilage is also made up of proteoglycan by 10% dry weight of the tissue makeup and gives it a compressive stiffness feature for withstanding mechanical loads [33][34].

PG contains a medial protein molecule, and at least, one Glycosaminoglycan (GAG) side chain is covalently attached to it (Fig. 2.2). Changes in the content of the PG affects the tissue performance and leads to serious cartilage and joint diseases. Among the PGs in cartilage matrix, Aggrecan is the major type and it appears as a massive aggregate of molecule [35]. The aggrecan and collagen interact equally and the relationship between both are mutually beneficial. Asides the movement restriction of PG molecules by collagen within cartilage matrix, PG as well covers the spaces within the collagen fibrils creating a fiber-reinforced composite. This makes the tissue stiff and prevents it from deforming.

Fig. 2.2: Structure of Aggrecan Proteoglycan (from Linus Awuniji thesis with permission)

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Among all structural macromolecules existing in articular cartilage, collagen is the most abundant. The entire collagen network has two vital roles; they ensure the tensile stiffness of cartilage tissue which is crucial for sustaining its structural integrity. Also, they regulate the rate of swelling produced by their negative fixed charge densities of PG aggregate [36].

Chondrocytes

Chondrocytes are the cells that generate and sustain the cartilaginous matrix [15]. They are very specialized and metabolically active cells important for the development, preservation, and repair of the ECM. Chondrocytes are sparsely distributed all over articular cartilage and make up about approximately 2% of its total volume [12]. They differ in size, form and concentration based on their position in articular cartilage [12] (Fig. 2.3). The arrangement of cells differ also between the zones, in deeper zones chondrocytes are packed into columns however in the superficial zones they are organized at random [37]. More so, the superficial zone has more flattened and elongated cells, while in deeper zones the cells look more spherical [12].

During regeneration of cartilage, chondrocytes play a vital role due to their capacity to synthesize collagen and other components of ECM required for the functional properties of cartilage [38]. On the other hand, chondrocytes harvested from persons may dedifferentiate and lose their properties. Furthermore, when chondrocytes age, they exhibit less metabolic activities and may not generate or generate insufficient functional proteins required to produce a desired ECM. Mesenchymal stem cells can also be utilized in the creation of chondrocytes and making cartilage regeneration feasible [38].

Fig. 2.3: Safranin O stained cartilage tissue with its specialized cells (chondrocytes)

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Imbalance in the function of these chondrocytes lead to OA [15]. In general, changes in the structure of chondrocytes may lead to OA and because of the huge socio-economic burden of OA, early diagnosis of OA is important.

2.1.2 Disease, diagnosis, and treatment

Osteoarthritis (OA) is a joint disease that causes excruciating pains affecting hundreds of millions of people worldwide [39]. Trauma could lead to OA, also due to ageing which comes from wear, tear and fatigue [13][40]. Other symptoms of OA can be joint stiffness, swelling, cartilage erosion, bones colliding on the surface of each other because there is no safe contact between bones, among others. Though pharmaceuticals are given for pain alleviation, presently, advanced stages of OA remain untreatable, but moderate exercise is often recommended as a preventive measure [10]. Therefore, timely detection of OA could aid clinicians to promptly administer suitable therapy.

Fig. 2.4: A healthy and osteoarthritic joint (https://theislander.net/osteoarthritis/)

Generally, in a healthy joint (Fig. 2.4), articular cartilage lines the end of the bones producing an easy gliding surface for movement and functions as a cushion between the bones. On the other hand, in OA for instance, it starts slowly as a minor degeneration of cartilage and in the

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final stages, cartilage is damaged (Fig. 2.4) leading to pains and swelling of the joint – this makes everyday living problematic.

During OA, changes in the joint’s structure and function can affect the whole joint within a few months to a few years [41][42]. Bone remodelling occurs to account for the increased wear and tear on other joint tissues, consequently resulting to harder joint movements, pain and swelling. OA often happens in knee, hip, and hand joints.

By clinical research, joint diagnosis is based on a physical examination; severity is often measured by pain, swelling and diminished joint movements [43][44]. It is usually confirmed by X-ray or MRI if required [45][46]. Because cartilage cannot be seen with conventional X- ray images, diagnosis depends only on the joint space narrowing and increase in the density of the subchondral bone. Yet, these observations are not detected until the advanced stages of OA [47]. Although MRI provides excellent tissue contrast, its low image resolution [48] and cost make it difficult to evaluate cartilage health [49]. Also, the initial signs of OA are not easily spotted using this diagnostic modality.

Since cartilage has minimal self-healing properties, it is critical to diagnose cartilage degeneration early to begin adequate repair or therapy [50]. It is possible to reduce potential risk factors for cartilage injury, such as obesity, muscle weakness, and repetitive and severe loading [51]. Reducing other factors like hereditary, ageing or gender is not feasible [52]. Anti- inflammatory and analgesic medications can help with OA symptoms like pain, while intra- articular hyaluronic injections can help with joint mobility, but the overall findings are not convincing [46].

Presently, there is no cure for OA, but drugs to alter the disease and delay its progression are constantly being developed [53]. For the repair of injured cartilage, surgical interventions such as mosaicplasty or autologous chondrocyte implantation have been created [54][55]. Surgical treatments, on the other hand, are costly and thus out of reach for most people. Effective diagnostic methods will be needed for future innovations of current drugs and surgical intervention, as well as for tracking the success of these therapies.

Table 2.1 Summary of ICRS scores [56]

Score Criterion

ICRS 0 Normal intact cartilage and no surface defects

ICRS 1 Surface fibrillation and/or softening of the surface, tissue swelling and fissures

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ICRS 2 Extended tissue defects up to < 50% of cartilage thickness ICRS 3 Defects extend > 50% of cartilage thickness but does not reach

the subchondral bone

ICRS 4 Defects expose the subchondral bone

In the clinics, arthroscopic procedures are used to patch ligament and meniscal tears in the joints. During these procedures, cartilage surfaces are checked for lesions. Owing to the use of visual inspection and manual palpation of cartilage surface, this test is unfortunately extremely qualitative and subjective [57][58]. Besides that, there is intra-observer and inter-observer subjectivity in arthroscopic assessment [59][60][61]. The International Cartilage Repair Society (ICRS) [56] rating system (Table 2.1) is used to grade cartilage injuries seen during arthroscopy. The recent diagnostic outcome is unsuccessful, and 75% of arthroscopists think quantitative methods should be used during arthroscopy [62]. More so, in recent times, optical vibrational spectroscopies such as Raman spectroscopy have gained interest to characterize the stage of the disease in deeper regions of the tissues. With this objective method, information can be extracted from the deeper region of cartilage tissue.

During the early stages of OA, there is loss of PGs and interference of the collagen network at the superficial zone of cartilage [63]. Hence, the tensile and compressive properties of cartilage tissue is decreased, making it vulnerable to subsequent damage. At this stage, the tissue swells, and surface fibrillation is also obvious. During the second stage, chondrocytes within the tissue matrix react by clearing the destroyed tissue matrix and further boosting collagen and PGs synthesis. The failure of chondrocytes to bring back homeostatic balance leads to the third stage disease progression [64]. The reduction in the activity of chondrocytes leads to the quick loss of PGs and improved fibrillation of articular cartilage surface [65]. In the end, cartilage layer is completely eroded, uncovering, and endangering the underlying bone.

The structure and composition of cartilage controls its function, with cells about 2% in cartilage synthesizing very slowly the ECM turnover and maintain the steady internal physical and chemical condition of the tissue. Imbalance in the function of these chondrocytes lead to degenerative diseases like OA. This thesis focuses on the relationship between vibrational spectroscopic technique such as Raman spectroscopy and chondrocytes for the early detection of OA.

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10 2.2 Fundamentals of Raman spectroscopy

Raman spectroscopy is a vibrational spectroscopy technique based on inelastic scattering of photons, often generated via laser irradiation [66]. It was named after C. V. Raman, an Indian physicist who first observed Raman scattering in 1928 with his research partner K. S. Krishnan.

This spectroscopic technique can be used to determine vibrational energy modes of molecules in a sample, but it can also be used to observe rotational and other low-frequency modes of structures. More so, Raman spectroscopy may provide chemical and structural details, as well as identify substances based on their Raman “fingerprint” [66]. The bond strength and identity of the atoms that contribute to the modes are reflected in the Raman peak frequencies and relative intensities of different vibrational modes, and thus are characteristic of a substance or molecule [67]. Raman spectroscopy may also be used for quantitative analysis because Raman peak intensities are proportional to the number or concentration of molecules. Raman spectroscopy extracts this information by detecting Raman scattering from the sample.

2.2.1 Theory of Raman scattering

Raman scattering, also known as the Raman effect, is the inelastic scattering of photons by matter, which involves an energy exchange and a shift in the direction of light [68]. As incident photons from a visible laser are transferred to lower energy, a molecule gains vibrational energy. Normal Stokes Raman scattering is the term for this phenomenon [68].

When it comes to Raman scattering, there are two ways to think about Physics: classical wave interpretation or quantum particle interpretation. Light is seen as electromagnetic radiation in the classical wave explanation, since it has an alternating electric field that works together with a molecule through its polarizability. The potential of an electron cloud to interact with an electric field determines its polarizability. For instance, soft molecules, such as benzene, are strong Raman scatterers, whereas harder molecules, such as water, are relatively weak Raman scatterers [69].

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Fig. 2.5: Comparing Raman scattering interpretations

A visual comparison of classical wave and quantum particle interpretations is shown in Fig.

2.5. When it comes to quantum particle interpretation, light is viewed as a photon that hits a molecule and then scatters inelastically. The number of scattered photons is proportional to the bond size in this interpretation. For instance, molecules with larger Pi bonds, like benzene would scatter a lot of photons, whereas water with smaller single bonds scatters very little.

To derive the Raman effect, it is best to start with the classical understanding, which considers a simple diatomic molecule as a mass on a spring with 𝑚 representing the atomic mass, 𝑥 representing the displacement and 𝐾 representing the bond strength [68].

Fig. 2.6: Diatomic molecule in the form of mass on a spring

Considering this approximation, Hooke’s law is used to express the displacement of the molecule as,

𝑚₁𝑚₂ 𝑚1+𝑚2 (^𝑑²^𝑥¹

𝑑𝑡² + ^𝑑²^𝑥²

𝑑𝑡²) = −𝐾(𝑥₁+ 𝑥₂), (1) CH3-CH2-OH

CH3-CH2-OH Classical wave interpretation

Quantum particle interpretation

𝑥₁ 𝑥₂

𝑚₁ 𝑚₂

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Substituting the reduced mass (𝑚₁𝑚₂⁄𝑚₁+ 𝑚₂) with 𝜇 and the total displacement (𝑥₁+ 𝑥₂) with 𝑞, equation (1) reduces to,

𝜇^𝑑²^𝑞

𝑑𝑡² = −𝐾𝑞, (2)

The solution of the differential equation (2) gives,

𝑞 = 𝑞_𝑜cos (2𝜋𝑣_𝑚𝑡), (3)

𝑣_𝑚 represents the molecular vibration and is expressed as,

𝑣_𝑚 = ¹

2𝜋√^𝐾_𝜇, (4)

The molecule vibrates in a cosine pattern with a frequency proportional to the bond strength and inversely proportional to the reduced mass, as shown by equations (3) and (4). As a result, each molecule would possess its own distinct vibrational signature, which is decided not only by the atoms in the molecule but as well by the features of individual bonds. Since a molecule’s polarizability 𝛼, is a function of displacement, 𝑞, these vibrational frequencies can be determined using the Raman effect. As incident light interacts with a molecule, it produces a dipole moment, 𝑃, equal to the product of the molecule’s polarizability and the electric field of the incident light source [70]. An expression of this is,

𝑃 = 𝛼𝐸_𝑜cos (2𝜋𝑣₀𝑡) (5)

Where 𝐸_𝑜 represents the intensity, and 𝑣₀ the frequency of the electric field. By small amplitude approximation, the polarizability can be defined as a linear function of displacement,

𝛼 = 𝛼_𝑜+ 𝑞 (^𝜕𝛼

𝜕𝑡)

𝑞=0+ ⋯, (6)

Combining equations (3) and (5) gives,

𝑃 = 𝛼_𝑜𝐸_𝑜cos(2𝜋𝑣₀𝑡) + 𝑞_𝑜cos(2𝜋𝑣_𝑚𝑡)𝐸_𝑜cos(2𝜋𝑣₀𝑡) (^𝜕𝛼

𝜕𝑡)

𝑞=0 (7)

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From equation (7), the interaction between the molecule and the incident light has two resulting effects. The first effect is the Rayleigh scattering, which is the most common, and hence there is no change in the frequency of the incident light [68]. The Raman scattered component is the second effect and can be expanded to,

𝑞_𝑜𝐸_𝑜(^𝜕𝛼

𝜕𝑡)

𝑞=0[𝑐𝑜𝑠(2𝜋{𝑣_𝑜− 𝑣_𝑚}𝑡) + 𝑐𝑜𝑠(2𝜋{𝑣_𝑜+ 𝑣_𝑚}𝑡)],

⁽⁸⁾

Equation (8) which is the Raman scattered component, reveals that there is a shift in the frequency of the incident light by plus or minus (+) the frequency of the vibration of the molecule. An Anti-Stokes shift is hereby characterized by the increase in frequency, while a Stokes shift is characterized by the decrease in frequency. The Raman effect now allows spectroscopists to precisely determine the vibrational frequency of a molecular bond by calculating the change in frequency from incident light (normally, the Stokes shift is the only effect used for this measurement) [70].

After the derivation of the Raman effect with the classical wave interpretation, the quantum particle interpretation helps to visualize better the process, establish, and verify additional information. The Raman effect is explained as an inelastic scattering of a photon of a molecular bond, and this stems from the excitation of the molecule into a virtual energy state by the incident photon [68].

Fig. 2.7: Quantum energy transitions for Rayleigh and Raman scattering Virtual State

Energy

hv0 hv0 hv0 hv0-hvm

hv0+hvm

hv0

E0+hvm

E0

Rayleigh Scattering

(elastic)

Stokes

Scattering Anti-Stokes Scattering

Raman (inelastic)

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When the excitation of the molecule by the incident photon happens, there are three distinct possible outcomes. The molecule can first relax back to its ground state and emit a photon with the same energy as the incident photon; the mechanism is elastic and is known as Rayleigh scattering. Next is that the molecule can relax to a natural phonon state and give out a photon with lower energy than the incident photon; this phenomenon is known as Stokes shifted Raman scattering. The third possible outcome is Anti-Stokes Raman scattering, in which the molecule already in an excited phonon state is excited to a higher virtual state. It then drops back to the ground state, releasing a photon with an energy greater than that of the incident photon. Since most molecules are in their ground state at room temperature, the likelihood of a photon being Anti-Stokes scattered is very low. Hence, most Raman measurements are conducted considering only the Stokes shifted light [70].

With additional consideration of the quantum understanding of the Raman effect, the power of the scattered light, 𝑃_𝑠, is equal to the product of the intensity of the incident photons 𝐼_𝑜, and a value referred to as the Raman cross-section, 𝜎_𝑅 which can be expressed as,

𝜎_𝑅 ∝ ¹

𝜆⁴, (9)

Where 𝜆 represents the wavelength of the incident photon. Thus,

𝑃_𝑠 ∝ ^𝐼^𝑜

𝜆⁴, (10)

Equation (10) shows a simple linear association between the power of the scattered light and the strength of the incident light, also an association between the power of the scattered light and the reciprocal of the wavelength to the fourth-order. Based on these relationships, it appears that using a short excitation wavelength and a high-power excitation source is often desirable, but this is not always the case.

2.2.2 Instrumentation

As compared to other optical interaction processes, including absorption, fluorescence, or elastic light scattering, the Raman effect is minimal [71]. As a result, Raman spectrometers produce a Raman signal from a sample by using high light intensity. A light source, sample, a dispersive part, and a detector are the basic components of a Raman spectrometer [71].

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Fig. 2.8: Schematic representation of the measurement principle in a Raman spectrometer From Fig. 2.8, the sample is illuminated by a laser light source, which interacts with the molecules. The dispersive element separates the inelastically dispersed light into different wavelengths; the detector analyzes various wavelengths and intensities of light and converts them into the final spectrum [72].

A laser is used as a light source in Raman spectrometers, with wavelengths ranging from visible to near-infrared (400nm – 1100nm). These wavelengths are monochromatic, coherent, and bright. The light is dispersed in all directions after the incident light interacts with the sample;

the dispersive element receives a portion of the scattered light. A diffraction grating in reflection or transmission geometry is commonly used to spatially separate scattered light rays, separating different wavelengths [73]. The detector could be made up of a photodiode, which converts the different intensity wavelengths into an electronic signal using the inner photoelectric effect. Single-element detectors, which can only detect one wavelength at a time and require a scanning technique to record a full spectrum, are standard in older instruments.

Newer instruments, on the other hand, use Charged Coupled Device (CCD) detector arrays like those used in cameras or InGaAs (Indium-Gallium-Arsenide) detectors, which can detect a specific range of the spectrum simultaneously [74]. A Raman spectrum is a graph in which the intensity (signal strength) is plotted against the reciprocal wavelength, which is proportional to the energy as a result of the measurement.

2.2.3 Basics of Raman spectroscopic measurements

Raman spectroscopy is an inelastic scattering mechanism. It works based on the Raman effect, which states that the frequency of a small proportion of scattered radiation differs from the frequency of monochromatic incident light. It is based on incident light scattering inelastically as it interacts with vibrating molecules. It uses molecular vibrations as a probe [75][76]. In

Light

source Sample Dispersive

Element Detector Spectrum

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Raman spectroscopy, a monochromatic laser beam is used to illuminate the sample, which interacts with the molecules and produces scattered light. The scattered light possessing a frequency that varies from that of the incident light (inelastic scattering) is utilized to create a Raman spectrum. This spectrum is produced by the inelastic interaction between incoming monochromatic light and sample molecules. After a collision with sample molecules, monochromatic radiation scatters in all directions. Rayleigh scattering occurs when the frequency of scattered radiation is equal to the frequency of incoming radiation. Just a small portion of scattered radiation possesses a frequency distinct from that of incident radiation and represents Raman scattering. Stokes lines arise in the Raman spectrum when the frequency of incident radiation is higher than the frequency of scattered radiation. Anti-Stokes lines arise in the Raman spectrum when the frequency of incident radiation is lower than the frequency of scattered radiation. The measurement of scattered radiation is normally done at a right angle to the incident radiation [77][78][67].

Stokes bands are more powerful than anti-Stokes bands because they entail transitions from lower to higher energy vibrational levels. Anti-Stokes bands are studied using fluorescing samples because fluorescence interferes with Stokes bands [77]. The magnitude of Raman shifts is independent of incident light wavelength [77]. The wavelength of incident light affects Raman scattering [75]. To obtain a Raman spectrum of a sample, a change in polarizability during molecular vibration is required. Water is a suitable solvent for dissolving materials because it has minimal Raman scattering.

2.3 Previous research: Raman spectroscopy in musculoskeletal diseases

Earliest study reveals a novel application of Raman spectroscopy using a murine animal model of osteoarthritis (transgenic mice) for examining harm to ocular collagen. These first findings imply that Raman can detect and measure abnormalities in eye collagen, suggesting that it could be used as a diagnostic tool for ocular collagen injury [79]. For a long time, researchers in rheumatology have utilized viscosity primarily to evaluate the physiochemical properties of synovial fluid both in osteoarthritic and normal patients. However, the limitation has been the availability of methods that are fast and generate several layers of information while using less sample volumes. Raman spectroscopy was then used to assess the biochemical makeup of synovial fluid taken from fourty individuals with clinical signs of knee OA at the time of elective surgical therapy. These findings suggested that Raman spectroscopy could be a viable option for assessing joint degeneration in knee osteoarthritis patients [80]. Further previous

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studies were conducted with an initial investigation into the diagnostic possibility of Raman spectroscopy for evaluating pathological articular cartilage. This study was conducted on five arthritic human tibial cartilages gotten after a total knee arthroplasty using near infrared (NIR) Raman spectroscopy energized with 647.1nm lines of Kr-ion laser. More so, as a control sample, a healthy cartilage gotten from a cadaver donor was analyzed. The result shows that the Raman spectroscopic method could be effective for detecting and quantifying the severity of OA in its early stages [81]. In recent years, researchers have continued studying Raman spectroscopy to improve its diagnostic and clinical significance. A recent study combined a home-made small-sized Raman spectrometer with machine learning algorithms to detect healthy and multi-period OA canine knee joints [82]. The result suggested that Raman spectroscopy in combination with machine learning could be a useful method for detecting multi-period OA in situ with high accuracy, precision and preclinical importance.

A review of previous research related to Raman spectroscopy reveals there are limited studies that utilize Raman spectroscopy to investigate the cellularity of articular cartilage. Hence, this thesis.

2.4 Characterization of articular cartilage cellular properties

The composition, structure and function of articular cartilage has a complex interdependence, hence, to predict how chondrocytes perceive their surroundings, one must be able to accurately quantify tissue and cell properties. Raman spectroscopy has shown potentials for characterizing the cellular properties of articular cartilage for early detection of OA. With Raman spectroscopy, there is a potential to subjectively estimate the cellularity of articular cartilage from Mankin score while objectively determining the cell count of the tissue using predictive models.

2.4.1 Cellularity assessment from Mankin score

Mankin score is regularly used for histopathological grading of the severity of osteoarthritic degeneration of articular cartilage [83][84]. This is a combined scoring system for evaluating the structure of articular cartilage (0 – 6 points), cellular abnormalities (0 – 3 points), matrix staining intensity (0 – 4 points), and tidemark integrity (0 – 1 point). The score increases with tissue degeneration; hence a score of zero suggests a healthy cartilage, while a score of fourteen indicates severely degenerated articular cartilage [84].

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On the modified Mankin scoring system, points (0 – 3) are distributed for cellular abnormalities, with 0 score given to a tissue with normal cellularity, 1 – hypercellulaity, including small superficial clusters, 2 – clusters and 3 – hypocellularity. This cellularity component of the Mankin score will be used as a reference in this thesis for estimating the cellularity of articular cartilage with Raman spectra.

According to the Mankin scoring system, the histopathological spectrum of the severity of OA is directly proportional to the metabolic condition of articular cartilage chondrocytes during the various phases of OA [83][85]. An essential limitation of the current implementation of the Mankin score is its accuracy which questions the consistency of the classification of articular cartilage lesions. Traditionally, the Mankin score is calculated on sections that are stained with Safranin O/Fast Green (SOFG) [84]. This method shows that the intensity of the SOFG stains corresponds truly with the concentration of proteoglycan [86]. Various parametric and nonparametric approaches exist for the evaluation of the accuracy of Mankin score [87][88][89]. An example is the intra and inter-observer accuracy of the Mankin score for lesions of articular cartilage [84].

2.4.2 Cell-count assessment

The chondrocytes, articular cartilage cells, are the key players in regulating the synthesis and degradation of articular cartilage matrix. More so, it is thought that most idiopathic cartilage pathologies are due to an inadequate response from the chondrocyte populations [90]. Hence, monitoring alterations in the chondrocyte population is pertinent for early diagnosis of articular cartilage diseases, such as OA [91][92]. The cell count assessment involves counting nuclei in defined sections of stained SOFG, which is then recorded as nuclei in a defined ROI [93].

2.5 Chemometrics

2.5.1 In general and on Raman spectroscopy

Chemometrics is the science of using data to derive information from chemical systems. A problem usually exists in this field of study which is constructing predictive models based on historical data in order to make predictions on new data for which we do not know the answer.

This predictive modelling can be expressed as the mathematical problem of estimating a mapping function (𝑓) from input variables (𝑥) to output variables (𝑦). More so, this branch of science can be used for the development of Raman spectroscopy analysis and design of calibration models. Raman spectroscopy, being a non-destructive optical measurement, could

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be used to rapidly examine the property of a material. The assessment is centered on a calibration model that creates a relationship between the Raman spectra (𝑥), referred to as the predictors, and the properties of interest (𝑦), also referred to as reference variables. The calibration model necessitates the gathering of both spectra and reference variables from a big enough sample pool. The reference variables must be accurately measured to build the model, as they represent the ground truth of the property that Raman spectroscopy is attempting to forecast. Moreover, the samples for the calibration model must cover the complete predicted variance of the reference variable, else the model will not be simplified to new samples. After the execution of the model is proven, it may be utilized for the planned application of predicting values of entirely different samples. The quality of the data and the modelling approach utilized have a big impact on the calibration model’s accuracy. Preprocessing and variable selection, on the other hand, can increase the model’s performance even further. Preprocessing is a series of actions that are performed to remove uninformative variation from the observed spectra. On the other hand, variable selection seeks to reduce the whole collection of predictors (like specific wavelengths in the spectrum) to a subset of the key predictors. One of the fundamental concepts in Chemometrics is merging preprocessing, variable selection, and modelling into an efficient pipeline.

2.5.2 Variable selection

The set of features that will be supplied into the calibration model is represented by the different wavelengths of the Raman spectra. While some of the characteristics in this feature space are closely related to the reference property, others do not. Variable selection, also known as feature extraction or dimensionality reduction, is the process of removing non-informative wavelengths. With variable selection, the number of features in a model is reduced, resulting in simpler regression or classification models, higher accuracy, and more stable functioning of the model. By highlighting the contribution of various wavelengths, the smaller feature space helps the model’s interpretation, delivering information on the chemical interactions between the Raman light and the measured material.

Much recent chemometric research has focused on creating and comparing various variable selection approaches [94][95]. Stepwise regression, genetic algorithms [96], signal decomposition [97], interval partial least squares [98], interval combination optimization [99], Monte Carlo Uninformative Variable Elimination (MCUVE) [100], are a few among the vast number of methods available today. Simpler approaches, such as stepwise regression adjust the

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number of features based on the model’s cross-validated performance. MCUVE, for example, uses Monte Carlo sampling to isolate the important features in a more complex variable selection [100].

2.5.3 Spectra preprocessing and model development

Chemometric models, like several other computational assessment tools, follow the computer science garbage in, garbage out (GIGO) principle, which states that faulty inputs to the model frequently produce incorrect outputs. Hence, during the development of the model, preprocessing is performed which seeks to improve the model’s overall performance by removing all external noise from the input spectra. Preprocessing spectral data entails a series of processes aimed at removing noise, scattering effects, and other non-informative causes of variation from the measured spectra. Although there are exceptions to the norm, most preprocessing procedures are unsupervised procedures that do not rely on the values of the reference variable. The most basic preprocessing techniques are based on a priori spectrum information. These include removing wavelength regions that are particularly noisy or saturated.

Scatter correction is a group of preprocessing techniques aimed at reducing the effect of particle size on the observed spectra. The term particle size effect concerns the existence of scattering particles in the measured material and might impact the path length of diffusely reflected Raman light. Because the size and distribution of these scatterers in materials that are diverse in content (e.g. biological tissue) is arbitrary, the inter-sample variance in spectra can be significant. Scatter correction is a type of spectrum normalization that removes inter-sample variations caused by scattering particles.

In spectroscopic data analysis, spectra derivatives are a common preprocessing tool. They are derived by differentiating the spectrum along the wavelengths, but only up to the first or second order. In a similar fashion to scatter correction, derivatives can also minimize particle size effects. The disadvantage of derivatives is that while they improve some aspects of the spectrum, they also significantly enhance noise, lowering the signal to noise ratio (SNR) of the spectrum.

Preprocessing in most applications entails a combination of procedures, such as scatter correction and filtering. While several preprocessing approaches have been thoroughly examined in the past, there is presently no clear agreement on the right order in which these procedures should be performed. Moreover, the probable combinations of approaches as well

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as the parameters of individual approaches allow an almost unlimited amount of preprocessing options. Though some degree of preprocessing will enhance model performance, it is also likely to overdo it by deleting key information from the spectra [101]. Hence, to achieve the best results, the preprocessing protocol should be customized for each application. Numerous chemometric studies have presented ways for determining the best preprocessing protocol in a systematic manner [102][103][104][105].

In general, the development of calibration models necessitates a significant number of samples with evenly dispersed reference variables. While building calibration models in principle, the training and test sets should be divided to ensure that they are sufficiently similar. The training and test sets can be chosen manually using predetermined conditions or using pre-existing algorithms like Shenk-Westerhaus [106] or Kennard-Stone [107]. The existence of outliers (singular influential samples) in the calibration dataset can drastically alter the result of a majority of statistical models. To establish robust and accurate models, it is crucial to detect and take out these types of significant outliers. Outlier samples by description statistically vary from the remaining samples, and this variation can be seen in the spectrum or in the reference variables. Visual examination or statistical outlier analytical methods such as leverage statistic, Cook’s distance, or Hotelling’s T2 diagnostics can be used to discover outliers.

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Chapter 3

3 Materials and methods

3.1 Sample preparation

Cartilage samples (𝑛 = 49) used in this study were obtained from the patella of intact bovine knee joints. In particular, osteochondral (cartilage-on-bone) plugs (Fig. 3.1) (20 × 10 × 10 𝑚𝑚³) were extracted from the upper and lower medial and lateral facets of the patella. To prevent degradation, the joints were preserved in a vacuumed bag and stored at 4⁰C before harvesting. Prior to Raman measurement and subsequent histopathological assessment, the specimens were stored at – 20⁰C in Phosphate-Buffered Saline (PBS, pH 7.4) supplemented with protease inhibitors. Moreover, the surface of the specimens was kept wet with PBS supplemented with protease inhibitors [19] during patella harvesting, sample preparation and Raman spectral measurements. For histological sample preparation, the samples were fixed and decalcified with Formalin-Ethylenediamine tetraacetic acid (EDTA) solution, followed by histological sectioning and Safranin-O staining.

Fig. 3.1: Image of cartilage-on-bone bovine sample

3.2 Raman measurement

The Raman spectra were measured from each bovine sample using a Raman spectrometer device (dispersive Raman-microscope thermo DXR2xi) (Fig. 3.2). The measurement was done pointwise with 10X objective; pointwise in the sense that the Raman spectra of the samples

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were collected from one spot on the surface of the samples. Each measurement was repeated three times for the sake of reproducibility and reducing operator’s error. Table 3.1 contains detailed specifications used for the Raman measurement.

Table 3.1 Specification for Raman measurement

Fig. 3.2: Dispersive Raman-microscope thermo DXR2xi

3.3 Histology

Prior to the Mankin scoring, light miscroscopy images of Safranin-O stained cartilage histological sections were acquired to extract the cell count. The measuements were conducted using a microscope with uniform light exposure across the entire measurements, which is part of standard protocol. All measurements were conducted in a dark room to avoid the interference of external light sources.

3.4 Cellularity

To obtain the cellularity score of the healthy and degenerated bovine articular cartilage samples, hispathological assessment was performed using the Mankin scoring system. The scoring of these samples was performed by four independent observers twice with a week interval between scoring to minimize the chances of memorizing the samples. The observers browsed through the samples from the surface to the calcified cartilage zone (Fig. 3.3) and scored them according to the modified Mankin scoring system in Table 3.2.

Laser wavelength

785 nm

Power 30 mW

Objective 10X

Resolution 50 µm confocal pinhole Exposure time 0.5 s

Accumulation 120

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Table 3.2 Modified Mankin score [84]

Structure

Normal 0

Irregular surface, including fissures into the radial layer 1

Pannus 2

Superficial cartilage layers (> 6) absent 3

Slight disorganization (cellular rows absent, some small superficial clusters) 4

Fissures into calcified cartilage layer 5

Disorganization (chaotic structure, clusters, osteoclast activity) 6 Cellular abnormalities

Normal 0

Hypercellularity, including small superficial clusters 1

Clusters 2

Hypocellularity 3

Matrix staining

Normal/slight reduction 0

Staining reduced in radial layer 1

Reduced in interterritorial matrix 2

Only present in pericellular matrix 3

Absent 4

After scoring the samples, those with cellularities of 2 and 3 from Mankin scores were labeled classes “clusters” and “hypocellularity” respectively.

Fig. 3.3: Safranin-O stained histological sections of a bovine cartilage showing different zones

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Image J was used to manually count the cells with a three-square box Region of Interest (ROI) moved across the superficial, middle, and deep zones (Fig. 3.4). After which, the mean across each zone was recorded as integers.

Fig. 3.4: Chondrocyte-counting with a square box ROI across superficial, middle and deep zones

3.6 Pre-processing of Raman spectra

The following spectra preprocessing was used; scatter correction, smoothing and derivatives.

For scatter correction, the baseline or mean spectrum was simply subtracted from the original spectrum using the Standard Normal Variate (SNV) method. SNV [108] and Multiplicative Scatter/Signal Correction (MSC) [109] are the two most widely utilized approaches. The correction with SNV is done according to the equation;

Superficial zone

Middle zone

Deep zone

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𝑥

_{𝑐𝑜𝑟𝑟}

=

^{𝑥− 𝜇}

𝜎 , (11)

𝑥_{𝑐𝑜𝑟𝑟} is the corrected spectrum, 𝑥 is the original spectrum, 𝜇 is the mean of the spectrum, and 𝜎 the standard deviation of the spectrum.

A simple moving average filter or convolution with another windowing function can smooth out randomly distributed instrumentation noise. In this study, Savitzky Golay filter [110] was used since it has proven a more prevalent an successful method in chemometrics. This filter iterates a moving window throughout the spectrum, replacing the original spectrum with a polynomial approximation usually second – fourth order produced using least squares regression at each window.

For spectral derivatives with the Raman spectra, two approaches were implemented. First, the raw spectra was used, then estimating its first and second order derivatives to emphasize tinier and less definite peaks while suppressing absorption from broader peaks. After that, these two spectra were incorporated into the chemometric analysis to see if they have any relationship with the cells and the model was developed afterwards.

3.7 Chemometric analysis

Chemometrics was used for data analysis for development of classification based and regression based models. Classification predictive models are normally tasked with estimating a mapping function (𝑓) from input variables (𝑥) to discrete output variables (𝑦). Labels or categories are terms used to describe the output variables. The class or category of an observation is predicted by the mapping function. A typical classification problem necessitates the classification of examples into one of two or multiple classes. On the other hand, regression predictive models are usually tasked with estimating a mapping function (𝑓) from input variables (𝑥) to continuous output variables (𝑦). This continuous output variable is real-valued, like integers or floating points, often quantities namely amounts and sizes.

There exists however an overlap between the two predictive models. The algorithm in a classification model may predict a continuous value, but that value is in the form of a class label probability. In like pattern, the algorithm in a regression model can predict a discrete value in the form of an integer quantity. The classification and regression predictive modelling approaches used in this study are Partial Least Squares-Discriminant Analysis (PLS-DA) and Partial Least Squares Regression (PLSR) respectively.

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PLS-DA is a resourceful and adaptable approach for predictive, descriptive and also discriminative variable selection. However, adaptability is both a benefit and a drawback, as the user must tune a plethora of parameters before arriving at dependable and accurate results [111]. PLS-DA has shown considerable success in modelling high-dimensional datasets for a variety of applications over the last two decades, including product authenticity in food analysis, disease categorization in medical diagnosis, and evidence assessment in forensic research [111]. The model’s performance is measured using metrics (also known as figures of merit), which are derived by comparing the model’s output to the expected values. In classification, accuracy, precision and sensitivity are the metrics of the model’s performance.

Classification metrics can be divided into calibration, cross-validation, and prediction metrics, just like regression metrics.

For PLSR, instead of using the original data, PLSR reduces the predictors to a smaller collection of uncorrelated components and conducts least squares regression on these components. When there are more predictors than observations, PLSR is very beneficial since regular least squares regression either gives coefficients with large standard errors or fails entirely. The chemical, drug, food and plastic industries are the most common users of PLSR.

A usual application is modelling the relationship between spectrum data (Raman, NIR, IR), which comprise many variables that are typically associated, and chemical composition or other physiochemical properties. In regression models, the most popular performance indicators are root mean squared error (RMSE), coefficient of determination (𝑅²), and correlation (Pearson or Spearman) coefficient.

We utilized Matlab for the Partial Least Square Discriminant Analysis (PLS-DA) to estimate cartilage cellularity from Mankin score. Matlab was also used for the Partial Least Square Regression (PLSR) analysis. To investigate the relationship between Raman spectra and cells, predictive modelling approaches was adopted. First, classification based models was used to investigate the relationship between Raman spectra and the cellularity (Mankin scores); then regression based predictive models was used to investigate the relationship between the Raman spectra and the cell count (cell count using Image J). In both of these predictive models, the predictors are the Raman spectra (𝑥) while the target variables or property of interest (𝑦) are the cellularity from Mankin score and cell count respectively. Training set (80% of the total samples, i.e. 39 samples) was used for creating the models, while the models were validated

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using a test set (20% of the total samples i.e. 10 samples). To improve the overall performance of the model and prevent producing inaccurate output because of inaccurate inputs, the spectra was preprocessed prior to building the models.

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Chapter 4

4 Results

4.1 Estimating articular cartilage cellularity from Raman spectra

Estimating the cellularity of articular cartilage from Raman spectra, histopathological assessment was performed to obtain the cellularity score of the samples which is crucial for the classification based model. Fig. 4.1 shows the distribution of the cellularity score among the samples.

Fig. 4.1: Distribution of cellularity score

Out of fourty-nine samples, twenty-seven (55%) were assigned a score of 2 and twenty-two (45%) samples were assigned a score of 3 which shows an exhibition of clustering and hypocellularity.

The scatter plots from PLS-DA classification model are presented in Figs. 4.2 – 4.4 for the three categories; zero derivative or raw spectra, first and second derivatives. The classification model for the zero derivative was created by using six partial least square (PLS) components while first and second derivatives were created by using four PLS components.

27 (55%)

22 (45%)

0 5 10 15 20 25 30

2 3

Number of samples

Mankin cellularity score

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Fig. 4.2: Plot showing classification of cartilage cellularity score based on Raman spectra with zero derivative

Fig. 4.3: Plot showing classification of cartilage cellularity score based on Raman spectra with first derivative

Sample plot (clusters vs hypocellularity)

● clusters

● hypocellularity

Sample plot (clusters vs hypocellularity)

● clusters

● hypocellularity

Estimating articular cartilage cellularity and cell count using Raman spectroscopy